The problem of universals

THE PROBLEM OF UNIVERSALS Edited and with an Introduction by CHARLES LANDESMAN Basic Books, Inc., Publishers NEW YORK : LONDON

@ 1971 by Basic Books, Inc. Library of Congress Catalog Card Number 72-158443 SBN 465-06361-6 Manufactured in the United States of America DESIGNED BY THE INKWELL STUDIO

CONTENTS

Introduction: The Problem of Universals PART ONE: The Theory of Universals 1. On the Relations of Universals and Particulars 2. Universals and Resemblances 3. On Concept and Object 4. Frege's Hidden Nominalism 5. Universals 6. Universals and Metaphysical Realism 7. Universals and Family Resemblances 8. Particular and General PART TWO: The Theory of Abstract Particulars 9. The Nature of Universals and Propositions 10. Are the Characteristics of Particular Things Universal or Particular?

11. The Relation of Resemblance 12. Qualities PART THREE Abstract Entities, Meaning, and Language 13. On What There Is 14. Empiricism, Semantics, and Ontology 15. The Languages of Realism and Nominalism 16. Grammar and Existence: A Preface to Ontology 17. A World of Individuals Bibliographical Notes Index -vi-

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Introduction THE PROBLEM OF UNIVERSALS IF one were to list the sorts of things that philosophers have characteristically disagreed about, one would find disagreements not only over the solutions to antecedently formulated problems but also over the very terms in which the problems are stated. Often, the very existence of a problem which has moved one generation of philosophers is doubted by the next. The problem of universals is no exception to this philosophical ambivalence. It is and has been a paradigm case of a metaphysical problem; yet in our time there has been a great deal of skepticism over the very possibility of metaphysics. Reasons that many philosophers have found persuasive have been offered to show that metaphysical speculation is either trival or fruitless or meaningless. In offering a collection of essays on the problem of universals, one has an obligation to justify the claim that there is such a problem. In what follows, the nature of the problem is explained and a defense of metaphysics is offered against some of the arguments of the skeptics.

I It is a truism that there is such a thing as recurrence or repetition in nature. The same colors, shapes, and sounds occur over and over again. We are continuously presented not only with novel things but with qualities and features of things that we have observed time and time again. And even the novel things very often belong to types—that is, to species and genera— which are quite familiar. As an example of natural recurrence, consider two leaves which are exactly alike in all their qualities; they have the same green color, the exact same shape, size, and feel. We have no difficulty in distinguishing between their qualities; a color, after all, is not a shape, a shape not a size; in other objects the same color coexists with different shapes, the same shapes with different sizes. In addition, we can easily distinguish between any one of these qualities and the thing itself—the leaf—which possesses it; we can distinguish between the leaf and its shape or its color; and we can imagine changes in quality—the color turning from green to brown in autumn or the shape being modified by a storm—though the object remains the same. The distinction between a particular thing and its qualities is well-entrenched in

our everyday thinking and speaking about the world. Things persist through space and time; qualities repeat themselves in different things at various times and places. The phenomenon of natural recurrence seems easily explained and accounted for. It consists of the fact that different objects have qualities in common: our two leaves, for example, have their color, shape, and size in common. It is the existence of common qualities which allows us to say that recurrence is literally repetition; the same quality literally appears over and over again. Common qualities have been given the technical name universals because of the fact that they are repeatable and can be possessed by diverse things. The spatiotemporal things which have the qualities are often called particulars or individuals or concrete entities; these are not repeatable at least in just the same way that universals are; no particular can be in totally different places at the same time, whereas a universal such as a shade of color is subject to no such restriction. The explanation of natural recurrence in terms of common qualities or universals, we shall call the theory of universals; it is also often called realism, because it asserts that universals are real. The opposite view, which tries to get by without universals, we shall call particularism. 1 It may be thought that the explanation of natural recurrence in terms of common qualities consists of a series of truisms which no sane man would want to deny. Nevertheless, at the very beginning of the western philosophical tradition, Plato found that, upon reflection, the truisms led to certain puzzles. In his dialogue Parmenides, Parmenides receives an affirmative

answer from Socrates to this question: But I should like to know whether you mean that there are certain ideas of which all other things partake, and from which they derive their names; that similars for example, become similar, because they partake of similarity; and great things become great, because they partake of greatness; and that just and beautiful things become just and beautiful, because they partake of justice and beauty. In this and other passages the Platonic ideas seem to be common qualities; a thing which has a certain quality is said to partake of or participate in the corresponding idea. Parmenides then proceeds to find difficulties in Socrates's theory. One difficulty he comes up with is especially relevant to the notion of a common quality. Then each individual partakes either of the whole of the idea or else of a part of the idea? Can there be any other mode of participation? There cannot be, Socrates said. Then do you think that the whole idea is one, and yet, being one, is in each one of the many? Why not, Parmenides? said Socrates. ____________________ 1The terminology of metaphysics is not standardized: different philosophers give different titles to the views they espouse or oppose. Other terms for realism are Platonism and the identity theory. The term nominalism is often used instead of particularism, but we shall use it later to designate one form that particularism can take. -4-

Because one and the same thing will exist as a whole at the same time in many separate individuals, and will therefore be in a state of separation from itself. Nay, but the idea may be like the day which is one and the same in many places at once, and yet continuous with itself; in this way each idea may be one and the same in all at the same time. I like your way, Socrates, of making one in many places at once. You mean to say, that if I were to spread out a sail and cover a number of men, there would be one whole including many—is not that your meaning? I think so. And would you say that the whole sail includes each man, or a part of it only, and different parts different men? The latter. Then, Socrates, the ideas themselves will be divisible, and things which participate in them will have a part of them only and not the whole idea existing in each of them? That seems to follow. Then would you like to say, Socrates, that the one idea is really divisible and yet remains one? Certainly not, he said. Suppose you divide absolute greatness, and that of the many great things, each one is great in virtue of a portion of greatness less than absolute

greatness— is that conceivable? No.... Then in what way, Socrates, will all things participate in the ideas, if they are unable to participate in them either as parts or as wholes? 2 Parmenides's argument has the form of a dilemma. The two leaves are both green. There are two alternatives for understanding this fact in terms of common qualities. Either the color green is possessed by each leaf as a whole or each possesses only a part of the color. But each alternative is absurd. The first is absurd because it implies that the same entity, the color green, can be in different and separated places at the same time, that it will be "in a state of separation from itself." The second is likewise absurd because it is unintelligible how something can be green by possessing not the quality green but only a part of the quality. In fact, it is not even clear what a part of a simple quality like green can be. The fact that realism is still a living option proves that philosophers have not taken Parmenides's argument to be conclusive. Realists usually accept the first alternative. Some deny that the allegedly absurd proposition that the same color can be in two or more places at once follows from it by asserting the universals do not have spatiotemporal location except insofar as the things that participate in them do. Others accept the implication but deny ____________________ 2Plato Parmenides, 131, Jowett translation. -5-

its absurdity. The supposition that it is absurd for a quality to be in two places at once comes from confusing qualities with particulars. For particulars, spatial separation is a criterion of nonidentity, but since qualities are different from particulars there is no reason to think that they are bound by the same identity criteria. Notice that this last response invokes a certain kind of argument which appears over and over in metaphysics. It is a category explanation. The question was raised, "How can the color green be in two different places at the same time?" The answer the realist gave was that green, being a quality, is not subject to spatial separation as a criterion of nonidentity. The question is answered first by specifying the category or ontological type to which green belongs and then pointing out that certain things are or fail to be true of it just because it belongs to that type. In general a category explanation of the question "How can some entity x have the feature F?" has the form: "x belongs to category C and its belonging to C entails that it has F." Someone might argue that a category explanation is not a final answer to the question since one can always ask how it is that something has F just because it belongs to C. But this would be a mistake; to raise this further question is like asking, "How is it that something is colored just because it is green?" or "How is it that something is rectangular just because it is square?" There are no answers to these questions other than pointing out that, given what these are, these relationships hold.

II Given this sketch of what realism amounts to, we can describe the problem of universals, or at least one form of it, in the history of philosophy as the question of whether realism provides an adequate account of natural recurrence. As it stands, however, the theory of universals hardly seems worthy of being classified as a theory. Despite the apparent difficulties that Parmenides found in it, it seems to consist of obvious truisms which are expressed in a somewhat technical vocabulary. Who can deny that things possess qualities in common, that many things can be red or green or square at the same time? The claim that this triviality is a metaphysical assertion seems pretentious. In order to explain why realism is not an uninteresting truism, it is necessary to distinguish between three things: the phenomenon to be explained, natural recurrence; our description of this phenomenon; and an explanation of it, the theory of universals. It is not easy to keep

these things separate, for the reason that almost every set of terms we use to point out the phenomenon of natural recurrence suggests one of the explanatory theories. The description and the explanation may both be formulated in the same vocabulary. For example, in indicating what we meant by natural recurrence at the very beginning of this essay, we used the vocabulary of common qualities. Thus our -6-

description is linguistically indistinguishable from the theory of universals. But there are other terms we could have used to point to the phenomenon. We could have said not that things have qualities in common, but that things resemble one another to a great degree. Or, instead of speaking of qualities or of resemblances, we could just as well have mentioned the fact that we often apply the same word to different things: we describe different things with the word "green" or with the word "square." That there is such a thing as natural recurrence is a truism; no one wishes to deny it. It is that which various metaphysical theories try to explain. The theory of universals, on the other hand, is not itself to be identified with the assertion of the existence of natural recurrence, but rather is one account of it. The situation is not unlike that in the sciences, in which the very phenomenon to be explained tends to be identified in terms of a current explanatory theory. To take an example from psychology, there are several theories attempting to explain the phenomenon of mental illness. But the very term "mental illness" already suggests a certain theoretical and practical point of view. A psychologist who rejects the point of view would naturally refuse to use the term "mental illness" to identify what he wants to explain; he will have to use another term such as "behavior problem" to indicate what he is after. If he should say that there is no such thing as mental illness, it sounds as if he is uttering a paradox, although in fact he is not rejecting the phenomenon but the theory. Similarly, a philosopher who refuses to accept the theory of universals is not necessarily denying that there is such a thing as natural recurrence, although he may wish to describe it in terms which suggest a different theory. These distinctions will not satisfy the skeptic who insists that realism is an uninteresting truism. He will say that even as an explanation of natural recurrence one cannot sensibly deny that different things are square because each possesses the shape square. That there is such a thing as the color red in virtue of which all red things are red can be ascertained just by opening one's eyes and looking. In order to demonstrate that the skeptic is again incorrect in his evaluation of the issue, it is necessary to introduce another distinction: that between commonsense and philosophical existence-claims. In everyday discourse such sentences as "The red color of that book is darker than the red color of this table" and "Both these leaves possess the same shape" may be used to make true statements which imply or presuppose the existence of certain abstract entities—colors and shapes. But these commonsense existence-claims do not yet constitute a philosophical theory, nor are they of any significance to metaphysics other than as data upon which to reflect. A philosopher may claim that statements which mention certain types of entity, such as qualities, and ostensibly presuppose their existence, are equivalent to statements which do not explicitly mention them; perhaps statements ostensibly about qualities are equivalent to statements asserting resemblances among particulars. If he can make out such a claim, then he is entitled to assert that, in a sense, there are no such things as qualities; there are only particulars. -7-

In general, if a philosopher can show that things of type A are reducible to things of type B, that A's are nothing but B's, or that statements which mention things of type A are translatable into statements which mention only things of type B, he is then entitled to say that, in a sense, things of type A do not exist but things of type B do. In a philosophical system, the types of entities out of which all other types of entities are "composed" are the system's ultimate categories. A philosophical existence-statement asserts the existence of members of the ultimate categories. The statement that qualities —e.g., colors and shapes —exist, if it is intended as a commonsense existence - statement, does not contradict the statement that qualities do not exist, if that is intended as the claim that qualities are not an

ultimate category. From the standpoint of the philosophical claim, our commonsense reference to qualities is a mere manner of speaking with which one can dispense for philosophical purposes. Therefore, the statements that the skeptic finds truistic and uninteresting are not the ones that the philosopher asserts; those that he asserts, although they often are compatible with commonsense existence-claims, are not identical with them. The skeptic is not yet finished; he may now make the notion of metaphysical explanation the target of his doubts. There are explanations of various sorts in everyday life and science. There are causal explanations when we explain a phenomenon by mentioning one of its causes, as when we explain why water turns to ice by citing the drop in temperature. There are motive explanations, as when we explain why a person did something by mentioning the aims and goals that he wanted to achieve by doing it. That there are these and other types of explanations is noncontroversial. But that there is something more we can do with a phenomenon, such as providing a metaphysical account of it, is problematic. Once we have stated something's causes or reasons, what else is there to know about it which a further explanation can accomplish? One source of the resistance to the very notion of metaphysical explanation is that such explanations are often couched in terms which make them appear as if they were rivals to the causal explanations in everyday life and science. In the passage from Plato quoted earlier there occurs the sentence, "Just and beautiful things become just and beautiful, because they partake of justice and beauty." This sounds as if Plato were offering a causal explanation of how things become just or beautiful. Yet clearly if we wanted instructions as to how to make a person just or how to make a painting beautiful, what Plato wrote would be useless. The metaphysical explanation sounds as if it belongs to primitive science which now can be replaced by sophisticated modern science. Thus Pears has written: "Because universals exist" is the answer to at least two general questions: "Why are things what they are?" and "Why are we able to name things as we do?" Though Plato and Aristotle sometimes distinguished these two questions, it was characteristic of Greek thought to confuse them. Yet they can be clearly distinguished, the first requiring a dynamic answer from scientists, and the second -8-

a static answer from logicians. Now philosophy has often staked premature claims in the territory of science by giving quick comprehensive answers to questions which really required laborious detailed answers. And clearly this is what happened to the first of the two questions. When detailed causal answers were provided to it, the comprehensive answer "Because universals exist" was no longer acceptable or necessary. 3 For skeptics like Pears, science has replaced metaphysics and has shown it to be superfluous. Now this skepticism would be justified only if its understanding of the function of metaphysics is correct; only if metaphysics had the same explanatory function as science could one claim that science has replaced metaphysics and shown it to be unnecessary. But if metaphysics can be shown to be doing something different from what science accomplishes, if its explanations can be shown not to be rivals of those provided by science, then this criticism misses the target. What then is a metaphysical explanation? The theory of universals provides us with a way of answering this question. It attempts to account for a general feature of our experience —natural recurrence—by stating the entities that that feature consists of—universals occurring in diverse particulars—where the entities are classified in terms of ultimate categories. In general, a metaphysical account is a redescription of some general and pervasive feature of our experience and of the world in terms of ultimate categories. These redescriptions are not rival causal explanations; they are not alternatives to the accounts provided by science; they give not antecedent causes but the ultimate categories from which our world (and any possible world) is constituted. In this sense, metaphysics tells about the nature of reality.

This account of metaphysics makes use of the notion of an ultimate category. Yet a commonsense philosopher who is skeptical of reductionism, who doubts philosophical claims of the form "A's are nothing but B's," may very well question whether this notion is meaningful or useful. He may say something like this: "Of course there are qualities; we speak about them all the time. Of course there are physical particulars; we constantly refer to them. Of course there are numbers, sets, propositions, events, relations; all these things are subjects of discourse. But there is no reason to think that any one of these sorts of thing can be 'reduced' to any other sort of thing. The assumption that there are any ultimate categories is an attempt to impose a simplified conception of discourse upon the multifarious uses and concepts of ordinary discourse." Now this argument of the antireductionist, rather than establishing that there are no ultimate categories, really shows, if it is correct, that there are many more such categories than those for which traditional systems allowed. If qualities, physical things, numbers, sets, propositions, events, and relations are types of entity independent of one another, then they are all ultimate categories. The antireductionist is a metaphysician despite himself. 3

D. F. Pears, "Universals," reprinted in A. G. N. Flew, ed., Logic and Language, Second Series (Oxford: Basil Blackwell, 1955), p. 52. -9-

III There is one more skeptical argument that is important enough to consider. Even if there is such a thing as a metaphysical account of things which is not simply a truistic commonsense existence-claim, nevertheless such accounts are uninteresting because it is pointless to deny them. Metaphysical theories are well known for the length of time they persist throughout the history of philosophy; they are also well known for their recalcitrance to clear-cut verification or refutation. The theory of universals and its alleged rivals have endured for most of the course of western philosophy. Each view still has its stanch advocates. This suggests that in fact the different theories are not really rivals after all. Perhaps they are different, though compatible, descriptions of the world; perhaps the actual ground for choosing one theory over another is not rational argumentation but something nonrational, such as aesthetic preference or interest of one sort or another. Just as the Eskimos have more terms in their language than we in our language for classifying a variety of types of snow because they have a greater interest in so doing, so different metaphysical systems are different, though compatible, ways of classifying the very same phenomena. 4 If this should be correct, then metaphysical systems would become uninteresting, in the sense that there would be no point in rejecting them or arguing about them. We do not reject the Eskimo classificatory scheme for snow; we simply fail to use it because it is not useful to us. Conceivably, for some purposes it might be useful to adopt a metaphysical scheme. But that one turns out to be useful and others not, does not mean that one is correct or true and the others incorrect or false. 5 This form of skepticism incorporates two distinct theses. First, it asserts that different metaphysical theories are not rivals because they are logically compatible with one another; second, it claims that such theories are not the sorts of things which can be verified or refuted. In order to rebut the first claim, it is sufficient to provide formulations of the various theories concerning qualities in such a way as to demonstrate that they are logically incompatible with one another. It is possible to provide a philosophically neutral identification of the sorts of entities the various theories of universals are about by pointing to examples of them. For instance, take any physical object and point to its color or its shape; these are the kinds of things meant by "quality." Realism asserts that qualities are universals. This claim can be interpreted as an identity criterion for qualities: the assertion that statements of the form "x is identical with y" or "x is numerically the ____________________ 4This view of metaphysics is suggested in certain writings of the linguist Benjamin Whorf and the Neo-Kantian philosopher Ernst Cassirer. See Whorf's Language, Thought and

Reality (New York: John Wiley and Sons, 1959) and Cassirer's The Philosophy of Symbolic Forms, Vol. I (New Haven: Yale University Press, 1953). point of view has received a sharp formulation in Carnap's "Empiricism, Semantics, and Ontology," reprinted in this volume.

5This

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same as y" can be true when "x" and "y" are names of qualities of different objects. This formulation of the theory of universals suggests a way of specifying an alternative account which we shall call the theory of abstract particulars. It says that when x and y are qualities of different objects, then it follows that x is not identical with y—that x is not numerically the same as y. In the words of G. F. Stout, qualities are abstract particulars; they are as particular as the things they qualify. 6 The theory of universals and the theory of abstract particulars are rivals in this precise sense: although both accept qualities as an ultimate category, the former asserts and the latter denies a certain identity criterion for qualities. They are saying different things about the same thing. We have made sure they are talking about the same thing by specifying what they are talking about in a philosophically neutral manner: a manner which does not commit one either to the existence of qualities as an ultimate category or to an identity criterion for qualities. They are, thus, logically incompatible with one another. This analysis yields another way in which metaphysical theories can be rivals. Instead of merely disagreeing about the identity conditions of some ultimate category, a philosopher may deny that this is an ultimate category in the first place; he may assert that there are no such things. And this is exactly what several forms of particularism do. Nominalism is based on the fact that there is such a thing as linguistic recurrence; there are general words in the vocabulary of any language which are applied to different particulars. The words "green," "square," and "leaf" are general in the sense that each applies to a variety of distinct individuals: green things, square things, and leaves. Nominalism explains natural recurrence as simply being linguistic recurrence ; qualities are reduced to general words, in the sense that the fact that two different things have the same quality is explained as consisting in the fact that the same word applies to both of them. 7 For the nominalist, general words are not names of qualities; rather, they are applied to or predicated on the concrete things that are commonsensically said to have the qualities. Consequently, for the nominalist the use of a general term does not presuppose the existence of qualities. Another version of particularism that rejects the category of quality is the resemblance theory. 8 In this view there is an objective basis—the resemblances between particulars—for applying general words to diverse particulars: we apply "green" to various things because they resemble one another in being green; we apply "square" to those things that resemble one another in being square. The resemblance theory, by providing an explanation of how linguistic recurrence is possible in terms of resemblances among particulars, could be looked upon as a corollary to nominalism. But it could also be formulated as a rival to nominalism in the following way. Suppose a philosopher thinks that the use of a general term in a sentence such as "This leaf is green" in some way ____________________ 6See the articles by Stout reprinted in this volume. 7See Quine's essay "On What There Is," reprinted in this volume. 8See H. H. Price's formulation in the selection reprinted in this volume. -11-

commits one to the existence of the quality green. But, as a particularist, he wants to avoid a philosophical commitment to qualities. He might then claim that the sentence can be translated into another one which does not presuppose qualities. For example, select some green object as an exemplar of green. Call the exemplar A. Then "This leaf is green" becomes something like "This leaf resembles A." 9 Qualities then are reduced to resembling particulars. The nominalist, having a different view of general terms, finds no need for such a reduction. In any case we now have four theories—realism and three forms of

particularism—which can be so formulated as to entail or presuppose logically incompatible theses. This dispenses with one of the claims of the skeptic. His second claim, that theories about universals are not the sorts of things that can be verified or refuted, is based on the fact that the problem has lasted a long time and disagreement still persists. Now there is a dialectical argument against this version of skepticism. The skeptic is presenting one theory about philosophy, but there are other theories as well which have endured through lengthy stretches of the history of philosophy. So, given the skeptic's own argument, his view is also not the sort of thing that can be verified or refuted. Thus we have no reason to accept it. Moreover, the fact that a problem has persisted a long time may be due to a variety of factors. It is characteristic of most philosophical problems, including the problem of universals, that they have a systematic nature: this means that what one says about one problem affects what one says about a variety of problems. One cannot solve philosophical problems piecemeal; one problem is not independent of others. This distinguishes philosophical problems from many of those in the sciences. Moreover, even in the sciences the fundamental problems, such as the ultimate constitution of matter and the nature of the human mind, have persisted as long as the problem of universals. While there tends to be more agreement at any given time within the scientific community than within the philosophical community, yet if one compares the sciences over a period of time one finds changes and disagreements as fundamental as in philosophy.

IV We have identified the problem of universals with the question of whether realism provides a satisfactory account of natural recurrence. A deeper insight into the nature of the problem depends on understanding the sorts of difficulties that particularists have found with realism. We shall now consider several of the more fundamental issues, examine the criticisms, and see how the realist would reply to them. ____________________ 9See Price's formulation for the details of the theory and for the various qualifications that have to be introduced. -12-

(a) Linguistic recurrence consists in the fact that there are general terms in language. In trying to understand the way language works and the way words apply to the world, realism tends to argue that general words are names of common qualities—of universals. 10 Consider the sentence: (1) This leaf is green. when it is used to make a true statement. The subject term "this leaf" is used to name (or stand for or refer to or denote) a given particular; similarly, the general term in the predicate position "green" is used to name a given universal. We apply the word "green" to the leaf by naming a quality of the leaf. General words apply to things by naming their qualities. Critics of the theory of universals argue that this semantical theory misunderstands how predicates actually function. The function of predicates is being confused with the function of subjects. This can be shown through the following argument. If general terms are names of qualities, then it follows that: (2) "Green" is a name of the quality green. Note also that: (3) "The quality green" is a name of the quality green. Since "green" and "the quality green" name the same thing, it follows that: (4) Green is identical with the quality green.

There is a rule of inference—the law of substitutivity—which says that words which name the same thing can be substituted for one another in sentences in which they occur, without turning a true statement into a false one. 11 One should be able, then, to substitute "the quality green" for "green" in (1). But if we do we come up with: (5) This leaf is the quality green. which is manifestly false. What went wrong? Neither (1) nor (3) nor the law of substitutivity are in doubt here. (4) follows from (2) and (3). The point of difficulty must be (2). To reject this is to say at least that in (1) the word "green" is not functioning as a name. Thus realism appears to rely upon an incorrect semantics. This is a persuasive argument. But it does not directly establish particularism. Realism is compatible with other views about the functioning of predicates. Someone who knows the meaning of (1) knows which quality the statement asserts the leaf to have. In general, someone who knows the meaning of a general word knows which quality something is asserted to have in a statement formulated with the general word as its predicate. For the realist ____________________ 10See Bergmann's "Frege's Hidden Nominalism," reprinted in this volume. 11There have been doubts whether this law holds unreservedly. But the context in which it is used in this discussion is not among those for which doubts have arisen. -13-

this implies that in some sense qualities enter into the meanings of general words. But it does not follow that the way they have meaning is by being names of qualities. The realist could say, for example, that in (1) both the singular and general terms function to introduce 12 certain entities into discourse : "this leaf" introduces a particular and "green" a universal. But there are different species of introduction, so that the way a singular term introduces an entity is not the same as the way a general term does so. "This leaf" introduces a particular by helping to single out which particular the sentence is about: it refers to or names that particular. Referring or naming is the function of singling out the subject of the sentence. On the other hand, "green" introduces a quality not by naming it but by ascribing it to the particular singled out by the subject term. Here ascribing is a different function from naming. This approach, which is here merely sketched, avoids the particularist's argument in this way: the law of substitutivity is interpreted to apply only to words which name or refer and not to words which ascribe. Since "green" in (1) is interpreted as ascribing a quality and not as naming it, then one cannot use the law to go from (1) to (5). (b) We have discussed the functions of the subject and predicate in (1), but not that of the copula "is." One of the functions of the copula is obviously to indicate tense. Another function, due to its position, is to signify that the sentence (1) is used to make an assertion or statement; if its position should be changed, as in "Is this leaf green?" instead of an assertion we have a question. In one version of realism, since the subject and predicate introduce distinct entities, the copula must also introduce that entity which connects them together. For this function, let us use Bergmann's term, exemplification. Sentence (1) asserts that the leaf exemplifies the quality green. Exemplification is the relation that holds between a quality and the things which have the quality. 13 Because exemplification connects entities of one ultimate category—universals—to those of another—particulars—it may be classified as a metaphysical tie. One motive for introducing the notion of exemplification is to answer the question, "How are universals related to particulars?" The question is answered by specifying the entity that does the relating. According to this way of thinking, whenever there is one entity related to a second entity, one can always ask for the entity which relates them. Thus we are entitled to raise the question of how exemplification is itself related to the entities it connects. This new question presents the realist with a dilemma. Either there is an entity which relates exemplification to the things it connects or there isn't. If there isn't, then exemplification fails to do the job it was introduced to do: to connect universals to particulars. But if there

is, then we can ask of this entity what relates it to the things it connects. And thus an infinite regress is gen____________________ 12The notion of introduction is Strawson's. See his Individuals, an Essay in Descriptive Metaphysics (London: Methuen & Co., 1959), p. 146. 13In systems employing the symbolism of mathematical logic, exemplification is represented not by the copula, since there isn't any, but by the juxtaposition of the predicate and subject terms. -14-

erated. To the particularist this dilemma indicates a fundamental difficulty with realism, which he solves by rejecting universals and thus avoiding the need for a metaphysical tie such as exemplification. The realist may try to respond by pointing out that not every infinite regress refutes the theory which generates it. There is no contradiction in the mathematical theory which says that there is no last number. Similarly, there is no contradiction in the supposition that, for every relation which connects entities to one another, there is another relation which connects the former to its terms. Although this reply suffices to rebut the charge of inconsistency, it is not satisfactory. For if the regress does not violate the laws of logic, it does seem to violate the principle of economy or simplicity sometimes known as Occam's razor. All things being equal, a theory without such a regress is more plausible than one that generates a regress. The regress is a complexity which is very difficult to understand. Particularism has the advantage, then, of not implying this bit of unintelligibility. But there are other ways out for realism. In the first place, a realist could argue that the infinite regress is merely verbal. It is a feature of English grammar that allows us to reiterate the verb "exemplifies" over and over again, as in "This leaf exemplifies the property of exemplifying green." Endless reiteration is a feature of other phrases in English, such as "it is true that." But just as "It is true that it is true that this is green" says no more than "It is true that this is green," so "This leaf exemplifies the property of exemplifying green" says no more than "This leaf exemplifies green." The regress is not one of an endless series of entities but of an endless series of sentences. As a corollary to this reply, the realist might claim in addition that the question which appeared to generate the regress is itself illegitimate. The question was, "What entity relates exemplification to the entities that it connects?" But, says the realist, exemplification is the sort of entity whose nature it is to connect other entities; it needs no further thing to achieve the connection. Here is another example of a category explanation; it is because exemplification is just the sort of thing it is that it has the ability to make the relevant connections. In the second place, there is another version of realism, one suggested by some of the writings of Frege. 14 In this view, qualities are unsaturated or incomplete ; it is their nature to be joined to particulars; a special tie is not required to make the connection. To the question, "How are qualities connected to particulars?" this view answers that by their very nature qualities are always qualities of something. If exemplification were indeed required as a tie, then it would always be an open question whether a given quality belonged to some particular. But this is absurd, since there cannot be colors or shapes without things which have that color or are of that shape. The dispute between these alternatives parallels the ancient dispute between Plato and Aristotle whether universals can exist independently of particulars. (c) In our earlier discussion of Parmenides's argument we noted that one ____________________ 14See Frege's essay "On Concept and Object," reprinted in this volume. -15-

way out of the dilemma was to deny that universals have spatiotemporal location in any direct sense. The color green, for example, may be said to be in a given place at a given time only in the sense that a green thing is in that place at that time. The spatiotemporal location of qualities is derived from that of the physical particulars that exemplify them, whereas the location of the physical particulars is direct. The tendency to deny location to universals reinforced another tendency one finds in Plato's philosophy: to claim that our knowledge of universals is based not on sense perception but on reason. Another road to this conclusion is that the theory of universals was often invoked 15 to explain how a priori knowledge is possible. Certain truths are known independently of experience; an example is, "Whatever is green is colored." These are said to assert connections among universals; our ability to know these truths is based on the fact that we can become acquainted with these universals by means of a nonsensory form of intuition. A distinguished logician has written: The extreme demand for a simple prohibition of abstract entities under all circumstances perhaps arises from a desire to maintain the connection between theory and observation. But the preference of (say) seeing over understanding as a method of observation seems to me capricious. For just as an opaque body may be seen, so a concept may be understood or grasped. 16 Realists have thus tended to be rationalists as well, claiming that there is a source of factual knowledge other than sense-perception. Particularists have tended to be empiricists, restricting our factual knowledge to what can be derived from sense. The bad reputation that rationalism has acquired as a result of doubts about the existence of a priori forms of cognition has tended to extend itself to realism. Thus the theory of universals has often been rejected on the grounds that it conflicts with an empiricist foundation of knowledge. The historical connection between realism and rationalism does not prove that they are logically interwoven. Quine has suggested that the fact that something is observable does not settle the question of to which metaphysical category it belongs. 17 That one can see qualities such as shapes, leaves open the question of their classification. Whether a quality is a universal or particular, whether it is reducible to some other type of entity depends upon systematic considerations and philosophical argument. Since a theory about qualities presupposes the ability to identify qualities through observation as a way of specifying what the theory is about, no adequate theory can end up by denying the possibility of observing them. (d) Earlier we considered two leaves which are exactly alike in every respect. According to realism, they possess the same qualities. But then, how ____________________ 15By Plato and by Bertrand Russell. See Russell's Problems of Philosophy (New York: Oxford University Press, 1912), Ch. 9 and 10. 16Alonzo Church, "The Need for Abstract Entities in Semantic Analysis," reprinted in J. A. Fodor and J. J. Katz, The Structure of Language (Englewood Cliffs: Prentice-Hall, 1964), p. 442. 17Word and Object (Cambridge: The M.I.T. Press, 1960), p. 236. -16-

is it that they are two, not one? This question, sometimes called the problem of individuation, is suggested by a principle apparently presupposed by realism that (P 1 ) it is logically possible for two different things to have the same qualities. This principle, together with what seems to be an obvious truism—that (P 2 ) things which are the same in every way are the same— makes us wonder how we have two leaves after all. Whereas the problem of universals is to explain how different things can have common qualities, the problem of individuation is to explain how things with all their qualities in common can be different. Since particularism does not accept (P 1 ), it does not generate the problem of individuation in just this form. Realists have adopted different solutions to the problem. One group of solutions accepts (P 1 ) and claims that when two objects have all their qualities in common, then there is something else about them which explains their difference. The theory of bare particulars 18 asserts that in addition to its qualities, a thing contains an individual which exemplifies them.

Different things, even if they should have the same qualities, contain different individuals. Many realists find it difficult to accept the idea of bare particulars because, although they can discern qualities in the objects of experience, they claim to be unable to find the individual which has them. For this group, a thing is just a bundle of qualities. If they accept (P 1 ) then what individuates can be neither a quality nor a bare particular but is rather a relation. Two things with the same qualities will stand in different spatiotemporal relations to other things; e.g., one will be to the left and the other to the right of some object in space. 19 Some realists have decided to reject (P 1 ) and argue that different particulars always have some difference in quality. One way of achieving this is to claim that the places and times at which a particular is located are among its qualities. 20 Another way is to hold that for every relation that holds between particulars, there is a relational quality in each of the particulars. These, then, are some of the issues that are implicit in the problem of universals. Since their resolution brings in questions about language, meaning, knowledge, space, and time, it is clear that the problem cannot be solved in any simple or neat way. But this explains why the problem is so interesting —why it has held the attention of philosophers throughout the entire history of philosophy. ____________________ 18Bergmann has advocated this view. See also Edwin B. Allaire, "Bare Particulars," Philosophical Studies (1963). 19This view is defended by Jack Meiland in "Do Relations Individuate?" Philosophical Studies (1966). Allaire's reply is contained in "Relations and the Problem of Individuation," Philosophical Studies (1968). 20Nelson Goodman, The Structure of Appearance (Indianapolis: Bobbs-Merrill, 1966), pp. 194-200. -17-

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PART ONE The Theory of Universals

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:1: ON THE RELATIONS OF UNIVERSALS AND PARTICULARS 1 BERTRAND RUSSELL THE purpose of the following paper is to consider whether there is a fundamental division of the objects with which metaphysics is concerned into two classes, universals and particulars, or whether there is any method of overcoming this dualism. My own opinion is that the dualism is ultimate; on the other hand, many men with whom, in the main, I am in close agreement, hold that it is not ultimate. I do not feel the grounds in favour of its ultimate nature to be very conclusive, and in what follows I should lay stress rather on the distinctions and considerations introduced during the argument than on the conclusion at which the argument arrives.

It is impossible to begin our discussion with sharp definitions of universals and particulars, though we may hope to reach such definitions in the end. At the beginning, we can only roughly indicate the kind of facts that we wish to analyse and the kind of distinctions that we wish to examine. There are several cognate distinctions which produce confusion by intermingling, and which it is important to disentangle before advancing into the heart of our problem. The first distinction that concerns us is the distinction between percepts and concepts, i.e., between objects of acts of perception and objects of acts of conception. If there is a distinction between particulars and universals, percepts will be among particulars, while concepts will be among universals. Opponents of universals, such as Berkeley and Hume, will maintain that concepts are derivable from percepts, as faint copies, or in some other way. Opponents of particulars will maintain that the apparent particularity of percepts is illusory, and that, though the act of perception may differ from the act of con ____________________ Reprinted from the Proceedings of The Aristotelian Society, XII (1911-1912), by courtesy of the Editor of The Aristotelian Society. Copyright © 1912, The Aristotelian Society. 1The thesis of the present paper is closely similar to that of Mr. Moore's paper "Identity," read before this Society in 1900-1901. My chief reason for thinking that the question demands a fresh discussion is that the statement of the grounds for the thesis appears to require some examination of the nature of sensible space as opposed to physical space.

ception, yet its objects differ only by their greater complexity, and are really composed of constituents which are, or might be, concepts. But the distinction of percepts and concepts is too psychological for an ultimate metaphysical distinction. Percepts and concepts are respectively the relata of two different relations, perception and conception, and there is nothing in their definitions to show whether, or how, they differ. Moreover, the distinction of percepts and concepts, in itself, is incapable of being extended to entities which are not objects of cognitive acts. Hence we require some other distinction expressing the intrinsic difference which we seem to feel between percepts and concepts. A cognate distinction, which effects part at least of what we want, is the distinction between things which exist in time and things which do not. In order to avoid any question as to whether time is relative or absolute, we may say that an entity x "exists in time" provided x is not itself a moment or part of time, and some such proposition as "x before y or simultaneous with y or after y" is true of x. (It is not to be assumed that before, simultaneous, and after are mutually exclusive: if x has duration, they will not be so.) Prima facie, a percept exists in time, in the above sense, while a concept does not. The object of perception is simultaneous with the act of perception, while the object of conception seems indifferent to the time of conceiving and to all time. Thus, prima facie, we have here the non-psychological distinction of which we were in search. But the same controversies will break out as in the case of percepts and concepts. The man who reduces concepts to percepts will say that nothing is really out of time, and that the appearance of this in the case of concepts is illusory. The man who reduces percepts to concepts may either, like most idealists, deny that anything is in time, or, like some realists, maintain that concepts can and do exist in time. In addition to the above distinction as regards time, there is a distinction as regards space which, as we shall find, is very important in connexion with our present question. Put as vaguely as possible, this is a distinction which divides entities into three classes: (a) those which are not in any place, (b) those which are in one place at one time, but never in more than one, (c) those which are in many places at once. To make this threefold division precise, we should have to discuss what we mean by a place, what we mean by "in," and how the different kinds of space—visual, tactile, physical—produce different forms of this threefold division. For the present I will merely illustrate what I mean by examples. Relations, obviously, do not exist anywhere in space. Our bodies, we think, exist in one place at a time, but not in more than one. General qualities, such as whiteness, on the contrary, may be said to be in many places at once: we may say, in a sense, that whiteness is

in every place where there is a white thing. This division of entities will be discussed later; for the present I merely wish to indicate that it requires examination. In addition to the above psychological and metaphysical distinctions, there are two logical distinctions which are relevant in the present enquiry. In the -22-

first place, there is the distinction between relations and entities which are not relations. It has been customary for philosophers to ignore or reject relations, and speak as if all entities were either subjects or predicates. But this custom is on the decline, and I shall assume without further argument that there are such entities as relations. Philosophy has, so far as I know, no common name for all entities which are not relations. Among such entities are included not only all the things that would naturally be called particulars, but also all the universals that philosophers are in the habit of considering when they discuss the relation of particulars to universals, for universals are generally conceived as common properties of particulars, in fact, as predicates. For our purpose it is hardly worth while to invent a technical term ad hoc; I shall therefore speak of entities which are not relations simply as nonrelations.

The second logical distinction which we require is one which may or may not be identical in extension with that between relations and non-relations, but is certainly not identical in intension. It may be expressed as the distinction between verbs and substantives, or, more correctly, between the objects denoted by verbs and the objects denoted by substantives. 2 (Since this more correct expression is long and cumbrous, I shall generally use the shorter phrase to mean the same thing. Thus, when I speak of verbs, I mean the objects denoted by verbs, and similarly for substantives.) The nature of this distinction emerges from the analysis of complexes. In most complexes, if not in all, a certain number of different entities are combined into a single entity by means of a relation. "A's hatred for B," for example, is a complex in which hatred combines A and B into one whole; "C's belief that A hates B" is a complex in which belief combines A and B and C and hatred into one whole, and so on. A relation is distinguished as dual, triple, quadruple, etc., or dyadic, triadic, tetradic, etc., according to the number of terms which it unites in the simplest complexes in which it occurs. Thus in the above examples, hatred is a dual relation and belief is a quadruple relation. The capacity for combining terms into a single complex is the defining characteristic of what I call verbs. The question now arises: Are there complexes which consist of a single term and a verb? "A exists" might serve as an example of what is possibly such a complex. It is the possibility that there may be complexes of this kind which makes it impossible to decide off-hand that verbs are the same as relations. There may be verbs which are philosophically as well as grammatically intransitive. Such verbs, if they exist, may be called predicates, and the propositions in which they are attributed may be called subjectpredicate propositions. If there are no such verbs as those whose possibility we have been considering, i.e., if all verbs are relations, it will follow that subject-predicate propositions, if there are any, will express a relation of subject to predicate. ____________________ 2This is the distinction which I formerly spoke of as the distinction between things and concepts, but these terms no longer seem to me appropriate, Cf. Principles of Mathematics, § 48. -23-

Such propositions will then be definable as those that involve a certain relation called predication. Even if there are subject-predicate propositions in which the predicate is the verb, there will still be equivalent propositions in which the predicate is related to the subject; thus

"A exists," for example, will be equivalent to "A has existence." Hence the question whether predicates are verbs or not becomes unimportant. The more important question is whether there is a specific relation of predication, or whether what are grammatically subjectpredicate propositions are really of many different kinds, no one of which has the characteristics one naturally associates with subject- predicate propositions. This question is one to which we shall return at a later stage. The above logical distinctions are relevant to our enquiry because it is natural to regard particulars as entities which can only be subjects or terms of relations, and cannot be predicates or relations. A particular is naturally conceived as a this or something intrinsically analogous to a this; and such an entity seems incapable of being a predicate or a relation. A universal, on this view, will be anything that is a predicate or a relation. But if there is no specific relation of predication, so that there is no class of entities which can properly be called predicates, then the above method of distinguishing particulars and universals fails. The question whether philosophy must recognize two ultimately distinct kinds of entities, particulars and universals, turns, as we shall see more fully later on, on the question whether non-relations are of two kinds, subjects and predicates, or rather terms which can only be subjects and terms which may be either subjects or predicates. And this question turns on whether there is an ultimate simple asymmetrical relation which may be called predication, or whether all apparent subject-predicate propositions are to be analysed into propositions of other forms, which do not require a radical difference of nature between the apparent subject and the apparent predicate. The decision of the question whether there is a simple relation of predication ought perhaps to be possible by inspection, but for my part I am unable to come to any decision in this way. I think, however, that it can be decided in favour of predication by the analysis of things and by considerations as to spatio-temporal diversity. This analysis and these considerations will also show the way in which our purely logical question is bound up with the other questions as to particulars and universals which I raised at the beginning of this paper. The common-sense notion of things and their qualities is, I suppose, the source of the conception of subject and predicate, and the reason why language is so largely based on this conception. But the thing, like other common-sense notions, is a piece of half-hearted metaphysics, which neither gives crude data nor gives a tenable hypothesis as to a reality behind the data. A thing, of the everyday sort, is constituted by a bundle of sensible qualities belonging to various senses, but supposed all to coexist in one continuous por -24-

tion of space. But the common space which should contain both visual and tactile qualities is not the space of either visual or tactile perception: it is a constructed "real" space, belief in which has, I suppose, been generated by association. And in crude fact, the visual and tactile qualities of which I am sensible are not in a common space, but each in its own space. Hence if the thing is to be impartial as between sight and touch, it must cease to have the actual qualities of which we are sensible, and become their common cause or origin or whatever vaguer word can be found. Thus the road is opened to the metaphysical theories of science and to the metaphysical theories of philosophy: the thing may be a number of electric charges in rapid motion, or an idea in the mind of God, but it is certainly not what the senses perceive. The argument against things is trite, and I need not labour it. I introduce it here only in order to illustrate a consequence which is sometimes overlooked. Realists who reject particulars are apt to regard a thing as reducible to a number of qualities coexisting in one place. But, apart from other objections to this view, it is doubtful whether the different qualities in question ever do coexist in one place. If the qualities are sensible, the place must be in a sensible space; but this makes it necessary that the qualities should belong to only one sense, and it is not clear that genuinely different qualities belonging to one sense ever coexist in a single place in a perceptual space. If, on the other hand, we consider what may be called "real" space, i.e. the inferred space containing the "real" objects which we suppose to be the causes of our perceptions, then we no longer know what is the nature of the qualities, if any, which exist in this "real" space, and it is natural to replace the bundle of qualities by a collection of pieces of matter having whatever characteristics the science of the moment

may prescribe. Thus in any case the bundle of coexisting qualities in the same place is not an admissible substitute for the thing. For our purposes, the "real" object by which science or philosophy replaces the thing is not important. We have rather to consider the relations of sensible objects in a single sensible space, say that of sight. The theory of sensible qualities which dispenses with particulars will say, if the same shade of colour is found in two different places, that what exists is the shade of colour itself, and that what exists in the one place is identical with what exists in the other. The theory which admits particulars will say, on the contrary, that two numerically different instances of the shade of colour exist in the two places: in this view, the shade of colour itself is a universal and a predicate of both the instances, but the universal does not exist in space and time. Of the above two views, the first, which does not introduce particulars, dispenses altogether with predication as a fundamental relation: according to this view, when we say "this thing is white," the fundamental fact is that whiteness exists here. According to the other view, which admits particulars, what exists here is something of which whiteness is a predicate—not, -25-

as for common sense, the thing with many other qualities, but an instance of whiteness, a particular of which whiteness is the only predicate except shape and brightness and whatever else is necessarily connected with whiteness. Of the above two theories, one admits only what would naturally be called universals, while the other admits both universals and particulars. Before examining them, it may be as well to examine and dismiss the theory which admits only particulars, and dispenses altogether with universals. This is the theory advocated by Berkeley and Hume in their polemic against "abstract ideas." Without tying ourselves down to their statements, let us see what can be made of this theory. The general name "white," in this view, is defined for a given person at a given moment by a particular patch of white which he sees or imagines; another patch is called white if it has exact likeness in colour to the standard patch. In order to avoid making the colour a universal, we have to suppose that "exact likeness" is a simple relation, not analysable into community of predicates; moreover, it is not the general relation of likeness that we require, but a more special relation, that of colour-likeness, since two patches might be exactly alike in shape or size but different in colour. Thus, in order to make the theory of Berkeley and Hume workable, we must assume an ultimate relation of colour-likeness, which holds between two patches which would commonly be said to have the same colour. Now, prima facie, this relation of colour-likeness will itself be a universal or an "abstract idea," and thus we shall still have failed to avoid universals. But we may apply the same analysis to colour-likeness. We may take a standard particular case of colour-likeness, and say that anything else is to be called a colour-likeness if it is exactly like our standard case. It is obvious, however, that such a process leads to an endless regress: we explain the likeness of two terms as consisting in the likeness which their likeness bears to the likeness of two other terms, and such a regress is plainly vicious. Likeness at least, therefore, must be admitted as a universal, and, having admitted one universal, we have no longer any reason to reject others. Thus the whole complicated theory, which had no motive except to avoid universals, falls to the ground. Whether or not there are particulars, there must be relations which are universals in the sense that (a) they are concepts, not percepts; (b) they do not exist in time; (c) they are verbs, not substantives. It is true that the above argument does not prove that there are universal qualities as opposed to universal relations. On the contrary, it shows that universal qualities can, so far as logic can show, be replaced by exact likenesses of various kinds between particulars. This view has, so far as I know, nothing to recommend it beyond its logical possibility. But from the point of view of the problem whether there are particulars, it has no bearing on the argument. It is a view which is only possible if there are particulars, and it demands only an easy re-statement of subject-predicate propositions: instead of saying that an entity has such and such a predicate, we shall have to say that there are entities to which it has such and such a specific likeness. I shall therefore in future ignore this view, which in any case assumes our main

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thesis, namely, the existence of particulars. To the grounds in favour of this thesis we must now return. When we endeavoured to state the two theories as to sensible qualities, we had occasion to consider two white patches. On the view which denies particulars, whiteness itself exists in both patches: a numerically single entity, whiteness, exists in all places that are white. Nevertheless, we speak of two white patches, and it is obvious that, in some sense, the patches are two, not one. It is this spatial plurality which makes the difficulty of the theory that denies particulars. Without attempting, as yet, to introduce all the necessary explanations and distinctions, we may state the argument for particulars roughly as follows. It is logically possible for two exactly similar patches of white, of the same size and shape, to exist simultaneously in different places. Now, whatever may be the exact meaning of "existing in different places," it is self-evident that, in such a case, there are two different patches of white. Their diversity might, if we adopted the theory of absolute position, be regarded as belonging, not to the white itself which exists in the two places, but to the complexes "whiteness in this place" and "whiteness in that place." This would derive their diversity from the diversity of this place and that place; and since places cannot be supposed to differ as to qualities, this would require that the places should be particulars. But if we reject absolute position, it will become impossible to distinguish the two patches as two, unless each, instead of being the universal whiteness, is an instance of whiteness. It might be thought that the two might be distinguished by means of other qualities in the same place as the one but not in the same place as the other. This, however, presupposes that the two patches are already distinguished as numerically diverse, since otherwise what is in the same place as the one must be in the same place as the other. Thus the fact that it is logically possible for precisely similar things to coexist in two different places, but that things in different places at the same time cannot be numerically identical, forces us to admit that it is particulars, i.e., instances of universals, that exist in places, and not universals themselves. The above is the outline of our argument. But various points in it have to be examined and expanded before it can be considered conclusive. In the first place, it is not necessary to assert that there ever are two exactly similar existents. It is only necessary to perceive that our judgment that this and that are two different existents is not necessarily based on any difference of qualities, but may be based on difference of spatial position alone; and that difference of qualities, whether or not it always in fact accompanies numerical difference, is not logically necessary in order to insure numerical difference where there is difference of spatial position. Again, it is not easy to state exactly what sort of spatial distribution in perceived space warrants us in asserting plurality. Before we can use space as an argument for particulars, we must be clear on this point. We are accustomed to concede that a thing cannot be in two places at once, but this -27-

common-sense maxim, unless very carefully stated, will lead us into inextricable difficulties. Our first business, therefore, is to find out how to state this maxim in an unobjectionable form. In rational dynamics, where we are concerned with matter and "real" space, the maxim that nothing can be in two places at once is taken rigidly, and any matter occupying more than a point of space is regarded as at least theoretically divisible. Only what occupies a bare point is simple and single. This view is straightforward, and raises no difficulties as applied to "real" space. But as applied to perceived space, such a view is quite inadmissible. The immediate object of (say) visual perception is always of finite extent. If we suppose it to be, like the matter

corresponding to it in "real" space, composed of a collection of entities, one for each point which is not empty, we shall have to suppose two things, both of which seem incredible, namely: (1) that every immediate object of visual (or tactile) perception is infinitely complex; (2) that every such object is always composed of parts which are by their very nature imperceptible. It seems quite impossible that the immediate object of perception should have these properties. Hence we must suppose that an indivisible object of visual perception may occupy a finite extent of visual space. In short, we must, in dividing any complex object of visual perception, reach, after a finite number of steps, a minimum sensible, which contains no plurality although it is of finite extent. Visual space may, in a sense, be infinitely divisible, for, by attention alone, or by the microscope, the immediate object of perception can be changed in a way which introduces complexity where formerly there was simplicity; and to this process no clear limit can be set. But this is a process which substitutes a new immediate object in place of the old one, and the new object, though more subdivided than the old one, will still consist of only a finite number of parts. We must therefore admit that the space of perception is not infinitely divided, and does not consist of points, but is composed of a finite though constantly varying number of surfaces or volumes, continually breaking up or joining together according to the fluctuations of attention. If there is a "real" geometrical space corresponding to the space of perception, an infinite number of points in the geometrical space will have to correspond to a single simple entity in the perceived space. It follows from this that, if we are to apply to the immediate objects of perception the maxim that a thing cannot be in two places at once, a "place" must not be taken to be a point, but must be taken to be the extent occupied by a single object of perception. A white sheet of paper, for example, may be seen as a single undivided object, or as an object consisting of two parts, an upper and a lower or a right hand and a left hand part, or again as an object consisting of four parts, and so on. If we on this account consider that, even when the sheet appeared as an undivided object, its upper and lower halves were in different places, then we shall have to say that the undivided object was in both these places at once. But it is better to say that, when the -28-

sheet appeared as an undivided object, this object occupied only one "place," though the place corresponded to what were afterwards two places. Thus a "place" may be defined as the space occupied by one undivided object of perception. With this definition, the maxim that a thing cannot be in two places at once might seem to reduce to a tautology. But this maxim, though it may need rewording, will still have a substantial significance, to be derived from the consideration of spatial relations. It is obvious that perceived spatial relations cannot hold between points, but must hold between the parts of a single complex object of perception. When the sheet of paper is perceived as consisting of two halves, an upper and a lower, these two halves are combined into a complex whole by means of a spatial relation which holds directly between the two halves, not between supposed smaller subdivisions which in fact do not exist in the immediate object of perception. Perceived spatial relations, therefore, must have a certain roughness, not the neat smooth properties of geometrical relations between points. What, for example, shall we say of distance? The distance between two simultaneously perceived objects will have to be defined by the perceived objects between them; in the case of two objects which touch, like the two halves of the sheet of paper, there is no distance between them. What remains definite is a certain order; by means of right and left, up and down, and so on, the parts of a complex object of perception acquire a spatial order, which is definite, though not subject to quite the same laws as geometrical order. The maxim that a thing cannot be in two places at once will then become the maxim that every spatial relation implies diversity of its terms, i.e., that nothing is to the right of itself, or above itself, and so on. In that case, given two white patches, one of which is to the right of the other, it will follow that there is not a single thing, whiteness, which is to the right of itself, but that there are two different things, instances of whiteness, of which one is to the right of the other. In this way our maxim will support the conclusion that there must be particulars as well as universals. But the above outline of an argument needs some amplification before it can be considered conclusive. Let us therefore examine, one by one, the steps of the argument.

Let us suppose, for the sake of definiteness, that within one field of vision we perceive two separated patches of white on a ground of black. It may then be taken as quite certain that the two patches are two and not one. The question is: Can we maintain that there are two if what exists in each is the universal whiteness? If absolute space is admitted, we can of course say that it is the difference of place that makes the patches two; there is whiteness in this place, and whiteness in that place. From the point of view of our main problem, which is as to the existence of particulars, such a view would prove our thesis, since this place and that place would be or imply particulars consituting absolute space. But from the point of view of our immediate problem, which is concerned with plurality in perceived space, we might reject the above view on -29-

the ground that, whatever may be the case with "real" space, perceived space is certainly not absolute, i.e., absolute positions are not among objects of perception. Thus the whiteness here and the whiteness there cannot be distinguished as complexes of which this place and that place are respectively constituents. Of course the whiteness may be of different shapes, say one round and one square, and then they could be distinguished by their shapes. It will be observed that, with the view adopted above as to the nature of perceived space, it is perfectly possible for a simple object of perception to have a shape: the shape will be a quality like another. Since a simple object of perception may be of finite extent, there is no reason to suppose that a shape must imply spatial divisibility in the object of perception. Hence our two patches may be respectively round and square, and yet not be spatially divisible. It is obvious, however, that this method of distinguishing the two patches is altogether inadequate. The two patches are just as easily distinguished if both are square or both are round. So long as we can see both at once, no degree of likeness between them causes the slightest difficulty in perceiving that there are two of them. Thus difference of shape, whether it exists or not, is not what makes the patches two entities instead of one. It may be said that the two patches are distinguished by the difference in their relations to other things. For example, it may happen that a patch of red is to the right of one and to the left of the other. But this does not imply that the patches are two unless we know that one thing cannot be both to the right and to the left of another. This, it might be said, is obviously false. Suppose a surface of black with a small white space in the middle. Then the whole of the black may form only one simple object of perception, and would seem to be both to the right and to the left of the white space which it entirely surrounds. I think it would be more true to say, in this case, that the black is neither to the right nor to the left of the white. But right and left are complicated relations involving the body of the percipient. Let us take some other simpler relation, say that of surrounding, which the black surface has to the white patch in our example. Suppose we have another white patch, of exactly the same size and shape, entirely surrounded by red. Then, it may be said, the two patches of white are distinguished by difference of relation, since one is surrounded by black and the other by red. But if this ground of distinction is to be valid, we must know that it is impossible for one entity to be both wholly and immediately surrounded by black and wholly and immediately surrounded by red. I do not mean to deny that we do know this. But two things deserve notice—first, that it is not an analytic proposition; second, that it presupposes the numerical diversity of our two patches of white. We are so accustomed to regarding such relations as "inside" and "outside" as incompatible that it is easy to suppose a logical incompatibility, although in fact the incompatibility is a characteristic of space, not a result of logic. I do not know what are the unanalysable spatial relations of objects of perception, whether visual or tactile, but whatever they are they must have -30-

the kind of characteristics which are required in order to generate an order. They, or some of them, must be asymmetrical, i.e., such that they are incompatible with their converses: for example, supposing "inside" to be one of them, a thing which is inside another must not also be outside it. They, or some of them, must also be transitive, i.e., such that, for example, if x is inside y and y is inside z, then x is inside z—supposing, for the sake of illustration, "inside" to be among fundamental spatial relations. Probably some further properties will be required, but these at least are essential, in view of the fact that there is such a thing as spatial order. It follows that some at least of the fundamental spatial relations must be such as no entity can have to itself. It is indeed self-evident that spatial relations fulfil these conditions. But these conditions are not demonstrable by purely logical considerations: they are synthetic properties of perceived spatial relations. It is in virtue of these self-evident properties that the numerical diversity of the two patches of white is self-evident. They have the relation of being outside each other, and this requires that they should be two, not one. They may or may not have intrinsic differences—of shape, or size, or brightness, or any other quality—but whether they have or not they are two, and it is obviously logically possible that they should have no intrinsic differences whatever. It follows from this that the terms of spatial relations cannot be universals, but must be particulars capable of being exactly alike and yet numerically diverse. It is very desirable, in such discussions as that on which we are at present engaged, to be able to talk of "places" and of things or qualities "occupying" places, without implying absolute position. It must be understood that, on the view which adopts relative position, a "place" is not a precise notion. But its usefulness arises as follows: Suppose a set of objects, such as the walls and furniture of a room, to retain their spatial relations unchanged for a certain length of time, while a succession of other objects, say people who successively sit in a certain chair, have successively a given set of spatial relations to the relatively fixed objects. Then the people have, one after the other, a given set of properties, consisting in spatial relations to the walls and furniture. Whatever has this given set of properties at a given moment is said to "occupy" a certain place, the "place" itself being merely a fixed set of spatial relations to certain objects whose spatial relations to each other do not change appreciably during the time considered. Thus when we say that one thing can only be in one place at one time, we mean that it can only have one set of spatial relations to a given set of objects at one time, It might be argued that, since we have admitted that a simple object of perception may be of finite extent, we have admitted that it may be in many places at once, and therefore may be outside itself. This, however, would be a misunderstanding. In perceived space, the finite extent occupied by a simple object of perception is not divided into many places. It is a single place occupied by a single thing. There are two different ways in which this place may "correspond" to many places. First, if there is such a thing as -31-

"real" space with geometrical properties, the one place in perceived space will correspond to an infinite number of points in "real" space, and the single entity which is the object of perception will correspond to many physical entities in "real" space. Secondly, there is a more or less partial correspondence between perceived space at one time and perceived space at another. Suppose that we attend closely to our white patch, and meanwhile no other noticeable changes occur in the field of vision. Our white patch may, and often does, change as the result of attention—we may perceive differences of shade of other differentiations, or, without differences of quality, we may merely observe parts in it which make it complex and introduce diversity and spatial relations within it. We consider, naturally, that we are still looking at the same thing as before, and that what we see now was there all along. Thus we conclude that our apparently simple white patch was not really simple. But, in fact, the object of perception is not the same as it was before; what may be the same is the physical object supposed to correspond to the object of perception. This physical object is, of course, complex. And the perception which results from attention will be in one sense more correct than that which perceived a simple object, because, if attention reveals previously unnoticed differences, it may be assumed that there are corresponding differences in the "real" object which corresponds to the object of perception. Hence the perception resulting from attention gives more information about the "real" object than the

other perception did: but the object of perception itself is no more and no less real in the one case than in the other—that is to say, in both cases it is an object which exists when perceived, but which there is no reason to believe existent except when it is perceived. In perceived space, the spatial unit is not a point, but a simple object of perception or an ultimate constituent in a complex object of perception. This is the reason why, although two patches of white which are visibly separated from each other must be two, a continuous area of white may not be two. A continuous area, if not too large, may be a single object of perception not consisting of parts, which is impossible for two visibly separated areas. The spatial unit is variable, constantly changing its size, and subject to every fluctuation of attention, but it must occupy a continuous portion of perceived space, since otherwise it would be perceived as plural. The argument as to numerical diversity which we have derived from perceived space may be reinforced by a similar argument as regards the contents of different minds. If two people are both believing that two and two are four, it is at least theoretically possible that the meanings they attach to the words two and and and are and four are the same, and that therefore, so far as the objects of their beliefs are concerned, there is nothing to distinguish the one from the other. Nevertheless, it seems plain that there are two entities, one the belief of the one man and the other the belief of the other. A particular belief is a complex of which something which we may call a subject is a constituent; in our case, it is the diversity of the subjects that produces the diversity of the beliefs. But these subjects cannot be mere bundles of general -32-

qualities. Suppose one of our men is characterized by benevolence, stupidity, and love of puns. It would not be correct to say: "Benevolence, stupidity, and love of puns believe that two and two are four." Nor would this become correct by the addition of a larger number of general qualities. Moreover, however many qualities we add, it remains possible that the other subject may also have them; hence qualities cannot be what constitutes the diversity of the subjects. The only respect in which two different subjects must differ is in their relations to particulars: for example, each will have to the other relations which he does not have to himself. But it is not logically impossible that everything concerning one of the subjects otherwise only concerning universals might be true of the other subject. Hence, even when differences in regard to such propositions occur, it is not these differences that constitute the diversity of the two subjects. The subjects, therefore, must be regarded as particulars, and as radically different from any collection of those general qualities which may be predicated of them. It will be observed that, according to the general principles which must govern any correspondence of real things with objects of perception, any principle which introduces diversity among objects of perception must introduce a corresponding diversity among real things. I am not now concerned to argue as to what grounds exist for assuming a correspondence, but, if there is such a correspondence, it must be supposed that diversity in the effects—i.e., the perceived objects—implies diversity in the causes—i.e., the real objects. Hence if I perceive two objects in the field of vision, we must suppose that at least two real objects are concerned in causing my perception. The essential characteristic of particulars, as they appear in perceived space, is that they cannot be in two places at once. But this is an unsatisfactory way of stating the matter, owing to the doubt as to what a "place" is. The more correct statement is that certain perceptible spatial relations imply diversity of their terms; for example, if x is above y, x and y must be different entities. So long, however, as it is understood that this is what is meant, no harm is done by the statement that a thing cannot be in two places at once. We may now return to the question of particulars and universals with a better hope of being able to state precisely the nature of the opposition between them. It will be remembered that we began with three different oppositions : (1) that of percept and concept, (2) that of entities existing in time and entities not existing in time, (3) that of substantives and verbs. But in the course of our discussion a different opposition developed itself, namely, (4) that between entities which can be in one place, but not in more than one, at a given time, and

entities which either cannot be anywhere or can be in several places at one time. What makes a particular patch of white particular, whereas whiteness is universal, is the fact that the particular patch cannot be in two places simultaneously, whereas the whiteness, if it exists at all, exists wherever there are white things. This opposition, as stated, might be -33-

held not to apply to thoughts. We might reply that a man's thoughts are in his head; but without going into this question, we may observe that there certainly is some relation between a man's thoughts and his head (or some part of it) which there is not between his thoughts and other things in space. We may extend our definition of particulars so as to cover this relation. We may say that a man's thought "belongs to" the place where his head is. We may then define a particular in our fourth sense as an entity which cannot be in or belong to more than one place at one time, and a universal as an entity which either cannot be in or belong to any place, or can be in or belong to many places at once. This opposition has certain affinities with the three earlier oppositions, which must be examined. (1) Owing to the admission of particulars in our fourth sense, we can make an absolute division between percepts and concepts. The universal whiteness is a concept, whereas a particular white patch is a percept. If we had not admitted particulars in our fourth sense, percepts would have been identical with certain concepts. (2) For the same reason, we are able to say that such general qualities as whiteness never exist in time, whereas the things that do exist in time are all particulars in our fourth sense. The converse, that all particulars in our fourth sense exist in time, holds in virtue of their definition. Hence the second and fourth senses of the opposition of particulars and universals are co- extensive. (3) The third opposition, that of substantives and verbs, presents more difficulties, owing to the doubt whether predicates are verbs or not. In order to evade this doubt, we may substitute another opposition, which will be co - extensive with substantives and verbs if predicates are verbs, but not otherwise. This other opposition puts predicates and relations on one side, and everything else on the other. What is not a predicate or relation is, according to one traditional definition, a substance. It is true that, when substance was in vogue, it was supposed that a substance must be indestructible, and this quality will not belong to our substances. For example, what a man sees when he sees a flash of lightning is a substance in our sense. But the importance of indestructibility was metaphysical, not logical. As far as logical properties are concerned, our substances will be fairly analogous to traditional substances. Thus we have the opposition of substances on the one hand and predicates and relations on the other hand. The theory which rejects particulars allows entities commonly classed as predicates—e.g. white—to exist; thus the distinction between substances and predicates is obliterated by this theory. Our theory, on the contrary, preserves the distinction. In the world we know, substances are identical with particulars in our fourth sense, and predicates and relations with universals. It will be seen that, according to the theory which assumes particulars, there is a specific relation of subject to predicate, unless we adopt the view— considered above in connexion with Berkeley and Hume—that common sensible qualities are really derivative from specific kinds of likeness. Assum -34-

ing this view to be false, ordinary sensible qualities will be predicates of the particulars which are instances of them. The sensible qualities themselves do not exist in time in the same sense in which the instances do. Predication is a relation involving a fundamental logical difference between its two terms. Predicates may themselves have predicates, but the predicates of predicates will be radically different from the predicates of substances. The predicate, on this view, is never part of the subject, and thus no true subject-predicate proposition is analytic. Propositions of the form "All A is B" are not really subject-predicate propositions, but express relations of predicates; such propositions may be analytic, but the

traditional confusion of them with true subject-predicate propositions has been a disgrace to formal logic. The theory which rejects particulars, and assumes that, e.g., whiteness itself exists wherever (as common sense would say) there are white things, dispenses altogether with predication as a fundamental relation. "This is white," which, on the other view, expresses a relation between a particular and whiteness, will, when particulars are rejected, really state that whiteness is one of the qualities in this place, or has certain spatial relations to certain other qualities. Thus the question whether predication is an ultimate simple relation may be taken as distinguishing the two theories; it is ultimate if there are particulars, but not otherwise. And if predication is an ultimate relation, the best definition of particulars is that they are entities which can only be subjects of predicates or terms of relations, i.e., that they are (in the logical sense) substances. This definition is preferable to one introducing space or time, because space and time are accidental characteristics of the world with which we happen to be acquainted, and therefore are destitute of the necessary universality belonging to purely logical categories. We have thus a division of all entities into two classes: (1) particulars, which enter into complexes only as the subjects of predicates or the terms of relations, and, if they belong to the world of which we have experience, exist in time, and cannot occupy more than one place at one time in the space to which they belong; (2) universals, which can occur as predicates or relations in complexes, do not exist in time, and have no relation to one place which they may not simultaneously have to another. The ground for regarding such a division as unavoidable is the self-evident fact that certain spatial relations imply diversity of their terms, together with the self-evident fact that it is logically possible for entities having such spatial relations to be wholly indistinguishable as to predicates. -35-

:2: UNIVERSALS AND RESEMBLANCES H. H. PRICE WHEN we consider the world around us, we cannot help noticing that there is a great deal of recurrence or repetition in it. The same colour recurs over and over again in ever so many things. Shapes repeat themselves likewise. Over and over again we notice oblong-shaped things, hollow things, bulgy things. Hoots, thuds, bangs, rustlings occur again and again. There is another and very important sort of recurrence which we also notice. The same pattern or mode of arrangement is found over and over again in many sets of things, in many different pairs of things, or triads, or quartets, as the case may be. When A is above B, and C is above D, and E is above F, the above-and-below pattern or mode of arrangement recurs in three pairs of things, and in ever so many other pairs of things as well. Likewise we repeatedly notice one thing inside another, one preceding another, one thing between two others. These recurrent features sometimes recur singly or separately. The same colour recurs in this tomato, that sunset sky, and this blushing face; there are few other features, if any, which repeat themselves in all three. But it is a noteworthy fact about the world that there are conjoint recurrences as well as separate ones. A whole group of features recurs again and again as a whole in many objects. Examine twenty dandelions, and you will find that they have many features in common; likewise fifty cats have very many features in common, or two hundred lumps of lead. In such cases as these there is conjoint recurrence of many different features. Again and again they recur together in a clump or block. This is how it comes about that many of the objects in the world group themselves together into Natural Kinds. A Natural Kind is a group of objects which have many (perhaps indefinitely many) features in common. From observing that an object has some of these features, we can infer with a good deal of probability that it has the rest.

These constant recurrences or repetitions, whether separate or conjoint ones, are what make the world a dull or stale or boring place. The same old ____________________ This selection consists of Chapter 1 of H. H. Price's Thinking and Experience (London: Hutchinson's University Library, 1953), reprinted by permission of the publisher.

features keep turning up again and again. The best they can do is to present themselves occasionally in new combinations, as in the black swan or the duck-billed platypus. There is a certain monotony about the world. The extreme case of it is found where the same old feature repeats itself in all parts of a single object, as when something is red all over, or sticky all through, or a noise is uniformly shrill throughout its entire duration. Nevertheless, this perpetual repetition, this dullness or staleness, is also immensely important, because it is what makes conceptual cognition possible. In a world of incessant novelty, where there was no recurrence at all and no tedious repetitions, no concepts could ever be acquired; and thinking, even of the crudest and most primitive kind, could never begin. For example, in such a world nothing would ever be recognizable. Or again, in so far as there is novelty in the world, non-recurrence, absence of repetition, so far the world cannot be thought about, but only experienced. Hitherto I have been trying to use entirely untechnical language, so that we may not commit ourselves unawares to any philosophical theory. But it is at any rate not unnatural, it is not a very wild piece of theorizing, to introduce the words "quality" and "relation" for referring to those facts about the world to which I have been trying to draw the reader's attention. A quality, we say, is a recurrent feature of the world which presents itself in individual objects or events taken singly. Redness or bulginess or squeakiness are examples. A relation, on the other hand, is a recurrent feature of the world which presents itself in complexes of objects or events, such as this beside that, this preceding that, or B between A and C. It is also convenient sometimes to speak of relational properties. If A precedes B, we may say that A has the relational property of preceding B, and B has the converse relational property of succeeding A. One further remark may be made on the distinction between qualities and relations. I said just now that a quality presents itself in individual objects or events taken singly, and a relation in complexes of objects or events. But it must not be forgotten that an individual object or event usually (perhaps always) has an internal complexity. In its history there is a plurality of temporal phases, and often it has a plurality of spatial parts as well. And there are relations between these parts, or these phases, which it has. Such relations within an individual object or event are sometimes said to constitute the "structure" of the object or event. For scientific purposes, and even for purposes of ordinary common sense prediction, what we most need to know about any object or process is its structure. And from this point of view the chief importance of qualities, such as colour or hardness or stickiness, is that they often enable us to infer the presence of a structure more minute than our unaided senses would reveal. It has often been maintained that sensible qualities are "subjective." But subjective or not, they have a most important function. They give us a clue to what the minute structure of objects and events is. If a gas smells like rotten eggs, we can infer that it is sulphuretted hydrogen. -37-

The terms "quality" and "relation" enable us to give a simple analysis of change. The notion of change has puzzled some philosophers greatly, ever since Heracleitus, or some disciple of his, remarked long ago that πàντa ̕ρ∊î, "all things flow." Indeed, it has sometimes led them to suppose that this world is a world of perpetual novelty after all, and not the tedious or boring or repetitious world which it has to be, if conceptual cognition is to be possible. They

have, therefore, concluded—rightly, from their premises—that all conceptual cognition is radically erroneous or illusory, a kind of systematic distortion of Reality; so that whatever we think, however intelligent or however stupid we may be, we are in error. On this view, only non-conceptual cognition—immediate experience or direct intuition—can be free from error. These conclusions are so queer that we suspect something is wrong with the premises. We can now see what it is. The notion of Change, as Plato pointed out, has itself to be analysed in terms of the notions of Quality and Relation. In qualitative change, as when an apple changes from being green to being red, an object has quality q 1 at one time and a different quality q 2 at a later time. In relational change, an object A has a relation R 1 to another object B at one time, and a different relation R 2 to B at a later time. At 12 o'clock, for example, it is six inches away from B, at 12.5 it is a mile away from B; at one time the relation it has to B is the relation "hotter than," at another the relation "as hot as," at another the relation "cooler than." It is not necessary for our present purposes to enquire whether there are other recurrent features of the world which are neither qualities nor relations nor analysable in terms of these. Some philosophers have thought, for instance, that causality (in its various determinate forms, hitting, bending, pushing, pulling, attracting, repelling, etc.) was such an ultimate and irreducible feature of the world, recurring or repeating itself in many situations. Others have undertaken to give a purely relational analysis of causality (the "Regularity" theory). For our present purpose, however—which is merely to explain why philosophers have thought it worth while to talk about recurrent features of the world at all—it is not necessary to decide how many irreducibly different types of recurrents there might be. It will be enough to consider just qualities and relations. We may now sum up the results of this ontological discussion so far by introducing another technical term, again not so very technical, the term "characteristic." Characteristics, we say, are of at least two different types, qualities and relations. What has been said so far then comes to this: there are recurrent characteristics in the world, which repeat themselves over and over again in many different contexts. Is it not just an obvious fact about the world, something we cannot help noticing whether we like it or not, that there are recurrent characteristics? Now these recurrent characteristics have been called by some philosophers universals. And the line of thought we have been pursuing leads very naturally to the traditional Aristotelian doctrine of universalia in rebus, "universals in things." (To provide for universals of relation, "things" must be understood to cover complexes as well as individuals. -38-

The res which the universal "beside" is in is not this, nor that, but this-and - that.) I do not propose to discuss the Platonic doctrine of universalia ante rem, "universals anterior to (or independent of) things." This is not because I think it uninteresting or unimportant, but merely because it is more remote from common sense and our ordinary everyday habits of thought than the Aristotelian theory of universalia in rebus. It is a sufficiently difficult task in these days to convince people that there is any sense in talking of universals at all, even in the mild and moderate Aristotelian way. The doctrine of universalia in rebus may, of course, be mistaken, or gravely misleading. There certainly are objections to it, as we shall find presently. But I cannot see that it is in the least absurd or silly, as the most approved thinkers nowadays seem to suppose. Nor can I see that it arises entirely from erroneous views about language, as the same thinkers seem to suppose; for example, from the superstition that all words are names, from which it would follow that general or abstract words must be names of general or abstract entities. On the contrary, this philosophy seems to me to be the result, and the very natural result, of certain ontological reflections. It seems to me to arise from reflections about the world; from consideration of what things are, and not— or certainly not merely—from consideration of the way we talk about them. On the contrary, it could be argued that we talk in the way we do, using general terms and abstract terms, because of what we find the world to be; because we find or notice recurrences in it.

Let us now consider how the doctrine of universalia in rebus might mislead us, although it arises in this natural and plausible way from the ontological considerations which we have been discussing. One danger of it obviously is that universals may be regarded as a sort of things or entities, over and above the objects or situations in which they recur. We may indeed emphasize the word "in." We may insist that universals are in things, and not apart from them as the doctrine of universalia ante rem maintains. But is the danger of supposing that they are themselves things or quasi-things entirely removed? Does it not arise over again as soon as we reflect upon the implications of the word "in" itself? If it is our profession to be misled—as, of course, it is the profession of philosophers—we shall be liable to suppose that redness is in the tomato somewhat as juice is in it, or as a weevil is in it. And if so, what can be meant by saying that redness is recurrent? How can it be in thousands of other tomatoes as well, or hundreds of post boxes, or dozens of blushing faces? It does not make sense to say that a weevil is in many places at once. Again, when the tomato begins to decay and turns brown, where has the redness gone to, which used to be in it? (The weevil has gone somewhere else; you will find him in the potato basket.) Likewise, where has the brownness come from? If we prefer to say that the tomato has redness, rather than "redness is in -39-

it," we shall again mislead these literal-minded persons, and in the same sort of way. Does the tomato have redness as Jones has a watch? If so, how can millions of other things have it too? I confess that I do not think much of these difficulties. The meaning of "in" and "have" in this context can be quite easily exhibited by examples, just as their literal meaning can, when we say that there is a weevil in the tomato, or I have a watch. Surely we all know quite well what is being referred to when two things are said to have the same colour? And is it really so very difficult to recognize what is meant by saying that the same colour is in them both? It is true no doubt that the words "in" and "have" are here being used in a metaphorical sense, though not, I think, extravagantly metaphorical. But we must use metaphorical words, or else invent new and technical terms (which are themselves usually metaphorical words taken from a dead language, Greek or Latin). Our ordinary language exists for practical ends, and it has to be "stretched" in one way or other if we are to use it for purposes of philosophical analysis. And if our metaphors can be cashed quite easily by examples, as these can, no harm whatever is done. It could, however, be argued that the terminology of "characteristics," which was current in the last philosophical epoch, some twenty years ago, is better than the more ancient terminology of "universals." A characteristic is pretty obviously a characteristic of something or other, and cannot easily be supposed to be an independent entity, like the weevil. Nor can we be easily misled into supposing that when something "has" a characteristic, i.e. is characterized by it, this is at all analogous to the having of a watch. In the technical symbolism of Formal Logic, the most appropriate expression for referring to one of these recurrent features of the world is not a single letter, such as ϕ or R, which might possibly be mistaken for the name of an entity, but a propositional function, such as ϕx, or xRy, or R(x,y,z). Here the x, y and z are variables, so that the propositional function is an overtly incomplete expression. To complete it, one must replace the variable by a constant, denoting some object which satisfies the function; or if there are several variables, as in xRy or R(x,y,z), each of these must be replaced by a constant. The terminology of characteristics is an approximate equivalent in words to the non-verbal symbolism of propositional functions, and has much the same advantages; whereas if we use the more traditional terminology of universals, there is some danger (though not, I think, unavoidable) that we may be led to speak of them as though they were in themselves complete and independent entities. Henceforth, the Aristotelian theory of universalia in rebus will be called "the Philosophy of Universals" for short. If our argument so far has been correct, the Philosophy of Universals is drawing our attention to certain important facts about the world. Yet it is at the same time

proposing an analysis of those facts. We cannot dispute the facts, nor can we dispute their funda -40-

mental importance. We cannot deny that something which may be called "the recurrence of characteristics" is genuinely there. We must also admit that if it were not there, conceptual cognition could not exist. If the world were not like this, if there were no recurrence in it, it could be neither thought about nor spoken about. We could never have acquired any concepts; and even if we had them innately (without needing to acquire them) they could never have been applied to anything. But though we cannot dispute the facts, nor their importance, we may, nevertheless, have doubts about the analysis of them which the Philosophy of Universals proposes. At any rate, another and quite different analysis of them appears to be possible. It is the analysis offered by what one may call the Philosophy of Ultimate Resemblances. (Henceforth I shall call this "the Philosophy of Resemblances" for short.) This is the analysis which most contemporary philosophers accept, so far as they consider the ontological side of the Problem of Universals at all. It is also accepted by Conceptualists, like Locke. The Philosophy of Resemblances is more complicated than the Philosophy of Universals, and more difficult to formulate. It involves one in long and cumbrous circumlocutions. Yet it claims, not unplausibly, that it keeps closer to the facts which have to be analysed. The unkind way of putting this, the one its critics prefer, is to say that it is "more naturalistic." Let us now consider the Philosophy of Resemblances in more detail. When we say that a characteristic, e.g. whiteness, recurs, that it presents itself over and over again, that it characterizes ever so many numerically different objects, what we say is admittedly in some sense true. But would it not be clearer, and closer to the facts, if we said that all these objects resemble each other in a certain way? Is not this the rock-bottom fact to which the Philosophy of Universals is drawing our attention, when it uses this rather inflated language of "recurrent characteristics"? The Philosophy of Universals of course agrees that all the objects characterized by whiteness do resemble one another. But according to it, resemblance is always derivative, and is just a consequence of the fact that the very same characteristic—whiteness, in this case—characterizes all these objects. To use more traditional language, it says that when A resembles B, this is because they are both instances of the same universal. Now this is all very well where the resemblance is exact, but what are we to say when it is not? Let us consider the following series of examples: a patch of freshly fallen snow; a bit of chalk; a piece of paper which has been used for wrapping the meat in; the handkerchief with which I have been dusting a rather dirty mantelpiece; a full evening dress bow tie which has been left lying about for several years on the floor. All these, we say, are white objects. But are they exactly alike in their colour, if white may be counted as a colour for the purpose of this discussion? Clearly they are not. They are, of course, more or less alike. In fact there is a very considerable degree of colour-likeness between them. But certainly they are not exactly alike in -41-

colour. And yet if the very same characteristic, whiteness, is present in them all (as the Philosophy of Universals, apparently, says it is) ought it not to follow that they are exactly alike in colour? To make quite clear what the point at issue is, we shall have to distinguish, rather pedantically perhaps, between exact resemblance in this or that respect and total or complete resemblance. To put it in another way, resemblance has two dimensions of variation. It may vary in intensity; it may also vary in extent. For example, a piece of writing paper and an envelope, before one has written on either of them, may be exactly alike in colour, and perhaps also in texture. These likenesses between them have the maximum degree of intensity. But the two objects are not completely or totally alike. For one thing, they are unlike in shape. Moreover, the envelope is stuck together with gum and has gum on its flap,

while the piece of writing paper has no gum on it. It might perhaps be thought that two envelopes from the same batch are completely alike; and certainly they come nearer to it than the envelope and the piece of notepaper. All the same, there is unlikeness in respect of place. At any given time, envelope A is in one place and envelope B is in a different place. On the Relational Theory of Space, this is equivalent to saying that at any given time A and B are related in unlike ways to something else, e.g. the North Pole, or Greenwich Observatory. According to Leibniz's Principle of the Identity of Indiscernibles, complete or total likeness is an ideal limit which can never quite be reached, though some pairs of objects (the two envelopes, for example) come closer to it than others. For if per impossible two objects were completely alike, place and date included, there would no longer be two objects, but only one. Whether Leibniz's Principle is correct, has been much disputed. But we need not concern ourselves with this dispute. It is sufficient to point out that if there were two objects which resembled each other completely, in date and place as well as in all other ways, and this complete resemblance continued throughout the whole of the histories of both, there could not possibly be any evidence for believing there were two of them. So in this discussion we need not concern ourselves any more with complete or total resemblance, though it is of course an important fact about resemblances that they vary in extent, as well as in degree of intensity. What does concern us is intensity of resemblance. The maximum intensity of it is what I called "exact resemblance in this or that respect." Now some people appear to think that even this is an ideal limit. They seem to think that no two objects are ever exactly alike even in one way (e.g. colour, or shape) though, of course, many objects are closely alike in one way or in several. I do not see what evidence we could have for believing such a sweeping negative generalization. It is true that sometimes, when we thought at first that there was an exact likeness in one or more respects between two objects, we may find on more careful examination that there was not. We may have thought that two twins were exactly alike in the conformation of -42-

their faces. We look more closely, and find that John's nose is a millimetre longer than William's. But still, there are many cases where there is no discoverable inexactness in a resemblance. We often find that two pennies are indistinguishable in shape, or two postage stamps indistinguishable in colour. And we should not confine ourselves to cases where two or more objects are being compared. There is such a thing as monotony or uniformity within a single object. For example, a certain patch of sky is blue, and the same shade of blue, all over. It is monotonously ultramarine. In other words, all its discernible parts are exactly like each other in colour; at any rate, we can discover no unlikeness of colour between them. Again, there is often no discoverable unlikeness of pitch between two successive phases of the same sound. Will it be said that such monotony is only apparent, not real? But what ground could we have for thinking that no entity is ever really "monotonous" in this sense, not even in the smallest part of its extent, or throughout the smallest phase of its duration? Thus there is no good ground for maintaining that resemblance of maximum intensity never occurs at all, still less for maintaining that it never could occur. Nevertheless, it is not so very common for two objects to be exactly alike even in one way, though monotony within a single object or event is more frequent. What we most usually find in two or more objects which are said to be "alike" is close resemblance in one respect or in several. We can now return to the controversy between the Philosophy of Resemblances and the Philosophy of Universals. It is argued that if the Philosophy of Universals were right, exact resemblance in one or several respects (resemblance of maximum intensity) ought to be much more common than it is; indeed, that inexact resemblance in a given respect, say colour or shape, ought not to exist at all. Of course, there could still be incomplete or partial resemblance, resemblance between two objects in one respect or in several, and lack of resemblance in others. But whenever two objects do resemble each other in a certain respect, it would appear that the resemblance ought to be exact (of maximum intensity), if the Philosophy of Universals were right; either it should be exact, or else it should not exist at all. The Philosophy of Universals tells us that resemblance is derivative, not ultimate; that when two objects resemble each other in a given respect, it is because the very same

universal is present in them both. This seems to leave no room for inexact resemblance. Now if we consider the various white objects I mentioned before—the whole series of them, from the freshly fallen snow to the unwashed bow-tie— how can anyone maintain that the very same characteristic, whiteness, recurs in all of them? Clearly it does not. If it did, they must be exactly alike in their colour; and quite certainly they are not. If we are to use the language of universals or characteristics, shall we not have to say that each of the objects in this series, from the snow to the unwashed tie, is characterized by a different characteristic, or is an instance of a different universal? In this case, -43-

then, the resemblance seems to be ultimate and underivative, not dependent on the presence of a single universal in all these objects, although they certainly do resemble each other. Let us consider another example. Two pennies may be exactly alike in their shape. If so, one may plausibly say that the very same characteristic, roundness, is present in both of them, and that their resemblance is dependent on this. But what about a penny and a sixpence? They certainly are alike in shape; but not exactly, because the sixpence has a milled edge and the penny a smooth one. So here again, it would seem, there is no single characteristic present in them both, upon which the resemblance could be dependent. This resemblance again seems to be ultimate and underivative. Thus the Philosophy of Universals, when it makes all resemblance derivative, appears to forget that resemblances have degrees of intensity. Resemblance is treated as if it were degreeless, either present in its maximum degree or else not present at all. In practice, the Philosopher of Universals concentrates his attention on close resemblances, and averts his attention from the awkward circumstance that few of them are exact; and resemblances of a lower degree than this (small or moderate ones, not intense enough to be called "close") are just neglected altogether. But is it not a glaringly obvious fact that resemblances do differ in degree or intensity? That being so, shall we not be inclined to reverse this alleged dependence- relation between "being alike" and "being characterized by"? Surely we shall be inclined to say that it is resemblance which is more fundamental than characterization, rather than the other way round. We shall, of course, be willing to go on using terms like "characteristic" and "characterized by"; they are part of ordinary language, and everyone has a sufficient understanding of them. But we shall define "characteristic" in terms of resemblance, and not conversely. Where a number of objects do happen to resemble each other exactly in one respect or three or fifteen, there, and in consequence, we shall be quite willing to say that they have one, or three, or fifteen "characteristics in common." But in other cases, where the resemblance is less than exact, we shall not be willing to say this. We shall just say that they resemble each other in such and such a degree, and stop there. In a given set of objects there is whatever degree or resemblance there is. Let us be content to take the facts as we find them. Turning for a moment to the epistemological side of the matter, surely it is obvious that the applicability of concepts does not require an exact resemblance in the objects which a concept applies to? Of course there does have to be a considerable degree of resemblance between all the objects which "satisfy" a given concept. As we say, there has to be a sufficient likeness between them, e.g. between all the objects to which the concept White applies. What degree of likeness is sufficient, and where the borderline comes between something which falls just within the concept's sphere of application and something else which just falls outside it, is often difficult to decide. For instance, one may wonder whether the very dirty bow-tie is white at all. In -44-

deed, it is difficult to see how such a question can be definitely answered, at least in the case of whiteness and many other familiar concepts. The right way to tackle it, perhaps, is to refuse to answer it as it stands. Perhaps we should rather say that a concept may be

"satisfied" in many different degrees; or, in more commonsensical language, that there are good instances and bad instances, better and worse ones, and some so bad that it is arbitrary whether one counts them as instances or not. Thus the piece of chalk is a better instance of whiteness than the rather dirty handkerchief is. The patch of freshly fallen snow is a better instance still, perhaps a perfect one. We may give it the mark a (+). Then αβ is about the right mark for the piece of chalk, and we will give the unwashed bow-tie γ=, to denote that it is just on the borderline between "pass" and "failure." It is not easy to see how the doctrine of universalia in rebus can make any room for this important and familiar notion of degrees of instantiation. But there is plenty of room for it in Conceptualism, which is the epistemological counterpart of the ontological Philosophy of Resemblances. We must add, in fairness, that there is also plenty of room for it in the Platonic doctrine of universalia ante rem. Indeed Plato, or perhaps Socrates, was the first philosopher who noticed that there are degrees of instantiation. This is one of the points, and a good point, which Conceptualism and Platonic Realism have in common. 1 In the last few pages, I have been discussing the difficulties which the Resemblance Philosophers find in the Philosophy of Universals. But the Philosophy of Resemblances has its difficulties too. The most important ones are concerned with resemblance itself. I shall discuss two of them, and the solutions proposed for them. The first arises from the phrase "resemblance in respect of...." It is obvious that we must distinguish between different resemblances. Objects resemble each other in different respects, as well as in different degrees. Red objects resemble each other in one respect, round objects in another respect. The members of a natural kind, for instance cats or oak trees, resemble each other in many respects at once. Thus it would be much too vague if we said that red objects, for example, are just a set of objects which resemble one another, or sufficiently resemble each other. That would not distinguish them from blue objects, or round objects, or any other class of objects one cares to name. We must specify what resemblance it is. Red objects are those which resemble each other "in a certain respect." But in what respect ? And now it looks as if we should have to introduce universals again. Our first answer would probably be that they resemble each other in respect of colour; and this looks very like saying that they are all instances of the universal Colouredness. That is bad enough; but we shall be driven to go ____________________ 1In Christian Platonism, where Plato's transcendent "forms" become concepts in the mind of God, the differences between Platonic Realism and Conceptualism are still further diminished, though they do not disappear altogether. -45-

farther, because we have not yet said enough to distinguish red objects from blue ones or green ones. Can we stop short of saying that red objects are just those objects which resemble each other in respect of redness? And here we seem to be admitting the very point which the Philosophy of Universals is so anxious to maintain; namely that the resemblance between these objects is after all derivative, dependent upon the presence of a single universal, Redness, in them all. To generalize the argument: whenever we say that A, B and C resemble each other in a certain respect, we shall be asked "In what respect?" And how can we answer, except by saying "in respect of being instances of the universal ϕ" or "in respect of being characterized by the characteristic ϕ"? We may try to get round the difficulty by saying that they resemble each other in a certain way (avoiding the word "respect"), or that there is a certain sort of resemblance between them. But when we are asked to specify in what way they resemble each other, or what sort of resemblance there is between them, surely we shall still have to answer by mentioning such and such a universal or characteristic? "The way in which red objects resemble each other is that all of them are instances of the universal Redness, or all of them are characterized by the characteristic Redness." This is one of the classical objections to the Philosophy of Resemblances. The argument purports to show that resemblance is not after all ultimate or underivative, but is dependent on the presence of a universal or characteristic which is common to the things which

resemble each other. There is something about this objection which arouses our suspicions. It comes perilously near to the tautology "red things are the things which are red." The Resemblance philosophers were not undertaking to deny this tautology. They do not deny that x is red entails x is red. They are only concerned to offer an analysis of x is red itself. Let us now consider the answer they might make to this celebrated objection. Roughly, it consists in substituting "resemblance towards ..." for "resemblance in respect of ..." Resemblance towards what? Towards certain standard objects, or exemplars as I shall call them—certain standard red objects, or standard round objects, or whatever it may be. It is agreed by both parties that there is a class of red objects. The question is, what sort of a structure does a class have? That is where the two philosophies differ. According to the Philosophy of Universals, a class is so to speak a promiscuous or equalitarian assemblage. All its members have, as it were, the same status in it. All of them are instances of the same universal, and no more can be said. But in the Philosophy of Resemblances a class has a more complex structure than this; not equalitarian, but aristocratic. Every class has, as it were, a nucleus, an inner ring of key-members, consisting of a small group of standard objects or exemplars. The exemplars for the class of red things might be a certain tomato, a certain brick and a certain British post- box. Let us call them A, B and C for short. Then a red object is any object which resembles A, B and C as closely as they resemble one another. The resemblance between the exemplars need not itself be a very close one, -46-

though it is of course pretty close in the example just given. What is required is only that every other member of the class should resemble the class - exemplars as closely as they resemble one another. Thus the exemplars for a class might be a summer sky, a lemon, a post-box, and a lawn. These do resemble one another, though not very closely. Accordingly there is a class consisting of everything which resembles these four entities as closely as they resemble each other. It is the class of coloured things, whereas the previous one was the class of red things. It may be thought that there is still a difficulty about the resemblance between the exemplar objects themselves. In what respect do the tomato, the brick and the post-box resemble each other? Surely this question still arises, even though it does not arise about the other members of the class? And how can one answer it, except by saying that these three objects resemble each other in respect of being red, or of being characterized by redness? But this assumes that we know beforehand what "being red" is, or what "being characterized by redness" amounts to. And this begs the question against the Resemblance Philosophy. The Resemblance Philosophers maintain that our knowledge of what it is for something to be red just consists in a capacity to compare any particular object X with certain standard objects, and thereby to discover whether X does or does not resemble these standard objects as closely as they resemble each other. It does not make sense to speak of comparing the standard objects with themselves, or to ask whether they resemble one another as closely as they do resemble one another. Yet that is just what we should be trying to do, if we tried to say "in what respect" they are alike. To say that they are red, or are characterized by redness, would not be an informative statement, but a tautology. This objection does however draw our attention to an important point. According to the Philosophy of Resemblances, there cannot be a class unless there are exemplar objects to hold the class together. Nevertheless, the same class may have alternative sets of exemplars. The class of red things, we said, consists of everything which resembles the post-box, the tomato and the brick as closely as they resemble each other. It could equally be said to consist of everything which resembles a certain bit of sealing wax, a certain blushing face and a certain sunset sky as closely as they resemble each other. In that case, it does make sense to ask whether the post-box, the tomato and the brick are red, or are characterized by redness. And the answer "Yes, they are" is now no longer tautologous. We are no longer trying, absurdly, to compare them with themselves. We are comparing them with three other things, and discovering that they do all have a sufficient degree of resemblance to these other things. But because there are (within limits) alternative sets of standard objects for the same class, we are led to suppose, erroneously, that a class can exist without any standard

objects at all. This or that set of standard objects can be deposed from its privileged position without destroying the unity of the class; and we then suppose, by a process of illegitimate generalization, that the class would still remain what it is if privilege -47-

were abolished altogether. There must be a set of standard objects for each class, though within limits it does not matter which set of objects have this status. Thus in the Philosophy of Resemblances, as well as the Philosophy of Universals, there does after all have to be something which holds a class together, if one may put it so. Where the two philosophies differ is, in their view of what that something is. In the Philosophy of Universals, what holds a class together is a universal, something of a different ontological type from the members. In the Philosophy of Resemblances there is no question of different ontological types. There are just particular objects, and there is nothing non-particular which is "in" them, in the way that a universal is supposed to be "in" the particulars which are its instances. What holds the class together is a set of nuclear or standard members. Anything which has a sufficient degree of resemblance to these is thereby a member of the class; and "resembling them sufficiently" means "resembling them as closely as they resemble each other." Again, to turn for a moment to epistemological considerations, it is their relationship to the standard objects or exemplars which enables all these objects to satisfy the same concept, e.g. the concept Red, and likewise enables the same word or other symbol, e.g. the word "red," to apply to them all. But this is to anticipate. The Philosophy of Resemblances is an ontological doctrine, though it may be used as the starting point for certain epistemological theories (Conceptualism, Imagism and Nominalism), just as the Philosophy of Universals may be used as the starting-point of a Realist epistemology. If the Philosophy of Resemblances is true at all, it might still have been true even if there had been no thinkers and no speakers. As it happens, there are thinkers and speakers too. But there may be many classes in the world, which do exist (because the requisite resemblances do happen to be there) although no mind happens to have formed the corresponding class - concepts, and no speaker has acquired the habit of using the corresponding class-symbols. Thus there is nothing subjectivist or anthropocentric about the Philosophy of Resemblances. It denies that there are universals in rebus, but it asserts that there are resemblances inter res. Certain objects really are as like the objects A, B and C as these are to one another, whether anyone notices the fact or not. Known or not, spoken of or not, the relationship is there; just as in the Philosophy of Universals objects are instances of universals whether they are known to be so or not. In this respect, both these philosophies are equally "realistic." We must now turn to the second of the classical objections against the Philosophy of Resemblances, an objection so familiar that one might almost call it notorious. It is concerned with resemblance itself. Surely resemblance is itself a universal, present in many pairs or groups of resemblant objects? It is of course, a universal of relation. The instances of it are not individual -48-

objects taken singly, but complexes, and each of these complexes is composed of two objects or more. In their attempt to "get rid of universals," the Philosophers of Resemblance seem to concentrate their attention on universals of quality (e.g. redness, colour, shape) and say little or nothing about universals of relation. Hence they have failed to notice that resemblance itself is one of them. But if we are obliged to admit that resemblance at any rate is a genuine universal, a relation which does literally recur in many different situations or complexes, what ground have we for denying that there are other universalia in rebus as well? It may seem audacious to question this formidable argument, which has convinced many illustrious men. But is it as strong as it looks? The Resemblance philosophers might very well reply that it begs the question at issue, that it just assumes what it purports to prove. For after all, what reason is given for the crucial assertion that resemblance is a universal? Apparently none. It is not enough just to say "surely resemblance at any rate is a universal."

Could any reason be given? We might perhaps try to find one by starting from the linguistic side of the matter. The word "resemblance," we might say, is an abstract word, like the words "redness" and "proximity"; therefore it must stand for a universal or characteristic (a relational one, of course). But if this is the argument, it seems to beg the question. For if one does start from a linguistic point of view, the very question at issue is whether abstract words and general words do stand for universals. And if the argument is to be cogent, it ought to be an argument about the noun "resemblance" in particular, or about the verb "to resemble" in particular. We ought to be shown that it is somehow peculiarly obvious that this word at any rate (or this pair of words) stands for a universal, even though it may be less obvious that other general words do. Perhaps it will be said, the peculiar obviousness consists in this, that even the people who try to get rid of universals have to use this general word at least, or equivalent general words such as "similar," "like." True enough, one cannot speak in a language consisting entirely of proper names and demonstratives. One cannot say anything at all without using some general words. As an observation about the nature of language, this is perfectly indisputable. But the question is, what are its implications? Does it follow that because we must use general words, there are, therefore, general somethings in rerum natura which they stand for? That is just the point at issue. One cannot just assume that the answer is "Yes." Of course the Philosophy of Resemblances admits that we do use general words, and cannot avoid using them if we are to speak at all. It does not at all deny the fact. But it does deny the conclusion which the Philosophy of Universals draws from it— namely that because we use general words, there must be general somethings (universals) which they mean. Has anything been done to show that this denial is mistaken? Nothing. The Philosophy of Universals has just repeated over again the principle which has to be proved, the principle that every -49-

general word stands for a universal; adding—what is obvious—that if this principle is true, the word "resemblance" is an illustration of it. Of course. But is the principle true? If the Philosopher of Resemblances is asked to explain how the general word "resemblance" is used, or what kind of meaning it has, he will presumably point out that there are resemblances of different orders. Two cats, A and B, resemble each other, and two sounds, C and D, also resemble each other. These are first-order resemblances. But it is also true that the two-cat situation resembles the two-sound situation, and resembles many other situations too. This is a second-order resemblance. The A-B situation and the C-D situation really are alike, though the constituents of the one are unlike the constituents of the other. In virtue of this second-order likeness (a likeness between likeness-situations) we may apply the same general word to both of them; and the word we happen to use for this purpose is the word "resemblance," in a second-order sense. There is nothing wrong or unintelligible in the notion of second-order resemblance. Or if it be said that there is, we can reply with the tu quoque argument that universality must itself be a universal. When it is said that "cathood is a universal" the word "universal" is itself a general word, just as "cat" is when we say "Pussy is a cat." So according to the Philosophy of Universals, there must be a universal called "universality." And if it is a universal, universality must accordingly be an instance of itself. But this is a contradiction. For according to this Philosophy, anything which is an instance of a universal is ipso facto a particular, and not a universal. To get out of this difficulty, the Philosophy of Universals must introduce the notion of "different orders" too. The word "universal," it has to say, stands for a second-order universal, whereas "green" or "cat" or "in" stand for first-order ones. This is equivalent to saying that the expression "a universal," or the propositional function " ϕ is a universal," can occur only in a metalanguage. This suggests another way in which the Philosophy of Resemblances might reply to the objection that "resemblance is itself a universal." The objection assumes that resemblance is just one relation among others: a relation of the same type as "on top of," or "near to," or "side by side with." But according to the Philosophy of Resemblances, resemblance is not just one relation among others. Indeed, according to this philosophy, it would be misleading to call it "a relation" at all. It is too fundamental to be called so. For what we ordinarily call "relations" (as well as what we call "qualities") are themselves founded upon or analysable into resemblances. For example, the relation "being inside of" is founded upon the resemblance between the Jonahwhale complex, the room-house complex, the match-

matchbox complex, etc. Moreover, the Philosophy of Universals itself does not really hold that resemblance is just one relation among others, and in pretending that it does, it is abandoning one of its own fundamental principles; indeed it is abandoning the very one which this argument ("resemblance is itself a universal") is ultimately intended to establish, the principle, namely, that all resemblance -50-

is derivative. In the Philosophy of Universals itself, resemblance has a status quite different from relations like "side by side with" or "on top of." Resembling is connected with being an instance of ... in a way that ordinary relations are not. When A resembles B and C, this is supposed to be a direct consequence of the fact that A, B and C are all instances of the same universal ; and not only when A, B and C are individual objects (in which case the universal is a universal of quality) but also when they are complexes, so that the universal they are instances of is a relational one, such as "being inside of." If resemblance, in the Philosophy of Universals, is to be called a relation at all, it is a relation of a very special sort, quite different from anything to which the word "relation" is ordinarily applied. We should have to say that it is a "formal" or "metaphysical" relation (as opposed to a "natural" or empirical one) just as the relation of instantiation is, if that can be called a relation at all. So much for the reply the Philosophy of Resemblances might make to this celebrated argument that "resemblance is itself a universal." First, it might be objected that the argument begs the question, by just assuming (what it ought to prove) that because "resemblance" is admittedly a general word, it must stand for a universal. Secondly, the argument overlooks the fact that there are resemblances of different orders. Thirdly, it treats resemblance as one relation among others, parallel in principle to "side by side with" or "on top of," whereas the Philosophy of Resemblances maintains that it is too fundamental to be called a relation at all, in the ordinary sense of the word "relation." Fourthly, the Philosophy of Universals itself admits, in its own way, that resemblance does not have the same status as other relations, in spite of maintaining in this argument that it has. Thus the Philosophy of Resemblances has an answer to these two classical objections, the one about "resemblance in respect of" and the one we have just discussed "that resemblance is itself a universal." But the Philosophy of Universals also has an answer to the objection about inexact resemblances, and to the complaint that it ignores the different degrees of intensity which resemblances may have. We must consider this answer if we are to do justice to both parties. The first step is to distinguish between determinable and determinate characteristics. Universals or characteristics, it is said, have different degrees of determinateness. The adjectives "determinable" and "determinate" are too fundamental to be defined. But their meaning can be illustrated. Thus the characteristic of being coloured is a determinable, and the characteristic of being red is a determinate of it. Being red is again a sub-determinable, and has under it the determinates being scarlet, being brick-red, being cherry-red, etc. Likewise, being a mammal is a determinable characteristic, a highly complex one this time. There are many different ways of being a mammal. Being a dog, being a whale, being a man are some of the determinates of this determinable. -51-

Now whenever two objects resemble each other with less than the maximum intensity (i.e. whenever they have what was called an "inexact" resemblance) we can always say that the same determinable characteristic characterizes them both, though not the same determinate one. Two objects may each have a different shade of red. A is scarlet, and B is brick-red. They resemble each other fairly closely, but by no means exactly. That is because redness itself is a determinable characteristic, a sub-determinable falling under the higher determinable colouredness. The two objects do have this determinable characteristic in common, though each of them has a different determinate form of it. So we can still maintain that this resemblance, though inexact, is a derivative, dependent on the presence of the same determinable universal in both objects.

Let us apply these considerations to the two examples given earlier: (1) the various white objects; (2) the penny and the sixpence. It may now be maintained that all my different white objects—from the freshly fallen snow at one end of the series to the unwashed bow-tie at the other—do have a determinable characteristic in common; though "whitish," rather than "white," would be the appropriate word for it. "White" might be taken to mean pure white. And pure white is only one determinate of the determinable whitish. We certainly should not say that all the objects in this series are pure white. At the most, only the freshly fallen snow is pure white, but not the piece of chalk, or the rather messy bit of paper, or the rather dirty handkerchief, or the very dirty unwashed bow-tie. But we should admit that all of them are "whitish." Let us now consider my other example, the penny and the sixpence, which resemble each other in shape, but inexactly. The penny with its smooth edge and the sixpence with its milled (slightly serrated) edge have different determinate shapes. How is it, then, that they do still resemble each other in shape, though inexactly, and both would be called "round coins" in ordinary speech? Because the same determinable shape—we might more appropriately call it "roundish"—characterizes both of them; and it characterizes many other things as well, e.g. slightly buckled bicycle wheels, cogwheels with not too large teeth, which resemble each other a good deal less closely than the penny and the sixpence do. By this expedient the Philosophy of Universals is able to maintain its thesis that all resemblances, inexact ones too, are derivative, and not ultimate, as the Philosophy of Resemblances would have them. Inexact resemblance, we are invited to say, depends upon or is derived from the presence of the same determinable characteristic in a number of objects; exact resemblance (resemblance of maximum intensity) depends upon their being characterized by the same determinate characteristic. Perhaps this will also enable us to dispense with the notion of "degrees of instantiation" which was mentioned earlier. It was not easy to see what could be meant in the Philosophy of universalia in rebus by saying that one object is a better instance of so-and-so than another, though this notion fits well -52-

enough into the Platonic theory of universalia ante rem, and into Conceptualism too. Perhaps it could now be suggested that the determinates of some determinables, e.g. "whitish," "roundish," are serially ordered. Thus the various determinates of whitishness which characterize the patch of snow, the piece of chalk, the paper, etc., may be arranged in a series beginning with "pure white." After this comes "nearly pure white" (the colour the piece of chalk has), then "farther from pure white" and then "farther still from pure white," until we come to a characteristic which is as far from pure whiteness as it can be without ceasing to be a determinate of whitishness at all. The system of marking (a+, a, a—, β+, etc.) which we suggested for indicating the "goodness" or "badness" of instances can still be used: only it is now applied not to the objects themselves, but to the determinate characteristics by which they are respectively characterized. Thus this objection to the Philosophy of Universals, that it can make no room for inexact resemblances (resemblances of less than the maximum intensity), turns out after all to be indecisive, although it looked so convincing at first sight. The facts to which this argument draws our attention are of course perfectly genuine, and important too. It is, for example, an important fact about language that most of our general words apply to sets of objects which inexactly resemble one another; and it is an important fact about thinking that the various objects which "satisfy" a given concept, e.g. the concept of Crow, do not have to be exactly alike. Nevertheless, this argument does not at all refute the Philosophy of Universals, as it is often supposed to do. All it does is to point out what was lacking in our first rough-and ready formulation of that philosophy. Certainly the Philosophy of Universals would be quite unworkable without the distinction between determinable and determinate universals. The doctrine that universals or characteristics have different degrees of determinacy is an indispensable part of it. But the distinction between determinables and determinates is perfectly consistent with the contention that there are recurrent characteristics in the world, and with the accompanying doctrine that resemblances are derivative, not ultimate. Indeed,

it could be argued, the fact that recurrent characteristics do differ in their degree of determinateness is just as obvious as the fact of recurrence itself. Finally, it is worth repeating that the phrases "inexact resemblance" "not exactly alike" are sometimes used in another way, to mean incomplete or partial resemblance. If A and B are closely alike in a large number of respects, but unlike or not closely alike in one or two, we sometimes say that they are very like each other but not exactly like each other. For example, within the same species of bird we often find that there are slight differences of size or colouring between two individual specimens, although they also resemble each other closely in very many ways. It is obvious that if the phrase "inexact resemblance" is used in this sense, the Philosophy of Universals has no difficulty at all about inexact resemblances. We merely have to say that many universals are common to the two birds, or recur in both of them; and consequently the -53-

two individuals resemble each other in a great many respects. We then add that bird A is also an instance of a certain universal ϕ, while bird B is not an instance of this, but of a certain other universal ψ; and consequently there is a respect in which they are not alike. (It may be found, of course, and in this example it almost certainly will be, that though ϕ and ψ are different determinate universals, they are determinates of the same determinable universal, say "mottled.") It must not be forgotten that every individual object is an instance of several universals at once, and often of very many at once. When we compare it with another object, we may easily find that some universals are common to both of them, and other universals are not. It would be a strange misunderstanding of the Philosophy of Universals to suppose that in this philosophy every particular is held to be an instance of only one universal. When we say that something is a cat, we are saying that it is an instance of many universals conjointly, and not just of one. Our discussion has been long and complicated. What conclusion shall we draw from it? It would seem that there is nothing to choose between these two philosophies, the Philosophy of Universals or characteristics (universalia in rebus) 2 on the one hand, and the Philosophy of Ultimate Resemblances on the other. At any rate, it would seem that there is nothing to choose between them so long as they are considered as purely ontological doctrines, which is the way we have been considering them in this chapter. Both seem to cover the facts, though only when both are stated with sufficient care. Moreover, they both cover the same facts. This strongly suggests that they are two different (systematically different) terminologies, two systematically different ways of saying the same thing. It does not follow that both alike are just pieces of solemn and elaborate trifling. On the contrary, the thing which they both say is of the first importance, and we do need a way of saying it. The efforts which each party has made to provide us with a systematic terminology for saying it have not been a waste of time. For if there were no recurrent characteristics, or no resemblances between different objects— whichever way you choose to put it—there could be no conceptual cognition, and no use of general symbols either. Now if there is only a (systematic) difference of terminology between these two philosophies, it is well to be familiar with both. Each of them may have its misleading features; and when we are in danger of being misled by the one, we may save ourselves by changing over to the other. The danger of the terminology of Universals has been pointed out already. If we can only do our philosophizing in this terminology, we may be led to regard universals as things or entities. We reduce this danger by using the word "characteristic" instead; or by using phrases like "being red" "being a cat" "being side by side with ..." instead of noun-substantives like "redness," ____________________ 2It may be worth while to remind the reader that the phrase "the Philosophy of Universals," as it has been used in this chapter, is not intended to cover the Platonic doctrine of universalia ante rem. -54-

"cathood," "side-by-sideness," which do look like names for entities; or by using the propositional function notation ϕx, xRy, R(x,y,z), etc., where "x," "y" and "z" are variables. But perhaps we do not avoid the danger altogether, especially when we make very general statements, as we have to in philosophy; for example "characteristics are divided into two sorts, qualities and relations" or even "the characteristic of being red entails the characteristic of being coloured." Such statements may mislead us into supposing that "there are" characteristics in the sense in which "there are" dogs, or planets. We can avoid these dangers by changing over to the terminology of Resemblances, and by recalling that everything which can be said in the language of Universals or Characteristics can also be said (though usually less elegantly) in the language of Resemblances. Perhaps there is another danger as well. The Philosophy of Universals may tend to make us think that the world is a more neat and tidy place than it is. If one may say so, there is sometimes a certain air of infallibility or omni - competence about its exponents, as if the basic structure of the universe were perfectly clear to them, and only a few rather unimportant details remained to be settled. The Philosophy of Resemblances delivers us from this danger, by reminding us that most of the resemblances we think and talk of are by no means exact ones. It restores to human thought and language that fuzziness or haziness, that absence of hard and fast boundaries, which do belong to them, and even in a way to the world itself. On the other hand, the terminology of Resemblances has its defects too. It is clumsy, complicated, and difficult to handle. Moreover, it tends to make us too much preoccupied with the inexactitude of resemblances; and so we may come to forget the vastly important fact that after all they are resemblances, and some of them pretty close ones too. There is such a thing as too much attention to "marginal cases." Attention to them is a philosophical virtue, but exclusive preoccupation with them is a philosophical vice. If that is our temptation, we may escape it by changing over to the terminology of Universals. In this terminology, we remind ourselves, there are determinable characteristics and not only determinate ones; so that even where objects resemble each other inexactly, there is still recurrence. -55-

:3: ON CONCEPT AND OBJECT GOTTLOB FREGE IN a series of articles on intuition and its psychical elaboration, Benno Kerry has several times referred to my Grundlagen der Arithmetik and other works of mine, sometimes agreeing and sometimes disagreeing with me. I cannot but be pleased at this, and I think the best way I can show my appreciation is to take up the discussion of the points he contests. This seems to me all the more necessary, because his opposition is at least partly based on a misunderstanding, which might be shared by others, of what I say about the concept; and because, even apart from this special occasion, the matter is important and difficult enough for a more thorough treatment than seemed to me suitable in my Grundlagen. The word "concept" is used in various ways; its sense is sometimes psychological, sometimes logical, and sometimes perhaps a confused mixture of both. Since this licence exists, it is natural to restrict it by requiring that when once a usage is adopted it shall be maintained. What I decided was to keep strictly to a purely logical use; the question whether this or that use is more appropriate is one that I should like to leave on one side, as of minor importance. Agreement about the mode of expression will easily be reached when once it is recognized that there is something that deserves a special term. It seems to me that Kerry's misunderstanding results from his unintentionally confusing his own usage of the word "concept" with mine. This readily gives rise to contradictions, for

which my usage is not to blame. Kerry contests what he calls my definition of "concept." I would remark, in the first place, that my explanation is not meant as a proper definition. One cannot require that everything shall be defined, any more than one can require that a chemist shall decompose every substance. What is simple cannot be decomposed, and what is logically simple cannot have a proper definition. Now something logically simple is no more given us at the outset than most of the chemical elements are; it is reached only by means of scientific work. If something has been discovered that is simple, or at least must count as ____________________ First published in the Vierteljahrsschrift fiir wissenschaftliche Philosophie (1892); this translation is reprinted from Translations from the Philosophical Writings of Gottlob Frege, edited by Peter Geach and Max Black (Oxford: Basil Blackwell, 1952) by permission of the publisher.

simple for the time being, we shall have to coin a term for it, since language will not originally contain an expression that exactly answers. On the introduction of a name for something logically simple, a definition is not possible; there is nothing for it but to lead the reader or hearer, by means of hints, to understand the words as is intended. Kerry wants to make out that the distinction between concept and object is not absolute. "In a previous passage," he says, "I have myself expressed the opinion that the relation between the content of the concept and the concept-object is, in a certain respect, a peculiar and irreducible one; but this was in no way bound up with the view that the properties of being a concept and of being an object are mutually exclusive. The latter view no more follows from the former than it would follow, if, e.g., the relation of father and son were one that could not be further reduced, that a man could not be at once a father and a son (though of course not, e.g., father of the man whose son he was)." Let us fasten on this simile! If there were, or had been, beings that were fathers but could not be sons, such beings would obviously be quite different in kind from all men who are sons. Now it is something like this that happens here. The concept (as I understand the word) is predicative. 1 On the other hand, a name of an object, a proper name, is quite incapable of being used as a grammatical predicate. This admittedly needs elucidation, otherwise it might appear false. Surely one can just as well assert of a thing that it is Alexander the Great, or is the number four, or is the planet Venus, as that it is green or is a mammal? If anybody thinks this, he is not distinguishing the usages of the word "is." In the last two examples it serves as a copula, as a mere verbal sign of predication. (In this sense [the German word ist] can sometimes be replaced by the mere personal suffix: cf. dies Blatt ist grün and dies Blatt grünt.) We are here saying that something falls under a concept, and the grammatical predicate stands for this concept. In the first three examples, on the other hand, "is" is used like the "equals" sign in arithmetic, to express an equation. 2 In the sentence "The morning star is Venus," we have two proper names, "morning star" and "Venus," for the same object. In the sentence "the morning star is a planet" we have a proper name, "the morning star," and a concept-word, "planet." So far as language goes, no more has happened than that "Venus" has been replaced by "a planet"; but really the relation has become wholly different. An equation is reversible; an object's falling under a concept is an irreversible relation. In the sentence "the morning star is Venus," "is" is obviously not the mere copula; its con____________________ 1It is, in fact, the reference of a grammatical predicate. 2I use the word "equal" and the symbol " = " in the sense "the same as," "no other than" "identical with." Cf. E. Schroeder Vorlesungen ueber die Algebra der Logik (Leipzig 1890), Vol. 1, No. 1. Schroeder must however be criticized for not distinguishing two fundamentally different relations; the relation of an object to a concept it falls under, and the subordination of one concept to another. His remarks on the Vollwurzel are likewise open to objection. Schroeder's symbol

does not simply take the place of the copula. -57-

tent is an essential part of the predicate, so that the word "Venus" does not constitute the whole of the predicate. 3 One might say instead: "the morning star is no other than Venus"; what was previously implicit in the single word "is" is here set forth in four separate words, and in "is no other than" the word "is" now really is the mere copula. What is predicated here is thus not Venus but no other than Venus. These words stand for a concept; admittedly only one object falls under this, but such a concept must still always be distinguished from the object. 4 We have here a word "Venus" that can never be a proper predicate, although it can form part of a predicate. The reference 5 of this word is thus something that can never occur as a concept, but only as an object. Kerry, too, would probably not wish to dispute that there is something of this kind. But this would mean admitting a distinction, which it is very important to recognize, between what can occur only as an object, and everything else. And this distinction would not be effaced even if it were true, as Kerry thinks it is, that there are concepts that can also be objects.

There are, indeed, cases that seem to support his view. I myself have indicated (in Grundlagen, § 53, ad fin.) that a concept may fall under a higher concept—which, however, must not be confused with one concept's being subordinate to another. Kerry does not appeal to this; instead, he gives the following example: "the concept 'horse' is a concept easily attained," and thinks that the concept "horse" is an object, in fact one of the objects that fall under the concept "concept easily attained." Quite so; the three words "the concept 'horse' " do designate an object, but on that very account they do not designate a concept, as I am using the word. This is in full accord with the criterion I gave—that the singular definite article always indicates an object, whereas the indefinite article accompanies a concept-word. 6 Kerry holds that no logical rules can be based on linguistic distinctions; but my own way of doing this is something that nobody can avoid who lays down such rules at all; for we cannot come to an understanding with one another apart from language, and so in the end we must always rely on other people's understanding words, inflexions, and sentenceconstruction in essentially the same way as ourselves. As I said before, I was not trying to give a definition, but only hints; and to this end I appealed to the general feeling for the German language. It is here very much to my advantage that there is such good accord between the linguistic distinction and the real one. As regards the indefinite article there are probably no exceptions to our rule at all for us to remark, apart from obsolete formulas like Ein edler Rath ["Councillor"]. The matter is not so simple for the definite article, especially in the plural; but then my criterion does not relate to this case. In the singular, so far as I can see, the matter is doubtful only when a singular takes the place of a ____________________ 3Cf. my Grundlagen, § 66, footnote. 4Cf. my Grundlagen, § 51. 5Cf. my paper, "On Sense and Reference" (Ueber Sinn und Bedeutung), shortly to appear in the Zeitschrift fiir Phil. und phil. Kritik. 6Grundlagen, § 51; § 66, footnote; § 68, footnote on p. 80. -58-

plural, as in the sentence, "the Turk besieged Vienna," "the horse is a four - legged animal." These cases are so easily recognizable as special ones that the value of our rule is hardly impaired by their occurrence. It is clear that in the first sentence "the Turk" is the proper name of a people. The second sentence is probably best regarded as expressing a universal judgment, say "all horses are four-legged animals" or "all properly constituted horses are four-legged animals"; these will be discussed later. 7 Kerry calls my criterion unsuitable; for surely, he says, in the sentence "the concept that I am now talking about is an individual concept" the name composed of the first eight words stands for a concept; but he is not taking the word "concept" in my sense, and it is not in what I have laid down that the contradiction lies. But nobody can require that my mode of expression shall agree with Kerry's. It must indeed be recognized that here we are confronted by an awkwardness of language, which I admit cannot be avoided, if we say that the concept horse is not a concept, 8 whereas, e.g., the city of Berlin is a city, and the volcano Vesuvius is a volcano. Language is here in a predicament that justifies the departure from custom. The peculiarity of our case is indicated by Kerry himself, by means of the quotation-marks around "horse"; I use italics to the same end. There was no reason to mark out the words "Berlin" and "Vesuvius" in a similar way. In logical discussions one quite often needs to assert something about a concept, and to express this in the form usual for such assertions—viz. to make what is asserted of the concept into the content of the grammatical predicate. Consequently, one would expect that the reference of the grammatical subject would be the concept; but the concept as such cannot play this part, in view of its predicative nature; it must first be converted into an object, 9 or, speaking more precisely, represented by an object. We designate this object by prefixing the words "the concept"; e.g.: ____________________

7Nowadays

people seem inclined to exaggerate the scope of the statement that different linguistic expressions are never completely equivalent, that a word can never be exactly translated into another language. One might perhaps go even further, and say that the same word is never taken in quite the same way even by men who share a language. I will not enquire as to the measure of truth in these statements; I would only emphasize that nevertheless different expressions quite often have something in common, which I call the sense, or, in the special case of sentences, the thought. In other words, we must not fail to recognize that the same sense, the same thought, may be variously expressed; thus the difference does not here concern the sense, but only the apprehension, shading, or colouring of the thought, and is irrelevant for logic. It is possible for one sentence to give no more and no less information than another; and, for all the multiplicity of languages, mankind has a common stock of thoughts. If all transformation of the expression were forbidden on the plea that this would alter the content as well, logic would simply be crippled; for the task of logic can hardly be performed without trying to recognize the thought in its manifold guises. Moreover, all definitions would then have to be rejected as false. 8A similar thing happens when we say as regards the sentence "this rose is red": The grammatical predicate "is red" belongs to the subject "this rose." Here the words "The grammatical predicate 'is red' " are not a grammatical predicate but a subject. By the very act of explicitly calling it a predicate, we deprive it of this property. 9Cf. my Grundlagen, p. x. -59-

"The concept man is not empty." Here the first three words are to be regarded as a proper name, 10 which can no more be used predicatively than "Berlin" or "Vesuvius." When we say "Jesus falls under the concept man," then, setting aside the copula, the predicate is: "someone falling under the concept man" and this means the same as: "a man." But the phrase "the concept man" is only part of this predicate. Somebody might urge, as against the predicative nature of the concept, that nevertheless we speak of a subject-concept. But even in such cases, e.g. in the sentence "all mammals have red blood" we cannot fail to recognize the predicative nature 11 of the concept; for we could say instead: "whatever is a mammal has red blood" or: "if anything is a mammal, then it has red blood." When I wrote my Grundlagen der Arithmetik, I had not yet made the distinction between sense and reference; 12 and so, under the expression "a possible content of judgment," I was combining what I now designate by the distinctive words "thought" and "truth-value." Consequently, I no longer entirely approve of the explanation I then gave (Grundlagen, p. 77), as regards its wording; my view is, however, still essentially the same. We may say in brief, taking "subject" and "predicate" in the linguistic sense: A concept is the reference of a

predicate; an object is something that can never be the whole reference of a predicate, but can be the reference of a subject. It must here be remarked that the words "all," "any," "no," "some," are prefixed to concept-words. In universal and particular affirmative and negative sentences, we are expressing relations between concepts; we use these words to indicate ____________________ 10I call anything a proper name if it is a sign for an object. 11What I call here the predicative nature of the concept is just a special case of the need of supplementation, the "unsaturatedness," that I gave as the essential feature of a function in my work Funktion und Begriff (Jena, 1891). It was there scarcely possible to avoid the expression "the function f(x)," although there too the difficulty arose that what this expression stands for is not a function. 12Cf. my essay "On Sense and Reference" in the Zeitschrift fiir Phil. und phil. Kritik. -60-

the special kind of relation. They are thus, logically speaking, not to be more closely associated with the concept-words that follow them, but are to be related to the sentence as a whole. It is easy to see this in the case of negation. If in the sentence "all mammals are land-dwellers" the phrase "all mammals" expressed the logical subject of the predicate are land-dwellers, then in order to negate the whole sentence we should have to negate the predicate: "are not land-dwellers." Instead, we must put the "not" in front of "all"; from which it follows that "all" logically belongs with the predicate. On the other hand, we do negate the sentence "The concept mammal is subordinate to the concept land-dweller" by negating the predicate: "is not subordinate to the concept land-dweller." If we keep it in mind that in my way of speaking expressions like "the concept F" designate not concepts but objects, most of Kerry's objections already collapse. If he thinks (cf. p. 281) that I have identified concept and extension of concept, he is mistaken; I merely expressed my view that in the expression "the number that applies to the concept F is the extension of the concept like-numbered to the concept F" the words "extension of the concept" could be replaced by "concept." Notice carefully that here the word "concept" is combined with the definite article. Besides, this was only an incidental remark; I did not base anything upon it. Thus Kerry does not succeed in filling the gap between concept and object. Someone might attempt, however, to make use of my own statements in this sense. I have said that to assign a number involves an assertion about a concept; 13 I speak of properties asserted of a concept, and I allow that a concept may fall under a higher one. 14 I have called existence a property of a concept. How I mean this to be taken is best made clear by an example. In the sentence "there is at least one square root of 4," we have an assertion, not about (say) the definite number 2, nor about —2, but about a concept, square root of 4; viz. that it is not empty. But if I express the same thought thus: "The concept square root of 4 is realized," then the first six words form the proper name of an object, and it is about this object that something is asserted. But notice carefully that what is asserted here is not the same thing as was asserted about the concept. This will be surprising only to somebody who fails to see that a thought can be split up in many ways, so that now one thing, now another, appears as subject or predicate. The thought itself does not yet determine what is to be regarded as the subject. If we say "the subject of this judgment," we do not designate anything definite unless at the same time we indicate a definite kind of analysis; as a rule, we do this in connexion with a definite wording. But we must never forget that different sentences may express the same thought. For example, the thought we are considering could also be taken as an assertion about the number 4: ____________________ 13Grundlagen, § 46. 14Grundlagen, § 53. -61-

"The number 4 has the property that there is something of which it is the square." Language has means of presenting now one, now another, part of the thought as the subject; one of the most familiar is the distinction of active and passive forms. It is thus not impossible that one way of analysing a given thought should make it appear as a singular judgment; another, as a particular judgment; and a third, as a universal judgment. It need not then surprise us that the same sentence may be conceived as an assertion about a concept and also as an assertion about an object; only we must observe that what is asserted is different. In the sentence "there is at least one square root of 4" it is impossible to replace the words "square root of 4" by "the concept square root of 4"; i.e. the assertion that suits the concept does not suit the object. Although our sentence does not present the concept as a subject, it asserts something about it; it can be regarded as expressing the fact that a concept falls under a higher one. 15 But this does not in any way efface the distinction between

object and concept. We see to begin with that in the sentence "there is at least one square root of 4" the predicative nature of the concept is not belied; we could say "there is something that has the property of giving the result 4 when multiplied by itself." Hence what is here asserted about a concept can never be asserted about an object; for a proper name can never be a predicative expression, though it can be part of one. I do not want to say it is false to assert about an object what is asserted here about a concept; I want to say it is impossible, senseless, to do so. The sentence "there is Julius Caesar" is neither true nor false but senseless; the sentence "there is a man whose name is Julius Caesar" has a sense, but here again we have a concept, as the indefinite article shows. We get the same thing in the sentence "there is only one Vienna." We must not let ourselves be deceived because language often uses the same word now as a proper name, now as a concept-word; in our example, the numeral indicates that we have the latter; "Vienna" is here a concept-word, like "metropolis." Using it in this sense, we may say: "Trieste is no Vienna." If, on the other hand, we substitute "Julius Caesar" for the proper name formed by the first six words of the sentence "the concept square root of 4 is realized," we get a sentence that has a sense but is false; for the assertion that something is realized (as the word is being taken here) can be truly made only about a quite special kind of objects, viz. such as can be designated by proper names of the form "the concept F." Thus the words "the concept square root of 4" have an essentially different behaviour, as regards possible substitutions, from the words "square root of 4" in our original sentence; i.e. the reference of the two phrases is essentially different. 16 What has been shown here in one example holds good generally; the behaviour of the concept is essentially predicative, even where something is ____________________ 15In my Grundlagen I called such a concept a second-order concept; in my work Funktion und Begriff I called it a second-level concept, as I shall do here. 16Cf. my essay "On Sense and Reference" (cited above). -62-

being asserted about it; consequently it can be replaced there only by another concept, never by an object. Thus the assertion that is made about a concept does not suit an object. Second-level concepts, which concepts fall under, are essentially different from first-level concepts, which objects fall under. The relation of an object to a first-level concept that it falls under is different from the (admittedly similar) relation of a first-level to a second-level concept. (To do justice at once to the distinction and to the similarity, we might perhaps say: An object falls under a first-level concept; a concept falls within a second-level concept.) The distinction of concept and object thus still holds, with all its sharpness. With this there hangs together what I have said (Grundlagen, § 53) about my usage of the words "property" and "mark"; Kerry's discussion gives me occasion to revert once more to this. The words serve to signify relations, in sentences like " Φ is a property of r" and "Φ is a mark of Ω." In my way of speaking, a thing can be at once a property and a mark, but not of the same thing. I call the concepts under which an object falls its properties; thus "to be Φ is a property of Γ" is just another way of saying: "r falls under the concept of a Φ." If the object r has the properties Φ, X, and Ψ, I may combine them into Ω; so that it is the same thing if I say that Γ has the property Ω, or, that Γ has the properties Φ, X, and Ψ. I then call Φ, X, and Ψ marks of the concept Ω, and, at the same time, properties of Γ. It is clear that the relations of Φ to r and to Ω are quite different, and that consequently different terms are required. r falls under the concept Φ; but Ω, which is itself a concept, cannot fall under the first-level concept Φ; only to a second-level concept could it stand in a similar relation. Ω is, on the other hand, subordinate to Φ. Let us consider an example. Instead of saying:

"2 is a positive number" and "2 is a whole number" and "2 is less than 10" we may also say "2 is a positive whole number less than 10." Here to be a positive number, to be a whole number, to be less than 10, appear as properties of the object 2, and also as marks of the concept positive whole number less than 10. -63-

This is neither positive, nor a whole number, nor less than 10. It is indeed subordinate to the concept whole number, but does not fall under it. Let us now compare with this what Kerry says in his second article (p. 224). "By the number 4 we understand the result of additively combining 3 and 1. The concept object here occurring is the numerical individual 4; a quite definite number in the natural number-series. This object obviously bears just the marks that are named in its concept, and no others besides— provided we refrain, as we surely must, from counting as propria of the object its infinitely numerous relations to all other individual numbers; 'the' number 4 is likewise the result of additively combining 3 and 1." We see at once that my distinction between property and mark is here quite slurred over. Kerry distinguishes here between the number 4 and "the" number 4. I must confess that this distinction is incomprehensible to me. The number 4 is to be a concept; "the" number 4 is to be a concept-object, and none other than the numerical individual 4. It needs no proof that what we have here is not my distinction between concept and object. It almost looks as though what was floating (though very obscurely) before Kerry's mind were my distinction between the sense and the reference of the words "the number 4." But it is only of the reference of the words that we can say: this is the result of additively combining 3 and 1. Again, how are we to take the word "is" in the sentences "the number 4 is the result of additively combining 3 and 1" and " 'the' number 4 is the result of additively combining 3 and I"? Is it a mere copula, or does it help to express a logical equation? In the first case, "the" would have to be left out before "result," and the sentences would go like this: "The number 4 is a result of additively combining 3 and 1"; " 'The' number 4 is a result of additively combining 3 and 1." In that case, the objects that Kerry designates by "the number 4" and " 'the' number 4" would both fall under the concept result of additively combining 3 and 1. And then the only question would be what difference there was between these objects. (I am here using the words "object" and "concept" in my accustomed way.) I should express as follows what Kerry is apparently trying to say: "The number 4 has those properties, and those alone, which are marks of the concept: result of additively combining 3 and 1."

I should then express as follows the sense of the first of our two sentences: "To be a number 4 is the same as being a result of additive combination of 3 and 1." -64-

In that case, what I conjectured just now to have been Kerry's intention could also be put thus: "The number 4 has those properties, and those alone, which are marks of the concept a number 4." (We need not here decide whether this is true.) The inverted commas around the definite article in the words " 'the' number 4" could in that case be omitted. But in these attempted interpretations we have assumed that in at least one of the two sentences the definite articles in front of "result" and "number 4" were inserted only by an oversight. If we take the words as they stand, we can only regard them as having the sense of a logical equation, like: "The number 4 is none other than the result of additively combining 3 and 1." The definite article in front of "result" is here logically justified only if it is known (i) that there is such a result; (ii) that there is not more than one. In that case, the phrase designates an object, and is to be regarded as a proper name. If both of our sentences were to be regarded as logical equations, then, since their right sides are identical, it would follow from them that the number 4 is "the" number 4, or, if you prefer, that the number 4 is no other than "the" number 4; and so Kerry's distinction would have been proved untenable. However, it is not my present task to point out contradictions in his exposition ; his way of taking the words "object" and "concept" is not properly my concern here. I am only trying to set my own usage of these words in a clearer light, and incidentally show that in any case it differs from his, whether that is consistent or not. I do not at all dispute Kerry's right to use the words "concept" and "object" in his own way, if only he would respect my equal right, and admit that with my use of terms I have got hold of a distinction of the highest importance. I admit that there is a quite peculiar obstacle in the way of an understanding with my reader. By a kind of necessity of language, my expressions, taken literally, sometimes miss my thought; I mention an object, when what I intend is a concept. I fully realize that in such cases I was relying upon a reader who would be ready to meet me halfway—who does not begrudge a pinch of salt. Somebody may think that this is an artificially created difficulty; that there is no need at all to take account of such an unmanageable thing as what I call a concept; that one might, like Kerry, regard an object's falling under a concept as a relation, in which the same thing could occur now as object, now as concept. The words "object" and "concept" would then serve only to indicate the different positions in the relation. This may be done; but anybody who thinks the difficulty is avoided this way is very much mistaken; it is only shifted. For not all the parts of a thought can be complete; at least one must be "unsaturated," or predicative; otherwise they would not hold to -65-

gether. For example, the sense of the phrase "the number 2" does not hold together with that of the expression "the concept prime number" without a link. We apply such a link in the sentence "the number 2 falls under the concept prime number"; it is contained in the words "falls under," which need to be completed in two ways—by a subject and an accusative; and only because their sense is thus "unsaturated" are they capable of serving as a link. Only when they have been supplemented in this twofold respect do we get a complete sense, a thought. I say that such words or phrases stand for a relation. We now get the same

difficulty for the relation that we were trying to avoid for the concept. For the words "the relation of an object to the concept it falls under" designate not a relation but an object; and the three proper names "the number 2," "the concept prime number," "the relation of an object to a concept it falls under," hold aloof from one another just as much as the first two do by themselves; however we put them together, we get no sentence. It is thus easy for us to see that the difficulty arising from the "unsaturatedness" of one part of the thought can indeed be shifted, but not avoided. "Complete" and "unsaturated" are of course only figures of speech; but all that I wish or am able to do here is to give hints. It may make it easier to come to an understanding if the reader compares my work Funktion und Begriff. For over the question what it is that is called a function in Analysis, we come up against the same obstacle; and on thorough investigation it will be found that the obstacle is essential, and founded on the nature of our language; that we cannot avoid a certain inappropriateness of linguistic expression; and that there is nothing for it but to realize this and always take it into account. -66-

:4: FREGE'S HIDDEN NOMINALISM * GUSTAV BERGMANN SOME philosophical pieces are like symphonies, others like quartets. This one is merely an ontological theme with variations. After I have introduced the theme, it will be seen that Exemplification versus Mapping is a very good name for it. The phrase does not signify, though, except to one already familiar with the theme. That is why I did not choose it as a title. All but the last of the variations are comments on Frege's ontology, though as such they are highly selective. 1 This is one reason for the title I chose. The other is that I hope to draw expository advantage from its shock value.

I In ontological discourse two clusters of very ordinary words are used philosophically. First of all, therefore, I shall state how I propose to handle these words. One cluster contains "thing," "object," "entity," "existent." When I do not wish to indicate anybody's ontological commitment, I use entity. When I wish to speak of what philosophers, speaking philosophically, assert to "exist," I use existent. Frege uses both "object" and "function" philosophically; and he holds, either explicitly, or very nearly so, that every entity (not, existent!) is either an object or a function. 2 The other cluster contains "naming," "denoting," "designating," "referring." Nor are the philosophical uses of the two clusters independent. Some philosophers, for instance, maintain that an existent is what is or could be named (denoted, ____________________ Reprinted with the permission of the author and the editor from The Philosophical Review, LXVII (1958). *I have profited from discussions with Mr. Reinhardt Grossmann. 1An excellent detailed exposition may be found in R. Wells, "Frege's Ontology," Rev. Metaphys., IV (1957), 537-573. References to this study are by page number, preceded by the letter W. 2In rendering Frege's terms I follow the well-known Translations from the Philosophical Writings of Gottlob Frege by M. Black and P. Geach (Oxford, 1952). References to this volume are by page number, preceded by the letter F.

designated) by a word or expression. When I wish to speak without indicating ontological commitment, I avoid all these verbs and borrow instead Frege's standing for. If they followed this use, the philosophers just mentioned could say that a name is a word or expression which stands for an existent.

Consider "This is green." On one occasion, "this" may stand for an apple; "green," for its color. Some hold that, on another occasion, the two words could stand for what they call a sensum and one of its qualities, respectively. Others disagree. The difference makes no difference for my purpose. So I shall entirely ignore it in calling the sort of thing "this" and "green" stand for, on all occasions, an individual and a character, respectively. Also, I shall in this essay use the two words without ontological commitment even though, in the case of "individual," that is admittedly unusual. For Frege, individuals are one kind of object; characters, one kind of function. But there are in his world still other kinds of objects and of functions. Some ontologists, including Russell (and myself) though not Frege, make much of a distinction between simple and complex characters. For what I am about it is irrelevant, so I shall disregard it. There is also the distinction between types of characters and functions. Both Frege and Russell pay attention to it. But again, with one glancing exception, it is irrelevant for what I am about, so I shall virtually ignore it. This shows how selective I shall be in my remarks about Frege. Even in ontological discourse the terms realism and nominalism are used in two ways; once strictly, once broadly. The ontologist's first business is to list all kinds of existents (not, all existents). If he discerns many kinds, perhaps too many, one calls him a realist. If he lists but few, perhaps too few, one calls him a nominalist. This is the broad use. In the strict sense, an ontologist is a realist if he counts characters, or at least some characters (for example, simple ones), as a kind of existent. A nominalist in the strict sense holds, conversely, that no characters are existents. In this essay, unless there be a qualification to the contrary, both terms are always used strictly. Two things about Frege are beyond reasonable doubt. Had he used "existent" as I do (as far as I know he did not use it at all), he would have agreed that everything he calls an object is an existent. This is the first thing. Of objects there are in his world many kinds. Nor are the distinctions among them "ordinary," like that between cats and dogs. They are even more sweeping than that between physical and phenomenal objects, which surely is sweeping enough and, according to some, anything but ordinary. His distinctions are so sweeping indeed that, if the word is to have any meaning at all, one cannot but call them ontological. This is the second thing beyond reasonable doubt. Specifically, Frege distinguishes (at least) the following (ontological) kinds (of objects): individuals, numbers, truth values, value ranges (classes of objects), senses, propositions (thoughts), concept correlates. 3 Many philosophers think that with the sole exception of individuals all these kinds are odd. Or, to say the same thing differently, they refuse to consider ____________________ 3As far as I know, the term is Wells's. -68-

the odd kinds of entities as existents. Still differently, these philosophers (including myself) reject Frege's exaggerated realism (broad sense). It is not my purpose to rehearse their arguments, or to improve on them, or to invent new ones; even though I shall permit myself, en passant, to call attention to two oddities about truth values. As far as Frege is concerned, my purpose is rather to give some reasons for my belief that, for all his exuberant realism in the broad sense, he was in the strict sense at least implicity a nominalist. My primary concern, though, is neither biographical nor textual. What I shall really argue, therefore, is that the structure of Frege's ontology though not, as will transpire, of Church's emendation of it, 4 is nominalistic. Everything said so far is merely preliminary. I shall proceed as follows. In the next section the theme is introduced and used to exhibit what I take to be the root of Frege's nominalism. In the third section I shall show that in one case this very nominalism forces upon Frege that multiplication of entities (or rather of existents) which is so characteristic of his ontology. In the fourth section I shall show that what is, broadly speaking, the most serious as well as the most obvious intrinsic flaw of the system is but another consequence of its author's hidden nominalism. I say intrinsic because this flaw is of course not that

exuberant realism (broad sense) which, as I said, I shall not question except once and incidentally. In the last section I shall vary my theme, very briefly and very sketchily, by sounding it as a background for the siren songs of a more recent nominalism.

II Where one arrives depends in part on where he starts. A philosopher's starting point depends in part on his basic paradigm. Frege's is very different from the realist's. My theme builds on this difference or, rather, contrast. I present first the realist, because it helps to bring out the contrast more forcefully. Some realists, including myself, propose an explication of the philosophical use of "exist" upon which all individuals and (some of) their characters but no higher characters are existents. 5 The realist I present is of this sort. My case does not depend on the limitation. But again, it helps to bring out the theme more clearly by freeing it from some bywork that otherwise would have to be introduced. The realist starts from individuals and their characters. That is, he starts from entities Frege calls objects (and from their characters), though not from those objects which with Frege's critics I called odd. "Peter is blond" may thus serve as the realist's paradigm. What claims does it suggest to him? What do and what don't these claims imply? What reasons can he give for them? I shall take up the three questions in this order. ____________________ 4A. Church, Introduction to Mathematical Logic (Princeton, 1957). 5See "Elementarism," J. Phil, and Phen. Res., XVIII (1957), 107-114. -69-

First. "Peter" and "blond" both stand for existents. Generally, both individuals and characters are existents. This is one major claim. Many realists, including myself, also hold that every existent is either an individual or a character; but for the purpose at hand that does not matter. What "Peter is blond" stands for comes about if two existents, one of each kind, enter into a certain "relation," or, as I would rather say, nexus. This nexus the realist calls exemplification. Obviously it is a very fundamental feature of his world. This is another major claim. To see that it is not independent of the first, notice that to say of something that it does or may enter into a nexus is to presuppose that it exists. Notice also that when I spoke of a sentence "standing for" something, I quite deliberately paid with clumsiness for the agreed- upon neutrality of the phrase. Second. (a) An individual may or may not exemplify a character. To say that a character exemplifies an individual is nonsense. The very nexus between the two kinds is thus asymmetrical. This alone shows that individuals and characters are not alike in all respects which concern the ontologist. Nor do the realist's claims imply that they are. Obviously not, I should say. For, if they were, what point would there be in distinguishing between them? (b) In the paradigm, the copula or, as I prefer to say, the predicative "is" stands for exemplification. In a much larger number of cases, to say the least, the verbal image of this nexus between things is predication, that is, the grammatical relation between subject and predicate. That follows from the realist's claims. Third. An articulate realist has of course many reasons for the position he takes. Fortunately they do not all matter for my purpose. What matters is that every time he discovers some respect in which individuals and characters are alike, he has discovered a reason. I shall state two such reasons, the two which I think carry most weight. (a) Just as we are never presented with an individual that is not qualitied, that is, does not exemplify a character, so we are never presented with a character that is not exemplified by some individual with which we are also presented. Notice that I speak of entities being presented to us, that is, as one says, epistemologically. Had I not promised to keep out the distinction between simple and complex characters and had I limited myself to the former, I could have spoken ontologically: Just as there is no individual that is not qualitied, so there is no character that is not exemplified. This is one fundamental likeness. (b) Consider the three entities that "Peter," "blond," and "Peter is blond" stand for. The differences among them are ontologically significant. With that Frege agrees. For, if he did not, he would not, as an ontologist, either distinguish concepts from objects or set aside truth values as a kind of

object. The realist says the same thing differently. Neither an individual nor a character is the kind of entity (notice the noncommittal word!) a sentence stands for. This is a second likeness. (b) The reader is assumed to be familiar with Frege's distinction between saturated and unsaturated expressions. "Blond" or, as he would really have to say, "is blond," is unsaturated. "Peter" is saturated. (So is, very importantly, "Peter is blond"; but that does not yet enter into my argument.) Primarily at -70-

least, the dichotomy is between expressions, not between entities. If one wants to apply it to entities, one must specify what in this case the two terms are to mean. For instance, one may propose "Individuals and characters are equally unsaturated" as an alternative way of stating the second fundamental likeness. An unsophisticated realist may object to this on the ground that, since individuals and characters are both existents, they really are both equally saturated. We know that he merely proposes another meaning for one (!) of the two terms as applied to entities. But his proposal has the merit of showing not only that this application serves no purpose but also the dangers that beset it. 6 The realist's gambit has a further consequence, which gives rise to an objection, which in turn leads to a clarification. It will pay later if in introducing the matter I change the paradigm to "Peter is a boy." The objector points out that one who takes the predicative "is" to stand for exemplification ought to admit that the paradigm and the sentence "Peter exemplifies the character of being a boy" stand for one and the same entity. After a fashion, the realist does admit that. He even admits it for the sentence "The individual (object) Peter exemplifies the character (concept) of being a boy," and, if he used the two words in parentheses, he would also admit it for the further variations they make possible. Now the objector taunts the realist with a Bradleyan regress. It seems, he says, that in order to grasp what exemplification is, he must first grasp what it means for the (relational) character of being exemplified to be exemplified. The realist answers as follows. Exemplification is a very peculiar character. (That is why I called it a nexus and only once, in quotation marks, a relation.) Its peculiarity is the same as that of such "characters" as being an individual or a character. To be an individual, for instance, is not to be of an "ordinary" kind, as is being a cat or a dog, but to be the sort of entity expressions of a certain grammatical kind stand for. The expressions for these peculiar kinds are therefore all expendable and the several alternatives for the paradigm need not be considered unless one speaks in a language containing them about another language and what its expressions stand for. I need not on this occasion endorse this answer. Nor would I on any occasion endorse it in this crude form. (That is why I said the realist admits what I made him admit "after a fashion.") I merely mention this answer because, being familiar and thus permitting me to communicate quickly about what does not matter for what I am about, it helps me to prepare the ground for what does. So much for the realist. Frege starts from numbers and their functions. "x2" may thus serve as his paradigm. That numbers are objects and therefore existents he takes for granted. Questionable as that is, I need not question it. My concern is with functions, mathematical and otherwise. The current mathematical name for the crucial idea is mapping. The square function, for instance, maps each number onto another, namely its square. Generally, given two classes of entities which may but need not coincide or overlap, a function is a mapping rule, mapping each member of one of the two classes upon one (and, in the ____________________ 6See "Propositional Functions," Analysis, XVII (1956), 43-48. -71-

paradigmatic case, only one) member of the other. Let me now for a moment speak as a poet might, using some very loaded words very freely. A rule is a thing totally different from the things to which it applies. A mapping rule, in particular, is a thing much more shadowy, much less real, less palpable, less substantial than the things mapped and mapped upon. This more and these less, rather than the questionable status of numbers, is the heart of the

matter. So I shall try to state it, not as a poet but as a philosopher might. Numbers and their functions differ from each other in the two fundamental respects in which, as we saw, individuals and characters are alike. (a) Just as there is no unexemplified character, so there is no unqualified individual. But there are of course numbers whether or not they be either arguments or values of functions. (b) The two notions of an individual and of a character, containing or presupposing each other to exactly the same extent, are equally "saturated" or "unsaturated." The notion of a number neither contains nor presupposes that of a function. The latter, however, contains and presupposes that of the two ranges (of numbers). (c) The realist's basic paradigm involves two entities, an individual and a (nonrelational) character. So does a function of one variable, which is Frege's basic paradigm. Or, rather, this is so after an argument has been chosen and the corresponding value computed by means of the function. The need for this additional step, which Frege never tires of emphasizing, increases the "ontological distance" between objects and functions. In Frege's paradigm, moreover, though not in the realist's, the two existents involved, the argument and "its" value, are existents of the same kind. This further increases the impression of disparity between them and the entity which is the function. Still another circumstance subtly undermines the ontological status of functions. What mathematicians say about the latter often has a subjective ring. As they speak, it is they who do the mapping or, as it is often put, establish the correlation. "Rule" itself, in most of its uses, has the same ring or tinge. This is an occasion for comment. First. Dangerous as that subjective ring or tinge may be philosophically, it is of course quite harmless as long as the mathematicians attend to their own business. What makes it even more harmless is that in fact mathematicians are not all busy establishing or making functions. The vast bulk of their work consists in demonstrating what further properties a function has, assuming that it has some others. Second. The realist pulls the fangs of this potentially dangerous talk by construing functional expressions as, in the Principia sense, indefinite descriptions, 7 either mathematical or otherwise (the square of x, the father of x). Descriptions in turn contain expressions standing for characters. And there is nothing subjective about characters (including, of course, relations), least of all in the case of numbers. As Russell put it, in a justly celebrated passage about the order relation, "we ____________________ 7"The father of x" is in this sense an indefinite description; "a son of Peter" is not, irrespective of how many sons, if any, Peter has. A. J. Ayer's "Individuals," reprinted in his Philosophical Essays (New York, 1954), makes one wonder whether he appreciates the distinction. What he calls indefinite descriptions seem to be predicative expressions which happen to be true for several subjects. -72-

can no more 'arrange' the natural numbers than we can the starry heavens." 8 Notice, though, that even if starting from numbers in one sense, one who accepts this clarification starts in another sense from the realist's paradigm. Third. I spoke quite deliberately of the subjective tinge or blur from which some of the mathematicians' phrases suffer. My purpose was to give an objector his opportunity. Frege, this objector reminds us, insists over and over again that not only his odd objects but also functions, though they are not objects, are yet objective. I know that this is one of his guiding ideas. And I admire the steadfastness with which he wielded it as a weapon against the psychologism rampant in the Germany of his day. One may appreciate all this, as of course I do, and yet consistently hold, as I also do, that while within his system at least Frege succeeded in securing full ontological status for his odd objects, he did not so succeed, even within the system, in the case of functions. That is what I mean by his hidden nominalism. Notice that I call it hidden or implicit. Remember, too, that in this section I merely undertook to state it and to trace it to what I take to be its root, namely, the contrast between exemplification and mapping. The evidence will be found in the next two sections. But I am not quite done with the business at hand. Nominalism is a thesis about characters. Nothing will be lost if we limit ourselves to nonrelational ones. Frege calls them concepts. What, then, does he have to say about concepts? The realist, we just saw, construes functions in terms of characters (concepts). Frege, proceeding in the opposite direction, as it were, construes concepts as a kind of

function. In this way, the nominalism I have shown to be implicit in any analysis that starts from mapping is spread to concepts (characters). This is the point. Or, if you please, this is the last bar of my theme. Frege's execution of the idea is familiar. If "Peter is blond" is to be construed in analogy to "the square of 3," then we must look for an object that goes with Peter as the value 9 goes with the argument 3. This object is the truth value of the sentence. This is one motive for Frege's "creation" of the two odd objects T and F. It fits nicely with another. He wants every saturated expression to stand for an object; sentences are saturated expressions; so the truth value of a sentence can serve as the object it stands for. Though Frege had still other motives for the "reification" of T and F, structurally these two are undoubtedly the most important. I should like to suggest that the first, that is, the need to make good the precarious analogy between concepts and functions, goes even deeper than the second. I turn from things to words. The alleged analogy between characters and functions is not reflected in our language. If it were, we would have to say "blond of Peter," just as we say "the square of 3," and not, as we do, "Peter is blond." (The reader who can anticipate the sequel will be struck by the irony of our propensity, if we consider such verbal violence at all, to say "the blond[-ness] of Peter.") The culprit in the case is the predicative "is." ____________________ 8B. Russell, Introduction to Mathematical Philosophy, p. 30 of the 1919 edition. The whole page repays reading in this context. -73-

From where the realist stands, we remember, it reflects very nicely the nexus of exemplification and is a, if not perhaps the, fundamental use of "is." 9 For Frege it is but a clumsily disguised "of." In "Peter is the father of John," on the other hand, as in "3 2 = 9" and, alas, in "Peter is blond = T," "is" reflects very nicely, from where Frege stands, what it is used to speak about. To express identity thus becomes the or at least a fundamental use of "is." In the last section I shall give some reasons why I believe that all nominalists are forced to consider it, more or less covertly, the fundamental use of "is." This is the place to call attention to two oddities about truth values. First, let "P" stand for a sentence and consider the series is true, so are all members of the series. If the arithmetical analogue were to hold, the

If P

members of the series would also all be true. Yet they are not even well formed. This is odd. Second, senses and propositions (thoughts) are in the system two kinds of objects, kindred in that a proposition is, as it were, the sense of a sentence. This is familiar. 10 Now there is a passage (F 64) in which I take Frege to assert, as I believe consistently he must, that "P" and "P = T" have (express) the same sense. If the arithmetical analogue held, so would therefore "3 2" and "32 = 9." Yet the former denotes a number, the second, T. Thus they do not even denote the same kind of object. This, too, is odd. If one has already accepted the system he will probably not boggle at such oddities. But if he hasn't, they may make him even more averse to the reification of T and F and to what, as we saw, is at the bottom of it all, Frege's analysis of exemplification in terms of mapping.

III A nodding acquaintance with Frege's work, or even with what is currently being said about it, leaves two impressions. The first is of the multiplication of entities due to his distinction between reference and sense, that is, between the objects denoted and the objects expressed by such saturated expressions as, say, "the Morning Star" and "Peter is blond." The second impression is that the main intellectual motive for the multiplication is the hope that, by means of it, it will be possible to conquer the difficulties that arise in inten____________________ 10See Sections III and IV.

9It

becomes the fundamental use if the Leibniz-Russell explication of identity is considered adequate. -74-

sional contexts, that is, in contexts mentioning either modalities or propositional attitudes, such as believing, knowing, and so on. Considering the system as a whole, that certainly is a motive. But if the two impressions are as widely spread as I believe them to be, then it is probably worth pointing out that Frege was first forced into that business of multiplying entities by the very logic of his nominalism in a case much simpler and more fundamental, which has nothing whatsoever to do with either modalities or propositional attitudes. This is the case of classes ( extensions, value ranges). Corresponding to each concept, which according to him is not an object and (if I am right) at least implicitly not an existent, Frege "creates" another entity, which according to him is an object, namely, the class of all objects which, as he says, fall under the concept. 11 In this section I shall give two reasons why his nominalism, made explicit, forces him to do just that. Such reasons, if sound, are of course the kind of structural evidence one must accumulate in order to establish that the system is, at least implicitly, nominalistic. Consider the two functional expressions "x 2" and "x2 — x + x" and the equation "x 2 = x2 — x + x." After a fashion, we all know what the equation stands for. Practicing mathematicians, without giving the matter much thought, say either that the two functions have the same extension, that is, the class of ordered pairs [(1,1), (2,4) ... ], or, alternatively, that the two functions are equal (the same, identical). Strictly speaking, from where Frege stands, the second alternative makes no sense. A function is a mapping rule. Following one of the two rules mentioned, one obtains the value by squaring the argument. Following the other, one first squares the argument, then subtracts it from the square, then adds it to the intermediate result. Considered as rules, the two functions are thus not the same. Generally, two rules are never the same, in a sense both strict and intelligible, unless they are, as one says, two tokens of the same type. All one can mean by calling them so, is, therefore, that they yield the same result (have the same extension). I conclude that, if he wants to be consistent, Frege cannot, as in fact he does not, specify conditions of identity for concepts and functions. Or, rather, he would have to hold that an assertion of identity between two (concepts or) functions is true if and only if the two expressions mentioned are different tokens of the same type. Of this more later. For the moment we notice that had he stopped at this point, Frege could not have preserved what as a mathematician he surely wanted to preserve, namely, the equation "x 2 = x2 — x + x" and the truism for which it stands. His way out is to interpret it as an identity not between the two functions but, rather, between their extensions. (Technically, he introduces a special notation for the latter and rewrites the equation as a statement of identity between them.) The possibility of this interpretation he thinks is indemonstrable. So he appeals to a fundamental law of logic. The words and the phrase italicized are his (F 26). This is the first reason I undertook to adduce. It shows how the nominalism implicit in any analysis that starts ____________________ 11The limitation to first-level concepts which this formulation entails does not affect my purpose. -75-

from mapping creates the need for the new entities. The second reason will show that they must be objects. Frege does not specify the fundamental law of logic to which he appeals. What then is it? Does he use the phrase merely to dignify what is done in this case? Or is there a general principle involved? Even though his words at this place seem to suggest the first alternative, the second is I believe the right one. Consider the following three propositions. 1. To be a name and to be an expression standing for an existent is one and the same thing. 2. For a statement of identity, "α = β" to be true, "α" and "β" must denote existents. 3. For "α =β" to be a statement (to be well-formed, or to be meaningful), "α" and "β" must denote (or

purport to denote) existents. Obviously, 3 is stronger than 2. Many ontologists endorse either 2 or 3, depending on the stand they take on issues which do not concern us. I would not even endorse 2. 12 That, however, is beside the point. The point is that either 1 and 3 or, perhaps, 1 and 2 follow deductively from the way many ontologists tended and still tend to use "existent," "name," and "identity." Add now, as a fourth proposition, that every saturated expression is a name; in the first three propositions replance "existent" by "object," and you obtain four principles, or four aspects of one principle, which underlie, either explicitly or very nearly so, all of Frege's analysis. This, I believe, is quite uncontroversial. Assume now that this principle is the fundamental law of logic to which Frege appealed. It follows that extensions (value ranges, classes) must be objects. This is the second reason I promised to adduce. Moreover, I have made it plausible, to say the least, that Frege uses "object" as many ontologists use "existent." Concepts and functions in general, we remember, though objective, are not objects. It follows that, at least implicitly, the system is nominalistic. This concludes the main argument of the section. I proceed to four comments. First. Let a 1 , a 2 , ... be all the objects that are blond; b 1 , b 2 , ... all those that are not. The class one ordinarily associates with the character blond is that of the a, [a 1 , a 2 , ... ]. It can be argued that the class Frege associates with the concept blond is that of all ordered pairs (a, T) and (b, F). If so, in his world what sort of object is an ordered pair of objects? Probing deeply in some such directions, one is eventually led to the Russell paradox and the question as to what, if anything, Frege can do about it. I realize all that. Clearly, these subtleties do not matter for what I am about. That is why I proceeded as I did. But it may hurt my thesis if I appear ignorant where I am merely selective. That is why I mention the matter. Second. Frege (F 50) feels the need to distinguish "the relation of an object to a first-level concept that it falls under ... from the (admittedly similar) relation of a first-level concept to a second-level concept." So he proposes that in the former case we speak of falling under, in the latter of falling within. His purpose, he tells us, is to preserve the distinction of con____________________ 12To this point I hope to return on another occasion. See "Sameness, Meaning, and Identity," in the Proceedings of the Twelfth International Congress of Philosophy (Venice, 1958). Reprinted in Meaning and Existence. -76-

cept and object "with all its sharpness" or, as I would put it, to increase the ontological distance between them. Taken by itself, the passage may be read as merely a plea for pervasive type distinctions. In context it provides subsidiary evidence for my thesis. Third. An objector might argue as follows: "True, Frege does not specify conditions of identity for functions. But, then, neither does he specify such conditions or criteria for senses. (I follow you in using 'sense' for propositions (thoughts) as well as for what is expressed by nonsentential saturated expressions such as 'the Morning Star'.) Yet senses are objects. This greatly weakens your argument." Wells (W 544) shrewdly anticipates part of the answer. Frege, he reminds us, had an additional reason, which does not, or at least not directly, apply to functions, for not specifying criteria for the identity of senses. To grasp this reason, remember that one of Frege's intellectual motives was to solve the problems of intentional contexts. In this enterprise the reification of senses is merely a first step. The decisive second step is to specify criteria of identity among senses. This second step Frege never took, simply because (or so I believe) he could not think of any that were acceptable to him and did the job. In any case he examined and rejected two. By one of them, two expressions have (express) the same sense if and only if they are analytically equivalent. This criterion he recognized as too broad. By the other, two expressions have the same sense if and only if they are different tokens of the same type. If we accepted this criterion, logic, he thinks (F 46), "would simply be crippled," if only because "all definitions would then have to be rejected as false." 13 However that may be, Frege had an additional reason for not specifying a criterion of identity for senses. This is part of the answer I would give to the objector. For the rest, I would remind him of what was pointed out at the beginning of this section, namely, that its main argument is completely independent of what does or does not hold for senses.

Fourth. Frege, who started from mapping, was forced to reify classes. Does the realist who starts from exemplification find himself compelled? If the answer were no, it would greatly add to the poignancy of my theme. The answer, I believe, is no. However, this is not the place to go into the reasons for that belief. So I shall merely hint at what is rather familiar. Our realist may so explicate the philosophical use of "exist" that only what undefined terms stand for exists in this very peculiar sense. (This is an issue I promised to keep out of the main argument.) When Russell supported his contention that classes do not exist by defining the expressions standing for them in terms of predicative expressions, he was at least implicitly guided by this explication of "exist." 14 A realist who accepts Russell's analysis of the class notion together with the ____________________ 13I do not subscribe to the dogma. This, though, is another story. See "Intentionality," in Semantica (Archivio di Filosofia, 1955), 177-216; "Elementarism," I.c.; and "Concepts," Phil. Studies, VII (1957), 19-27 (jointly with H. Hochberg). Reprinted in Meaning and Existence. 14See "Particularity and the New Nominalism," Methodos, VI (1954), 131-148. Reprinted in Meaning and Existence. -77-

explication of "exist" it implies or at least suggests need not therefore, like the Fregean nominalist, reify classes. The contrast adds depth to that between mapping and exemplification.

IV Consider the phrase "the concept blond" and the sentence "The concept blond is a concept." As Wells points out (W 550), one would think that the latter is not only true but truistic. Frege, as he must, disagrees. Like every saturated expression beginning with "the," the phrase is a name. A name denotes an object (existent). These two principles, we saw, Frege never questions. But a concept is not an object (existent). Hence, the supposed truism is false. Perhaps it is even nonsensical. That leaves two alternatives. One is to declare the sentence expendable. The other is to create a new kind of odd objects. Frege chose the second. The new objects are the concept correlates. A concept correlate "represents" its concept. Or it is obtained by "converting" the concept into an object. These are Frege's words. Nor must the correlate of a concept be confused with its extension. Starting with one entity, the concept, which as I argue does not exist, Frege thus ends up with two more which indubitably do exist, namely, the concept's correlate and its extension. The need for the creation of this further kind of odd object is, to my mind, the most obvious intrinsic flaw of the system as it stands. By calling it intrinsic I indicate, as before, that I do not on this occasion wish to challenge the odd kinds merely because to some of us they seem odd. Nor do I call it a flaw merely because this particular reification is patently ad hoc. For so is that of the two truth values. My point is that, once the new kind, the concept correlate, has been introduced, one cannot escape answering the question in what relation, or connection—use any word you wish—it stands to the other two, the concept itself and its extension. Yet there is no answer. This is the flaw I have in mind. It is as obvious as it is serious. One cue to its being a flaw is the opacity of the two metaphors, representation and conversion. This is not to say that I blame Frege just for speaking metaphorically. Many philosophers sometimes do, and sometimes it helps. I merely wish to say that these two metaphors do not help me in the least. Nothing comes through. The way I presented the matter leaves no doubt that the need for concept correlates is a consequence of what I claim is the implicit nominalism of the system. In this respect there is no difference between concept correlates and classes (extensions). But there is in another. Notice that I spoke of the system "as it stands." In the case of concept correlates, though not of classes, a very slight emendation eliminates the need for their reification as a further kind of objects. I shall next use this circumstance to argue that the nominalism which, -78-

if it were explicitly present in the system, would necessitate the reification, actually is present in it, at least implicitly. Take (α) "Peter," (β) "Peter is blond," (γ) "blond." They exemplify Frege's three basic grammatical categories. Let the Greek letters stand for these categories. Every α and β expression has a reference and a sense. It denotes the former, expresses the latter. The reference of a β expression is a truth value, its sense a proposition (thought). Senses are objects. Hence they can be named. In the case of the paradigm, their names are "the sense Peter" 15 and "the proposition Peter is blond" 16 respectively. Being a name, each of these two expressions has in turn a sense. We have entered upon an infinite regress. Within the system, though, that is no difficulty. Nor does it disturb the lucidity of the pattern. The difficulty is, rather, that the pattern does not apply to the unsaturated expressions γ. There (I limit myself to concepts) it is disturbed by that dangling third entity, the concept correlate. Assume now that concepts are existents. If so, they can be named and the pattern can be extended as follows. A γ expression, say "blond," denotes its extension and expresses its sense, which is the concept itself, which in turn is denoted by "the concept blond." With this emendation the same pattern applies to all three categories. Moreover, the need for concept correlates has disappeared. The emendation is in substance the one Church proposed. With all the respect due to him, it

does not seen very far-fetched, at least by hindsight. Nor is it overdoing the respect we owe to Frege's ingenuity to believe that it was not, even by foresight, beyond his grasp. Why, then, one must ask, did he not take this almost obvious step? The answer I propose will not come as a surprise. He balked at the one assumption which as I have shown the step implies, namely, that concepts, though not objects, are yet full-fledged existents. This concludes the main argument of the section. I proceed to two comments. First. Wells reports (W 546) Church to have argued as early as 1939, in a paper not generally accessible, that Frege's concepts are full-fledged existents. In other words, he disagreed sharply with my thesis. I am neither surprised nor disturbed. As emended by Church, the system is indeed no longer nominalistic in structure. That merely proves that Church is not a nominalist. It proves nothing about the system as it stands. I also grant and even insist that the emendation is nearly obvious. That explains why Church did not want to charge his master with what he must have considered a flaw. But it does not explain why Frege himself put up with an obvious and serious flaw rather than take Church's nearly obvious step. My thesis does explain that. Second. What can the realist do about Frege's problem? To answer, I first state the problem in the way it impressed itself upon Frege. Consider "Fido is a dog." If "dog" and "the concept dog" stood for the same entity, they ____________________ 15Or, as one says rather, the concept Peter. It is obvious why I avoid that locution. 16Or, in intentional contexts, that Peter is blond. -79-

would have to be interchangeable salva veritate. This is another principle Frege never questioned. Yet, "Fido is the concept dog" is nonsense. (Frege, everyone knows, was tremendously and of course quite rightly impressed with the contrast between the definite and the indefinite article. That is why I changed the paradigm.) The concept correlates are an obvious way out of the difficulty. The realist does not need them. Admitting, for the sake of the argument, that "dog" and "the concept dog" stand for the same entity, he need not therefore abandon the principle. He merely adds the proviso, which I introduced in Section II, that whenever such a substitution is made, "exemplifies" must, in the nature of things, be substituted for "is." In this way he obtains, quite smoothly, "Fido exemplifies the concept dog." The reason the realist finds this answer is that, unlike Frege who starts from mapping, he can do justice to that fundamental feature of our world from which he starts. Thus we are once more led back to the contrast between mapping and exemplification.

V Consider "This is red." Frege and the realist agree that the demonstrative denotes an existent. By the realist's account, so does the adjective. Frege, we saw, disagrees, at least implicitly. The root of the matter, we also saw, is that he starts from mapping. The inspiration of this alternative to exemplification is mathematical. In this his nominalism is unique. All other varieties I know of—I am tempted to call them the ordinary varieties —operate with the doctrine of common names. Or, as I would rather say, there are really only two kinds of nominalism, Frege's and the doctrine of common names. The difference between the two is by no means negligible. Both kinds, though, in addition to being nominalisms, which to my mind is a weakness, share still another weakness. Neither does justice to the predicative "is," which stands for exemplification. Both, therefore, more or less covertly take identity to be the fundamental meaning of "is." In Section II, I showed this for Frege. In this section I shall show it for the doctrine of common names, first generally, then by analyzing an essay of Quine's, 17 Assume that when I said "This is red" I pointed at an individual, say, a red apple. The demonstrative and the adjective are both names of the apple. The only difference is that while the former is (serves as) a "proper name," the latter is a "common name." A proper name is a label arbitrarily attached to one and only one individual. A common name applies indifferently to each of several individuals, namely, all those sharing a character. This is the doctrine of common names. It runs into an objection and a difficulty. ____________________ 17"Identity, Ostension, and Hypostasis," reprinted in From a Logical Point of View (Cambridge, Mass., 1953). References to this volume are by page number, preceded by the letter Q. -80-

A common name applies to an individual if and only if that individual has a certain character. Hence it is not an arbitrary label, in the sense in which a proper name is one, unless it be, as the realist insists and the nominalist denies, the name or label of the character itself. What, then, the realist asks the defender of the doctrine, is there "objectively" in or about each of the several individuals by virtue of which the common name is properly applied to each of them? Some nominalists answer (Q 68) that upon hearing and seeing a common name applied, we learn to apply it ourselves "by induction." The realist retorts that for such learning to occur, there must be a clue common to all individuals to which the learner hears and sees the common name applied. That leaves the issue where it was before. The doctrine of common names has no answer to this objection. Frege answered it, after a fashion, by insisting that functions, though not objects (existents), are yet "objective." That is why his nominalism is so superior to the other kind and, being superior, can remain "hidden." That much for the objection. The difficulty relates to what I am about. Assume that an individual has two names, say "Napoleon" and "Bonaparte." Consider "Napoleon is Bonaparte." In this sentence "is" stands for identity. Generally, if an individual has two names, what way is there of combining them into a sentence except by the "is" of identity? This suggests that proponents of the doctrine may be tempted to

assimilate the predicative "is" to that of identity. Notice that I just spoke of names, without distinction between common and proper ones. I did this because I do not really understand what it means for a word to be a common name. Or, to say the same thing differently, a name, in the only use of the term I understand, is a word attached as a label to one and only one entity. Or, still differently, in the manner of speaking I wish to discourage, every name, whatever it may name, is a proper name. Notice, second, that I spoke of suggestion. In other words, not every proponent of the doctrine asserts that in "This is red" the copula stands for identity. To claim anything of the sort would be unreasonable indeed. For is it not the very purpose of the doctrine of common names to prevent this collapse of the two uses of "is?" Only its proponents still somehow think of "common names" as "names." Therein, I claim, lies a temptation, or a suggestion, or perhaps even a compulsion in the direction of that collapse. This claim is not at all unreasonable. To substantiate it, I shall present two series of comments, the first about classical (Aristotelian) logic, the second about the essay by Quine. 1. For Aristotle, there is an important difference between "This is green" and "Socrates is a man." For my purpose the difference does not matter. Even so, consider the second sentence, if only because everyone knows that classical logic cannot cope with it except by the device of subsuming it, rather artificially, under the A-sentence. To do that is to construe the predicative "is" as the "is" (or "are") of the A-, E-, I-, and O-sentences. For Aristotle, this third use of "is" is the fundamental one. It is, if I may so put it, the only one for which he can account. (Frege and the realist both construe it as a com -81-

bination of two predicative uses with a quantifier.) Be that as it may, formally or logically the device does the trick. But it does not even touch the heart of the difficulty, which is ontological rather than logical. Within the hylomorphic scheme, the problem of individuation is insoluble. 18 One may of course abandon individuals. That is the way Scotus took. But it can be argued that in taking it he also abandoned hylomorphism. The original terminists did not wish to go that far. Yet they faced up to the Parmenidean illusion, which is one of the roots, if not perhaps the root, of the classical difficulty, that every occurrence of the copula indicates an identity. Moreover, they insisted, like Frege, that any two names of an individual must be substitutable for each other salva veritate in all contexts; and they noticed that, say, "this" and "red" are not so substitutable. Thus they were led to the distinction which is the core of their doctrine of signification. Connotatively, they held, the adjective signifies indifferently each of the several red things; denotatively it, or, rather, its abstractum "redness," signifies the character itself. Deny now that characters are existents. Then there is nothing for the adjective (or its abstractum) to signify denotatively and you arrive at the doctrine of common names. This is the step Ockham took. 2. An apple is, in a familiar sense, spatio-temporally extended. Its color and shape, as the realist conceives them, are not. For Quine, to be an existent and to be spatio-temporally extended, or, for brevity's sake I shall say, to be extended or an extension, are one and the same thing. This is the guiding idea of his ontology. It has an important corollary. The sum of any number of extensions is itself extended. Roughly, sum here means set-theoretical sum. Precisely, it is the function axiomatized in the so-called meromorphic calculus. This subtlety we can safely ignore. Notice, though, that the notion of a function, in the Fregean sense of the term, is needed to state the intuitive core of this ontology. Assume now once more that, pointing at an apple, I say "This is red." Or for the matter, assume that, pointing at a certain volume of water, I say "This is the Iowa River." Quine holds (Q 69) that there is in principle no difference between the two "ostensions." Just as the Iowa River is the sum of certain watery extensions, so the color may be thought of as the sum of all red ones. Which extensions we are meant to sum we learn in either case "by induction" from watching what is being pointed at ( Q 68). Pointing, however, is ambiguous (Q 67). Taking advantage of the ambiguity, Quine says that one who speaks and points as by assumption I do "identifies" for the purpose of the discourse what he points at with the sum in question (Q 71). Notice how subtle it all is. Quine does not tell us that the copula in "This is red" ____________________

18This

is by now at least a respectable opinion. See, for all this, "Some Remarks on the Ontology of Ockham," Philos. Rev., LIII (1954), 560-571; "Russell's Examination of Leibniz Examined," Philosophy of Science, XXIII (1956), 175-203; "Some Remarks on the Philosophy of Malebranche," Rev. Metaphys., X (1956), 207-226. Reprinted in Meaning and Existence. Leibniz, it is true, manages to accommodate both kinds of existent. But he pays the price of having to maintain that in a sense every predication is analytic (Predicatum inest subjecto). -82-

stands for identity. Of course he doesn't. As a logician, he knows better than that. Yet he says obliquely, by means of the opaque metaphor of "identification," that what I really point at is the sum. If this were so and if the color could be conceived as the sum in question, then "This is red" would indeed state an identity. Quine is convinced that nobody in his right mind would "hypostatize" characters as the realist does. So he must explain why such hypostasis ever seemed plausible. The explanation takes the form of an anthropological fable. Its hero is misled by a faulty analogy (Q 73). As it happens, some adjectives may be thought of as standing for a sum of extensions. So he is led to hope that this is so for all adjectives. Quine constructs a simple universe in which the sum of all triangles coincides with the sum of all squares ( Q 72). Negatively, this frustrates that hope. Positively, we are told (Q 75) that "in ostensively explaining 'square' ... we say each time 'This is square' without imputing identity of indicated object from one occasion to the next." Again the metaphor is opaque. I do not really know what it means to impute identity. I do know, though, that we are left with two alternatives. Either "square" stands for a character as the realist conceives it; or, even though there is no such character, we learn "inductively" how to use the common name. Quine rejects the first alternative, chooses the second (Q 75). Thus he lays himself open to the classical objection which I rehearsed earlier. Quine's nominalism is clearly a doctrine of common names. That makes it very different from Frege's. Yet there are also two points of contact. The first is that, sums being functions, the Fregean notion of function is an ingredient of the intuitive core of the doctrine. The other point of contact seems at first rather verbal. Quine is fond of the formula that while sentences are either true or false, a predicate is either true or false of something. For Frege, we remember, the predicative "is" is merely a clumsily disguised "of." Ofness, if I may coin a word, thus plays a crucial role in both systems. One may wonder whether this similarity is merely a chance product of the idiom. -83-

:5: UNIVERSALS F. P. RAMSEY THE purpose of this paper is to consider whether there is a fundamental division of objects into two classes, particulars and universals. This question was discussed by Mr. Russell in a paper printed in the Aristotelian Society's Proceedings for 1911. 1 His conclusion that the distinction was ultimate was based upon two familiar arguments, directed against the two obvious methods of abolishing the distinction by holding either that universals are collections of particulars, or that particulars are collections of their qualities. These arguments, perfectly sound as far as they go, do not however seem to me to settle the whole question. The first, which appears again in The Problems of Philosophy, shows as against the nominalists that such a proposition as "This sense-datum is white" must have as one constituent something, such as whiteness or similarity, which is not of the same logical type as the sense- datum itself. The second argument, also briefly expounded in McTaggart's The Nature of Existence, proves that a man cannot be identified with the sum of his qualities. But although a man cannot be one of his own qualities, that is no reason why he should not be a quality of something else. In fact material objects are described by Dr. Whitehead as "true Aristotelian adjectives"; so that we cannot regard these two arguments as rendering the

distinction between particular and universal secure against all criticism. What then, I propose to ask, is the difference between a particular and a universal? What can we say about one which will not also be true of the other? If we follow Mr. Russell we shall have to investigate three kinds of distinction, psychological, physical and logical. First we have the difference between a percept and a concept, the objects of two different kinds of mental acts; but this is unlikely to be a distinction of any fundamental importance, since a difference in two mental acts may not correspond to any difference whatever in their objects. Next we have various distinctions between objects based on their relations to space and time; for instance, some objects can only be in one place at a time, others, like the colour red, can be in many. Here again, in spite of the importance of the subject, I do not think we can have reached the essence of the matter. For when, for instance, Dr. Whitehead ____________________ Reprinted from The Foundations of Mathematics (London: Routledge & Kegan Paul Ltd. and New York: Humanities Press, Inc., 1950) by permission of the publishers. Original source: Mind, n.s. XXXIV (1925), Gilbert Ryle, editor. 1[See the paper by Russell reprinted in this volume.—ED.].

says that a table is an adjective, and Mr. Johnson that it is a substantive, they are not arguing about how many places the table can be in at once, but about its logical nature. And so it is with logical distinctions that our inquiry must mainly deal. According to Mr. Russell the class of universals is the sum of the class of predicates and the class of relations; but this doctrine has been denied by Dr. Stout. 2 But Dr. Stout has been already sufficiently answered. 3 So I shall only discuss the more usual opinion to which Mr. Russell adheres. According to him terms are divided into individuals or particulars, qualities and relations, qualities and relations being grouped together as universals; and sometimes qualities are even included among relations as one-termed relations in distinction from two-, three-, or many-termed relations. Mr. Johnson also divides terms into substantives and adjectives, including relations as transitive adjectives, and he regards the distinction between substantive and adjective as explaining that between particular and universal. But between these authorities, who agree so far, there is still an important difference. Mr. Johnson holds that although the nature of a substantive is such that it can only function in a proposition as subject and never as predicate, yet an adjective can function either as predicate or as a subject of which a secondary adjective can be predicated. For example, in "Unpunctuality is a fault" the subject is itself an adjective—the quality of unpunctuality. There is thus a want of symmetry between substantives and adjectives, for while a predicate must be an adjective, a subject may be either a substantive or an adjective, and we must define a substantive as a term which can only be a subject, never a predicate. Mr. Russell, on the other hand, in his lectures on Logical Atomism, 4 has denied this. He says that about an adjective there is something incomplete, some suggestion of the form of a proposition; so that the adjective-symbol can never stand alone or be the subject of a proposition, but must be completed into a proposition in which it is the predicate. Thus, he says, the appropriate symbol for redness is not the word "red" but the function "x is red," and red can only come into a proposition through the values of this function. So Mr. Russell would say "Unpunctuality is a fault" really means something like "For all x, if x is unpunctual, x is reprehensible"; and the adjective unpunctuality is not the subject of the proposition but only comes into it as the predicate of those of its parts which are of the form "x is unpunctual." This doctrine is the basis of new work in the Second Edition of Principia Mathematica. Neither of these theories seems entirely satisfactory, although neither could ____________________ 2"The Nature of Universals and Propositions," Proc. British Academy, 1921-22 (reprinted in Studies in Philosophy and Psychology, 1930). [Reprinted in this volume—ED.] 3See the symposium between G. E. Moore, G. F. Stout & G. Dawes Hicks in Aristotelian Society Supplementary Volume III, 1923. [The contributions of Moore and Stout are reprinted

in this volume—ED.] and 1919.

4The Monist, 1918

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be disproved. Mr. Russell's view does, indeed, involve difficulties in connection with our cognitive relations to universals, for which reason it was rejected in the First Edition of Principia; but these difficulties seem to me, as now to Mr. Russell, by no means insurmountable. But I could not discuss them here without embarking upon innumerable questions irrelevant to the main points which I wish to make. Neither theory, then, can be disproved, but to both objections can be raised which may seem to have some force. For instance, Mr. Russell urges that a relation between two terms cannot be a third term which comes between them, for then it would not be a relation at all, and the only genuinely relational element would consist of the connections between this new term and the two original terms. This is the kind of consideration from which Mr. Bradley deduced his infinite regress, of which Mr. Russell apparently now approves. Mr. Johnson might reply that for him the connectional or structural element is not the relation but the characterizing and coupling ties; but these ties remain most mysterious objects. It might also be objected that Mr. Johnson does not make particulars and universals different enough, or take into account the peculiar incompleteness of adjectives which appears in the possibility of prefixing to them the auxiliary "being"; "being red," "being a man" do not seem real things like a chair and a carpet. Against Mr. Russell it might be asked how there can be such objects as his universals, which contain the form of a proposition and so are incomplete. In a sense, it might be urged, all objects are incomplete; they cannot occur in facts except in conjunction with other objects, and they contain the forms of propositions of which they are constituents. In what way do universals do this more than anything else? Evidently, however, none of these arguments are really decisive, and the position is extremely unsatisfactory to any one with real curiosity about such a fundamental question. In such cases it is a heuristic maxim that the truth lies not in one of the two disputed views but in some third possibility which has not yet been thought of, which we can only discover by rejecting something assumed as obvious by both the disputants. Both the disputed theories make an important assumption which, to my mind, has only to be questioned to be doubted. They assume a fundamental antithesis between subject and predicate, that if a proposition consists of two terms copulated, these two terms must be functioning in different ways, one as subject, the other as predicate. Thus in "Socrates is wise," Socrates is the subject, wisdom the predicate. But suppose we turn the proposition round and say "Wisdom is a characteristic of Socrates," then wisdom, formerly the predicate, is now the subject. Now it seems to me as clear as anything can be in philosophy that the two sentences "Socrates is wise," "Wisdom is a characteristic of Socrates" assert the same fact and express the same proposition. They are not, of course, the same sentence, but they have the same meaning, just as two sentences in two different languages can have the same meaning. Which sentence we use is a matter either of literary style, or of the point of view from which we approach the fact. If the centre of our interest -86-

is Socrates we say "Socrates is wise," if we are discussing wisdom we may say "Wisdom is a characteristic of Socrates"; but whichever we say we mean the same thing. Now of one of these sentences "Socrates" is the subject, of the other "wisdom"; and so which of the two is subject, which predicate, depends upon what particular sentence we use to express our proposition, and has nothing to do with the logical nature of Socrates or wisdom, but is a matter entirely for grammarians. In the same way, with a sufficiently elastic language any proposition can be so expressed that any of its terms is the subject. Hence there is no essential distinction between the subject of a proposition and its predicate, and no fundamental classification of objects can be based upon such a distinction. I do not claim that the above argument is immediately conclusive; what I claim is that it throws doubt upon the whole basis of the distinction between particular and universal as deduced from that between subject and predicate, and that the question requires a new

examination. It is a point which has often been made by Mr. Russell that philosophers are very liable to be misled by the subject-predicate construction of our language. They have supposed that all propositions must be of the subject-predicate form, and so have been led to deny the existence of relations. I shall argue that nearly all philosophers, including Mr. Russell himself, have been misled by language in a far more far-reaching way than that; that the whole theory of particulars and universals is due to mistaking for a fundamental characteristic of reality what is merely a characteristic of language. Let us, therefore, examine closely this distinction of subject and predicate, and for simplicity let us follow Mr. Johnson and include relations among predicates and their terms among subjects. The first question we have to ask is this: what propositions are they that have a subject or subjects and a predicate? Is this the case with all propositions or only with some? Before, however, we go on to answer this question, let us remind ourselves that the task on which we are engaged is not merely one of English grammar; we are not school children analysing sentences into subject, extension of the subject, complement and so on, but are interested not so much in sentences themselves, as in what they mean, from which we hope to discover the logical nature of reality. Hence we must look for senses of subject and predicate which are not purely grammatical, but have a genuine logical significance. Let us begin with such a proposition as "Either Socrates is wise or Plato is foolish." To this, it will probably be agreed, the conception of subject and predicate is inapplicable; it may be applicable to the two parts "Socrates is wise," "Plato is foolish," but the whole "Either Socrates is wise or Plato is foolish" is an alternative proposition and not one with a subject or predicate. But to this someone may make the following objection: In such a proposition we can take any term we please, say Socrates, to be the subject. The predicate will then be "being wise unless Plato is foolish" or the propositional function " ̂x is wise or Plato is foolish." The phrase "being wise unless Plato is foolish" will then stand for a complex universal which is asserted to characterize -87-

Socrates. Such a view, though very frequently held, seems to me nevertheless certainly mistaken. In order to make things clearer let us take a simpler case, a proposition of the form "aRb"; then this theory will hold that there are three closely related propositions; one asserts that the relation R holds between the terms a and b, the second asserts the possession by a of the complex property of "having R to b," while the third asserts that b has the complex property that a has R to it. These must be three different propositions because they have different sets of constituents, and yet they are not three propositions, but one proposition, for they all say the same thing, namely that a has R to b. So the theory of complex universals is responsible for an incomprehensible trinity, as senseless as that of theology. This argument can be strengthened by considering the process of definition, which is as follows. For certain purposes "aRb" may be an unnecessarily long symbol, so that it is convenient to shorten it into " ϕb." This is done by definition, ϕx = aRx, signifying that any symbol of the form ϕx is to be interpreted as meaning what is meant by the corresponding symbol aRx, for which it is an abbreviation. In more complicated cases such an abbreviation is often extremely useful, but it could always be dispensed with if time and paper permitted. The believer in complex universals is now confronted with a dilemma: is "ϕ," thus defined, a name for the complex property of x which consists in a having R to x? If so, then ϕx will be the assertion that x has this property; it will be a subject-predicate proposition whose subject is x and predicate ϕ; and this is not identical with the relational proposition aRx. But as ϕx is by hypothesis defined to be short for aRx this is absurd. For if a definition is not to be interpreted as signifying that the definiendum and the definiens have the same meaning, the process of definition becomes unintelligible and we lose all justification for interchanging definiens and definiendum at will, on which depends its whole utility. Suppose on the other hand " ϕ," as defined above, is not a name for the complex property; then how can the complex property ever become an object of our contemplation, and how can we ever speak of it, seeing that " ϕ," its only possible name, is not a name for it at all but short for something else? And then what reason can there be to postulate the existence of this thing?

In spite of this reductio ad absurdum of the theory, it may still be worth while to inquire into its origin, and into why it is held by so many people, including formerly myself, without its occurring to them to doubt it. The chief reason for this is I think to be found in linguistic convenience; it gives us one object which is "the meaning" of " ϕ." We often want to talk of "the meaning of 'ϕ'," and it is simpler to suppose that this is a unique object than to recognize that it is a much more complicated matter, and that "ϕ" has a relation of meaning not to one complex object but to the several simple objects which are named in its definition. There is, however, another reason why this view is so popular, and that is the imaginary difficulty which would otherwise be felt in the use of a variable propositional function. How, it might be asked, are we to interpret such a statement as "a has all the properties of b," except on the supposition that there are properties? The answer -88-

is that it is to be interpreted as being the logical product of all propositions which can be constructed in the following way: take a proposition in which a occurs, say ϕa, change a into b and obtain ϕb, and then form the proposition ϕb . ⊃. ϕa. It is not really quite so simple as that, but a more accurate account of it would involve a lot of tiresome detail, and so be out of place here; and we can take it as a sufficient approximation that "a has all the properties of b" is the joint assertion of all propositions of the form ϕb . ⊃ . ϕa, where there is no necessity for ϕ to be the name of a universal, as it is merely the rest of a proposition in which a occurs. Hence the difficulty is entirely imaginary. It may be observed that the same applies to any other case of apparent variables some of whose values are incomplete symbols, and this may explain the tendency to assert that some of Mr. Russell's incomplete symbols are not really incomplete but the names of properties or predicates. I conclude, therefore, that complex universals are to be rejected; and that such a proposition as "Either Socrates is wise or Plato foolish" has neither subject nor predicate. Similar arguments apply to any compound proposition, that is any proposition containing such words as "and," "or," "not," "all," "some"; and hence if we are to find a logical distinction between subject and predicate anywhere it will be in atomic propositions, as Mr. Russell calls them, which could be expressed by sentences containing none of the above words, but only names and perhaps a copula. The distinction between subject and predicate will then arise from the several names in an atomic proposition functioning in different ways; and if this is not to be a purely grammatical distinction it must correspond to a difference in the functioning of the several objects in an atomic fact, so that what we have primarily to examine is the construction of the atomic fact out of its constituents. About this three views might be suggested; first there is that of Mr. Johnson according to whom the constituents are connected together by what he calls the characterizing tie. The nature of this entity is rather obscure, but I think we can take it as something which is not a constituent of the fact but represented in language by the copula "is," and we can describe this theory as holding that the connection is made by a real copula. Next there is the theory of Mr. Russell that the connection is made by one of the constituents; that in every atomic fact there must be one constituent which is in its own nature incomplete or connective and, as it were, holds the other constituents together. This constituent will be a universal, and the other particulars. Lastly there is Mr. Wittgenstein's theory that neither is there a copula, nor one specially connected constituent, but that, as he expresses it, the objects hang one in another like the links of a chain. From our point of view it is the second of these theories that demands most attention; for the first and third do not really explain any difference in the mode of functioning of subject

and predicate, but leave this a mere dogma. Only on Mr. Russell's theory will there be an intelligible difference between particular and universal, grounded on the necessity for there to be in each fact a copulating term or universal, corresponding to the need for every -89-

sentence to have a verb. So it is Mr. Russell's theory that we must first consider. The great difficulty with this theory lies in understanding how one sort of object can be specially incomplete. There is a sense in which any object is incomplete; namely that it can only occur in a fact by connection with an object or objects of suitable type; just as any name is incomplete, because to form a proposition we have to join to it certain other names of suitable type. As Wittgenstein says: "The thing is independent, in so far as it can occur in all possible circumstances, but this form of independence is a form of connection with the atomic fact, a form of dependence. (It is impossible for words to occur in two different ways, alone and in the proposition.)" 5 And Johnson: "Ultimately a universal means an adjective that may characterize a particular, and a particular means a substantive that may be characterized by a universal." 6 Thus we may admit that "wise" involves the form of a proposition, but so does "Socrates," and it is hard to see any ground for distinguishing between them. This is the substance of Mr. Johnson's criticism that Mr. Russell will not let the adjective stand alone, and in treating "s is p" as a function of two variables takes the arguments to be not s and p, but s and "̂x is p." In reply to this criticism Mr. Russell would, I imagine, use two lines of argument, whose validity we must examine. The first would dwell on the great convenience in mathematical logic of his functional symbolism, of which he might say there was no explanation except that this symbolism corresponded to reality more closely than any other. His second line of argument would be that everyone can feel a difference between particulars and universals ; that the prevalence of nominalism showed that the reality of universals was always suspected, and that this was probably because they did in fact differ from particulars by being less independent, less self-contained. Also that this was the only account of the difference between particulars and universals which made them really different kinds of objects, as they evidently were, and not merely differently related to us or to our language. For instance, Mr. Johnson describes the particular as presented to thought for its character to be determined in thought, and others might say a particular was what was meant by the grammatical subject of a sentence; and on these views what was particular, what universal would depend on unessential characteristics of our psychology or our language. Let us take these lines of argument in reverse order, beginning with the felt difference between particular and universal, and postponing the peculiar symbolic convenience of propositional functions. Anyone, it may be said, sees a difference between Socrates and wisdom. Socrates is a real independent entity, wisdom a quality and so essentially a quality of something else. The first thing to remark about this argument is that it is not really about objects at all. "Socrates is wise" is not an atomic proposition, and the symbols ____________________ 5Tractatus Logico-Philosophicus, 2.0122. 6Logic Part I, p. 11. -90-

"Socrates" and "wise" are not the names of objects but incomplete symbols. And according to Wittgenstein, with whom I agree, this will be the case with any other instance that may be suggested, since we are not acquainted with any genuine objects or atomic propositions, but merely infer them as presupposed by other propositions. Hence the distinction we feel is one between two sorts of incomplete symbols, or logical constructions, and we cannot infer without further investigation that there is any corresponding distinction between two sorts of names or objects. We can, I think, easily obtain a clearer idea of the difference between these two sorts of

incomplete symbols (Wittgenstein calls them "expressions") typified by "Socrates" and "wise." Let us consider when and why an expression occurs, as it were, as an isolated unit. For instance "aRb" does not naturally divide into "a" and "Rb," and we want to know why anyone should so divide it and isolate the expression "Rb." The answer is that if it were a matter of this proposition alone, there would be no point in dividing it in this way, but that the importance of expressions arises, as Wittgenstein points out, just in connection with generalization. It is not "aRb" but "(x) . xRb" which makes Rb prominent. In writing (x) . xRb we use the expression Rb to collect together the set of propositions xRb which we want to assert to be true; and it is here that the expression Rb is really essential because it is this which is common to this set of propositions. If now we realize that this is the essential use of expressions, we can see at once what is the difference between Socrates and wise. By means of the expression "Socrates" we collect together all the propositions in which it occurs, that is, all the propositions which we should ordinarily say were about Socrates, such as "Socrates is wise," "Socrates is just," "Socrates is neither wise nor just." These propositions are collected together as the values of " ϕ Socrates," where ϕ is a variable. Now consider the expression "wise"; this we use to collect together the propositions "Socrates is wise," "Plato is wise," and so on, which are values of "x is wise." But this is not the only collection we can use "wise" to form; just as we used "Socrates" to collect all the propositions in which it occurred, we can use "wise" to collect all those in which it occurs, including not only ones like "Socrates is wise" but also ones like "Neither Socrates nor Plato is wise," which are not values of "x is wise" but only of the different function " ϕ wise," where ϕ is variable. Thus whereas Socrates gives only one collection of propositions, wise gives two: one analogous to that given by Socrates, namely the collection of all propositions in which wise occurs; and the other a narrower collection of propositions of the form "x is wise." This is obviously the explanation of the difference we feel between Socrates and wise which Mr. Russell expresses by saying that with wise you have to bring in the form of a proposition. Since all expressions must be completed to form a proposition, it was previously hard to understand how wise could be more incomplete than Socrates. Now we can see that the reason for this is that whereas with "Socrates" we only have the idea of completing it in any manner into a proposition, with "wise" we have not only this but also an -91-

idea of completing it in a special way, giving us not merely any proposition in which wise occurs but also one in which it occurs in a particular way, which we may call its occurrence as predicate, as in "Socrates is wise." What is this difference due to, and is it a real difference at all? That is to say, can we not do with "Socrates" what we do with "wise," and use it to collect a set of propositions narrower than the whole set in which it occurs? Is this impossible, or is it merely that we never in fact do it? These are the questions we must now try to answer. The way to do it would seem to be the following. Suppose we can distinguish among the properties of Socrates a certain subset which we can call qualities, the idea being roughly that only a simple property is a quality. Then we could form in connection with "Socrates" two sets of propositions just as we can in connection with "wise." There would be the wide set of propositions in which "Socrates" occurs at all, which we say assert properties of Socrates, but also there would be the narrower set which assert qualities of Socrates. Thus supposing justice and wisdom to be qualities, "Socrates is wise," "Socrates is just" would belong to the narrower set and be values of a function "Socrates is q." But "Socrates is neither wise nor just" would not assert a quality of Socrates but only a compound characteristic or property, and would only be a value of the function "ϕ Socrates," not of "Socrates is q." But although such a distinction between qualities and properties may be logically possible, we do not seem ever to carry it out systematically. Some light may be thrown on this fact by a paragraph in Mr. Johnson's Logic in which he argues that, whereas "we may properly construct a compound adjective out of simple adjectives, yet the nature of any term functioning as a substantive is such that it is impossible to construct a genuine compound

substantive." 7 Thus from the two propositions "Socrates is wise," "Socrates is just" we can form the proposition "Neither is Socrates wise nor is Socrates just," or, for short, "Socrates is neither wise nor just"; which still, according to Mr. Johnson, predicates an adjective of Socrates, is a value of "ϕ Socrates" and would justify "(∃ϕ). ϕ Socrates," or "Socrates has some property." If, on the other hand, we take the two propositions "Socrates is wise," "Plato is wise" and form from them "Neither Socrates is wise nor Plato is wise"; this is not a value of "x is wise" and would not justify "(∃x) . x is wise," or "Someone is wise." So

inasmuch as "Socrates is neither wise nor just" justifies "Socrates has some adjective" we can say that "neither wise nor just" is a compound adjective; but since "Neither Socrates nor Plato is wise" does not justify "something is wise," "neither Socrates nor Plato" cannot be a compound substantive any more than nobody is a compound man. If, however, we could form a range of qualities as opposed to properties, "Socrates is neither wise nor just" would not justify "Socrates has some quality" and "neither wise nor just" would not be a quality. Against this Mr. Johnson says that there is no universally valid criterion by which we can distinguish qualities from other properties; and this is certainly a very ____________________ 7Part II, p. 61. -92-

plausible contention when we are talking, as we are now, of qualities and properties of logical constructions such as Socrates. For the distinction is only really clear in connection with genuine objects; then we can say that ϕ represents a quality when ϕa is a two-termed atomic proposition, and this would distinguish qualities from other propositional functions or properties. But when the subject a is a logical construction and ϕa a compound proposition of which we do not know the analysis, it is hard to know what would be meant by asking if ϕ were simple, and calling it, if simple, a quality. It would clearly have to be a matter not of absolute but of relative simplicity. Yet it is easy to see that, in theory, an analogous distinction can certainly be made for incomplete symbols also. Take any incomplete symbol "a"; this will be defined not in isolation but in conjunction with any symbol of a certain sort x. Thus we might define ax to mean aRx. Then this incomplete symbol "a" will give us two ranges of propositions: the range ax obtained by completing it in the way indicated in its definition; and the general range of propositions in which a occurs at all, that is to say, all truth-functions of the propositions of the preceding range and constant propositions not containing a. Thus in the two famous cases of descriptions and classes, as treated in Principia Mathematica, the narrower range will be that in which the description or class has primary occurrence, the wider range that in which it has any sort of occurrence primary or secondary, where the terms "primary" and "secondary" occurrence have the meanings explained in Principia. In brief with regard to any incomplete symbol we can distinguish its primary and secondary occurrences, and this is fundamentally the same distinction which we found to be characteristic in the adjective. So that any incomplete symbol is really an adjective, and those which appear substantives only do so in virtue of our failing whether through inability or neglect to distinguish their primary and secondary occurrences. As a practical instance let us take the case of material objects; these we are accustomed to regard as substantives, that is to say we use them to define ranges of propositions in one way only, and make no distinction between their primary and secondary occurrences. At least no one made such a distinction until Dr. Whitehead declared that material objects are adjectives of the events in which they are situated, so that the primary occurrence of a material object A is in a

proposition "A is situated in E." From such propositions as this we can construct all other propositions in which A occurs. Thus "A is red" will be "For all E, A is situated in E implies redness is situated in E," in which A has secondary occurrence. So the distinction between primary and secondary occurrence is not merely demonstrated as logically necessary, but for this case effected practically. The conclusion is that, as regards incomplete symbols, the fundamental distinction is not between substantive and adjective but between primary and secondary occurrence; and that a substantive is simply a logical construction between whose primary and secondary occurrences we fail to distinguish. So that to be a substantive is not an objective but a subjective property in the -93-

sense that it depends not indeed on any one mind but on the common elements in all men's minds and purposes. This is my first conclusion, which is I think of some importance in the philosophy of nature and of mind; but it is not the conclusion which I most want to stress, and it does not answer the question with which I began my paper. For it is a conclusion about the method and possibility of dividing certain logical constructions into substantives and adjectives, it being in connection with these logical constructions that the idea of substantive and adjective traditionally originated. But the real question at issue is the possibility of dividing not logical constructions but genuine objects into particulars and universals, and to answer this we must go back and pick up the thread of the argument, where we abandoned it for this lengthy digression about logical constructions. We saw above that the distinction between particular and universal was derived from that between subject and predicate which we found only to occur in atomic propositions. We then examined the three theories of atomic propositions or rather of atomic facts, Mr. Johnson's theory of a tie, Mr. Russell's that the copulation is performed by universals, of which there must be one and only one in each atomic fact, and Mr. Wittgenstein's that the objects hang in one another like the links of a chain. We observed that of these theories only Mr. Russell's really assigned a different function to subject and predicate and so gave meaning to the distinction between them, and we proceeded to discuss this theory. We found that to Mr. Johnson's criticisms Mr. Russell had two possible answers; one being to argue that his theory alone took account of the difference we feel there to be between Socrates and wisdom, the other that his notation was far more convenient than any other and must therefore correspond more closely to the facts. We then took the first of these arguments, and examined the difference between Socrates and wisdom. This we found to consist in the fact that whereas Socrates determined only one range of propositions in which it occurred, wise determined two such ranges, the complete range "f wise," and the narrower range "x is wise." We then examined the reason for this difference between the two incomplete symbols Socrates and wise, and decided that it was of a subjective character and depended on human interests and needs. What we have now to consider is whether the difference between Socrates and wise has any such bearing on the composition of atomic facts as Mr. Russell alleges it to have. This we can usefully combine with the consideration of Mr. Russell's other possible argument from the superior convenience of his symbolism. The essence of this symbolism, as Mr. Johnson has observed, consists in not letting the adjective stand alone, but making it a propositional function by attaching it to a variable x. A possible advantage of this procedure at once suggests itself in terms of our previous treatment of the difference between substantive and adjective; namely, that attaching the variable x helps us to make the distinction we require to make in the case of the adjective, but not in the case of the substantive, between the values of ϕx and -94-

those of f (ϕ̂Z) where f is variable. Only so, it might be said, can we distinguish (x) . ϕx from

( f) . f(ϕ̂Z) But very little consideration is required to see that this advantage is very slight and of no fundamental importance. We could easily make the distinction in other ways; for instance by determining that if the variable came after the ϕ it should mean what we now express by ϕx, but if before the ϕ what we express by f (ϕ̂Z); or simply by deciding to use the letters "x," "y," "z," in one case, "f," "g," "h," in the other. But, although this supposed advantage in the functional symbolism is imaginary, there is a reason which renders it absolutely indispensable. Take such property as "either having R to a, or having S to b"; it would be absolutely impossible to represent this by a simple symbol "ϕ." For how then could we define ϕ? We could not put ϕ = Ra . v . Sb because we should not know whether the blanks were to be filled with the same or different arguments, and so whether ϕ was to be a property or relation. Instead we must put ϕx. = . xRa . v . xSb; which explains not what is meant by ϕ by itself but that followed by any symbol x it is short for xRa . v . xSb. And this is the reason which makes inevitable the introduction of propositional functions. It simply means that in such a case " ϕ" is not a name but an incomplete symbol and cannot be defined in isolation or allowed to stand by itself. But this conclusion about xRa . v . xSb will not apply to all propositional functions. If ϕa is a two-termed atomic proposition, "ϕ" is a name of the term other than a, and can perfectly well stand by itself; so, it will be asked, why do we write " ϕx" instead of "ϕ" in this case also? The reason for this lies in a fundamental characteristic of mathematical logic, its extensionality, by which I mean its primary interest in classes and relations in extension. Now if in any proposition whatever we change any individual name into a variable, the resulting propositional function defines a class; and the class may be the same for two functions of quite different forms, in one of which " ϕ" is an incomplete symbol, in the other a name. So mathematical logic, being only interested in functions as a means to classes, sees no need to distinguish these two sorts of functions, because the difference between them, though all-important to philosophy, will not correspond to any difference between the classes they define. So because some ϕ's are incomplete and cannot stand alone, and all ϕ's are to be treated alike in order to avoid useless complication, the only solution is to allow none to stand alone. Such is the justification of Mr. Russell's practice; but it is also the refutation of his theory, which fails to appreciate the distinction between those functions which are names and those which are incomplete symbols, a distinction which, as remarked above, though immaterial for mathematics is essential for philosophy. I do not mean that Mr. Russell would now deny this distinction; on the contrary it is clear from the Second Edition of Principia that he would accept it; but I think that his present theory of universals is the relic of his previous failure to appreciate it. It will be remembered that we found two possible arguments for his theory of universals. One was from the efficiency of the functional notation; this -95-

clearly lapses because, as we have seen, the functional notation merely overlooks an essential distinction which happens not to interest the mathematician, and the fact that some functions cannot stand alone is no argument that all cannot. The other argument was from the difference we feel between Socrates and wise, which corresponds to a difference in his logical system between individuals and functions. Just as Socrates determines one range of propositions, but wise two, so a determines the one range ϕa, but ϕ̂Z the two ranges ϕx and f (ϕ̂Z). But what is this difference between individuals and functions due to? Again simply to the fact that certain things do not interest the mathematician. Anyone who was interested not only in classes of things, but also in their qualities, would want to distinguish from among the others those functions which were names; and if we called the objects of which they are names qualities, and denoted a variable quality by q, we should have not only the range ϕa but also the narrower range qa, and the difference analogous to that between "Socrates" and "wisdom" would have disappeared. We should have complete symmetry

between qualities and individuals; each could have names which could stand alone, each would determine two ranges of propositions, for a would determine the ranges qa and ϕa, where q and ϕ are variables, and q would determine the ranges qx and fq, where x and f are variables. So were it not for the mathematician's biassed interest he would invent a symbolism which was completely symmetrical as regards individuals and qualities; and it becomes clear that there is no sense in the words individual and quality; all we are talking about is two different types of objects, such that two objects, one of each type, could be sole constituents of an atomic fact. The two types being in every way symmetrically related, nothing can be meant by calling one type the type of individuals and the other that of qualities, and these two words are devoid of connotation. To this, however, various objections might be made which must be briefly dealt with. First it might be said that the two terms of such an atomic fact must be connected by the characterizing tie and/or the relation of characterization, which are asymmetrical, and distinguish their relata into individuals and qualities. Against this I would say that the relation of characterization is simply a verbal fiction. "q characterizes a" means no more and no less than "a is q," it is merely a lengthened verbal form; and since the relation of characterization is admittedly not a constituent of "a is q" it cannot be anything at all. As regards the tie, I cannot understand what sort of a thing it could be, and prefer Wittgenstein's view that in the atomic fact the objects are connected together without the help of any mediator. This does not mean that the fact is simply the collection of its constituents but that is consists in their union without any mediating tie. There is one more objection suggested by Mr. Russell's treatment in the new edition of Principia. He there says that all atomic propositions are of the form R 1 (x), R 2 (x, y), R 3 (x, y, z), etc., and so can define individuals as terms which can occur in propositions with any number of terms; whereas of course an n-termed relation could only occur in a proposition with n + 1 terms. But this assumes his theory as to the con -96-

stitution of atomic facts, that each must contain a term of a special kind, called a universal; a theory we found to be utterly groundless. The truth is that we know and can know nothing whatever about the forms of atomic propositions; we do not know whether some or all objects can occur in more than one form of atomic proposition; and there is obviously no way of deciding any such question. We cannot even tell that there are not atomic facts consisting of two terms of the same type. It might be thought that this would involve us in a vicious circle contradiction, but a little reflection will show that it does not, for the contradictions due to letting a function be its own argument only arise when we take for argument a function containing a negation which is therefore an incomplete symbol not the name of an object. In conclusion let us describe from this new point of view the procedure of the mathematical logician. He takes any type of objects whatever as the subject of his reasoning, and calls them individuals, meaning by that simply that he has chosen this type to reason about, though he might equally well have chosen any other type and called them individuals. The results of replacing names of these individuals in propositions by variables he then calls functions, irrespective of whether the constant part of the function is a name or an incomplete symbol, because this does not make any difference to the class which the function defines. The failure to make this distinction has led to these functional symbols, some of which are names and some incomplete, being treated all alike as names of incomplete objects or properties, and is responsible for that great muddle the theory of universals. Of all philosophers Wittgenstein alone has seen through this muddle and declared that about the forms of atomic propositions we can know nothing whatever. -97-

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UNIVERSALS AND METAPHYSICAL REALISM ALAN DONAGAN The point of philosophy is to start with something so simple as not to seem worth stating, and end with something so paradoxical that no one will believe it. —BERTRAND RUSSELL, The Monist (1918) THE late Friedrich Waismann once remarked that, while you may confute and kill a scientific theory, a philosophy dies only of old age. The realist theory of universals, which G. E. Moore and Bertrand Russell revived in the brilliant fifteen years which preceded the first World War, 1 seems to have aged more rapidly than its authors, and to have died, or fallen into oblivion, during the 'forties. In the United States, the very different conception of realism propounded by Professor Quine and Goodman, 2 and nicknamed by Quine "Plato's Beard," has displaced it, leaving Professor Bergmann almost alone to defend it. 3 In Britain, a polished essay by Mr. Pears seems to have been received as its epitaph. 4 In this paper I propose to re-examine Moore's and Russell's principal argument for the reality of universals, in order to determine whether any spark of life remains in it. Is it truly dead, or only neglected? ____________________ Reprinted from The Monist, 47, no. 2 (1963), with the permission of The Open Court publishing Co., La Salle, Illinois, and of the author. 1G. E. Moore, "The Nature of Judgment," Mind, 8 (1899), esp. pp. 178-83; "Identity," Proc. Aris. Soc., 1 (1900-1), esp. pp. 105-15; Some Main Problems of Philosophy (London, 1953), hereafter cited as Main Problems, pp. 301-5, 312-77 (composed in 1910-1); and Bertrand Russell, "On the Relations of Universals to Particulars" (composed 1911) in Logic and Knowledge, ed. Robert C. Marsh (London, 1956); The Problems of Philosophy (London, 1912), chs. 8-10. 2W. V. Quine, From a Logical Point of View (Cambridge, Mass., 1951), chs. 1, 6; Nelson Goodman, The Structure of Appearance (Cambridge, Mass., 1951), ch. 2. 3Gustav Bergmann, Meaning and Existence (Madison, Wis., 1959), esp. chs. 4, 13. My debts in this essay to Professor Bergmann, particularly in what I say about the attempts of Professors Quine and Goodman to shave Plato's Beard, are heavy and obvious, though no doubt he would reject most of my conclusions. 4D. F. Pears, "Universals," in Logic and Language, 2nd series, ed. Antony Flew (Oxford, 1953).

I Russell's The Problems of Philosophy is a convenient and familiar point of departure. Lucidly and simply, it states the position which Moore and Russell held, and their reason for holding it. In its eighth chapter, Russell wrote this: Suppose, for instance, that I am in my room. I exist, and my room exists; but does "in" exist? Yet obviously the word "in" has a meaning; it denotes a relation which holds between me and my room. This relation is something, although we cannot say that it exists in the same sense in which I and my room exist. The relation "in" is something which we can think about and understand, for, if we could not understand it, we could not understand the sentence "I am in my room." 5 The conclusion that we are to investigate is that the relation denoted by "in" is, or is real. Russell's distinction between being and existence, according to which the relation denoted by "in" has being (is or is real) but does not exist, is notoriously difficult, and we shall defer investigating it. Yet, even apart from that distinction, Russell's argument and conclusion are puzzling.His reasoning seems to have been as follows: i. Some propositions of the form "x is in y," where "x" and "y" deputize for names or descriptions of things which in a familiar sense exist, can be thought about and

understood. They could not be thought about or understood unless the word "in" were thought about and understood; i.e. "in" is not redundant. iii. Some propositions in the form "x is in y" are true. (I take this to be presupposed in Russell's opening injunction: "Suppose, for instance, that....") iv. The non-redundant elements of true propositions denote things that are real or have being, if not things that exist. v. Therefore, "in" denotes something which is or is real, if not something which exists; and since if "in" denotes anything at all it is a relation, it follows that at least one relation is or is real. ii.

If relations are real, then universals are real: for "a universal will be anything which may be shared by many particulars"; 6 and at least two pairs of particulars, namely, Russell and his room, and Moore and his room, may share the relation denoted by "in." Neither Russell nor Moore believed that all universals were relational. In The Problems of Philosophy Russell had much to say of justice and whiteness, which he considered to be non-relational qualities; and in Some Main Problems of Philosophy Moore strove to demonstrate that in some sense ____________________ 5Bertrand Russell, The Problems of Philosophy (London, reset edn. 1946), hereafter cited as Problems, p. 90. 6Russell, Problems, p. 93; cf. Moore, Main Problems, p. 304. -99-

whiteness is a universal which is neither a relation (like in) nor a relational property (like in Russell's room). Yet both Moore and Russell considered the being of relations and relational properties to be far more evident than that of non-relational (qualitative) universals; and both ascribed the nominalist tendencies in the work of Berkeley and Hume to their error that, unlike qualities, relations are evidently the work of the mind. 7 Russell plainly agreed with Moore that "it is ... comparatively easy to distinguish universals of both these two sorts [relations and relational properties]; and if it were quite clear that they were the only sorts, the whole question about universals would be ... comparatively simple." 8 Simple or not, it is the question we are to investigate. In doing so, I shall assume that Moore and Russell were in the right when they declared that whether or not there are qualities which are irreducible to relational properties has not the slightest bearing on whether or not there are universals. Despite Russell's lucidity, there are obscurities in his argument as I have analysed it. It only applies to expressions which are non-redundant, i.e. which must be thought about and understood if the meaning of the sentences in which they occur is to be thought about and understood. Clearly if, instead of saying "I am in my room," Russell had added some expletive to "room," e.g. "God-forsaken," that expletive would have been redundant, and his argument would not have shown that there is something which "God-forsaken" denotes. To show that, it would be necessary to produce a true statement in which "God-forsaken" was not redundant. But is it enough to exclude redundant expressions? Some expressions, for example in mathematics, are rigorously defined. If the definition of "triangle" were substituted for the word "triangle" in a theorem of Euclid, the meaning of that theorem would remain unchanged. Are we to interpret Russell's argument as showing that there is a universal denoted by "triangle," as well as those denoted by "figure," "plane," and "threesided?" In his later work Russell construed his argument as applying only to expressions which are primitive. Hence, the fact that you can think about and understand the expression "in" shows either that "in" denotes something that is real or has being, or that "in" is definable, and that the primitive expressions by which it is ultimately to be defined denote things that are real or have being. Even after this clarification, the scope of Russell's argument remains obscure. Suppose that the sentences with which Russell began were, "You are or I am in my room" or "I am an individual (or a particular)." The expressions "or" and "individual" (or "particular") are, in

Russell's own view, not redundant. Once more, we must turn to his later works for guidance. If all logical connectives such as "and," "or," "if ... then" be interpreted truth- functionally, then they must be excluded from the fundamental propositions from which compound propositions are constructed. It must be conceded that a difficulty remains about the sentence, " 'I am in my room' is true." To un____________________ 7Russell, Problems, pp. 95-7; Moore, Main Problems, pp. 305, 313-4. 8Moore, Main Problems, p. 353; cf. Russell, Problems, pp. 93-4, 97. -100-

derstand that sentence, it is necessary to understand the expression "true"; and if truthfunctional analyses of the logical connectives are to be admitted, such sentences must be indispensable. However, Russell might plead that the expressions "true" and "false," which signify, not properties of objects, but properties of propositions about objects, call for separate elucidation and interpretation. I shall therefore assume that his argument applies neither to them nor to their derivatives. Expressions like "individual," "particular," and "universal" must also be treated separately. Frege's technique of quantification enables us to dispense with them as they most commonly occur in such sentences as, "Some individual both took office under Caesar and conspired to murder him," by replacing them with variables, e.g. "For some value of 'x,' 'x took office under Caesar and x conspired to murder Caesar' is true." As for sentences which cannot be so analysed, e.g. "Brutus is an individual," what they say is shown by allowing certain expressions, e.g. "Brutus," to be substituted for certain variables, e.g. "x" in the above function; and it may be expressed in the formal mode by such sentences as, "The expression 'Brutus' is a legitimate value of the variable 'x'." Russell was to accept Wittgenstein's view that expressions like "individual," "particular," and "universal," which can be eliminated by such devices, signify formal concepts, 9 and should not be mistaken for predicates signifying properties which a thing may or may not possess. These elucidations affect only the scope of Russell's argument. What of its nature? If our analyses and clarifications are sound, it asserts that the reality of the universal in follows from three facts: (i) that the sentence "I am in my room" can be thought about and understood; (ii) that on the occasion when Russell wrote it he expressed a true proposition; and (iii) that the word "in" neither is definable nor is a logical connective nor signifies a formal concept, and is predicable of many particulars (henceforth I shall call such expressions "primitive predicates"). That universals are real is held to follow from these facts by the general principle that the non-redundant elements of true propositions denote things that are real or have being. That principle, however, applies to proper names as well as to predicates. Russell's argument requires only a narrower principle, which I shall henceforth call "the Realist Principle"; namely, that primitive predicates occurring non-redundantly in true propositions denote real things, or, as Moore liked to say, "real constituents of the world." It is plain why Russell and Moore adhered to this Principle. They could not conceive how otherwise propositions containing primitive predicates could state facts about the world. 10 And certainly this consideration is weighty. If the ultimate non-logical and non-formal constituents of true propositions refer to nothing in the world, in what can the truth of such propositions consist? Before proceeding to consider objections to Russell's argument one more ____________________ 10Russell, Problems, pp. 90 (cf. 80-8), 97-8; Moore, Main Problems, pp. 303-5. 9Ludwig Wittgenstein, Tractatus Logico-Philosophicus (London, 1922), 4.126- 4.12721. -101-

elucidation is called for. While it presupposes that there are true propositions containing expressions which stand for universals, it does not stipulate that those propositions must

assert that those universals are exemplified. In his example Russell laid it down that the relation in was supposed to be exemplified ; for he invited his readers to suppose that he was in his room. But, since "in" is as much a constituent of the negative proposition "Russell is not in his room," as of the affirmative one, "Russell is in his room," the reality of the relation in would seem to follow from the truth of either one. This point can be generalized. Let "... R ..." signify a relational expression, and let the only true propositions containing "... R ..." be of the form ˜R(x,y) or ˜xRy. In other words, let it be true that ˜(∃x,y) xRy. Six years after writing The Problems of Philosophy, Russell stoutly maintained the possibility that there are negative facts, i.e. that there are facts expressible by propositions of the form ˜fa, which cannot be reduced to facts expressible by propositions that contain no sign of negation. 11 If that is possible, then it is logically possible that the only true propositions containing a given predicative expression, whether "F... ," or "R(... , ...)" or some other, should be negative. By Russell's argument, such an unexemplified universal would have exactly the same claim to being or reality as exemplified ones. Both in The Problems of Philosophy and "The Philosophy of Logical Atomism" Russell avoided admitting this by adopting the Principle of Acquaintance, namely, that "in every proposition that we can apprehend (i.e., not only in those whose truth and falsity we can judge of, but in all that we can think about) all the constituents are really entities with which we have immediate acquaintance." 12 It follows that we cannot think about any proposition the primitive expressions in which do not stand for constituents with which we are acquainted; and we can be acquainted with the constituent denoted by a qualitative or relational expression only if that constituent is exemplified and we are acquainted with an instance of it. In short, we cannot even think about a negative proposition containing "... R ... ," e.g. "˜aRb," unless we have been acquainted with a state of affairs asserted by a proposition of the form "xRy." The metaphysical problem, however, cannot be dodged in that way. First, the question whether universals have being or are real is quite distinct from the question whether every universal of which we have formed a concept has been exemplified somewhere at some time. Nothing in Russell's argument confines its application either to affirmative propositions, or to propositions we know. Of course, he might stipulate that its application be so confined; but such an arbitrary stipulation would carry no weight. Secondly, the problem of unexemplified universals can be propounded even if the Principle of Ac____________________ 11Russell, Logic and Knowledge, pp. 211-6, esp. 213. 12Russell, Problems, p. 58; Logic and Knowledge, pp. 195, 270-80. For a criticism of the Principle of Acquaintance see Max Black, Language and Philosophy (Ithaca, 1949), pp. 130-4. -102-

quaintance be accepted. That Principle entails neither that any given language, English say, contains expressions for all exemplified qualities and relations, nor that speakers of English are acquainted with instances of all of them. It cannot, therefore, forbid a speaker of English to opine that two objects, say the Atlantic and the Pacific Oceans, stand to each other in some relation with which he is not acquainted. It follows that somebody who said, in English, "(∃R) the Atlantic Ocean R the Pacific Ocean, and I am not acquainted with R," would make an intelligible statement. Now if you can opine that a pair of objects exemplifies a relation with which you are not acquainted, you can equally opine that it does not. For example, you might intelligibly say:

(1) "( 3 R) ˜R (the Atlantic Ocean, the Pacific Ocean) and I am not acquainted with R." Having said that, you might generalize it: (2) "( 3R)(x,y) ˜R(x,y) and I am not acquainted with R." If (2) were true, an infinite number of statements of the form ˜R (x,y) would be true, in each of which the value of the variable "R" would signify an unexemplified relation. The Principle of Acquaintance entails, not that there is no such relation, but that no language contains a predicate denoting it. Although the limits of my language may be the limits of my world, they are not the limits of the world. Since I am not tempted to endorse any metaphysical Principle of Plenitude, I am inclined to think the proposition (2) above to be true. If it is, then there are innumerable negative facts which, if the Principle of Acquaintance be true, nobody will ever know. From that, if Russell's argument is sound, it follows that an unexemplified relation is a real constituent of the world. Those who countenance Russell's argument can escape this conclusion in only two ways: either by demonstrating that unexemplified universals are impossible (not merely that they cannot be directly known), or by demonstrating that all negative propositions are reducible to affirmative ones. Up to now, neither has been established.

II Realist arguments like Russell's have been rejected for such a variety of reasons that I cannot here examine them all. I shall, therefore, select those few which I judge to be cardinal. I cannot even justify my selection; for to do so it would be necessary to show that none of the objections I do not discuss has more weight than any of those I do. The four objections I have selected are: (1) the classical difficulty, with which Plato struggled, that the very concept of a unitary universal which is -103-

"shared by" many particulars appears to be self-contradictory; (2) that although some realist principle may be true, the Realist Principle which Russell held is false; (3) that Russell's argument depends on features peculiar to certain languages, which may be dispensed with in an artificial language, and perhaps is in some natural languages; (4) that Russell's theory of universals, as a whole, is "circular and uninformative." (1) The Classical Difficulty. In the Philebus Plato drew attention to two difficulties in his theory of forms: if there are many things in which a form may be said to be present, it would seem that "we must think [either] that [the form] is dispersed and has become many," or "that it is still entire and divided from itself, which latter would seem to be the greatest impossibility of all" (ibid. 15B). Russell's theory appears to avoid the first difficulty, but not the second. He recognized a universal denoted by "in" which may be "shared" or, to avoid metaphor, "exemplified" by, many pairs of particulars, e.g. by Russell and his room, and by Moore and his. However, he did not think that only part of the universal in would be exemplified by each pair that exemplifies it: that is, he did not think that it could be "dispersed" among those pairs, and so "become many." A universal remains unitary. Yet, since Russell did think that Moore could be in his room at the very same time as he was in his, the two rooms being necessarily at different places, he could not avoid concluding that at the same time the unitary universal in could be exemplified at different places. Does that not imply what to Plato seemed "the greatest impossibility of all," that it is "still entire and yet divided from itself?" A tempting way out of this difficulty is to deny that because the in is exemplified by Russell and his room, both of which are at a certain place, the universal itself must be at that place, or at any place. Yet that way lies destruction. It is true that the question form, "Where is the universal?" has no established use in non-philosophical discourse. But then, neither has the term "universal" such a use; and questions of the impugned form naturally arise out of Russell's theory. Moreover, there is a strong reason for thinking that if universals are

exemplified in space and time, they are where they are exemplified. You can verify the statement that Russell is in his room by looking into it and seeing him there. When you look, you see not only him and his room, but also that he is in it. It is true that it is not good English to say that you see in, along with Russell and his room; but, as the late J. L. Austin once pointed out, neither is it good English to say that you do not see it, or that you intuit it. "I [see] what in English is described by means of two demonstrative pronouns and an adverbial phrase. To look for an isolable entity corresponding to the latter is a bad habit...." 13 Now, if what you see includes what is described by the adverbial phrase "... is in ... ," i.e. a universal, must it not be where you are looking? And if one man was to see that Russell was in his room at the same time as another was to see Moore in his, would it not follow that the universal in was in the two different places ____________________ 13J. L. Austin, Philosophical Papers (Oxford, 1961), p. 18. -104-

where the two were looking? If so, would not the universal in be both "entire and yet divided from itself"? At this juncture, realists should act on the principle that the best defense is attack, and protest that by its very nature a universal is the sort of thing that can be exemplified by particulars in different places at the same time. To say that it is "entire and yet divided from itself" is objectionable, because it presupposes that to be exemplified in two different places at once implies being divided. It is true that a particular can only be in two places at once if one part of it is at one place, and another part at the other; but, by their very nature, universals are not divisible into parts. Exasperated, the Platonic Mephistopheles may retort that what is seen to be exemplified at two different places is seen at those places; and that, since what is seen at one place is not what is seen at the other, the in which is seen to be exemplified in Russell's room cannot be the same as the in which is seen to be exemplified in Moore's room. In his turn, a realist may reply that the second premise of this argument, namely that what is seen at one place is not what is simultaneously seen at the other, holds for particulars but not for universals. If he is asked how that can be, he need not hesitate to reply that you cannot explain what is fundamental. At a certain time Russell is in his room and Moore is in his; and one and the same relation, namely that denoted by "in," is a constituent of both facts. If that is impossible, then all discourse is impossible. Even this resounding affirmation may not exorcise the Platonic imp. We have supposed that realists may avoid metaphorical expressions like "share" and "participate in" when speaking of the connexion between particulars and universals, and have employed instead the non-metaphorical "exemplify." But what does "exemplify" denote? In his 1911 essay "On the Relations of Universals and Particulars," Russell wrote that, ... according to the theory which assumes particulars, there is a specific relation of subject to predicate ... [Ordinary sensible qualities will be predicates of the particulars which are instances of them.... Predication is a relation involving a fundamental logical difference between its two terms ... [T]he question whether predication is an ultimate simple relation may be taken as distinguishing the two theories [i.e. that there are particulars and that there are not]; it is ultimate if there are particulars (Logic and Knowledge, p. 123). Plainly Russell's "predication" has the same sense as our "exemplification" ("exemplification" is better because it is convenient to reserve "predication" for the relation between a linguistic expression and what it is predicated of); and Russell is saying that predication (or exemplification) itself is an "ultimate simple relation." In the first of his articles on Plato's Parmenides, Professor Ryle showed that there cannot be such a relation. 14 By Russell's own exposition, it would be anomalous. Whereas ordinary relations relate particulars (John is to the left of James) or universals (Yellow is a lighter colour than red), exempli____________________

14Gilbert

Ryle, "Plato's Parmenides," Mind, 48 (1939) pp. 137-8. -105-

fication is supposed to relate particulars to universals. Suppose, nevertheless, that there is such a relation. Applying this supposition to Russell's example, exemplification will relate the two particulars, Russell and his room, to the relation in, and the two particulars, Moore and his room, to the same relation. It follows that exemplification is a universal. For, although Russell defined a universal as "anything which may be shared by many particulars," by explicitly acknowledging that "predicates themselves may have predicates," 15 i.e. that there may be universals which are exemplified only by universals, he showed that he considered it a sufficient condition of universality that a thing be predicable of or exemplifiable by many other things whether particulars or not.The ultimate simple relation of exemplification is then a constituent of each of the two facts: i. The relation in is exemplified by Russell and his room; ii. The relation in is exemplified by Moore and his room. It follows that, ia. The relation of exemplification is exemplified by Russell, his room, and the relation in, and that, iia. The relation of exemplification is exemplified by Russell, his room, and the relation in. But the facts (ia) and (iia) are stated in sentences which contain the expression "is exemplified by." What does that expression denote? It cannot denote the relation of exemplification which is said to be exemplified, because a relation cannot relate anything to itself. It must therefore denote either nothing at all or a second-order relation of exemplification. It cannot denote nothing at all, if the first-order relation of exemplification is genuine, as it must be if universals are related to what they exemplify by an ultimate simple relation. Hence it must denote a second-order relation of exemplification. Manifestly, this regress is interminable and vicious. For, since second-order exemplification must in turn be a genuine universal, exemplified by Russell, his room, the relation in, and first-order exemplification, there must be a third-order relation of exemplification, and so ad infinitum. 16

Since vicious infinite regresses cannot be stopped, they must not be al____________________ 15Logic and Knowledge, p. 123; cf. Problems, pp. 102-3. 16Ryle truly observed that his regress is not the same as F. H. Bradley's celebrated regress of relations, "though reminiscent of it" (loc. cit. p. 138). The question which generated Bradley's regress, namely, How can "a more or less independent" relation relate its terms? arises from Bradley's doctrine that a relation between A and B "implies really a substantial foundation within them" (Appearance and Reality [Oxford, 1946], pp. 17-18). Neither Russell nor Ryle saw any difficulty in the "independence" or externality of relations. -106-

lowed to start. Once you concede to the Platonic imp that particulars and universals need a further universal, and an anomalous one at that, to relate them, you cannot deny that that further universal requires yet a further one, and so ad infinitum. Nor will it help to plead that the relation of exemplification is unique. It is not unique in the only respect that matters: namely, that many sets of universals and particulars share it or exemplify it. Why did Russell postulate a relation of exemplification at all? Presumably because he perceived that even if he and his room are real particulars, and the relation in a real universal, it does not follow that he is in his room, any more than it follows that he is not in his room. The relation in is a constituent of both the positive and the negative fact. What is the difference between those facts? It is natural to suggest that in the positive fact the relation in is tied to Russell and his room by an ultimate simple relation, and that in the negative fact it is not. But by accepting that suggestion, you generate Ryle's regress. The only possible escape is to deny that the statement "Russell is in his room" asserts any

relation, whether ultimate or not, between the relation in and the particulars it is said to relate. The relation in may relate Russell and his room, or it may not; but, supposing it does relate them, it does not follow that some further relation relates it to them. In the same way, a certain rose may be red or not; but, supposing it is red, it does not follow that being red is related to it. Ryle's regress can only be forestalled by conceiving the exemplification of a universal by a particular or set of particulars as non-relational. Language inevitably misleads us here. Having recognized that expressions like "... is red" and "... is in ..." denote constituents of facts, it is tempting to think that the difference between the facts asserted by the pairs of sentences: "a is red" and "a is not red," "a is in b" and "a is not in b," must be found in the presence or absence of some further constituent, the relation of exemplification. That would be a mistake. The fact, if it be a fact, that a is red, has exactly the same constituents as the fact, if it be a fact, that a is not red. There is an ultimate difference between the two facts, but it is not a difference in their constituents. I have argued: (1) that Plato's objection to the realist theory of universals does not arise if it is presupposed that a universal may be simultaneously exemplified by many particulars without being divided from itself; and (2) that Ryle's regress cannot begin if it is presupposed that the difference between the facts asserted by propositions of the forms f(x) and ~f(x) is not a difference in their constituents, i.e. is not a relational difference. Neither presupposition seems to me to be inconsistent. Whether or not Russell's Realist Principle is true, Plato's objection does not refute it. (2) Even if some realist principle is true, must it be Russell's? It is well -107-

known that, ever since the Nominalist controversy vexed the medieval Schools, most of those who have claimed to be realists have adopted a position less extreme than Russell's. The most familiar form of "moderate" realism is that commonly ascribed to Aristotle. According to it, while something in the world must correspond to a true proposition, that correspondence need not be point for point. As Aquinas urged, "Alius est enim modus intellectus in intelligendo quam rei in essendo." If "Russell is in his room" is true, then something in the world must correspond to that proposition; but there need not be a constituent in the world for each constituent of the proposition. If we take the true propositions "Socrates is a man," and "Plato is a man," there must once have been something in the world corresponding to each of them. But it was not that the particulars Socrates and Plato each exemplified the universals denoted by the primitive predicates into which "is a man" is supposedly analysable. (Nor was it that the particulars of which the complex particulars Socrates and Plato are supposedly composed exemplified the universals denoted by certain primitive predicates.) Rather, it was that the essence man, which in itself is neither universal nor particular, was in rerum natura individuated in Socrates and Plato, as well as in other men. In rerum natura the same essence may therefore be multiplied. However, when somebody forms the proposition that Socrates is a man, or that Plato is a man, he does so by abstracting the individuated essence both from the different parcels of matter which it informed and from the accidents with which it was associated. Since the abstracted essence of Socrates is the same as that of Plato or of any other man, it is universal. It follows that an essence exists in two distinct ways: in rerum natura as a many, and in the mind as a one. The universal term "man" stands for the essence man as it exists in the mind abstractly. The essence itself, being neutral with respect to universality and particularity, can exist in rerum natura as individuated in Socrates, Plato, and other men. 17 Against this theory, Russell would presumably argue that it is unintelligible to suppose that a neutral essence should be capable of existing both as many individuals, and as an abstract unitary universal. In what sense can the same neutral thing exist as both a many and a one? An Aristotelian would retort that this seems absurd only because of the dogma that

everything is either universal or particular. If Russell may protest that universals are unitary and yet exemplified by many things, why may not an Aristotelian protest that essences, while neither universal nor particular, may exist in the world as many particulars and in the mind as unitary universals? Set against Russell's, the Aristotelian theory has two drawbacks. First, it postulates not merely one problematic entity, as Russell's does, but one problematic entity and two problematic forms of existence for it. By Ockham's ____________________ 17The traditional Aristotelian doctrine is clearly explained by Henry B. Veatch in Intentional Logic (New Haven, 1952), pp. 105-13, esp. 111-3. Fr. Joseph Owens, C.Ss.R., has argued that the "Aristotelian" doctrine really was Aristotle's: see The Doctrine of Being in the Aristotelian Metaphysics (Toronto, 1957) pp. 242-3. -108-

Razor, Russell's theory, if tenable at all, is preferable. Secondly, the question cannot be suppressed: If the essence man is individuated in Socrates and Plato, are Socrates and Plato nothing but two individuals? Are they not both men? And if they are both men, can you stop short with saying that the essence man is individuated? Must you not add that the individuals, Socrates and Plato, exemplify the same thing, namely man? A very different criticism of Russell's Realist Principle has been made by Goodman and Quine. 18 Like Russell, they hold that in some way true statements correspond in their structure to the structure of the world, but they altogether reject Russell's doctrine that there must be real universals which correspond to the primitive predicates of true propositions. In their view, only one part of any statement carries ontological commitment: its quantified variables. To find out what a man's ontological commitments are, you must find over what variables the statements he believes to be true compel him to quantify. "Entities of a given sort," Quine wrote, are ontologically assumed by a theory "if and only if some of them must be counted among the values of the variables in order that the statements affirmed in the theory be true." 19 On this view, if in the proposition, "Russell is in his room," you permit "Russell" and "his room" to be replaced by the non-predicative name variables "x" and "y," and those variables to be quantified, i.e. if you assert that (3 x,y) x is in y, you commit yourself to a world containing individuals, but not to the reality of the relation in. It is true that in "(∃ x,y) x is in y," you use the word "in," and presuppose that it has meaning. But Quine has insisted that "there is a gulf between meaning and naming." 20 In the same spirit, Goodman has defined nominalism as "the refusal to countenance any entities other than individuals," while at the same time allowing "the nominalist's language" to contain "one-place and many-place predicates of individuals." 21 He can consistently do so, because, like Quine, he does not consider predicates to stand for any entity. 22 In the opinion of both Goodman and Quine, then, a philosopher would commit himself to rejecting nominalism only if he were to allow "... is in ..." to be replaced by a variable, and that variable to be quantified, as in "( 3 R) Russell R his room," for only by doing so would he expressly assert that there is some relation (and relations are universals) in which Russell stands to his room. This position can be assailed from several directions. Professor Sellars, for example, has forcibly argued that to quantify over a variable does not commit you to accepting the values of that variable as denoting anything real. 23 Russell would approach the matter from another quarter. Holding, as he does, ____________________ 18W. V. Quine, From a Logical Point of View, pp. 9-14, 102-29, esp. 122-4; Nelson Goodman, The Structure of Appearance, pp. 33-41. 19Quine, op. cit. p. 103.

20Ibid.

p. 9.

21Goodman,

op. cit., pp. 33-4. pp. 34-5. 23W. S. Sellars, "Grammar and Existence: A Preface to Ontology," Mind, 69 ( 1960), esp. pp. 499-503, 507-17. Although my position in this paper is reactionary 22Ibid.

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that what you quantify over has no special ontological significance, he might nevertheless urge that the alleged gulf between admitting predicates of individuals and quantifying over predicate variables is imaginary. Of course a logician may for his own convenience eschew such quantification. Russell himself discovered that unrestricted quantification over predicate variables generates the paradox which bears his name, nor could he deny force to Quine's charge that "our precautions against [such] contradictions [e.g. Russell's Theory of Types] are ad hoc devices, justified only in that, or in so far as, they seem to work." 24 Yet he might rejoin that to prohibit all quantification over predicate variables because unrestricted quantification gives rise to contradiction would be a remedy worse than the disease. Quine himself admits such facts as that more than one dog is white, and that roses and sunsets are red. Well, if it is true both that Fido is white and that Rover is white, must it not also be true that there is some colour which Fido and Rover both have? More generally, if Fa and Fb are both true, must it not be true that (∃ f)fa and fb? It will not do for a logician to say: in my system, quantification over predicate variables is forbidden. The device of quantification is not private property; and any logician may be called upon to answer whether the result of a particular quantification is or is not true. Prima facie, that Fido and Rover are both white is a sufficient condition of the truth of the proposition ( ∃ f)f (Fido) and f (Rover); and if any proposition expressed by means of quantification over predicates is true, then some quantification over predicates is legitimate, and no considerations of elegance or convenience can justify prohibiting it. By arguing against Quine in this way, Russell would not surrender to Quine's criterion of ontological commitment. He might continue to hold the Realist Principle that the primitive predicates of true propositions must each denote something real. He would overcome Quine's criterion by showing that, rightly employed, it yields exactly the same results as his own. If by asserting the truth of a proposition containing a primitive predicate you oblige yourself to assert the truth of a proposition containing a quantified predicate variable, then quantified variables are not unique in disclosing ontological commitments. Yet Quine has another argument. "We may say," he wrote, "that some dogs are white and not thereby commit ourselves to recognizing either doghood or whiteness as entities. 'Some dogs are white' says that some things that are dogs are white; and in order that this statement be true, the things over which the bound variable 'something' ranges must include some white dogs, but ____________________ while his is revolutionary, my debt to Sellars' writings and conversation is too great to be indicated in detail: in particular, his criticism over many years at Minnesota showed me that realism is still an issue, and that Russell's and Moore's views deserve serious consideration. 24Russell did not, however, plead guilty. "The theory of logical types," he wrote, "... has also a certain consonance with common sense which makes it inherently credible." (Principia Mathematica [2nd ed., Cambridge, 1927], p. 37.) -110-

need not include doghood or whiteness." 25 Russell of course knew that in the proposition "Something is white," the bound variable "something" does not range over a class of things which includes whiteness; and wisely, he did not couch his argument in terms of abstract nouns like whiteness or doghood. His rejoinder to Quine would be: If some things that are dogs are white, is there not some quality which things that are dogs have? Otherwise how do white dogs differ from those which are not white? How can it be a fact that this dog and that are white, if the predicate "... is white" does not stand for something which dogs can either

be or not be? (3) Does Russell's argument depend on features peculiar to certain languages? Russell began by defining a universal as "anything which may be shared by many particulars." Now it is manifest that in English, as in all modern European languages, innumerable true propositions can be expressed by joining predicative expressions like verbs, adjectives, and common nouns, to proper names or demonstrative pronouns; and that in many of the sentences so constructed the same predicative expression, used in the same sense, is joined to a variety of proper names and demonstrative pronouns. Inasmuch as those propositions are faithfully reflected in English (or French, or German, or Italian) sentences which express them, there must by the Realist Principle be universals corresponding to those predicative expressions. Russell evidently recognized this; for he wrote that, "broadly speaking, proper names stand for particulars, while other substantives, adjectives, prepositions, and verbs stand for universals." 26 But what if the very same propositions which are expressed in English by predicative expressions can be expressed in some other language, whether artificial or not, without them? A suggestion with which Russell toyed in An Inquiry into Meaning and Truth is to the point here. Imagine a language in which what is expressed in English by "That wall is white" is expressed, not by a predicative expression corresponding to "... is white," but by a proper name, say "White," which is taken to be the name of a spatially and temporally discontinuous particular. This particular can be said to be wherever any part of it is, much as a salesman can be said to be in a house if he has his foot in the door. Instead of saying, as in English, "That wall is white," speakers of our imaginary language would say "White is there," pointing to that wall (or possibly, "White and Wall are there"). In An Inquiry into Meaning and Truth (London, 1940), Russell proposed a similar interpretation of many statements in modern European languages. "I wish to suggest," he wrote, "that 'this is red' is not a subject-predicate proposition, but is of the form 'redness is here'; [and] that 'red' is a name, not a predicate ..." (p. 97). In Three Philosophers, Miss G. E. M. Anscombe attributed an apparently similar view to Aristotle. "It would be closer to [Aristotle's] view," she wrote, "if we ascribed to him an alternative ____________________ 25Quine, op. cit. p. 13. 26Russell, Problems, p. 93. -111-

that Plato proposes: namely, that a single form is divided up and becomes many.... Thus if there were only one large lump of [gold] in the world, the division of it would make gold, which had been only one thing, become many" (pp. 31-2). Prima facie, an expression like "White" in this imaginary language would not denote anything which may be shared by many particulars. It is not shared by many places; for while White is in many places, a different part of it is at each of them. And although it would seem very strange to us to speak of In, say, as being where Russell and his room are, it is not obviously impossible that a language could be constructed in which even relational predicates like "... is in ..." would be replaced by proper names of discontinuous particulars. If this could be done, there would be no reason to suppose that there are any constituents of reality which may be exemplified by many particulars. That supposition would be dismissed as an illusion created by the structure of certain languages. It could not survive the discovery that non-predicative structures are possible. Unfortunately, not even in imaginary languages can predicative expressions be completely replaced by names of particulars. Suppose there to be a language in which everything said in English about what is white or not white is said by means of a proper name "White" of the kind I have described, i.e. the name of a spatially and temporally discontinuous particular. We may then inquire how saying that this particular is in two places is synonymous with saying that two different regions are white. Obviously, if the discontinuous particular "White" were many-coloured, the two could not be synonymous. "The particular White is both here and there" could express the same proposition as "This region and that region are

white," only if the particular White were of one colour, and that colour were white. But that condition cannot even be stated in our imaginary language. Manifestly, to introduce a further discontinuous particular, Albus say, and to lay it down that Albus is wherever White is, would only put off the evil day; for the regions where Albus is need not be white unless Albus itself is white all over. Neither the belief that predicative expressions could be replaced by names of discontinuous particulars, nor Russell's notion that logically "This is white" is "not a subject-predicate proposition, but is of the form '[Whiteness] is here,' " 27 would be tempting were not the predicative expression itself, or one of its derivatives, used as the name of the discontinuous particular. Suppose that particular to be named "Jack." The proposition "Jack is here" can only express the same proposition as "This is white" if Jack fulfills certain conditions. Those conditions can be stated in English, by means of the predicative expression, "... is white"; but I cannot conceive how they could be stated except by predicative expressions or their equivalents, i.e. by combining the same linguistic element used in the same sense with a number of other linguistic elements, in order to say the same thing about the things for ____________________ 27Russell, An Inquiry into Meaning and Truth, p. 97. -112-

which those other linguistic elements stand. The nature of the elements and the modes of combining them fall within the province of grammar, and Russell placed no limitation on their variety. He presupposed only that any language in which what can be said in modern European languages can be said, must contain predicative expressions or their equivalents. That presupposition has not been shown to be false by any argument known to me. (4) The objection that Realism is "circular and uninformative." Having survived, bloody but unbowed, the objections of candid friends like Plato, and nominalist foes like Goodman and Quine, it would be an anti-climax if realism should succumb to the objection, not that it is inconsistent, but that it is trivial. Yet Mr. D. F. Pears has put that objection vigorously: [R]ealism is necessarily a circular explanation of naming ... [Ultimately there must be some exit from the maze of words, and, whenever this exit is made, it will be impossible to give an informative reason except by pointing ... [It is true that] at the place where the exit is made it is always possible to give a detailed reason like "we are able to call things red because they are red," ... [but that] is too obviously circular to look informative.... What philosophers who propose the existence of universals do is to propose a general reason which looks informative because it shifts to another level, but unfortunately it is not. It merely marks time.... 28 The form of realism which Pears chose to attack is not precisely Russell's. Russell's premise was not that we are able to call things red, but that some propositions containing the primitive predicate "... is red" are true; and his argument did not purport to explain such truths, but only to exhibit a necessary condition of their existence. However, it is beyond doubt that Pears would be willing to adapt his objection to Russell's theory. In one respect, Pears is less than clear. He accuses realists like Russell of proposing a "reason which looks informative because it shifts to another level, but unfortunately it is not." Literally, this means that, because it shifts to a new level, Russell's reason looks informative, although in fact it is not. In other words, Russell argued that a necessary condition of the truth of propositions of the form "x is red" is that the universal red be real: this "shifts to another level," i.e. shifts from the level of words like "... is red" to the level of real beings, and so looks informative. Pears, however, contends that it is not. But if Russell's argument does shift to a new level, is it not informative ? To be told that real beings correspond to the primitive predicates of true propositions—is not that information? A second interpretation of Pears' objection is possible. If the clause "because it shifts to another level" falls within the scope of the verb "looks," then what Pears meant is that Russell's "reason" only seems to shift to another level, and so is not informative, although it

seems so. Pears' example of a detailed realist "reason" supports this interpretation: "it is always pos____________________ 28D. F. Pears, "Universals" in Logic and Language, 2nd series, ed. Antony Flew (Oxford 1953), pp. 53-4. -113-

sible to give a detailed reason like 'We are able to call things red because they are red.' " Observe that he does not write, "we are able to call things 'red' because they are red"; for, if he had, he could not have added that this "is too obviously circular even to look informative." By placing quotation marks around the word "red," he would have shown that his realist is looking to a fact about the world to explain a fact about language, i.e. that he does "shift to another level." Pears did not leave the matter there. He went on to dismiss as vain all realist efforts to escape from the maze of words by postulating real entities corresponding to primitive predicates, on the ground that entities so postulated would be no more than "shadows" of their corresponding predicates. 29 Realism is "like a dream"—a dream the "manifest content [of which] is little more than a harmless caprice, but ... [the] latent content [of which] is a serious error." 30 I doubt whether I understand what Pears meant by this simile; but I interpret him as meaning that a universal is like a dream-object, an unreal image constructed in the realist's mind, which, since it merely reproduces a fact about the objects from which it has been derived, i.e. that they are called by the same name, "taken literally ... seems to be of little importance." 31 Its manifest content is therefore harmless. But, since it easily passes over into full-blown Platonism, thus becoming both important and false, its latent content is dangerous. This criticism is odd, not because it affirms anything paradoxical, but because it affirms nothing (so far as its "manifest content" goes) which Russell need deny. Russell himself would reject full-blown Platonism, 32 i.e. the doctrine that only universals are real, and that objects in the world of sights and sounds are "between unbeing and being." Nor would he deny that universals are "shadows" of primitive predicates in the sense that the reality of universals is inferred from the fact that primitive predicates are irreducible components of true propositions. Of course he would deny that universals are shadows of primitive predicates in the sense that if the predicates had never been conceived, then the universals would not be real. That universals are in that sense shadows is the harmful latent content of Pears' simile. Let it be conceded that the latent content of realism is false: to Russell, that was never in question. Is its manifest content, Russell's theory as I have elucidated it, also false? Pears' only objection to that manifest content, namely, that it is circular, that it only seems to escape from the maze of words, I think I have shown to be false. Realism asserts that something in the world corresponds to, and in that sense is a shadow of, every primitive predicate; but that assertion is neither circular nor uninformative. ____________________ 29Ibid. p. 54. 30Ibid, p. 58. 31Ibid. p. 58. 32"These mystical developments [i.e. Platonism] are very natural, but the basis of the theory is in logic, and it is based in logic that we have to consider it" (Russell, Problems, p. 92). -114-

III Wise philosophers defer to plain men; but a plain man who has accompanied us so far will hardly contain his derision. To swallow the doctrine that universals are constituents of the

world, just as a certain morsel of flour is a constituent of a pudding mixture, is painful, even when it is stipulated that the universals in question be exemplified. But that unexemplified universals are as much constituents of the world as exemplified ones! Is not that as though you were to say that flour is a real constituent of ice-cream because it is true that ice-cream is not made of it? Should our plain man turn for aid and comfort to Moore's Some Main Problems of Philosophy, he would be confirmed in his outrage. Moore there invited his readers to distinguish two kinds of objects we can think about: "those which do have being, and those which simply have not got it, are purely imaginary, and don't belong to the Universe at all." To the second class he assigned "pure fiction[s]" like griffins and chimaeras. He then proceeded: If you fix clearly in your mind the sense in which there certainly are no such things as griffins and chimaeras, ... it seems to me quite plain ... that universals are not in any way to be classed with griffins and chimaeras; that, on the contrary, there is the most fundamental difference in the world between the two, a difference ever so much more important than that which separates universals from particulars (p. 373). At this, any plain man who has learned a little Russellian logic will protest: "The fictitiousness, the non-being, of griffins and chimaeras consists in the fact that nothing is a griffin or a chimaera; but in your argument that universals are real you don't even attempt to show that they are all exemplified; in fact, it has been urged that your argument proves that unexemplified universals are as much constituents of the world as exemplified ones." Such a protest is certainly justified. Moore himself, in his essay "The Conception of Reality," later accepted Russell's and Frege's view that the question whether or not griffins and chimaeras are real is the same as the question whether or not the predicates "... is a griffin" and "... is a chimaera" are each truly predicable of something. 33 And it is quite clear that the Realist Principle on which Russell's argument for the reality of universals depends, namely, that primitive predicates occurring non-redundantly in true propositions denote real constituents of the world, does not mean that such predicates are truly predicable of something. To show this, it is not necessary, although it is sufficient, to demonstrate that nothing in Russell's argument precluded its application to negative facts involving unexemplified universals. One need only point out that Russell began by supposing that he was in his room, i.e. that the relational predicate "... is in ..." was truly predicable of something, namely, himself and his room. It follows that if by his conclusion that ____________________ 33G. E. Moore, Philosophical Studies (London, 1911), p. 212. -115-

the relation in is a real constituent of the world he had meant no more than that it is exemplified, then his argument would have been a gross petitio principii. To attribute such a blunder to Russell would be ridiculous. Moore, then, was simply wrong when he implied that the sense in which realists claim to prove that universals are real constituents of the world is the sense in which griffins and chimaeras are not. Whether universals are real or have being in the sense of Russell's (and Moore's) proof is a question altogether distinct from the question whether they are or are not exemplified. We may go further. Expressions like "real constituent of the world," and descriptions of the task of Philosophy or Ontology as being "to give a general description of the whole of the Universe, mentioning all the most important kinds of things which we know to be in it," 34 inevitably suggest that philosophers are looking for the ingredients of which the world is composed, much as a chemist looks for the ingredients of a chemical mixture, or perhaps a zoologist for the species of fauna inhabiting a given region. Plain men are led to expect that philosophers will place before them a list of distinct ingredients or species, like flour and sugar, or lions and antelopes, although of course it is not required that they be material or even observable. And indeed some philosophers, for example the neo-Platonists and

Aristotle and his medieval followers, with their hierarchies of beings, have done something like that. For example, Aquinas's catalogue—God or Esse subsistens, the Separate Substances or pure subsisting forms, and material substances or beings whose forms actualize matter —together with his account of their ordering with respect to one another, is in the ordinary sense a general description of the whole Universe, mentioning all the most important kinds of things which Aquinas believed he knew to be in it. Since the sense in which Aquinas believed God and the Separate Substances to be "in the Universe" (he would not, of course, have used that phrase) is the same as that in which Moore believed griffins and chimaeras not to be in it, namely that the predicates "... is God" and "... is a Separate Substance" are each truly predicable of something, we have already shown that Russell did not even profess to prove that universals are real in that sense. In what sense, then, did he profess to prove it? According to his Realist Principle, the non-redundant primitive predicates of true propositions denote things that are real or have being: but how are the expressions "things that are real," "things that have being" to be understood? If Moore, who in 1910 was as close to Russell as any man was, nevertheless misunderstood, have we any hope of doing better? Wittgenstein once alleged that "Nothing is more likely than that the verbal expression of the result of a mathematical proof is calculated to delude us with a myth"; 35 and whether he was right or wrong about mathematics, his remark holds good of Russell's proof of the reality of universals. Wittgen____________________ 34Moore, Main Problems, p. 1. 35Ludwig Wittgenstein, Remarks on the Foundations of Mathematics (Oxford, 1956), II, 26 (p. 77). -116-

stein's prescription for getting rid of such delusions was to look at the proof. "[T]he sense of the result is not to be read off from [the result] by itself, but from the proof." 36 Why did Russell accept his Realist Principle? What proof did he give of it? He seems to have thought that a proof of it would fall into two parts. First, it would be necessary to show that predicative expressions could not all be analysed into non-predicative ones. Both Russell and Moore held that traditional nominalism, e.g. that of Berkeley and Hume, had attempted such analyses, and had failed, because it had not been able to dispense with the relational predicate "... is similar to. ..." 37 Secondly, it would be necessary to show that whether or not a proposition is true depends on how the world is, and not on how anybody, plain or scientific, chooses to think about it. If "F" and "G" are primitive predicates, then what "Fa" says about the world is different from what "Ga" says about it. The difference in what they say can only arise from the difference of their predicates. Suppose both to be true: then the world is as they say it is, and what they say it is depends in part on their predicates. Suppose either or both to be false, then the world will be as the negatives of either or both say it is, and that too depends in part on their predicates. This argument does not show that any bit of the world is named by "F" or "G"; for it is not about the elements or ingredients of the world in the way in which a chemical analysis is about the elements or ingredients of a chemical compound or mixture. But it does show that "F" and "G" refer to the world in the sense that they are descriptive and not merely formal parts of statements about it, the truth of those statements being determined by how the world is. And since, for any predicate "f" and any individual name "x," it is true either that fx or that ˜fx, every primitive predicate must be a descriptive and not merely a formal part of a true full description of the world, the truth of that description being determined by how the world is. That, if anything, is what Russell's proof proves; and that is what I think he meant when he asserted that a universal like in "is something, although we cannot say that it exists in the same sense in which I and my room exist." 38 Russell confirmed this interpretation of his theory of universals in an almost mocking remark in his "Reply to Criticisms" in P. A. Schilpp's The Philosophy of Bertrand Russell. If it is true [he wrote], as it seems to be, that the world cannot be described without the use of the word "similar" or some equivalent [i.e. without the use

of predicates], that seems to imply something about the world, though I do not know exactly what. This is the sense in which I still believe in universals (p. 688). In this passage, Russell took the realist theory of universals to consist in repudiating two errors: the nominalist error that predicates can be dispensed with in a true description of the world; and what we may call the "idealist" ____________________ 36Ibid. II, 25 (p. 76). 37Russell, Problems, pp. 95-7; Moore, Main Problems, pp. 313-7. 38Russell, Problems, p. 90. -117-

error that the repudiation of the nominalist error implies nothing about the world, because the truth of a description depends, not on how the world is, but on how thinkers think. Even if I have interpreted Russell's theory correctly, I have not shown that it is true; for I have proved neither that predicates cannot be dispensed with in a true description of the world, nor that whether a description of the world is true depends on how the world is. However, Moore's and Russell's criticism of Berkeley and Hume, and the difficulties I have pointed out in the proposal to replace qualitative predicates by the names of discontinuous particulars, show how difficult it is to carry out the nominalist programme. As for what I have called "the idealist error," like Moore and Russell I consider it to merit exposure rather than refutation. A plain man might accept all my explanations, and yet object that the realist theory of universals, although true, is of little importance. In one respect, he would be right. The major questions of metaphysics are either about the substance of the world (e.g., What sorts of individuals does it contain? What are the space and time in which some, if not all, of them exist? Do they persist through time? Are they substances or processes? Are any or all of them phenomenal?) or about mind and knowledge (e.g., What is a mind? How are minds related to bodies? Is thinking a physical process? How can we think of individuals, their kinds, and their properties? How is thinking related to perceiving?). The realist theory of universals does not lead to a solution of any of these problems. Its importance, like its character, is negative. If you reject it, that is, if you accept the nominalist or the idealist theories that conflict with it, you cannot avoid serious errors when you try to answer the major questions. Although negative, it is fundamental. 39 ____________________ 39Although I doubt whether any of them will agree with most of my conclusions, this essay originated in conversations with my colleagues Herbert Hochberg, Reinhardt Grossmann, Henry B. Veatch and Roger C. Buck, and both in design and in particular points is heavily indebted to them. -118-

:7: UNIVERSALS AND FAMILY RESEMBLANCES RENFORD BAMBROUGH I believe that Wittgenstein solved what is known as "the problem of universals," and I would say of his solution, as Hume said of Berkeley's treatment of the same topic, that it is "one of the greatest and most valuable discoveries that has been made of late years in the republic of letters."

I do not expect these claims to be accepted by many philosophers. Since I claim that Wittgenstein solved the problem I naturally do not claim to be making an original contribution to the study of it. Since I recognise that few philosophers will accept my claim that Wittgenstein solved it, I naturally regard it as worth while to continue to discuss the problem. My purpose is to try to make clear what Wittgenstein's solution is and to try to make clear that it is a solution. Philosophers ought to be wary of claiming that philosophical problems have been finally solved. Aristotle and Descartes and Spinoza and Berkeley and Hume and the author of the Tractatus Logico-Philosophicus lie at the bottom of the sea not far from this rock, with the skeletons of many lesser men to keep them company. But nobody suggests that their journeys were vain, or that nothing can be saved from the wrecks. In seeking for Wittgenstein's solution we must look mainly to his remarks about "family resemblances" and to his use of the example of games. In the Blue Book he speaks of "our craving for generality" and tries to trace this craving to its sources: This craving for generality is the resultant of a number of tendencies connected with particular philosophical confusions. There is— (a) The tendency to look for something in common to all the entities which we commonly subsume under a general term.—We are inclined to think that there must be something in common to all games, say, and that this common property is the justification for applying the general term "game" to the various games; whereas games form a family the members of which have family likenesses. Some of them have the same nose, others the same eyebrows and others ____________________ Reprinted from the Proceedings of The Aristotelian Society, LXI (1960-61) by courtesy of the Editor of The Aristotelian Society. Copyright © 1961, The Aristotelian Society.

again the same way of walking; and these likenesses overlap. The idea of a general concept being a common property of its particular instances connects up with other primitive, too simple, ideas of the structure of language. It is comparable to the idea that properties are ingredients of the things which have the properties; e.g., that beauty is an ingredient of all beautiful things as alcohol is of beer and wine, and that we therefore could have pure beauty, unadulterated by anything that is beautiful. (b) There is a tendency rooted in our usual forms of expression, to think that the man who has learnt to understand a general term, say, the term "leaf," has thereby come to possess a kind of general picture of a leaf, as opposed to pictures of particular leaves. He was shown different leaves when he learnt the meaning of the word "leaf"; and showing him the particular leaves was only a means to the end of producing "in him" an idea which we imagine to be some kind of general image. We say that he sees what is in common to all these leaves; and this is true if we mean that he can on being asked tell us certain features or properties which they have in common. But we are inclined to think that the general idea of a leaf is something like a visual image, but one which only contains what is common to all leaves. (Galtonian composite photograph.) This again is connected with the idea that the meaning of a word is an image, or a thing correlated to the word. (This roughly means, we are looking at words as though they all were proper names, and we then confuse the bearer of a name with the meaning of the name.) (Pp. 17-18). In the Philosophical Investigations Wittgenstein again speaks of family resemblances, and gives a more elaborate account of the similarities and differences between various games:

66. Consider for example the proceedings that we call "games." I mean board- games, card-games, ball-games, Olympic games, and so on. What is common to them all?—Don't say: "there must be something common, or they would not be called 'games' "—but look and see whether there is anything common to all.— For if you look at them you will not see something that is common to all, but similarities, relationships, and a whole series of them at that. To repeat: don't think, but look!—Look for example at board-games, with their multifarious relationships. Now pass to card-games; here you find many correspondences with the first group, but many common features drop out, and others appear. When we pass next to ball-games, much that is common is retained, but much is lost.—Are they all "amusing"? Compare chess with noughts and crosses. Or is there always winning and losing, or competition between players? Think of patience. In ball games there is winning and losing; but when a child throws his ball at the wall and catches it again, this feature has disappeared. Look at the parts played by skill and luck; and at the difference between skill in chess and skill in tennis. Think now of games like ring-a-ring-a-roses; here is the element of amusement, but how many other characteristic features have disappeared! And we can go through the many, many other groups of games in the same way; can see how similarities crop up and disappear. And the result of this examination is: we see a complicated network of similarities overlapping and criss-crossing: sometimes overall similarities, sometimes similarities of detail. 67. I can think of no better expression to characterise these similarities than "family resemblances"; for the various resemblances between the members of a family: build, features, colour of eyes, gait, temperament, etc. etc. overlap and criss-cross in the same way.—And I shall say: "games" form a family. -120-

Wittgenstein expounds his analogy informally, and with great economy. Its power can be displayed in an equally simple but more formal way by considering a situation that is familiar to botanical taxonomists. 1 We may classify a set of objects by reference to the presence or absence of features ABCDE. It may well happen that five objects edcba are such that each of them has four of these properties and lacks the fifth, and that the missing feature is different in each of the five cases. A simple diagram will illustrate this situation: e ABCD

d ABCE

c ABDE

b ACDE

a BCDE

Here we can already see how natural and how proper it might be to apply the same word to a number of objects between which there is no common feature. And if we confine our attention to any arbitrarily selected four of these objects, say edca, then although they all happen to have B in common, it is clear that it is not in virtue of the presence of B that they are all rightly called by the same name. Even if the actual instances were indefinitely numerous, and they all happened to have one or more of the features in common, it would not be in virtue of the presence of the common feature or features that they would all be rightly called by the same name, since the name also applies to possible instances that lack the feature or features. The richness of the possibilities of the family resemblances model becomes more striking still if we set it out more fully and formally in terms of a particular family than Wittgenstein himself ever did. Let us suppose that "the Churchill face" is strikingly and obviously present in each of ten members of the Churchill family, and that when a family group photograph is set before us it is unmistakable that these ten people all belong to the same family. It may be that there are ten features in terms of which we can describe "the family face" (high forehead, bushy eyebrows, blue eyes, Roman nose, high cheekbones, cleft chin, dark hair, dimpled cheeks, pointed ears and ruddy complexion). It is obvious that the unmistakable presence of the family face in every single one of the ten members of the family is

compatible with the absence from each of the ten members of the family of one of the ten constituent features of the family face. It is also obvious that it does not matter if it happens that the feature which is absent from the face of each individual member of the family is present in every one of the others. The members of the family will then have no feature in common, and yet they will all unmistakably have the Churchill face in common. This example is very artificial, and it may seem at first sight that its artificiality plays into my hands. But on the contrary, the more natural the example is made the more it suits my purpose. If we remember that a family face does not divide neatly into ten separate features, we widen rather than reduce ____________________ 1I have profited from several discussions with Dr. S. M. Walters on taxonomy and the problem of universals. On the more general topics treated in this paper I have had several helpful discussions with Mr. R. A. Becher. Miss G. E. M. Anscombe kindly lent me the proofs of her essay on Aristotle, which is to appear in Three Philosophers by Miss Anscombe and Mr. P. T. Geach. -121-

the scope for large numbers of instances of the family face to lack a single common feature. And if we remember that what goes for faces goes for features too; that all cleft chins have nothing in common except that they are cleft chins, that the possible gradations from Roman nose to snub nose or from high to low cheekbones are continuous and infinite, we see that there could in principle be an infinite number of unmistakable Churchill faces which had no feature in common. In fact it now becomes clear that there is a good sense in which no two members of the Churchill family need have any feature in common in order for all the members of the Churchill family to have the Churchill face. The passages that I have quoted contain the essence of Wittgenstein's solution of the problem of universals, but they are far from exhausting his account of the topic. Not only are there other places where he speaks of games and of family resemblances: what is more important is that most of his philosophical remarks in The Blue and Brown Books and in the Philosophical Investigations are concerned with such questions as "What is the meaning of a word?" "What is language?" "What is thinking?" "What is understanding?" And these questions are various forms of the question to which theories of universals, including Wittgenstein's theory of universals, are meant to be answers. There is a clear parallel between what Wittgenstein says about games and what he says about reading, expecting, languages, numbers, propositions; in all these cases we have the idea that there is a common element or ingredient, and Wittgenstein shows us that there is no such ingredient or element. The instances that fall under each of these concepts form a family. It is already clear that the point Wittgenstein made with the example of games has a much wider range of application than that example itself. But exactly how wide is its application meant to be? Wittgenstein's own method of exposition makes it difficult to answer this question. In his striving to find a cure for "our craving for generality," in his polemic against "the contemptuous attitude towards the particular case," he was understandably wary of expressing his own conclusions in general terms. Readers and expositors of Wittgenstein are consequently impelled to make use of glosses and paraphrases and interpretations if they wish to relate his work to philosophical writings and doctrines that are expressed in another idiom; that is to say, to most other philosophical writings and doctrines. I believe that this is why Wittgenstein's solution of the problem of universals has not been widely understood, and why, in consequence, it has not been widely seen to be a solution. 2 In avoiding the generalities that are characteristic of most philosophical discussion he also avoided reference to the standard "problems of philosophy" and to the "philosophical theories" which have repeatedly been offered as answers to them. He talks about games and families ____________________ 2Of recent writings on this topic I believe that only Professor Wisdom's Metaphysics and Verification (reprinted in Philosophy and Psycho-analysis) and Mr. D. F. Pears' Universals

(reprinted in Flew, Logic and Language, Second Series) show a complete understanding of the nature and importance of Wittgenstein's contribution. -122-

and colours, about reading, expecting and understanding, but not about "the problem of universals." He practised an activity which is "one of the heirs of the subject which used to be called 'philosophy,' " but he did not relate the results of his activity to the results of the enquiries to which it was an heir. He did not, for example, plot the relation between his remarks on games and family resemblances and the doctrines of those philosophers who had been called Nominalists and Realists. When I claim that Wittgenstein solved the problem of universals I am claiming that his remarks can be paraphrased into a doctrine which can be set out in general terms and can be related to the traditional theories, and which can then be shown to deserve to supersede the traditional theories. My purpose in this paper is to expound such a doctrine and to defend it. But first I must return to my question about the range of application of the point that is made by the example of games, since it is at this crucial first stage that most readers of Wittgenstein go wrong. When we read what he says about games and family resemblances, we are naturally inclined to ask ourselves, "With what kinds of concepts is Wittgenstein contrasting the concepts of game, language, proposition, understanding?" I shall consider three possible answers to this question. The first answer is suggested by Professor Ayer's remarks about games and family resemblances on pp. 10-12 of The Problem of Knowledge. Ayer contrasts the word "game" with the word "red," on the ground that the former does not, while the latter does, mark "a simple and straightforward resemblance" between the things to which the word is applied. He claims that, "The point which Wittgenstein's argument brings out is that the resemblance between the things to which the same word applies may be of different degrees. It is looser and less straightforward in some cases than in others." Now this contrast between simple and complicated concepts is important, and the games example is a convenient means of drawing attention to it, but I am sure that this is not the point that Wittgenstein was making with his example. In the Brown Book (p. 131) he asks, "Could you tell me what is in common between a light red and a dark red?" and in the Philosophical Investigations (Section 73) he asks, "Which shade is the 'sample in my mind' of the colour green—the sample of what is common to all shades of green?" Wittgenstein could as easily have used the example of red things as the example of games to illustrate "the tendency to look for something in common to all the entities which we commonly subsume under a general term." Just as cricket and chess and patience and ring-a-ring-a-roses have nothing in common except that they are games, so poppies and blood and pillar-boxes and hunting-coats have nothing in common except that they are red. A second possible answer is implied by a sentence in Mr. P. F. Strawson's Individuals: "It is often admitted, in the analytical treatment of some fairly specific concept, that the wish to understand is less likely to be served by the search for a single strict statement of the necessary and sufficient conditions of its application than by seeing its applications—in Wittgenstein's simile—as -123-

forming a family, the members of which may, perhaps, be grouped around a central paradigm case and linked with the latter by various direct or indirect links of logical connexion and analogy." (p. 11). The contrast is not now between simple and complex concepts, but between two kinds of complex concepts: those which are definable by the statement of necessary and sufficient conditions and those which are not. But once again the contrast, although it is important, and is one which the family resemblances simile and the example of games are well able to draw, is not the point that Wittgenstein is concerned with. In the sense in which, according to Wittgenstein, games have nothing in common except that they are games, and red things have nothing in common except that they are red, brothers have nothing in common except that they are brothers. It is true that brothers have in common

that they are male siblings, but their having in common that they are male siblings is their having in common that they are brothers, and not their having in common something in addition to their being brothers. Even a concept which can be explained in terms of necessary and sufficient conditions cannot be ultimately explained in such terms. To satisfy the craving for an ultimate explanation of "brother" in such terms it would be necessary to define "male" and "sibling," and the words in which "male" and "sibling" were defined, and so on ad infinitum and ad impossible. What then is the contrast that Wittgenstein meant to draw? I suggest that he did not mean to draw a contrast at all. Professor Wisdom has remarked that the peculiar difficulty of giving a philosophical account of universals lies in this: that philosophers are usually engaged in implicitly or explicitly comparing and contrasting one type of proposition with another type of proposition (propositions about minds with propositions about bodies, propositions of logic with propositions about matters of fact, propositions about the present and the past with propositions about the future, etc.) whereas propositions involving universals cannot be compared or contrasted with propositions that do not involve universals, since all propositions involve universals. 3 If we look at Wittgenstein's doctrine in the light of this remark we can understand it aright and can also see why it has been misunderstood in just those ways that I have mentioned. It is because of the very power of the ways of thought against which Wittgenstein was protesting that philosophers are led to offer accounts of his doctrine which restrict the range of its application. They recognise the importance of Wittgenstein's demonstration that at least some general terms can justifiably be applied to their instances although those instances have nothing in common. But they are so deeply attached to the idea that there must be something in common to the instances that fall under a general term that they treat Wittgenstein's examples as special cases, as rogues and vagabonds in the realm of concepts, to be contrasted with the general run of law-abiding concepts which do mark the presence of common elements in their instances. ____________________ 3Professor Wisdom has pointed out to me that further discussion would be necessary to show that claims of the form "This is Jack" are not exceptions to this rule. -124-

Here we come across an ambiguity which is another obstacle to our getting a clear view of the problem of universals and of Wittgenstein's solution of it. Ayer remarks, in the passage to which I have already referred, that, "It is correct, though not at all enlightening, to say that what games have in common is their being games." It is certainly correct, but I strongly deny that it is unenlightening. It is of course trivially and platitudinously true, but trivialities and platitudes deserve emphatic affirmation when, as often in philosophy, they are explicitly or implicitly denied, or forgotten, or overlooked. Now the platitude that all games have in common that they are games is denied by the nominalist, who says that all games have nothing in common except that they are called games. And it is not only the nominalist, but also his opponent, who misunderstands the central importance of the platitude that all games have in common that they are games. When he is provoked by the nominalist's claim that all games have nothing in common except that they are called games, and rightly wishes to insist that games have something more in common than simply that they are called games, he feels that he must look for something that games have in common apart from being games. This feeling is entirely misplaced. The very terms of the nominalist's challenge require only that the realist should point out something that games have in common apart from being called games, and this onus is fully discharged by saying that they are games. Although the feeling is misplaced, it is a very natural feeling, as we can see by considering the kinds of case in which we most typically and ordinarily ask what is in common to a set of objects. If I ask you what these three books have in common, or what those four chairs have in common, you will look to see if the books are all on the same subject or by the same author or pubblished by the same firm; to see if the chairs are all Chippendale or all three legged or all marked "Not to be removed from this room." It will never occur to you to say that the books have in common that they are books or the chairs that they are chairs. And if you find after close inspection that the chairs or the books do not have in common any of the features I have mentioned, and if you cannot see any other specific feature that they have in common, you will say that as far as you can see they have nothing in common. You

will perhaps add that you suppose from the form of my question that I must know of something that they have in common. I may then tell you that all the books once belonged to John Locke or that all the chairs came from Ten Rillington Place. But it would be a poor sort of joke for me to say that the chairs were all chairs or that the books were all books. If I ask you what all chairs have in common, or what all books have in common, you may again try to find a feature like those you would look for in the case of these three books or those four chairs; and you may again think that it is a poor sort of joke for me to say that what all books have in common is that they are books and that what all chairs have in common is that they are chairs. And yet this time it is not a joke but an important philosophical truth. -125-

Because the normal case where we ask "What have all these chairs, books or games in common?" is one in which we are not concerned with their all being chairs, books or games, we are liable to overlook the extreme peculiarity of the philosophical question that is asked with the words "What do all chairs, all books, all games have in common?" For of course games do have something in common. They must have something in common, and yet when we look for what they have in common we cannot find it. When we try to say what they have in common we always fail. And this is not because what we are looking for lies deeply hidden, but because it is too obvious to be seen; not because what we are trying to say is too subtle and complicated to be said, but because it is too easy and too simple to be worth saying: and so we say something more dramatic, but something false, instead. The simple truth is that what games have in common is that they are games. The nominalist is obscurely aware of this, and by rejecting the realist's talk of transcendent, immanent or subsistent forms or universals he shows his awareness. But by his own insistence that games have nothing in common except that they are called games he shows the obscurity of his awareness. The realist too is obscurely aware of it. By his talk of transcendent, immanent or subsistent forms or universals he shows the obscurity of his awareness. But by his hostility to the nominalist's insistence that games have nothing in common except that they are called games he shows his awareness. All this can be more fully explained by the application of what I will call "Ramsey's Maxim." F. P. Ramsey, after mapping the course of an inconclusive dispute between Russell and W. E. Johnson, writes as follows: Evidently, however, none of these arguments are really decisive, and the position is extremely unsatisfactory to any one with real curiosity about such a fundamental question. In such cases it is a heuristic maxim that the truth lies not in one of the two disputed views but in some third possibility which has not yet been thought of, which we can only discover by rejecting something assumed as obvious by both the disputants. (The Foundations of Mathematics, pp. 115-116). It is assumed as obvious by both the nominalist and the realist that there can be no objective justification for the application of a general term to its instances unless its instances have something in common over and above their having in common that they are its instances. The nominalist rightly holds that there is no such additional common element, and he therefore wrongly concludes that there is no objective justification for the application of any general term. The realist rightly holds that there is an objective justification for the application of general terms, and he therefore wrongly concludes that there must be some additional common element. Wittgenstein denied the assumption that is common to nominalism and realism, and that is why I say that he solved the problem of universals. For if we deny the mistaken premiss that is common to the realist's argument and the nominalist's argument then we can deny the realist's mistaken conclusion and deny the nominalist's mistaken conclusion; and that is another way of saying that we can affirm the true premiss of the nominalist's argument and can also affirm the true premiss of the realist's argument. -126-

The nominalist says that games have nothing in common except that they are called games. The realist says that games must have something in common, and he means by this that they must have something in common other than that they are games. Wittgenstein says that games have nothing in common except that they are games. Wittgenstein thus denies at one and the same time the nominalist's claim that games have nothing in common except that they are called games and the realist's claim that games have something in common other than that they are games. He asserts at one and the same time the realist's claim that there is an objective justification for the application of the word "game" to games and the nominalist's claim that there is no element that is common to all games. And he is able to do all this because he denies the joint claim of the nominalist and the realist that there cannot be an objective justification for the application of the word "game" to games unless there is an element that is common to all games (universalia in rebus) or a common relation that all games bear to something that is not a game (universalia ante res). Wittgenstein is easily confused with the nominalist because he denies what the realist asserts: that games have something in common other than that they are games. When we see that Wittgenstein is not a nominalist we may easily confuse him with the realist because he denies what the nominalist asserts: that games have nothing in common except that they are called games. But we can now see that Wittgenstein is neither a realist nor a nominalist: he asserts the simple truth that they both deny and he also asserts the two simple truths of which each of them asserts one and denies the other. I will now try to put some flesh on to these bare bones. The value and the limitations of the nominalist's claim that things which are called by the same name have nothing in common except that they are called by the same name can be seen if we look at a case where a set of objects literally and undeniably have nothing in common except that they are called by the same name. If I choose to give the name "alpha" to each of a number of miscellaneous objects (the star Sirius, my fountain-pen, the Parthenon, the colour red, the number five, and the letter Z) then I may well succeed in choosing the objects so arbitrarily that I shall succeed in preventing them from having any feature in common, other than that I call them by the name "alpha." But this imaginary case, to which the nominalist likens the use of all general words, has only to be described to be sharply contrasted with the typical case in which I apply a general word, say "chair," to a number of the instances to which it applies. In the first place, the arbitrariness of my selection of alphas is not paralleled in the case in which I apply the word "chair" successively to the chair in which I am now sitting, the Speaker's Chair in the House of Commons, the chair used at Bisley for carrying the winner of the Queen's Prize, and one of the deck chairs on the beach at Brighton. In giving a list of chairs I cannot just mention anything that happens -127-

to come into my head, while this is exactly what I do in giving my list of alphas. The second point is that the class of alphas is a closed class. Once I have given my list I have referred to every single alpha in the universe, actual and possible. Although I might have included or excluded any actual or possible object whatsoever when I was drawing up my list, once I have in fact made my arbitrary choice, no further application can be given to the word "alpha" according to the use that I have prescribed. For if I later add an object that I excluded from my list, or remove an object that I included in it, then I am making a different use of the word "alpha." With the word "chair" the position is quite different. There are an infinite number of actual and possible chairs. I cannot aspire to complete the enumeration of all chairs, as I can arbitrarily and at any point complete the enumeration of all alphas, and the word "chair," unlike the word "alpha," can be applied to an infinite number of instances without suffering any change of use. These two points lead to a third and decisive point. I cannot teach the use of the word

"alpha" except by specifically attaching it to each of the objects in my arbitrarily chosen list. No observer can conclude anything from watching me attach the label to this, that, or the other object, or to any number of objects however large, about the nature of the object or objects, if any, to which I shall later attach it. The use of the word "alpha" cannot be learned or taught as the use of a general word can be learned or taught. In teaching the use of a general word we may and must refer to characteristics of the objects to which it applies, and of the objects to which it does not apply, and indicate which of these characteristics count for the application of the word and which count against it. A pupil does not have to consult us on every separate occasion on which he encounters a new object, and if he did consult us every time we should have to say that he was not learning the use of the word. The reference that we make to a finite number of objects to which the word applies, and to a finite number of objects to which the word does not apply, is capable of equipping the pupil with a capacity for correctly applying or withholding the word to or from an infinite number of objects to which we have made no reference. All this remains true in the case where it is not I alone, but a large number of people, or all of us, who use the word "alpha" in the way that I suggest. Even if everybody always called a particular set of objects by the same name, that would be insufficient to ensure that the name was a general name, and the claim of the name to be a general name would be defeated by just that necessity for reference to the arbitrary choices of the users of the name that the nominalist mistakenly claims to find in the case of a genuinely general name. For the nominalist is right in thinking that if we always had to make such a reference then there would be no general names as they are understood by the realist. The nominalist is also right in the stress that he puts on the role of human interests and human purposes in determining our choice of principles of classification. How this insistence on the rôle of human purposes may be reconciled with the realist's proper insistence on the objectivity of the similari -128-

ties and dissimilarities on which any genuine classification is based can be seen by considering an imaginary tribe of South Sea Islanders. Let us suppose that trees are of great importance in the life and work of the South Sea Islanders, and that they have a rich and highly developed language in which they speak of the trees with which their island is thickly clad. But they do not have names for the species and genera of trees as they are recognised by our botanists. As we walk round the island with some of its inhabitants we can easily pick out orange-trees, date-palms and cedars. Our hosts are puzzled that we should call by the same name trees which appear to them to have nothing in common. They in turn surprise us by giving the same name to each of the trees in what is from our point of view a very mixed plantation. They point out to us what they called a mixed plantation, and we see that it is in our terms a clump of trees of the same species. Each party comes to recognise that its own classifications are as puzzling to the other as the other's are puzzling to itself. This looks like the sort of situation that gives aid and comfort to the nominalist in his battle against the realist. But if we look at it more closely we see that it cannot help him. We know already that our own classification is based on similarities and differences between the trees, similarities and differences which we can point out to the islanders in an attempt to teach them our language. Of course we may fail, but if we do it will not be because we must fail. Now either (a) The islanders have means of teaching us their classifications, by pointing out similarities and differences which we had not noticed, or in which we had not been interested, in which case both classifications are genuine, and no rivalry between them, of a kind that can help the nominalist, could ever arise; or (b) Their classification is arbitrary in the sense in which my use of the word "alpha" was arbitrary, in which case it is not a genuine classification. It may be that the islanders classify trees as "boat-building trees," "house-building trees," etc., and that they are more concerned with the height, thickness and maturity of the trees than they are with the distinctions of species that interest us.

In a particular case of prima facie conflict of classifications, we may not in fact be able to discover whether what appears to be a rival classification really is a classification. But we can be sure that if it is a classification then it is backed by objective similarities and differences, and that if it is not backed by objective similarities and differences then it is merely an arbitrary system of names. In no case will it appear that we must choose between rival systems of genuine classification of a set of objects in such a sense that one of them is to be recognised as the classification for all purposes. There is no limit to the number of possible classifications of objects. (The nominalist is right about this.) 4 ____________________ 4Here one may think of Wittgenstein's remark that "Every application of every word is arbitrary," which emphasises that we can always find some distinction between any -129-

There is no classification of any set of objects which is not objectively based on genuine similarities and differences. (The realist is right about this.) The nominalist is so impressed by the infinite diversity of possible classifications that he is blinded to their objectivity. The realist is so impressed by the objectivity of all genuine classifications that he underestimates their diversity. Of course we may if we like say that there is one complete system of classification which marks all the similarities and all the differences. (This is the realist's summing up of what we can learn by giving critical attention to the realist and the nominalist in turn.) Or we may say that there are only similarities and differences, from which we may choose according to our purposes and interests. (This is the nominalist's summing up.) In talking of genuine or objective similarities and differences we must not forget that we are concerned with similarities and differences between possible cases as well as between actual cases, and indeed that we are concerned with the actual cases only because they are themselves a selection of the possible cases. Because the nominalist and the realist are both right and both wrong, each is driven into the other's arms when he tries to be both consistent and faithful to our language, knowledge and experience. The nominalist talks of resemblances until he is pressed into a corner where he must acknowledge that resemblance is unintelligible except as resemblance in a respect, and to specify the respect in which objects resemble one another is to indicate a quality or property. The realist talks of properties and qualities until, when properties and qualities have been explained in terms of other properties and other qualities, he can at last do nothing but point to the resemblances between the objects that are said to be characterised by such and such a property or quality. The question "Are resemblances ultimate or are properties ultimate?" is a perverse question if it is meant as one to which there must be a simple, single answer. They are both ultimate, or neither is ultimate. The craving for a single answer is the logically unsatisfiable craving for something that will be the ultimate terminus of explanation and will yet itself be explained. ____________________ pair of objects, however closely similar they may be. What might be called the principle of the diversity of discernibles guarantees that we can never be forced to apply the same word to two different things. -130-

:8: PARTICULAR AND GENERAL. 1 P. F. STRAWSON 1. THERE is a certain philosophical question which, if antiquity confers respectability, is as respectable as any. It was not long ago discussed by Ramsey in the form "What is the difference between a particular and a universal ?," 2 and more recently by Ayer in the form "What is the difference between properties and individuals?" 3 Ramsey decided that there was no ultimate difference; but perhaps he set the standard for an ultimate difference higher than we should wish to, or drew it from a theory we no longer wish to hold. Ayer, after some interesting suggestions, changed the subject, and discussed instead two other questions: viz., what is the difference in function between indicator words and predicates, and could we in principle say what we want to say without using the former? 4 It may be that the original question is made easier to start on, and more difficult to settle, by an initial failure to make even fairly clear what types or classes of things are to be included in the two general categories between which a satisfying difference is sought. The words of the questions I quoted are not very helpful. Universals are said to include qualities and relations. But if, for example, we take the words "quality," "relation" and "property" in their current uses, much that we should no doubt wish to include on the side of the general, as opposed to the particular, would be left out; and if we do not take them in their current uses, it is not clear how we are to take them. Thus snow, gold and clothing are not properties; nor is man, nor any other species; nor is chess nor furniture; ____________________ Reprinted from the Proceedings of The Aristotelian Society, LIV ( 1953-54) by courtesy of the Editor of The Aristotelian Society. Copyright © 1954, The Aristotelian Society. 1I am much indebted to Mr. H. P. Grice for his criticisms of an earlier version of this paper; and I owe much to the stimulus of an unpublished paper by Mr. Michael Dummett. For the errors and obscurities which remain in the present paper I am alone responsible. 2Ramsey, Foundations of Mathematics, pp. 112-134. 3Ayer, Individuals, Mind, 1952. 4To the second question Ayer's answer was affirmative; and, things being as they are, this is no doubt correct as a matter of what is theoretically practicable. Ayer also acknowledges (a) that in actual practice we could scarcely dispense with indicator words, and (b) that the attempt to do so would always involve a theoretical failure to individuate, since no elaboration of predicates rules out the theoretical possibility of reduplication. But I doubt if the original question can be answered unless we take these two facts more seriously than he does.

nor is the Union Jack—by which I mean, not the tattered specimen the porter keeps in a drawer, but the flag designed in the 19th century, examples of which are taken from drawers by porters and hung from windows. But all these are things which we might well wish to classify with properties correctly so-called, like inflammability, or with qualities correctly so-called, like prudence, when we contrast these latter with individuals or particulars. For there are individual flakes or drifts or falls of snow, pieces of gold, articles of clothing or furniture, games of chess, 5 members of species; and there are hundreds of Union Jacks. These are all (are they not?) particular instances of the general things named in their names. Sometimes the unlikeness of these general things to properties or qualities correctly so-called is masked by the introduction of expressions like "being (a piece of) gold," "being snow," "being a man," "being a Union Jack," "being a chair," "being a game of chess"—phrases like these being said to name properties. Now such expressions no doubt have a participial use; and some (e.g., "being a man") may have a use as noun-phrases, as singular terms. But it is dubious whether many of them have a use as singular terms; and it is dubious whether any of them can be regarded as names of properties. And however we resolve these doubts in different cases, the following dilemma arises in each. Either these verbal nouns (where they are nouns) have the same use as the general names they incorporate—and in that case they may as well be discarded in favour of those general names, which are more familiar, and about the use of which we are consequently less liable to be misled; or they have a different use from those general names— and in this case we still have on our hands, to be

differentiated, like properties correctly so-called, from particulars, the general things designated by those familiar general names. 2. This initial unclarity about the limits of the two great categories of general and particular shows itself also in that arbitrary narrowing of the field which must be presumed to occur whenever certain answers to our question seem plausible. I shall consider again some of these answers, which were dismissed by Ayer or Ramsey or both, not so much on the ground that they thought them false as on the ground that they did not think them fundamental. There is, for example, the suggestion that general, unlike particular, things cannot be perceived by means of the senses; and this seems most plausible if one is thinking of the things designated by certain abstract nouns. It is not with the eyes that one is said to see hope. But one can quite literally smell blood or bacon, watch cricket, hear music or thunder; and there are, on the other hand, certain particulars which it makes dubious sense to say one perceives. Then there is the suggestion that general, unlike particular, things, can be in several places at once. There can be influenza in London as well as in Birmingham, and gold in Australia as well as in Africa. But then so can many particulars be scattered over the surface of the table or the globe. Moreover, it makes dubious sense to say of some general things (e.g., solubility) that they are in any place, let alone in many; and equally dubious sense to say of ____________________ 5But a game of chess may be something which itself has instances. -132-

some particular things (a sudden thought, a mental image, the constitution of France) that they have a particular spatial location. It may be said that I have missed the point of both these theories; that, first, when we say we perceive general things, what we really perceive is individual instances of them, not the general things themselves; and, second, to say that general things can be in several places at once is to say that they may have different instances, differently located; whereas it makes no sense to speak of different instances of individuals. But so to explain these theories is to give them up. It is to fall back on saying that general things may have instances, and individual instances of general things may not. This is, perhaps, an unexceptionable statement of the general distinction between the two categories, but scarcely seems to count as an explanation of it. A third suggestion is that individual things, unlike general things, have dates or histories. But similar objections apply to this. We may speak of the history of dress or engineering, the origins of civilization, the invention of golf and the evolution of man. This theory, like the others (when taken at their face value), may draw a logically interesting distinction; but, like them, does not draw one that coincides with the categorial line between particular and general. A doctrine which might appear more promising, because more general, than these, is that individuals can function in propositions only as subjects, never as predicates; whereas general things can function as both. But it is not clear what this doctrine amounts to. Suppose, first, it is a grammatical point. Then if it says that the names of individuals never have adjectival or verbal forms, whereas names of general things do, it is false. If it says that individual names never form parts of grammatical predicates, or alternatively, never stand by themselves after the word "is" in a grammatical predicate, it is equally false. In any case, a grammatical point could scarcely be fundamental, since it is easy to imagine the elimination of those distinctions upon which such points must rely, in favour of the device of merely coupling names of appropriate types, in any order, in a singular sentence. We should not, by so doing, eliminate the category-distinction. For we might imagine changing the language once more, requiring that our names should stand on one side or the other of the phrase "is an instance of," and then simply distinguishing the individual names as those that could never stand on the right of this phrase. 6 So I think we must conclude that the point misleadingly made in the languages of grammar is simply once more the point that individuals, unlike general things, cannot have instances. To say that general things, unlike individuals, can be predicated of other things, is simply to paraphrase this; and neither expression seems more perspicuous than the other.

3. But will the word "instance" itself really bear the weight of this distinc____________________ 6Ramsey seems to suggest that this would simply be to manufacture an empty verbal distinction. (Cf. Foundations of Mathematics, pp. 132-133). But it would not. For it would not be an arbitrary matter to decide which names to put on which side of the coupling phrase. -133-

tion? Of course, as a philosopher's word, understood in terms of that distinction, it cannot fail to bear it; but then it ceases to explain the distinction for us. If we ask what expressions we actually use to refer to or describe an individual thing as an instance of a general thing, we find that they are many; and that perhaps none of them is appropriate in every case. They include: "a case of," "an example of," "a specimen of," "a member of," "a piece of," "a quantity of," "a copy of," "a performance of," "a game of," "an article of," and so on. Though each can be followed by the name of a general thing, many can also be followed by expressions we should hesitate to regard as the names of general things. This is true of the phrase "an instance of" itself. We may speak of a signal instance of generosity; but we may also speak of a signal instance of Smith's generosity. Similarly we may speak not only of a piece of gold and an article of clothing, but of a piece of Smith's gold and an article of Smith's clothing. So if we seek to draw our distinction in terms of the words actually used to play the part of the philosopher's word "instance"— including the word "instance" itself—then it will not be enough to say that general things may have instances. For so may non-general things. The point here may be put roughly as follows. We are tempted to explain the distinction between two types of things, T 1 and T 2 , by means of a certain relation R; by saying, that is, that only things belonging to T 2 can appear as the second term of this relation, whereas both things belonging to T 2 and things belonging to T 1 can appear as its first term. R is something like, but more general than, is characterized by or is a member of or the converse of is predicated of. But then it appears that we really have no notion of R except one which is useless for explanatory purposes since it is itself to be explained in terms of the difference between T 1 and T 2 ; this is what I called the philosopher's notion of "an instance of." What we have instead is a lot of notions which are either too restricted to serve our purpose (e.g., "has the property of"), or fail to be restricted in precisely the way in which we want them to be, or both. As a member of this set of notions, pre-eminent for its abstract character, we may take the logician's idea of class-membership. The difficulty is, roughly, that we can form closed classes on what principle we please; we could count almost any particular we are likely to mention as such a class, and hence as the second term of our relation. (These remarks are very rough and schematic; but they serve, I hope, to make the point in a general form). Consequently, we shall have to give up the idea of explaining the difference between the particular and the general in terms of such a relation. This will not lead us, as it perhaps led Ramsey, to despise the philosopher's notion of an instance, and to think that there is nothing in it; for it is easy enough to teach anyone the application of it, without precise explanations. But it will lead us to look further for such explanations. 4. To begin with, I want to draw a rough distinction between three classes of nouns, all of which would traditionally be regarded either as themselves the names of universals (general things) or—in the case of the nouns of group (2)—as closely linked to such names. The distinctions are indicated -134-

only by examples; and the three classes are by no means exhaustive of the field. But this does not matter for my purpose. 1. Examples of the first class are such partitive nouns as "gold," "snow," "water," "jam," "music." These I shall call material-names, and what they name, materials. 2. Examples of the second are certain articulative nouns such as "(a) man," "(an) apple," (a) cat." These I shall call substance-names, and what they apply to, substances.

3.

Examples of the third are such abstract nouns as "redness," (or "red"), "roundness," "anger," "wisdom." These I shall call quality- or property-names, and what they name, qualities or properties. 7 These three classes of nouns may be compared and contrasted with one another in a number of ways. But the contrast on which I wish to lay most emphasis is i. The contrast between the nouns of group (3) and those of groups (1) and (2). The nouns of group (3) are the most sophisticated and the most dispensable. They are derived from adjectives and the general things they name usually enter our talk by way of the adjectives from which their names are derived. When we consider the things which philosophers are prepared to count as individual instances of these general things, we find a considerable latitude in the categories of the things to which these instances may belong. Thus an instance of wisdom may be a man, a remark or an action. An instance of the colour red may be a material thing like a pillar-box, an event like a sunset, or a mental thing like an image. A word, a gesture, an expression, a man may all be instances of anger. In contrast, unsystematic ambiguities aside, there is no latitude at all about what category of thing can be an individual instance of a cat or an apple. There is some latitude, but one would often hesitate to call it a category-latitude, about what can be an individual instance of the general things named by the nouns of group (1). An instance of gold may be a vein, a piece or a quantity of gold; an instance of snow may be a drift, an expanse, a piece, and even a fall, of snow. ii. Next I want to emphasise a respect in which the nouns of group (2) differ from those of groups (1) and (3). Philosophers may speak of "an individual (particular) instance (example, specimen) of ϕ," where "ϕ" is replaced by a noun from any of these three groups. Suppose the noun is drawn from group (2). Then we have such phrases as "an instance of a horse" or "an instance of an apple." It is to be noticed that what follows the expression "an instance of" is a phrase which can and does by itself function as an indefinite designation of an individual instance. (An instance of a horse is the same as a horse.) This is not the case if the nouns are drawn from groups (1) or (3). (Gold is not the same as a piece of gold.) It seems as if, when we say that x is an instance of y, then when y is such that there is no choice about the sort of thing we can count as an instance of it, we feel no need of a true general- thing name for y, i.e., of a name differing from an indefinite designation of ____________________ 7The terminology, evidently, is not to be taken too seriously. Anger is a state, not a property or quality. -135-

an individual instance of y. (It is true that we have the expressions "the horse," "the apple," etc., names of species or kinds, obvious collectors of homogeneous individuals; but these follow less naturally after the expression "an instance of" than does the phrase containing the indefinite article). Philosophers have felt this difference, and tried to blur it with the invention of such expressions as "horseness" (cf. "being a horse"). But it should rather be treated as a clue until proved an anomaly. iii. Finally, I want to note the existence of a special class of individual instances of general things whose names belong to group (3). The simplest, though not the only recipe, for forming the names of members of this class is as follows: in the formula "the ... of ... ," fill the first gap with the property-name in question and the second gap with the definite designation of a suitable individual. Thus we may speak of the wisdom of Socrates as an instance of wisdom; of the redness of Smith's face as an instance of redness; and we may also speak of Jones' present mental state as an instance of anger. This class of individual instances of properties, or property-like things, will include the "particular qualities" which Stout defended. And an analogy may be found between referring to a horse as "an instance of a horse" and referring to Jones' present stage of anger as "an instance of anger." 5. Next, I want to make some general, and still propaedeutic, remarks about the notion of an individual or particular. 1. The idea of an individual is the idea of an individual instance of something general.

There is no such thing as a pure particular. (This truth is too old to need the support of elaboration.) The idea of an individual instance of ϕ is the idea of something which we are able in principle a. to distinguish from other instances of ϕ; and b. to recognise as the same instance at different times (where this notion is applicable). So, to have the idea of a particular instance of ϕ, we need (in general) a. criteria of distinctness, b. criteria of identity for a particular instance of ϕ. On the need for these criteria the following comments must be made: i.

It might be supposed that the distinction between the two kinds of criteria is a mistake; that there is no such distinction. For identity and difference are two sides of the same coin. It is possible, however, at least in some cases, to consider separately the criteria by which we distinguish and enumerate objects of the same sort, in a situation in which the question of identifying any one of them as, or distinguishing it from, the one which had such-and-such a history, does not arise or is not considered. It is to criteria of this kind that -136-

3.

I give the name "criteria of distinctness." They might also be called "criteria of enumeration." 8 ii. What the criteria of distinctness and identity for instances of ϕ may be is obviously closely connected with what ϕ is; but is not wholly determined by it in every case. That it is not so determined is obvious in the case of properties, qualities, states, etc.; we have already seen how wide a range of categories their instances may be drawn from (4 (i)). It is less obvious, but still true, in the case of general things named by material-names. The general question of the criteria of distinctness and identity of individual instances of snow or gold cannot be raised or, if raised, be satisfactorily answered. We have to wait until we know whether we are talking of veins, pieces or quantities of gold, or of falls, drifts or expanses of snow. There are cases, however, where this indeterminateness regarding the criteria of identity and distinctness does not seem to exist, where it seems that once ϕ is given, the criteria are given, too. And among these cases are those where " ϕ" is a substance-name (4(ii)). It should once more be noted that these are the cases where we do not find a true name of a general thing following the phrase "an instance of," but instead an expression which can by itself function as an indefinite designation of an individual instance (e.g., "a horse"). When it has been said that a particular must be an instance of something general, and that there must be criteria of distinctness and (where applicable) of identity for individual instances of a general thing, something of central importance still remains unsaid. In giving the relevant criteria—or sets of criteria—for individual instances of a certain general thing, we do not indicate how such particulars are brought into our discourse. Nor do we bring a particular into our discourse by mentioning these criteria. (To mention them is still to talk in general.) We bring a particular into our discourse only when we determine, select, a point of application for such criteria, only when we mention, refer to, something to which these criteria are to be applied; and no theory of particulars can be adequate which does not take account of the means by which we determine such a point of application as a point of application for these criteria.

6. In the rest of this paper I shall try to do two things. First, I shall try to show how, in the case of certain kinds of particulars (particular instances of certain kinds of general things), the notion of a particular may be seen as something logically complex in relation to other notions (a kind of compound of these notions). That is, I shall try to produce a partial

explanation (analysis) of the notion of an individual instance, for certain cases; and then I shall try to show how this notion, as explained for these cases, may be used in the explanation of the notion of individual in____________________ 8It might be true, if intelligible, that if we had so time-indifferent a perspective of things as to see them as four-dimensional objects in a space-time, then there would be no point in giving separate consideration to criteria of distinctness. But we do not have such a perspective. -137-

stances of other sorts of general things, and in the explanation of the notions of those other types of general things themselves. So in this part of the paper (sections 6-9), no general account is offered of the distinction we are concerned with. The procedure is essentially one of indicating, step by step, how certain types of notion can be seen as depending upon others; and it makes no claim at all to completeness. Second (section 12), this procedure is found to suggest a possible general account of the distinction we are concerned with; though the acceptability or otherwise of this general account seems to be independent of that of the step-by-step schema of explanation. Now it might seem that the difficulty of finding an explanation of the notion of an individual instance arises from the fact that the category distinction between general and individual is so fundamental that there is nothing logically simpler, or more fundamental, in terms of which this notion could be explained. But I think this view can be challenged for a certain range of important cases, which can then perhaps serve as the basis for the explanation of others. To challenge it successfully we have to envisage the possibility of making statements which (a) do not make use of the notion of individual instances, and (b) do not presuppose the existence of statements which do make use of this notion. The second condition may be held to rule out general statements; for though many general statements make no direct mention of individuals, they have often and plausibly been held in some sense to presuppose the existence of statements which do. So what we have to consider is the possibility of singular statements which make no mention of (i.e., contain no names for, or other expressions definitely or indefinitely referring to) individual instances of general things. Now there certainly does exist, in ordinary use, a range of empirical singular statements answering to this description. I suggest, as examples, the following:— It is (has been) raining. Music can be heard in the distance. Snow is falling. There is gold here. There is water here. All these sentences contain either the material-name of a general thing ("music," "snow") or a corresponding verb; but none contains any expression which can be construed as serving to make a definite or indefinite mention of individual instances of those general things (i.e., falls or drops of rain, pieces of gold, pools of water and so on). Of course, when these sentences are used, the combination of the circumstances of their use with the tense of the verb and the demonstrative adverbs, if any, which they contain, provides an indication of the incidence of the general thing in question. Such an indication must be provided somehow, if empirical singular statements are to be made at all. But it is important that it can be provided by means of utterance- centred indications which do not include noun-expressions referring definitely -138-

or indefinitely to individual instances. Such sentences as these do not bring particulars into our discourse. Languages imagined on the model of such sentences are sometimes called "propertylocation" languages. But I think the word "property" is objectionable here because (a) the

general things which figure in my examples are not properties, and (b) the idea of a property belongs, with the idea of an individual instance itself, to a level of logical complexity we are trying to get below. So I propose to substitute the less philosophically committed word "feature"; and to speak of feature-placing sentences. Though feature-placing sentences do not introduce particulars into our discourse, they provide the materials for this introduction. Suppose we compare a feature-placing sentence ("There is snow here") with a phrase ("This (patch of) snow") in the use of which an individual instance of the feature is mentioned. It seems possible, in this case, to regard the notion of the individual instance as something logically complex in relation to the two simpler notions of the feature and of placing. The logical complexity may be brought out in the following way. In making the feature-placing statement, we utter a completed sentence without mentioning individuals. If we merely mention the individual without going on to say anything about it, we fail to utter a completed sentence; yet what the feature-placing sentence does explicitly is, in a sense, implicit in this mere mention. So, as the basic step in an explanatory schema, we may regard the notion of a particular instance of certain sorts of general things as a kind of logical compound of the simpler notions of a feature and of placing. But what about the criteria of distinctness and identity which were said in general to be necessary to the notion of an individual instance of a general thing? The basis for the criteria of distinctness can already be introduced at the feature-placing level, without yet introducing particulars. For where we can say "There is snow here" or "There is gold here," we can also, perhaps, more exactly, though not more correctly, say "There is snow (gold) here— and here—and here." And when we can say "It snowed to-day," we can also, perhaps, more exactly, but not more correctly, say "It snowed twice to-day." The considerations which determine multiplicity of placing become, when we introduce particulars, the criteria for distinguishing this patch of snow from that, or the first fall of snow from the second. Of criteria of identity I shall say more in general later. It might be objected that it is absurd to speak of an imagined transition from feature-placing sentences to substantival expressions definitely designating particular instances of features as the introduction of particulars; that it is absurd to represent this imagined transition as part of a possible analysis of the notion of a particular instance, even for these simple cases of material- names which seem the most favourable; and that at most what is achieved is the indication of a possible way of looking at certain designations of certain particulars. For are not the particulars as much a relevant part of the situa -139-

tion in which a feature-placing sentence is employed as they are of a situation in which a substantival particular-designation is employed? To this I would reply by asking what philosophical question there would be about particulars if we did not designate them, could not make lists of them, did not predicate qualities of them and so on. What we have to explain is a certain mode of speech. 7. When we turn from material-names to substance-names, the attempt to provide an analogous explanation of the notion of an individual instance seems much harder. But though it is harder, it is perhaps worth making; for if it succeeds, we may find we have then an adequate basis for the explanation of the notion of an individual instance in other cases, and for the explanation of further kinds of general things. In order for the attempt to succeed, we must be able to envisage a situation in which, instead of operating with the notion of an individual instance of a cat or an apple, we operate with the notions of a corresponding feature and of placing. Ordinary language does not seem to provide us, in these cases, with feature-placing sentences. And it might be argued that the idea of such sentences was, in these cases, absurd. For (1) it might be pointed out that an all-important difference between such things as snow and such things as cats lay in the fact that different instances of snow are, in a sense, indefinitely additive, can be counted together as one instance of snow; while this is not true in the case of instances of cats; and it might be suggested that herein lay a reason for the possibility of feature-placing sentences in the case of snow and for their impossibility in the case of cats. And (2) it might be added that we have no name for a general thing which could count as the required feature in the case of cats. It is true that we speak of the cat in general; but "the cat" ranks as a species-name, and

the notion of a species as surely presupposes the notion of individual members as the notion of a property involves that of individual things to which the property belongs or might belong. It is also true that we may speak of an instance (specimen) of a cat, as we may speak of an instance of gold; but here what follows the phrase "an instance of" is not, as "gold" is, a general-thing name which could figure in a merely feature-placing sentence, but an expression which also serves as an indefinite designation of an individual. Does not all this strongly suggest that there could be no concept of the "cat-feature" such as would be required for the analysis to work, that any general idea of cat must be the idea of a cat, i.e., must involve criteria of identity and distinctness for cats as individuals and hence the notion of an individual instance? These objections have great force and importance; but I do not think them decisive. For they do not show that it is logically absurd to suppose that we might recognise the presence of cat or signs of the past or future presence of cat, without ever having occasion to distinguish one cat from another as the cat on the left, or identify a cat as ours or as Felix. 9 The second argument ____________________ 9Cf. Price, Thinking and Experience, pp. 40-41, on identity of individuals and of characteristics. -140-

merely reminds us that the resources of our language are such that on any actual occasion of this kind we in fact use, not a partitive noun, but the indefinite forms ("cat" or "a cat") of the articulative noun. But this fact can be explained in a way consistent with the advocated analysis (see section 10). Nevertheless, these arguments show something. The point about the species- name, for example, is sound; the notion of a species, like that of a property, belongs to a level of logical complexity we are trying to get below. Second, and more immediately important, the first argument shows that if there is to be a general concept of the cat-feature, corresponding in the required way to the notion of an individual instance, it must already include in itself the basis for the criteria of distinctness which we apply to individual cats. (Roughly, the idea of cat, unlike that of snow, would include the idea of a characteristic shape). But to concede this is not to concede the impossibility of the analysis. It is worth adding that sometimes we do find verbal indications of our use of featureconcepts such as those we are trying to envisage; as, e.g., when we speak of "smelling cat" or "hunting lion," or using the noun in the singular without the article. There might seem to exist a more general objection to this whole procedure. For it seems that it would always be possible in practice to paraphrase a given feature-placing sentence in use, by means of a sentence incorporating indefinite designations of particular instances; e.g., "There is gold here" by "There is a quantity of gold here"; "Snow has fallen twice" by "There have been two falls of snow"; "There is snow here—and here" by "There are patches (expanses) of snow here and here"; and so on. And if sentences incorporating definite or indefinite designations of particular instances bring particulars into our discourse; and if statements made by the use of feature- placing sentences are equivalent to statements made by the use of sentences incorporating indefinite designations of particular instances; then do not feature-placing sentences themselves bring particulars into our discourse? But this argument can be turned in favour of the explanation it is directed against. Suppose there is a statement S made by means of a feature-placing sentence; and an equivalent statement S' made by means of a sentence incorporating an indefinite particular-designation; and a statement T made by means of a sentence incorporating a definite designation of the particular indefinitely designated in S'. Now only if a language admits of statements like T can it admit of statements correctly described as I have described S'. (There are no indefinite designations of particulars where there are no definite designations of particulars.) But a language might admit of statements like S without admitting of statements like T. So the existence of statements like S', in a language which admits of both statements like S and statements like T, is not destructive of the analysis, but is a proof of its correctness. 8. If the argument so far is acceptable, then at least in the case of some materials and some substances, we can regard the notion of an individual instance as partially explained in terms of the logical composition of the two notions of a feature and of placing. When we turn to

properties and qualities, -141-

we may make use of a different kind of explanation which is also, in a sense, the completion of the first kind. I shall not, that is to say, try to explain the notion of individual instances of anger or wisdom or red in terms of the logical composition of a feature, such as anger or red, and placing. But nor shall I maintain that it would be wrong or impossible to do so. We might think of such general things as anger (or red) not primarily as qualities, properties, states or conditions of persons or things, but primarily as instantiated in, say, situations (or patches) which acquired their status as individuals from just such a logical composition. But though this is how we might think, it is not, for the most part, how we do think. It is natural, rather, to regard those general things which are properly called qualities, conditions, etc., as belonging at least to the same level of logical complexity as the idea of individual instances of the kinds we have so far been concerned with; to regard them, that is, as feature- like things, the incidence of which, however, is primarily indicated, not by placing, but by their ascription to individual instances of material or substantial features the incidence of which is primarily indicated by placing. 10 We have seen the notion of an individual instance of some materials and substances can be regarded as a logical compound of the notions of a feature and of placing. We have now to see the ascription of a quality (etc.) to such an individual as an operation analogous to the placing of a feature. Indeed, we may find in the possibility of this operation the point—or one important point—of that logical composition which yields us the particular. The individual instance of the simply placeable feature emerges as a possible location-point for general things other than the feature of which it is primarily an instance, and hence as also an individual instance of these general things, its properties or qualities or states. One might exaggeratedly say: the point of having the idea of individual instances of material or substantial features is that they may be represented as individual instances of property-like features. The individuals are distinguished as individuals in order to be contrasted and compared.Other notions call for other treatment. I consider two more. a. I mentioned, at 4 (iii), a rather special class of individual instances of properties or property-like things. We form the notion of such an instance when, for example, we speak not of a man or an action as an instance of wisdom or anger, but of the wisdom of Socrates as an individual (a case of wisdom) or of Jones' present mental state as an individual instance of anger. Here the notion of the individual instance can be seen as a new kind of logical compound, namely, a compound which includes as elements both the notion of the general thing (property) in question and that of the material or substantial individual which is an instance of it; it may sometimes include a further element of temporal placing (cf. "his present state of anger"). b. Instances of events, processes and changes I have so far scarcely mentioned. Most of our more familiar words for happenings strike us es____________________ 10These remarks, of course, apply only to some of the things correctly called properties, states, qualities, etc. -142-

sentially as names for the actions and undergoings of individual instances of material or substantial features. But there is a difference between these happening words and quality or state-words. A wise man is an instance of wisdom, but a dead or dying man is not an instance of death. Only death is that. As regards such happening-words as these, then, we have to see the idea of an individual instance as reached by a kind of logical composition analogous to that considered in the paragraph immediately above: an individual instance of a material or substantial feature is an element in the compound. But these, though perhaps the most important, are not the only kinds of happeningwords. 9. The general form of these explanations may be roughly indicated as follows. The notion of placing a feature is taken as basic, as consisting of the logically simplest elements with which we are to operate. It is pointed out that neither of these elements involves the notion of an individual instance, nor therefore the notions of certain types of general things, such as properties and species; and it is shown that the idea operating solely with these simplest

elements can be made intelligible for certain cases. (Features in fact of course belong to the class of general things; but so long as we remain at the feature-placing level, they cannot be assigned to it; for there is nothing to contrast the general with.) From this basis we proceed by composition and analogy. The designations of individual instances of (some) material and substantial features are first introduced, as expressions, not themselves complete sentences, which include placing-indications; and, complementarily, certain types of general things (e.g., properties and types of happening) are introduced as items the designations of which do not include placing-indications and which are ascribed to material or substantial individuals. The ascription of such a thing as a property to a substantial individual is represented simply as an operation analogous to the placing of a feature; so no circularity attends the word "ascription." Individuals of certain other types (e.g., events happening to substances, states of substances and "particularised" qualities) are then introduced as the designata of expressions which include the designations of individuals of earlier types, and hence indirectly include the notion of placing.There are many types of individual and of general thing besides these here considered. Some may admit of analogous treatment; and it might be possible to introduce others, on the basis already provided, by other methods of construction and explanation. But every introduction of a particular, in terms of such a schema, will either directly contain the notion of placing or will preserve, by way of individuals already introduced, the original link with this notion. Of course the value of this suggestion, as it stands, is small. For the notion of an individual instance extends itself indefinitely, by way of far more complicated connexions than I have so far indicated; and the limits of plausibility for the kinds of construction-procedure I have used would, no doubt, soon be reached, if they are not already overpassed. Nevertheless, I think this sketch of a procedure has certain merits: 1. Some of the difficulties which attend any attempt to elucidate the -143-

2.

3.

category-distinction between the particular and the general arise from the fact that these two classes include so many different category-distinctions within themselves. This fact creates a dilemma for the theorist of the distinction. On the one hand, he is tempted, in a way illustrated at the beginning of this paper, into drawing distinctions which indeed separate one or more sub-categories of one class from one or more sub-categories of the other, but which fail to yield the desired result if applied over the whole field. Or, on the other hand, in the effort to escape from this domination by irrelevant category differences, he is tempted by the prospect of a purely formal distinction, drawing for this purpose on the terms and concepts of grammar or of formal logic. But distinctions so drawn can only seem to succeed by forfeiting their formal character and silently incorporating the problematic category-distinction. The present procedure offers at least a hope of escape from this difficulty. For it fully allows for the differences between types of general thing and of individual; and instead of producing one single explanation, the same for every case, it offers a serial method of explaining later types of general or particular things on the basis of earlier ones, while preserving a continuous general differentiation between the two major categories in the course of the explanation. Too much must not be claimed for the suggested procedure, however ; in particular, it must not be thought that it has been so described as to provide a criterion for the distinction we are concerned with. Another characteristic of the schema of explanation is that it accords a central place to the notion of an individual instance of certain kinds of general things, viz., of material and substantial features. This (see section 8) is not an essential characteristic; it could be modified. But there is reason to think that it corresponds to our actual way of thinking; that these individuals are the "basic particulars." Why this should be so, and whether it might not be otherwise, are questions which I shall not now consider. Finally, while not itself providing for a criterion of general and particular, the schema points the way to a possible general distinction which might be defensible even if the procedure which suggests it should prove unsatisfactory. This general distinction I shall outline in section 12. Before I do so, some further points remain to be considered.

10. Something further must first be said on the subject of criteria of identity for individual instances of a general thing. We saw (5 (2)) how in many cases the question of the criteria of distinctness and identity of an individual instance of a general thing was incompletely determined when the general thing was named. This was particularly evident in the case of

some properties and was evident also in the case of materials. Where substance-names were concerned, however, this indeterminateness seemed not to exist; when the name was given, the criteria were fixed. And this was connected with the fact that in these cases there seemed to exist no true general-thing name, apart from expressions which ranked as species-names and obviously presupposed certain definite criteria of identity for individual members. As far as criteria of distinctness are concerned, this raises no particular difficulty. We saw, for -144-

example, how the idea of a simply placeable feature might include—might indeed be—the idea of a characteristic shape, and in this way provide a basis for criteria of distinctness for individual instances of the feature. But it is not so easy to account for the apparent determinateness of criteria of identity. The explanatory schema advanced required that we should theoretically be able to form concepts of some substance-features which were logically prior to, and independent of, the corresponding concepts of an individual instance of such features; and this requirement seems to clash with the apparent determinateness of the criteria of identity for such individuals. A parallel answer to that given in the case of criteria of distinctness is theoretically available, but is unattractively unplausible. If we reject this answer, and cannot find an alternative, then we must at least radically revise, though in a not unfamiliar direction, the basis of the explanatory schema. (The difficulty is essentially a more specific form of that encountered already in section 7.) I think, however, that an acceptable alternative can be found. For in all cases where a feature-concept can be assumed to be possible, the criteria of identity (and of distinctness) for an instance of the general thing in question—or the sets of such criteria, where there is more than one set—can be seen as determined by a combination of factors, viz., the nature of the feature itself, the ways in which the feature empirically manifests itself in the world, and—to adopt a possibly misleading mode of expression—the kind of incentives 11 that exist for having a notion of an individual instance of the feature in question. The relevance of this third factor even, perhaps, gives us the right to say that there is something arbitrary about the criteria we adopt, something which, given the other two factors, is—in at any rate a stretched sense—a matter of choice. In extreme cases this is obvious. Even those who had witnessed the whole of the affair under discussion might, for example, give varying answers to such a question as: Is this the same quarrel going on now as was going on when I left? The answer we choose may depend on just what distinctions we are interested in; and one can imagine many situations for this example, and many different things which might influence us. There may, on the other hand, be very many cases of features where the adoption of a certain particular set of criteria of identity (and distinctness) for their instances is so utterly natural that it would seem to be stretching the phrase "matter of choice" intolerably to apply it to them. But, even in these cases, the naturalness may still be seen as depending on the combination of factors I mentioned; and, if we bear this in mind, we can sometimes imagine the possibility of alternatives. (Here is a question which might with advantage be explored for many different types of case.) It seems reasonable to view substantial features as cases of this kind. If this view is acceptable, we can find in it an explanation of that difference be____________________ 11What I mean by "incentives" here may be illustrated from the convenience of the institution of property. Suppose there is a general feature, ϕ which human beings wish to make use of. Even if there is enough ϕ for all, friction may be avoided if criteria are used for distinguishing my ϕ from yours. ("Mine" is indeed one of the earliest individuating words used by children.) -145-

tween substance-names and certain other true general-thing names to which I have several times referred. Given a true general-thing name, like "gold" or "wisdom," the question of the criteria of identity of its instances cannot be answered until the kind of instance is specified, by such a phrase as "a piece of gold" or "a wise action." But where one set of criteria of

identity is peculiarly dominant, its adoption peculiarly compelling, we find no such non-committal general name in current, adult, unsophisticated use. All that we might wish to do with it, we can equally well do without it, by the use of the indefinite singular or plural forms of the ordinary substance-name (e.g., "a horse" or "horses"). 11. It is, perhaps, necessary to guard briefly against a misunderstanding. Of course, I am not denying that we can very well use individual-designations as such without being, or ever having been, in a position to make a relevant placing of some feature which, in terms of the explanatory schema I have defended, is immediately or ultimately relevant to the explanation of the type of instance concerned. To deny this would be absurd. It would be to deny, for example, that when we talk about remoter historical characters, we are really talking about individuals. But the view I am defending does not require such a denial. For this view seeks merely to explain the notion of an individual instance of a general thing in terms, ultimately, of feature-placing. It does not at all imply that we cannot make use of this notion in situations other than those in terms of which it is explained. In fact, of course, the expansiveness of our talk about individuals is in marked contrast with the restrictedness of our contacts with them. Both the possibility of, and the incentives to, this expansiveness have an empirical ground; in the variousness of individuals, the non-repetitiveness of situations. But this fact may nevertheless mislead us, may make the theoretical problem of individuation look more difficult than it is by distracting our attention from an essential element in the notion of an individual instance. The problem would scarcely seem difficult for the case of an imagined universe in which all that happened was the repetition of a single note, varying, perhaps, in volume. Individual instances could then be described only as, say, "the third before now" or "the next one to come." But in such a universe the incentives to forming the notion of an individual instance would be small. We might say that, in general, what is essential to the notion of an individual instance is not what is interesting about individuals. 12. To conclude. I remarked earlier that the explanatory schema I have sketched points the way to a possible general distinction between the two major categories we are concerned with. To recall, first, some vague, figurative and unsatisfactory terms I have already used: the schema suggests that the notion of a particular individual always includes, directly or indirectly, that of placing, whereas the notion of a general thing does not. Now placing is characteristically effected by the use of expressions the reference of which is in part determined by the context of their use and not by their meaning, if any, alone. And this suggests the possibility of formulating a general dis -146-

tinction in a more satisfactory way. We may say: it is a necessary condition for a thing's being a general thing that it can be referred to by a singular substantival expression, a unique reference for which is determined solely by the meaning of the words making up that expression; and it is a necessary condition of a thing's being a particular thing that it cannot be referred to by a singular substantival expression, a unique reference for which is determined solely by the meaning of the words making up that expression. This specification of mutually exclusive necessary conditions could be made to yield definitions by stipulating that the conditions were not only necessary, but also sufficient. But there is point in refraining from doing so. For as we consider substantival expressions increasingly remote from the simplest cases, there may be increasing reluctance to apply the distinction at all. Nor is this reluctance quite irrational; for the simplest cases are those which form the basis of the general distinction. (Hence, roughly, the association of particularity with concreteness.) We may admit that the traditional distinction was vague as well as unclear, and respect its well-founded vagueness in this way.To elucidate this quasi-definition of particular and general, I add some miscellaneous comments of varying degrees of importance. 1. It might be objected to the conditions given that expressions like "The third tallest man who ever lived or lives or will live" answer to the specifications for a general-thing designation. If they did, it would perhaps not be difficult to legislate them out, by suitable amendments of those specifications. But in fact they do not. For their meaning does not suffice to determine for them a unique object of reference. It is, if true, contingently true that there is a single thing answering to such a description. This case, however, does raise a problem about how the words "expression a unique reference for which is determined solely by the meaning" are to be construed. If we construe them as

"expression the existence of just one object of reference for which is guar anteed by the meaning," we may find ourselves in (possibly circumventable) trouble over, e.g., "phlogiston" and "the unicorn." Yet this is the construction at first suggested by the present case. 12 It will be better, therefore, to construe them as follows: "expression the (or a) meaning of which is such that it is both logically impossible for it to refer to more than one thing (in that meaning) 13 and logically impossible for the expression to fail to have reference because of the existence of competing candidates for the title." And the sense of "competing candidates" can be explained as follows: x, y and z are competing candidates (and the only competing candidates) for the title D if, if any two of them had not existed, D would apply to the third. 2. It may seem, perhaps, a more troublesome fact that the names we commonly employ for certain types, like Beethoven's Fifth Symphony, do not answer to the specifications given for a general-thing designation, although we ____________________ 12This difficulty was pointed out to me by Mr. H. P. Grice. 13This qualification allows for the possible case where there is no convenient unambiguous designation of the general thing in question; but is not strictly necessary since an unambiguous designation could always be framed. -147-

3. 4.

may be more than half inclined to count such types as general things; for these names include, as a part of themselves or of their explanation, proper names like "Beethoven." We have, however, an easy remedy here. We can regard the pattern of sounds in question as a general thing for which there might (perhaps does) exist a general description the meaning of which uniquely determines its reference; and then it will appear as the contingent truth it is that Beethoven stands to the general thing so designated in a certain special relation. This does not commit us to saying that it is a contingent truth that Beethoven's Fifth Symphony was composed by Beethoven; but the necessity here is simply a consequence of the fact that we ordinarily and naturally refer to the general thing in question by means of an expression which incorporates a reference to a particular individual who stands in a special relation to it. Analogous considerations apply to many other types. Of course, the alternative is always open to us of declining to apply the criterion in such cases. It is clear that numbers, if we apply our criterion to them, will emerge as general things. But this is a result which will disturb few, and will certainly disturb no one who continues to feel the charm of the class-of-classes analysis. If we choose to apply the test to facts, we get the not wholly unappealing result that, e.g., the facts that 2 + 2 = 4, that all crows are black and that crows exist (in one use of "exist") are general things, while the facts that Brutus killed Caesar and that all the people in this room are philosophers are particular things. For propositions, of course, the result is similar. The distinction will correspond roughly to the old distinction between those propositions (or facts) which are "truly universal" and those which are not. In the case of facts and propositions, however, we may well feel a very strong reluctance to classify in this way at all; and, if we do, there is no reason why we should struggle to overcome it. 14

Some points of more general significance remain. As historical evidence for the general correctness of this doctrine, we may note that Russell who, for so large a part of his philosophical life, showed an anxiety to equate meaning and reference in the case of names, finally inclined to the conclusion that the only true names are those of universals. 15 We do not, of course, need to adopt his idiosyncratic use of the word "name," in acknowledging the correctness of his implied view of universals. 6. It will be clear that the quasi-definition I am suggesting has points of contact with some of those more familiar ways of marking the distinction which turn out to be more or less unsatisfactory. For instance, it will not do ____________________ 14What I have said here of facts and propositions must not lead us to suppose that we should obtain a similar result for sentences. These, and expression-types generally, will emerge as general things (e.g., in virtue of the conventions for the use of inverted commas, 5.

the expression "the word 'and' " may be said to determine, by meaning alone, a unique object of reference). Inquiry into Meaning and Truth and Human Knowledge: Its Scope and Limits.

15See

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7.

to say that general things do not have spatio-temporal positions and limits, whereas particular things do. Some general things, those of appropriate categories, like gold, do have spatial distribution; and some may have temporal limits. It is rather that when we refer to general things, we abstract from their actual distribution and limits, if they have any, as we cannot do when we refer to particulars. Hence, with general things, meaning suffices to determine reference. And with this is connected the tendency, on the whole dominant, to ascribe superior reality to particular things. Meaning is not enough, in their case, to determine the reference of their designations; the extra, contextual element is essential. They are, in a quite precise sense, less abstract; and we are, on the whole, so constituted as to count the less abstract as the more real. Finally, we may, if we choose, revert to the original philosophical way of marking the distinction in terms of the concept of an instance, and give it a sense in terms of the final definition. Instantiability, in the philosophers' sense, ends precisely at the point at which contextual dependence of referring expressions begins, or where referring expressions, as being proper names of individuals, have meaning only in a sense in which it is altogether divorced from reference. So general things may have instances, while particular things may not. -149-

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PART TWO The Theory of Abstract Particulars

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:9: THE NATURE OF UNIVERSALS AND PROPOSITIONS G. F. STOUT THERE are various types or forms of unity which may all be regarded as partial phases of the unity of the universe. There is the unity of the complex of qualities qualifying the same thing or concrete individual. There is the unity of space and time or space-time. There is the teleological unity, exemplified in a living organism. And there are others which I need not enumerate. It is only with one of these that I am here directly concerned—the unity of a class or kind as including its members or instances. What I am going to mean by the term "universal" is either this unity itself, if it is taken as ultimate, or if it is not taken as ultimate, whatever principle is supposed to account for it. I mean what Mr. Bosanquet names the abstract universal in distinction from other forms of unity which he names concrete

universals. The so-called abstract universal is, no doubt, when considered by itself, relatively superficial and shallow. None the less, it is vitally important, inasmuch as it is presupposed in all other forms of unity, so that without it there can be no thought. Hence the view taken of it by a philosopher essentially contributes to determine his whole philosophical position. I hold myself that the unity of a class or kind is quite ultimate, and that any attempt to analyse it leads to a vicious circle. But this is not the traditional view, and it is not the view taken by leading philosophers of the present day such as Mr. Bradley, Mr. Bosanquet, Mr. Bertrand Russell, Mr. M'Taggart, and Mr. W. E. Johnson in his recent admirable work on Logic. According to these writers, qualities and relations, as such, are universals. They are so inasmuch as the same relation may severally and separately relate distinct sets of terms, and the same qualities may be common to many distinct particular things. A plurality of particular things, sharing a common character, is a logical class, signified by a general term. The diverse particulars are the denotation, and the common character is the connotation of the general or distributive term applicable to each member of the class. Thus, the unity of a class or kind is regarded as derivative, not ultimate. It is constituted by the identity of some character, simple or complex, characterising the ____________________ From G. F. Stout, Studies in Philosophy and Psychology (London: Macmillan & Co., Ltd., 1930); reprinted by permission of the publisher.

things denoted by the general name. The identity of the character is interpreted strictly and literally. There is no plurality of particular things. The common quality is regarded as indivisibly single. Two billiard balls are both round and smooth. So far as they are both round, the roundness of the one is the roundness of the other, and so far as they are both smooth, the smoothness of the one is the smoothness of the other. Abstract nouns, as standing for the quality in its singleness, without reference to any multiplicity of things qualified by it, are thus regarded as singular terms, like proper names. If we ask how, for example, shape can be identical both in square things and round things, the best answer is that of Mr. Johnson, who distinguishes between indeterminate and determinate characters. Shape is a single indeterminate character capable of being variously determined as square, round, or triangular. Similarly for relations. My nose is above my chin, and Smith's nose is above Smith's chin. His nose is distinct from mine, and the same is true of our chins. But there is the single identical relation of "above and below" which relates both my nose to my chin and his nose to his chin. The question whether relations are or are not characters predicable of things is not here relevant. In order, however, to explain my language in what follows, I may say that I hold them to be predicable characters. I agree entirely with Mr. Johnson's treatment of the question in his chapter on Relations. "My nose is above my chin" means "my nose is to my chin as above to below, the nose being above and the chin below." This whole doctrine which I have roughly outlined, of the singleness of characters, whether qualities or relations, seems to me fundamentally wrong. A character characterising a concrete thing or individual is as particular as the thing or individual which it characterises. Of two billiard balls, each has its own particular roundness separate and distinct from that of the other, just as the billiard balls themselves are distinct and separate. As Jones is separate and distinct from Robinson, so the particular happiness of Jones is separate and distinct from that of Robinson. What then do we mean when we say, for instance, that roundness is a character common to all billiard balls? I answer that the phrase "common character" is elliptical. It really signifies a certain general kind or class of characters. To say that particular things share in the common character is to say that each of them has a character which is a particular instance of this kind or class of characters. The particular instances are distributed amongst the particular things and so shared by them. It is true that the term "class" tends in ordinary usage to be applied to classes of things, whereas such words as "kind" or "sort" are naturally applied also to qualities and relations. My point is that these terms all express the same ultimate form of unity, the distributive unity which comprehends what are for that reason called members of a class, instances or examples of a sort or kind. To define a general term exclusively by reference to classes of things, therefore, involves a vicious circle. There is no generality in substances which is not entirely derivative. It is wholly constituted by the generality of the adjectives which -154-

qualify them, and the generality of adjectives does not consist ultimately in possessing other common adjectives. Abstract nouns are, on my view, not singular but general terms. Shape, for example, stands for "all shapes as such," and squareness stands for all square shapes as such. On the other hand, the shape of the table at which I am now writing is a singular term. Abstract nouns supply the appropriate verbal form for naming qualities and relations when they are to be themselves characterised by other qualities and relations, as when we say that "human happiness is transient." Adjectives and verbs supply the appropriate verbal form for attributing characters to things. The statement found in some text-books of Logic that adjectives are not names of qualities but of the things they qualify is, of course, nonsense. The position that characters are as particular as the concrete things or individuals which they characterise is common to me and the nominalists. But I differ from them essentially in maintaining that the distributive unity of a class or kind is an ultimate and unanalysable type of unity. The nominalists, on the contrary, say that it can be explained through the relation of resemblance. This view seems to me entirely indefensible. Distributive unity is signified by such words as "all," "every," "any," "some," and the indefinite article. Can the meaning of these words be stated adequately in terms of resemblance? This is plainly impossible. Consider the example "all triangles." It may be said that this means all shapes that resemble each other in a certain respect. But such formulas presuppose that the word "all" has a

meaning of its own that cannot be reduced to relations of similarity. It is precisely the concept of distributive unity which remains unexplained. The nominalist entirely fails to show how we can think of a class or kind as a whole without setting out before our mind each one of its members or instances so as to discern relations of similarity between them. Yet he cannot help tacitly assuming that this is not required for our apprehension of the class as a whole. Berkeley, for example, says that we take a given particular triangle as representing all other figures which resemble it in a certain respect. But this is nonsense unless we can think of all the other figures as one total object without severally apprehending each of them or indeed any one of them. What again is meant by resemblance in a certain respect? In what respect must figures resemble each other to be classed as triangles? Shall we say "by being enclosed by three lines"? The answer is a good one if we suppose that three-sidedness is a single quality indivisibly present in the plurality of things which it qualifies. But nominalism is based on a denial of this position. Hence in the mouth of the nominalist the answer can only mean that the figures must resemble each other inasmuch as they are all triangles—inasmuch as they are all members of the class "triangular figures." This is plainly a vicious circle, when what requires to be explained is precisely the meaning of the words "class" or "kind." How then, it may be asked, are relations of resemblance connected with -155-

the distributive unity of a class or kind? My own view is briefly as follows. A relation considered as subsisting between terms presupposes some complex unity within which both the terms and relations fall. This complex unity is the fundamentum relationis. For example, a relation of "above and below" as subsisting between a and b presupposes a spatial complex including both a and b and the spatial relation between them. In like manner, resemblance presupposes a complex unity of the peculiar type which I call the distributive unity of a class. The same holds for dissimilarity so far as this admits of degrees, as between colours, and does not amount to disparity which makes comparison impossible, as between colours and sounds. The unity of the complex as a whole ought not to be confused with relations between terms. Thus the resemblance is always between members of a class of things or particular instances of a kind of quality. The unity of the class or kind as a whole is not a relation at all. It is what, with Mr. Johnson's permission, I should like to call a "tie"—a fundamentum relationis. Agreeing with the nominalist that characters are as particular as the things or substances they characterise, the inference I draw from this thesis is not that there really are no universals, but that the universal is a distributive unity. I have now to defend this thesis and consider some of its implications. It will be convenient to begin with characters which consist in transient states, acts, or processes, e.g. a sneeze, the flight of a bird, the explosion of a mine. These are so obviously particular that they present a special difficulty for those who hold that qualities and relations are, as such, universals. The difficulty is so pressing that it has driven more than one recent writer to assert that transient states or acts are substances, not characters of substances. Mr. M'Taggart, for example, after defining a substance as that which has qualities or relations but is not itself a quality or relation, writes as follows (Nature of Existence, p. 73): "A sneeze would not usually be called a substance, nor would a party at whist, nor all red-haired archdeacons. But each of the three complies with our definition, since each of them has qualities and each is related without being a quality or relation." Mr. M'Taggart's definition is defective. If we are not to ignore a fundamental and relevant distinction we must add to it that a substance must be a particular existence and not a universal. This excludes the red-haired archdeacons. We may pass the whist party, considered as a group of men sitting at a table and playing a game. A sneeze is certainly particular. But it is equally certain that it is not a substance, even according to M'Taggart's definition. It may indeed have characters predicated of it: it may be violent and inconvenient. But it is also a character predicable of something else, the particular man who sneezes. It has its being only in its concrescence with the other qualities and relations of the concrete individual while he is sneezing. The sneeze cannot continue to exist in however altered a form apart from the sneezer, as a hand or eye may when severed from the body.

We may then assume that at least a large and important group of characters are as particular as the substances which they characterise. Is this true -156-

of all qualities and relations? It must be so, because there is no distinction of substances as separate particulars which does not involve a corresponding distinction of their characters as separate particulars. I apprehend two billiard balls as separate substances, inasmuch as each is taken to be in a separate place. One is here and the other there on the surface of the billiard table. How can I know or suppose this unless I know or suppose that the roundness, smoothness, and whiteness of the one ball is locally separate from the roundness, smoothness, and whiteness of the other, and that the relation of contact between the one ball and the cloth is locally separate from the contact between the other ball and the cloth? It has been objected that what is really the same indivisible quality may none the less appear separately in different times and places. There is here, I think, a serious confusion between two senses of the word "appear." We say that something may appear to be what it is not. So used, appearing is synonymous with seeming. But we also say not that something appears (i.e. seems) to exist, or to be this or that, but simply that it appears, meaning that it is an actual apparition, that it is actually presented or given in experience. In this sense, nothing can really appear except what really is, and really is as it appears. I may, in double vision, have two images of a single candle flame. There then appear or seem to be two candle flames, whereas in fact there is only one. But the visual presentations do not merely seem to exist and be separate. Both they and their separation really appear, are really presented or given, and must therefore really exist. It is only because the images really exist and are really separate that there appear or seem to be two flames. Now, when it is said that, for instance, the brightness of one light appears separately from the brightness of another, what is meant is simple appearance and not seeming. This must be so, because the separate appearance is taken as explaining how the qualities may seem to be separate though they are not, just as the double image explains why the single candle flame seems to be double. But the explanation refutes itself. If the qualities of separate things really appear separately, and if their separateness really appears, then they really are separate, and do not merely seem to be so. I may restate my general argument in another way. Whatever view may be held of the distinction of a substance from its qualities, it is almost universally admitted that the substance is nothing apart from its qualities. Mr. M'Taggart makes this proposition on the basis of an argument to show that substances cannot be diverse without being in some respect dissimilar. In this he may be right. But the same principle seems also to lead to a conclusion which he would reject, that qualities are distinct particulars, just as substances are. If substance is nothing apart from its qualities, to know the substance without knowing its qualities is to know nothing. It follows that we cannot distinguish substances from each other without discerning a corresponding distinction between their qualities. It follows also that if the distinction of the substances is not preconditioned by any discernible dissimilarity between their qualities, the qualities must be primarily known -157-

as separate particulars, not as universals. The universals will be involved only inasmuch as the qualities are particulars of the same general sort or kind. Now in looking, let us say, at a sheet of white paper, I am able to discern the several parts of the paper without discerning qualitative unlikeness between each part and every one of the others. Even if I am aware of qualitative unlikeness between one part and some other part I can clearly recognise that this is not the primary ground of the distinction between them. Whether I suppose the unlikeness to be great or almost imperceptible or quite absent, diversity is still discernible. Indeed if it were not presupposed, there could be no question of likeness or unlikeness. Nor can we say that each part is distinguishable by its distinctive relations to other parts. For in order that one particular may be known as related in the required way to other particulars, it

is a logical precondition that it shall itself be known as one particular among others. In this argument I have assumed that a thing is nothing apart from its characters, and that therefore there can be no knowledge of it which is not knowledge of its characters. But Mr. Bertrand Russell and, I believe, Mr. Moore reverse this reasoning. According to them, knowledge of a thing as in any way characterised is only knowledge about it, and presupposes a logically prior and independent knowledge of the things themselves, which they call acquaintance. Hence they would argue that inasmuch as things can be known independently of any knowledge of their characters, it cannot be true, as I have assumed, that they are nothing apart from their characters. Mere acquaintance with a thing is supposed to involve no apprehension of anything which could possibly be predicated of it. What is known in this way cannot be expressed in words. I am acquainted with a colour presentation while it is being presented, and with a toothache while I am feeling it. If, however, I am aware of the toothache as being painful or intense, or as felt, or as existing, or as mine, or as beginning, persisting, or ceasing, or as in any way distinct from or connected with anything else, or even as being "something or other," such awareness is knowledge about the toothache and not merely acquaintance with it. Acquaintaince with the toothache consists in the fact that it is felt, not in knowledge of this or any other fact. Acquaintance with a colour presentation consists in the fact that it is presented, not in knowledge of this fact or of any other. I do not at all doubt that what is here called acquaintance really exists. Without it there can be no knowledge; for if we were not acquainted with some things we could not know anything. It is what I have called actual appearance as distinguished from seeming. It constitutes the radical meaning of the word "experience" which gives distinctive significance to all its other applications. It is what, following Mr. Bradley, I have been accustomed to call immediate experience. But it cannot, I think, be properly regarded as knowledge. It is true that I can know about a toothache while I am actually experiencing it, as I cannot know about it while I am not experiencing it. And we may perhaps call this way of knowing, knowledge by acquaintance. Still, the knowledge -158-

is only knowledge about, and is distinct from the acquaintance which conditions it. How, indeed, can we know anything, if it is supposed that we know absolutely nothing about it? Let us, however, for the sake of argument, concede that acquaintance, as such, is knowledge. There is still no ground for regarding it as a knowledge merely of things, apart from their qualities and relations. It is true, indeed, that we do not know about the qualities and relations when we are merely acquainted with them. We do not know that they exist or what they are. We do not distinguish them from each other or from the things they characterise. If reasons of this sort prove that we do not know the qualities, they prove equally that we do not know the thing qualified. For in mere acquaintance, we do not know that the thing exists or what it is: we do not distinguish it from other things or from its qualities. If we can know the thing in this blind way, then in the same blind way we can know its characters. If we inquire what in mere acquaintance we are acquainted with, mere acquaintance itself, being blind and dumb, can supply no answer. The answer must be sought in analytic judgements which involve knowledge about. But these judgements never reveal a mere thing apart from its characters, but always the thing as in some way characterised. Both for mere acquaintance with things and for knowledge about them the principle holds good that a substance, being nothing apart from its adjectives, cannot be known apart from them. At this point we are confronted by the ultimate question, What is the distinction between a substance on the one hand, and its qualities and relations on the other? To me only one view appears tenable. A substance is a complex unity of an altogether ultimate and peculiar type, including within it all characters truly predicable of it. To be truly predicable of it is to be contained within it. The distinctive unity of such a complex is concreteness. Characters of concrete things are particular, but not concrete. What is concrete is the whole in which they coalesce with each other. This view of substance as a complex unity, when coupled with the doctrine that qualities and relations are universals, leads naturally, if not inevitably, to the denial of an ultimate plurality of substances. This is the line of thought which we find in Mr. Bradley and Mr. Bosanquet. Reality must be concrete and individual; the individual

cannot be constituted by any mere union of universals. Yet if we inquire what so-called finite individuals are, we find nothing but qualities and relations, which, as such, are taken to be universals. Hence, the true individual transcends the grasp of finite thought. There can be only one substance, the absolute and individual whole of being; all finite existences including finite selves are merely adjectives of this. If taken as ultimate they are mere appearances. On the other hand, those who maintain that there is an ultimate plurality of substances, and yet hold that characters are, as such, universals, seem logically bound to deny that a substance is the complex unity of all its qualities and relations. Thus Mr. M'Taggart, who occupies this position, asserts in his Nature of Existence, ch. v., that the complex unity is itself only a complex -159-

adjective, and therefore presupposes a subject ultimately distinct from itself. I have elsewhere criticised this view on the ground that it makes the whole being of substance consist in its relatedness to something else, to the characters which characterise it. Mr. M'Taggart now replies that when, for instance, "Smith is said to be happy," the fact that he is happy is the primary fact, and the fact that he is related to the quality of happiness is only derivative (p. 70). But this leaves my difficulty untouched. What Mr. M'Taggart calls the primary fact, the happy Smith, is, according to him, a complex containing two existences ultimately quite distinct from each other, the substance, on the one hand, and, on the other, all characters predicable of it. But two distinct existences within a complex can only be connected by a relation; and the relation in this case can be no other than what is directly expressed in such propositions as "Smith is happy." Mr. M'Taggart also directly attacks the alternative view that the substance is the complex unity comprehending what for that reason are called its characters. Unfortunately his argument starts with a misunderstanding. "It has," he says, "been maintained that we shall, if we take the right view, be able to dispense with the conception of substance and use only the conception of qualities." 1 This is certainly not what I take to be the right view. For me, the concrete complex containing all the characters of a thing is not a character but the thing itself. To say that the inclusive complex must itself be a predicable character, is like saying that a triangle must be the side of a triangle, that the class "horses" must be a horse. What remains of Mr. M'Taggart's argument, after we have allowed for such misunderstanding, amounts only to this, that a proposition such as "Smith is happy" cannot, without absurdity, be formulated in the language of my theory. We cannot, he urges, assert of the complex comprising all characters predicable of Smith that this complex is happy. We cannot. But this rendering of "Smith is happy" is not mine. Mine would rather be: "The concrete unity including the character of being known by the name of Smith also includes the character of being happy." This, I take it, is precisely what is meant by asserting that Smith is happy. The formula given by M'Taggart itself needs to be translated in terms of my theory. So translated it would run: "The complex including all the characters of Smith includes, besides these, another character of Smith, that of being happy." This is nonsense. But in my view there is no reason why it should be sense. There still remains one question which I have not yet considered, though it is of vital importance to my general argument. If I am right, what is meant by a character common to a class of things is a general kind of character of which a particular instance characterises each member of the class. It follows that the logical division of a wider class into mutually exclusive subclasses according to the same fundamentum divisionis is possible only through a corresponding division of a wider class of characters into subclasses of characters. This view is, of course, quite incompatible with the position of those ____________________ 1The Nature of Existence, p. 66. -160-

who regard a common character as a single quality or relation indivisibly belonging to each and all of the things it characterises. Have they any alternative explanation? I know of no other than that which is offered in Vol. i, ch. xi. of Mr. Johnson's Logic, on "The Determinable." Mr. Johnson begins by comparing the propositions "Red is a colour" and "Plato is a man." He inquires whether Red is asserted to be a member of a class called "colours," as Plato is asserted to be a member of the class "men." He simply takes for granted without discussion that redness at any rate, if not colour, is a singular term, standing for a single quality and not for a general kind of qualities. He thus, from my point of view, partially begs the question at issue from the outset. In his way of dealing even with the problem as he himself formulates it, there seems to be a similar petitio principii. He decides that "colours" does not stand for a class of which redness is a member. The sole reason which he gives is that whereas Plato, for example, is recognised as a man through the quality of humanity common to him and other men, it is not true that red is recognised as a colour through a quality distinct from itself and common to it and other colours such as blue and yellow. But this is merely to assert, what is in any case evident, that inasmuch as substances are not qualities, classes of substances are not classes of qualities. On any view, the division of substances into classes is in some way dependent on a corresponding distinction between their adjectives. It presupposes that, in some sense, a plurality of things share in a common character. The only question is, what is meant by their sharing in a common character? I take this to mean that each is characterised by a particular instance of a general kind or class of characters. We may if we choose apply the term class exclusively to general kinds of substances. But the real question is whether the words "kind" and "class" stand for the same ultimate type of distributive unity, which is found in substances only because it is found in their characters, and cannot therefore be ultimately different for substances and for characters. This is not Mr. Johnson's view. Does he offer any tenable alternative? Instead of the distinction between general and particular, and between more and less general, he would in dealing with characters substitute the distinction of the determinable and the completely or relatively determinate. "To predicate colour or shape of an object," he says, "obviously characterises it less determinately than to predicate of it red or circular; hence the former adjectives may be said negatively to be indeterminate as compared with the latter." 2 There is certainly a sense in which this distinction is valid and useful. If I know or consider merely the fact that something is a colour, this does not determine what special sort of colour it is. This is determined only by further propositions in which it is asserted to be red or to be blue. So understood, the distinction is relative to the knowing mind. It is what Mr. Johnson calls "epistemic." 3 In this sense I am myself prepared to use the terms determinable and determinate. But in this sense the distinction is applicable to sub____________________ 2Logic, Vol. i, p. 174. 3The proper form is "epistemonic," but the barbarism is convenient. -161-

stances as well as adjectives. If I consider something merely as being an animal, this leaves undetermined the question whether it is a mouse or a man. Mr. Johnson, of course, means far more than this. For him the relation of determinable is constitutive, not merely epistemonic. It is a relation between qualities as such; and for qualities it takes the place of the distinction between degrees of generality which is supposed to hold only for substances. According to Johnson, colour is not a general kind of quality comprising redness as a sub-kind. On the contrary, colour and redness are both singular, each standing for a single positive quality. Colour, he tells us, though negatively it may be said to be indeterminate, "is, metaphorically speaking, that from which the specific determinates, red, yellow, green, etc., emanate; while from shape emanate another completely different series of determinates such as triangular, square, octagonal, etc. Thus our idea of this or that determinable has a distinctly positive content, which would be quite inadequately represented by the word 'indeterminate.' " 4 On this view the proposition "red is a colour" means that a single positive quality red is related to another positive quality

colour by a peculiar relation appropriately named that of a determinate to its determinable. Now it seems to me that Mr. Johnson has not only failed to show that there is such a relation, but that he has also, in the course of his argument, suggested a cogent reason for denying it. He points out very clearly that red is not recognised as a colour through any quality distinct from itself and shared in common by it and all colours, as redness is shared by all red things. As he puts it, "the several colours... are given the same name colour, not on the ground of any partial agreement, but on the ground of the special kind of difference which distinguishes one colour from another." 5 I would add that there is a peculiar kind of resemblance as well as of difference. The point is that red and yellow do not resemble each other in one character and differ in another. The respect in which they are alike, i.e. colour, is also the respect in which they are dissimilar. The same holds for squareness and roundness. As the late Professor Cook Wilson used to say, "square shape is not squareness plus shape; squareness itself is a special way of being a shape." Are considerations of this sort inconsistent with my view that "redness" is a subclass of the more general class "colour" as "red things" is a subclass of "coloured things"? There would be an inconsistency only if it could be shown that a red thing is distinguished from a yellow thing not merely by its colour but by some other character. But, as Mr. Johnson himself expressly points out, this is not so. In the logical division of a class of things into subclasses, the fundamentum divisionis is always a determinable adjective predicated of every member of the class divided; and the subclasses are always distinguished by determinates of this determinable. It is true, indeed, that a concrete thing is, or implies, the concrete union of many characters which are not related to each other as determinable and determinate. Hence it is possible to select ____________________ 4Logic, Vol. i, pp. 174-5. 5Logic, Vol. i, p. 176. -162-

this or that indeterminate adjective, simple or complex, as a basis of division. Thus we divide books according to their size or according to their binding. But a subclass is never distinguished by the presence or absence of a fresh adjective which is not indeterminately applicable to all members of the wider class. When we divide books into bound or unbound, the fundamentum is the status of books as regards binding; the term unbound has a positive meaning as applied to books which it would not have if applied to coals or candles. There is nothing in these statements which is not fully accounted for if we suppose that the distinction of general and particular and of degrees of generality in things is constituted by, and therefore presupposes, a precisely corresponding distinction of general and particular, and of degrees of generality, in adjectives. On the other hand, Mr. Johnson's view is not really self-consistent. Assuming as he does that redness is a singular term, and denying that colour is a class including redness as a member, he is bound to regard colour also as a singular term. As such it can only stand for a single quality, just as redness stands for a single quality. What, then, can be meant by saying that red, green, or blue are colours? What is asserted cannot be that each is identical with colour. For they would, then, be identical with each other. We seem compelled to say that redness is in part identical with colour and in part different. It must be a complex including the indeterminate quality colour which is equally present in blue and green, and also a determining quality which distinguishes it from blue and green. But, as Mr. Johnson has himself shown, this is untrue. There is no determining quality which makes the determinable determinate. We must, therefore, give up the initial assumption that redness and colour are singular terms. They are both general, i.e. distributive terms. Redness, considered as a completely determinate general term, stands for the distributive unity of particular reds. To be a particular red is to be either this, that, or the other particular instance of redness. Redness in general is comprised within a more comprehensive unity called "colour in general," which also comprises yellowness and blueness. Every particular instance of redness is a particular instance of colour. Colour in general is nothing but the distributive unity of its specific subkinds, just as these are ultimately the distributive unity of their particular instances. To be a particular colour is to be a particular example either of this, that, or the other special kind

of colour. The words "either, or" mark the distributive tie, and exclude the conception of colour as a single though indeterminate quality. The distinction of the determinable and its determinates, though it presupposes generality, has none the less, as I said before, its own place and value if we regard it not as constitutive but epistemonic. In particular it is important in considering the nature of propositions. I have included this topic in my title. But I have left myself so little time, that I must be content with a brief indication of what I intended to say about it. A proposition, whatever else it may be, is something proposed or set before the mind as the object of certain subjective processes—questioning, doubting, -163-

asserting, supposing, and also practical deliberation and decision. Belief and will do not necessarily consist in such processes. I may be aware of myself as sitting at a table and writing, without mentally asserting that this is so, and without at all questioning whether it is so or not. There is knowledge about things without any explicit mental act of judging. Similarly, I may voluntarily shake hands with a friend without any thought of doing otherwise, and therefore without choosing or deciding to shake hands. What is thus taken for granted constitutes a vast and vague background from which propositions emerge here and there. Nothing takes shape as a proposition, either theoretical or practical, unless it is in some way suggested, however transiently, that from some general point of view it may or might be otherwise. If the thought of its being otherwise is prolonged, there is questioning or practical hesitation. If it is still further prolonged, and developed in detail, there is doubt or deliberation. Thus we may say that a proposition is apprehended as a possible alternative. What then is an alternative? There are two meanings of the word, distinct though inseparable. In one sense an alternative is such only relatively to the variable knowledge and interest of the individual. But this presupposes that the objective universe is so constituted as to present alternatives to the knowing and willing mind. Their existence is ultimately implied in the existence of general classes or kinds, of generalities as the distributive unity of particular instances and subclasses. To have shape is to have this, that, or the other special sort of shape. This holds good whether or not some one knows which special shape the thing in fact has. Even when the thing is known or believed to be square it is still true that it is either square or round or octagonal or so forth. But a mind interested in the specific shape, and already knowing it to be square, need not and does not concern itself with the existence of other alternatives, unless one is suggested, for example, by the words or behaviour of other persons. Otherwise the proposition that the thing is square will not be asserted at all as a separate proposition. In mere supposition, the mind attends to the nature and implications of an alternative as such, ignoring, either provisionally or entirely, the question whether it is realised or to be realised. Consider the following. "If I get this post I shall have no time for research work." "If I had been appointed to that post, I should have had no time for research work." "If there had been no carbon there would have been no organic life." "If there were no incompatible qualities, the logical law of contradiction would have no application." These are all statements that one possibility A is so connected with another possibility B that the realisation of A implies also the realisation of B. This is what "if" means. Such propositions rarely occur where the alternative A is already known or fully believed to be realised, or where it has already been practically decided that it shall be realised. On the contrary, they occur frequently where it is known that the alternative is not, and is not to be, realised. They are then called fictions. This view implies that there really are alternative possibilities. Now, in the most natural and common use of language the real and possible are correlated -164-

and opposed in such wise that it is as absurd to say that the possible qua possible is real, as it is to say that what is above is, as such, below. None the less, possibilities as such are not mere inventions of the understanding, or mere appearances. They really exist. Their

existence is not merely possible. When a man has to choose between death and apostasy, these alternatives are really contained in the general situation with which he is confronted. But only one of them is realised. Which of them it shall be depends on the man himself. Only determinism gone mad could deny that, to this extent, there is free-will. The meaning of the adjectives "true" and "false," in their ordinary use, presupposes the conception of the proposition as an alternative. Alternatives are such only in relation to some real fact. One of them, and not more than one, is identical with the real fact. A proposition is true when it is identical with the realised alternative. To assert, deny, doubt, or suppose that this alternative is realised, is to assert, deny, doubt, or suppose what is true. The unrealised alternatives are false propositions. Of course the distinction between truth and falsity holds also for the inarticulate domain of what is merely taken for granted. But it is only so far as alternatives are apprehended as such, i.e. as propositions, that we become aware of the distinction: then only can we consider and examine competing claims to truth. Even at this stage our assertions, denials, and doubts are, on the most important matters, conditioned and controlled by a vast background of what is merely taken for granted. If in this background there is anything which is incapable, from any point of view, of being apprehended as an alternative, then, though it may be transcendently important, we can never be aware of it as a proposition so as to express it in language and discuss it. A word in conclusion on the metaphysical bearings of the logical doctrine of universals. I have already indicated how the philosophy of those who maintain the unity of the universe is affected by the view that universals are qualities and relations. But it plays an equally important part with Mr. Russell, for whom there is no universe, but only an indefinite aggregate of disjointed items, each conceivably capable of existing by itself. As an integral part of this theory, he disjoins particulars and universals as two intrinsically independent realms of existence. He finds it possible to do this because, for him, qualities and relations are, as such, universals. Inasmuch as they are universals, they cannot in any way form part of the being of the particular things which they qualify or relate. On the other hand, inasmuch as they are qualities and relations, they cannot contain the particular things. Characters cannot contain what they characterise. It follows that the domain of concrete things and individuals in its own intrinsic being falls entirely apart from the domain of universals in their intrinsic being. From this point of view, we can understand Mr. Russell's distinction between acquaintance with things and knowledge about them, and his still more perplexing distinction between knowledge about and knowledge by description. Plainly, the nature of general and abstract ideas is a topic which has the -165-

same philosophical importance now that it had for Berkeley; and however defective his treatment of it was, some things which he said deserve to be repeated even now—though with a difference. -166-

: 10 : ARE THE CHARACTERISTICS OF PARTICULAR THINGS UNIVERSAL OR PARTICULAR? G. E. MOORE AND G. F. STOUT

Part One by G. E. Moore I understand that the object of this Symposium is to discuss a view advocated by Professor Stout in his Hertz Lecture to the British Academy on "The Nature of Universals and

Propositions." 1 He there advocates some view, which he seems to think can be properly expressed by the words: "Every character which characterizes either a concrete thing or a concrete individual is particular and not universal." And I understand that what we are wanted to do is to discuss the view which he expresses by those words. We are not to give to the words the sense or senses which we may think they ought to bear, and then to discuss whether the view or views they would then express is true or false. What we have to do is to try to discover what Professor Stout means by them, and then merely to discuss whether the view which he uses them to express is true or false, even though we may think that the view in question is one which cannot be properly expressed by them at all. Now I confess that I think it extremely difficult to be sure what Professor Stout does mean by those words. All that I can do, therefore, is to try to state as clearly as possible the only views which, so far as I can see, he might mean by them, and to discuss whether those are true or false. It is, of course, possible that I may have overlooked just the view which is what he really does mean; but, if so, I hope that what I shall say will at least have the use of making it easier for him to point out to us what he does mean. There are two main points as to which I feel doubt. The first is as to what precisely he means by the expression "is particular" (or "is a particular"; for he sometimes uses this latter expression also as equivalent to the former) in the sentence, "Every character which characterizes a concrete thing is par____________________ Reprinted from the Proceedings of The Aristotelian Society, Supplementary Volume III (1923), by courtesy of the Editor of The Aristotelian Society. Copyright © 1912, The Aristotelian Society. 1Proceedings of the British Academy, Vol. X, 1921-22. [Reprinted in this volume. —ED]

ticular." And the second is as to how, precisely, he uses the term "character." As regards the first point, I feel no doubt whatever that part, at least, of what he means by "is particular" is "characterizes one thing only." Part, at least, of what he means to assert with regard to every entity of which it can be truly said that it is "a character of a concrete thing," in the sense (whatever it may be) in which he is using the term "character," is, quite clearly, that every such entity characterizes one thing only; or (what is equivalent to this) that no such entity characterizes more than one thing—no such entity is a "common character" of two or more things. This notion, of characterizing one thing only, seems to me to be a perfectly clear conception; and hence, if only we can discover what Professor Stout means by "characters," we shall have one perfectly clear proposition, which is certainly part at least of what he means to assert, and which we can discuss. My only doubt is as to whether "characterizes one thing only" can be all that he means by "is particular" or "is a particular." But here I have to confess that, if Professor Stout does mean anything else, I have not been able to form the faintest notion of what else he does mean. I shall, therefore, have to content myself with discussing, with regard to certain classes of entities, whether it is or is not true of them that every such entity characterizes one thing only, although I recognize that this is probably only a part of what Professor Stout means to assert. It seems to me, I may explain, a wholly indefensible misuse of language, to use the expressions "is particular" or "is a particular" in such a way that the proposition "P is particular" or "P is a particular" implies "P characterizes one thing only." None of the various senses in which "is particular" can be properly used seems to me to carry with them this implication. But I think there is no doubt that Professor Stout is using them in some sense which does carry this implication; and, as I have said, I understand that we are to discuss only views which he does mean, and not views which we may think his words ought to mean. But there is one meaning which might be attached to the expressions "is particular" or "is a particular," with regard to which I think it is very important to point out that Professor Stout cannot, consistently with statements of his own, be using the expressions with that meaning. In the formulation of our question the phrase "particular things" is apparently used as a synonym for the phrase "concrete things," and Professor Stout himself so uses it. And I think that undoubtedly one correct usage of "is particular" or "is a particular" is as a

synonym for "is a particular thing" or "is a concrete thing." If Professor Stout were using the expressions in this sense, his statement "Every character of a concrete thing is particular" would, of course, mean the same as "Every character of a concrete thing is itself a concrete thing." And it might perhaps be thought that this is what he does mean. But he certainly cannot consistently mean this; since he declares that a sneeze certainly is "particular," while he implies that nevertheless it is not a "substance"—the expression "is a substance" being one which he uses throughout as equivalent to -168-

"is a concrete thing or individual." He implies, therefore, that a sneeze, while it is "particular" in the sense (whatever that may be) in which he maintains that all "characters" of concrete things are "particular," is not itself a "concrete thing." And in the same passage he employs a useful mark for distinguishing "characters" from "concrete things" or "concrete individuals." Nothing, he implies, can be a "character," unless it is predicable of something else; and nothing can be a "concrete thing" or "concrete individual" or "substance" if it is predicable of something else; from which it would again follow that, according to him, no character can be "particular" in the sense of being a concrete thing. It seems to me that the notion of being predicable of something else is a clear one, and that it is undoubtedly in accordance with usage to confine the term "character" to what is predicable of something else, and the terms "concrete thing," "concrete individual" and "substance" to what is not. I should myself be inclined to use the term "is a character" as equivalent to "is predicable of something else"; so that not only would every "character" be predicable of something else, but everything that is predicable of anything else would be a "character": I fully recognize, however, that it is legitimate to use the term "character" in a more restricted sense, so that some only of the entities which are predicable of something else would be "characters." But that nothing can be properly called a "character" unless it is predicable of something else, I do agree with Professor Stout; and that is why, by the way, I wholly dissent from his proposition that a sneeze is a "character." I may say of a given individual A: "It was A that sneezed that sneeze"; and here the words "sneezed that sneeze" may, I think, express a "character," since they may express something which is predicable of A. But that the sneeze itself is predicable of anything whatever, I wholly deny. What we mean by "sneezed that sneeze" is not the same as what we mean by "that sneeze." The sneeze itself is, I should say, quite clearly an event; and every event is quite as incapable of being predicated of anything else, as is a concrete thing or concrete individual or substance. All events, including sneezes and flashes of lightning, are, I should agree with Mr. Johnson, what he calls "substantives proper"—a category which excludes their being "characters," for the very reason that no "substantive proper" is predicable of anything else. But though all events are "substantives proper," it appears to me, as I gather it does to Mr. Johnson, a mere misuse of language to call events, as Dr. McTaggart does, "substances." When he asserted that Mr. Johnson says that a flash of lightning is a substance, Professor Stout must, I suppose, have been assuming that Mr. Johnson would use the term "substance" as a synonym for "substantive proper"; whereas, while Mr. Johnson does hold that a flash of lightning is not a "character," he also holds that it is not a "substance," since he recognizes a category of entities which he calls "occurrences," which, though they share with "substances" the characteristic that they are not predicable of anything, and are therefore not "characters," differ from "substances" in other respects. To return from this digression. The only meaning which I can see Professor Stout to be attaching to the expressions "is particular" or "is a particular" is -169-

the meaning "characterizes one thing only," and hence the only possible meanings of his sentence "Every character of a concrete thing or a concrete individual is particular," which I can discuss, will be meanings obtained by understanding "is particular" in this sense. But there remains the question: In what sense is he using the term "character?" The sentence "Every character of a concrete thing characterizes one thing only," would, I think, be naturally understood in a sense from which it would follow that, if A and B are two

different concrete things, then it cannot be true, e.g. both that A is round, and that B is round; both that A is red, and that B is red, etc. This is what would be naturally implied by saying that two concrete things never have a common character. But these propositions are obviously monstrously false, and I think it is quite plain that Professor Stout does not mean to assert that they are true. He is obviously willing to allow that, where "A" and "B" are names of two different concrete things, the expressions "A is round" and "B is round," may, nevertheless, each of them express a true proposition. But what, then, does he mean by saying that, if A and B are two different concrete things, every character which belongs to A belongs to A only, and every character which belongs to B, to B only? So far as I can see, there are only two possible alternatives as to his meaning. (1) He might possibly be meaning to say that, if, where "A" and "B" are names of two different concrete things, the expressions "A is round" and "B is round" both express true propositions, the sense in which "is round" is used in the one must be different from that in which it is used in the other. Or (2) he may be using the term "character" in a quite indefensibly restricted sense; so that, while admitting that what is predicated of A in a true proposition expressed by "A is round" may be exactly the same as what is predicated of B in a true proposition expressed by "B is round," he would maintain that what is, in such cases, predicated of both, cannot properly be called a "character." As regards (1), I think it is just possible that Professor Stout does mean to say this, because, in a former publication of his on the same subject 2 he has said something which seems to imply it. "When I assert," he there says, "that the sense-datum is red, I mean just that particular red with which I am immediately acquainted." This ought to mean, I take it, that if I have two different sense-data, one of which, A, presents to me a different particular shade, of red, R 1 , while the other, B, presents to me a different particular shade, R 2 , then what I should mean by the expression "is red," if I said of A "A is red," would be "A is characterized by R 1 ," while what I should mean by "is red," if I said of B "B is red," would be "B is characterized by R 2 ," and that, therefore, I should be using "is red," in the two cases, in different senses. But if Professor Stout does mean this, then I think what he means is obviously false. If I merely tell somebody that one of my sense-data is red, I am obviously not telling him what particular shade of red it is of. That is to say, I am not ____________________ 2Proceedings of The Aristotelian Society, 1914-15, p. 348. -170-

using "is red" as a name for the particular shade which it, in fact, presents to me. Suppose the shade in question is R 1 . I am not, as Professor Stout seems to imply, using "is red" as a name for R 1 . And what I am using it as a name for, is, I think, pretty obvious. I perceive with regard to R 1 that it has a certain character, P, which belongs also to the shade R 2 and to an immense number of other particular shades, and what I mean by "is red" is simply "has some character of the kind P." And what I am telling anybody, if I tell him, with regard to another sense-datum, B, which presents to me the shade R 2 , that it also is red, is precisely the same thing, namely, that B also "has some character of the kind P." It is true that how I know, in the case supposed, that the sense-datum A has some character of the kind P, and that the sense-datum B also has some character of the kind P, is because I know in the case of A that it has R 1 , and that R 1 has the character P, and in the case of B that it has R 2 , and that R 2 has the character P. But is it not obvious that this extra knowledge, which I, in fact, have with regard to A and B, namely, that A has the shade R 1 , and B the shade R 2 , forms no part of what I express by "A is red" or by "B is red"? The opposite view that what I express by "is red" in the one case is "has R 1 ," and in the other "has R 2 ," and is therefore something different in the two cases, can, I think, be refuted by a reductio ad absurdum as follows. Suppose R 1 and R 2 are not only shades of red, but also shades of scarlet. I can then truly use the words "A and B are both scarlet" as well as the words "A and B are both red." But if what I meant by "A is red and B is red" were "A has R 1 and B has R 2 ," then obviously what I shall mean by "A is scarlet and B is scarlet" would also be "A has R 1 and B has R 2 ." That is to say, the view that what I mean by "A is red" is something different from what I mean by "B is red," namely, in the one case "A has R 1 " and in the other "A has R 2 ," involves the absurd consequence that what I mean by "A is scarlet" is the same as what I mean by "A is red." Quite obviously this consequence is absurd, and

therefore the view which entails it is false. I doubt whether Professor Stout would really disagree with what I have just been saying. On the contrary, my contention that what we do mean by "is red" is just "has some character of the kind P" is, I think, part (not the whole) of what he himself is asserting to be true and taking Mr. Johnson to deny, when he says that "colour" and "redness" are "general kinds of quality" and are not "both singular, each standing for a single positive quality." Part of what he means by this is, I think, just that what "A is red" stands for is merely something of the form "A has some character of the kind P," and what "A is coloured" stands for is merely something of the form "A has some character of the kind Q"; though this is not the whole, since he conjoins with this contention a further view, which I think certainly false, as to the analysis of propositions of the form "A has some character of the kind P." What I want to insist on is that the view that "A is red" is to be analysed in this way, so far from supporting, is definitely incompatible with the view that, when I truly say, of two different concrete things, A and B, both "A is red" and "B is red," what I express by "is red" in the one sentence must be different from -171-

what I express by "is red" in the other. On the contrary, the character for which I use "is red" as a name is, in each case, precisely the same, namely, "has some character of the kind P." It follows that the first of the two alternatives as to Professor Stout's meaning, which seemed to me to be the only possible ones, is such that, if he does mean what it would suppose him to mean, then what he means is certainly false. It is false that what we express by "is red" is something which cannot characterize more than one concrete thing. And since what we express by "is red" certainly is a character, in any legitimate sense of the term "character," Professor Stout's sentence, "Every character of a concrete thing characterizes only one thing," can only be true if he is using "character" in some quite improperly restricted sense. That he is doing this—that just as he means by "is particular" something which nobody ought to mean by "is particular," so he means by "Every character" something which nobody ought to mean by "Every character"—was the second alternative as to his meaning which I distinguished above. And we can now see, I think, what the unduly restricted sense in which he is using the term "character" is. He is using it in such a sense that no generic character such as those which are expressed by "is red," "is round," "is coloured," etc., is, in his terminology, a character at all. Of such generic characters it is perfectly obvious that they may characterize two or more concrete things; and we saw that Professor Stout does not seem really to wish to deny this. It remains that when he says "Every character," what he really means must be "Every absolutely specific character"; where by "absolutely specific" we mean the same as "not generic." In other words, he is talking, quite unjustifiably, as if absolutely specific characters could alone be properly called "characters." And the proposition he really wants to maintain is this: "Every absolutely specific character, which characterizes a concrete thing or individual, characterizes one thing only." This, so far as I can see, is the only proposition which Professor Stout's arguments, if sound, could have any tendency to show. And I will try first, briefly, to explain my own attitude towards it, and then to deal with his arguments. That it is certainly false I see no way of proving. But the contention that it is true can, I think, obviously only be justified by the contention that it must be true; since it is obviously impossible to justify it by comparing every concrete thing in turn with every other concrete thing, and seeing that every absolutely specific character which belongs to each does in fact belong to no other. Professor Stout, therefore, must be holding that we can see, a priori, that an absolutely specific character, which characterizes a concrete thing, must characterize one thing only, or cannot be a common character. And this proposition, I think, I can see to be certainly false. In the case of two sense- data, A and B, both of which appear to me to be red, I often cannot tell that the most specific shade of red which A presents to me is not exactly the same as the most specific shade which B presents to me. I also cannot tell that the

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most specific shade which A presents to me is not an absolutely specific shade. And I think I can see quite clearly that it is logically possible both that it is an absolutely specific shade, and that it does in fact characterize both A and B. While I allow, therefore, that it may, as a matter of fact, be true that the same absolutely specific shade never does in such cases characterize both A and B, I contend that Professor Stout cannot possibly have any good reason for saying that it is so; and that, if he holds that it must be so, he is certainly wrong. Let us now turn to Professor Stout's arguments in favour of his proposition. With the first argument, since it only professes to prove that some absolutely specific characters of concrete things "are particular," we need not trouble ourselves. I have already explained that I think it fails to prove even this, because what Professor Stout there takes to be "characters," namely, such entities as "a sneeze, the flight of a bird, the explosion of a mine," are, in my view, clearly not "characters" at all, but events or occurrences. But even if Professor Stout had proved that some absolutely specific characters of concrete things characterize one thing only, this would clearly by itself have no tendency to prove that the same is true of all. The arguments which concern us, therefore, are only those where Professor Stout expressly sets out to prove that "all qualities and relations" "are particulars." And, so far as I can make out, he has only two such arguments. The point of the first is this. Professor Stout urges that, in the case of any two perceived concrete things, which I "know or suppose" to be "locally separate," I must also "know or suppose" that the specific colour or shape, which the one presents to me, is also "locally separate" from that which the other presents to me. And I suppose he infers that if the specific colour of A is "known or supposed" to be "locally separate" from the specific colour of B, it cannot be identical with the specific colour of B. But this inference seems to me to be a mere mistake. I admit the premiss that if A is locally separate from B, and if A really has the colour which it presents to me, and B really has the colour which it presents to me, then the colour which A presents to me really is "locally separate" from that which B presents to me. But I deny that, even if this is so, it follows that the colour of A is not identical with the colour of B. Professor Stout's whole point seems to me to rest on supposing that there is no distinction between the sense in which two concrete things can be said to be "locally separate," and that in which two characters can be said to be so. Of local separation or mutual externality, in the sense in which we use this term of concrete things, it does seem to me to be self-evident (though this is sometimes disputed) that it is a relation which nothing can have to itself. In other words, I admit, as Professor Stout seems to assume, that it is impossible for one and the same concrete thing to be in two different places at the same time. But when we speak of two qualities as "locally separate" we seem to me to be using the phrase in an entirely different sense. All that we mean, or can mean, by it, is, I think, that the first belongs to a concrete thing which is locally separate (in our first -173-

sense) from a concrete thing to which the second belongs. And with this sense of "locally separate" from itself: one and the same quality can be in two different places at the same time. Indeed, to deny that it can be is simply to beg the original question at issue. For if to say "the specific colour of A is locally separate from the specific colour of B" merely means that the specific colour of A belongs to a concrete thing which is locally separate from a concrete thing to which the specific colour of B belongs, it follows that the specific colour of A can be "locally separate" from itself, provided only it is true that the specific colour of A can belong to each of two concrete things. This answer, if sound, is, so far as I can see, an absolutely complete answer to Professor Stout's first argument, and makes it unnecessary for me to examine the argument by which he tries to show that the "same indivisible quality cannot appear separately in different times

and places," unless it really is locally or temporally separate. For I maintain that the same indivisible quality can really be locally or temporally separate; maintaining that all this means is that it can really belong to both of two concrete things or events which are, in the fundamental sense appropriate to concrete things or events, locally or temporally separate. Professor Stout must be assuming that absolutely specific characters can really be "locally separate" in the same sense in which "concrete things" are so, and "temporally separate" in the same sense in which events are so; and that, as a matter of fact, in a case where A and B are two "locally separate" coloured concrete things, the absolutely specific colour of A must always, in that sense, be "locally separate" from the absolutely specific colour of B. I admit that, if this were so, it would follow that the absolutely specific colour of A cannot be identical with that of B. But I deny that any two characters can ever be "locally separate" in the sense in which two concrete things can be, or "temporally separate" in the sense in which two events can be. It is clear, with regard to his second argument, that he starts with some premiss (1) which he expresses by the words "A substance is nothing apart from its qualities"; that he infers from this premiss some proposition (2) which he expresses by the words "to know a substance without knowing its qualities is to know nothing"; and that from (2), in its turn, he states that there follows a proposition (3) which he expresses by the words "we cannot distinguish substances from each other without discerning a corresponding distinction between their qualities." It is clear also that it is only by the help of (3) that he professes, in this argument, to be able to reach the conclusion that every absolutely specific character of a concrete thing characterizes one thing only. What, precisely, then, does (3) assert? It is clear that, whatever Professor Stout may mean by "discerning a corresponding distinction between their qualities," he means something which we cannot do, unless there is "a corresponding distinction between their qualities." He is, therefore, here asserting at least this: that we cannot ever distinguish two concrete things unless there is "a corresponding distinction be -174-

tween their qualities." But what exactly does he mean by this? I take it that what he must mean is at least this: that we can never distinguish two concrete things, A and B, unless A has at least one quality which is not possessed by B, and B at least one quality which is not possessed by A. He may, of course, mean more than this: he may mean that every quality which is possessed by A must be a quality which is not possessed by B, and vice versa. But he must mean, at least, what I have said: that, if we can distinguish A and B, then A must have at least one quality not possessed by B, and B at least one not possessed by A. But, then, returning to the question what he means by "discerning a corresponding distinction between their qualities," I think it is clear that he must at least mean this further thing by (3): namely, that we cannot ever distinguish two concrete things, A and B, unless at least one quality, which we perceive to belong to A, is not possessed by B, and at least one, which we perceive to belong to B, is not possessed by A. For you certainly cannot be said to "discern a distinction" between two qualities, unless you perceive both of them. What I am in doubt about is whether he also means to assert or not this further thing: that we cannot distinguish between A and B, unless, with regard to at least one quality, which we perceive to belong to A, we perceive that it does not belong to B, and, with regard to at least one quality, which we perceive to belong to B, we perceive that it does not belong to A. I think very likely he does not mean to assert this. But it is on the question, whether he does or does not, that my attitude towards his proposition (3) depends. If he does, then I wish to maintain that his proposition (3) is false. If he does not, I only wish to maintain that it is a proposition which there is no reason whatever to believe. First, then, I wish to maintain: That I certainly do, in some cases, distinguish between two concrete things, A and B, without perceiving, with regard to any quality, which I perceive to belong to A, that it does not belong to B, or vice versa. But I want to emphasize that it is only of qualities, strictly so- called, as opposed to relational properties, that I wish to maintain this. That I can ever distinguish between two concrete things, A and B, without perceiving,

with regard to some relational property, which I perceive to belong to A, that it does not belong to B, I do not wish to assert. But I think it is clear that Professor Stout, if he is to prove his point, must maintain that his proposition (3) is true of qualities, strictly so-called, as opposed to relations; since his conclusion is that every absolutely specific character of a concrete thing, including, therefore, absolutely specific qualities, characterizes one thing only; and plainly this conclusion cannot be proved by any premiss which makes no assertion about qualities. This being understood, I should propose to prove my proposition by reference to cases of the very kind to which Professor Stout immediately goes on to refer. He insists (and I fully agree) that there are cases in which I can distinguish between two concrete things, A and B (as, for instance, when I distinguish between two different parts of a sheet of white paper), although -175-

I cannot perceive that A is qualitatively unlike B in any respect whatever— either in shape, or size, or colour. But to say that I cannot perceive A to be qualitatively unlike B in any respect whatever is, according to me, the same thing as to say that whatever quality I take, which A appears to me to possess, I cannot perceive that just that quality does not also belong to B, and that whatever quality I take, which B appears to me to possess, I cannot perceive that just that quality does not also belong to A. And if these two propositions are identical, then my proposition is proved. Does Professor Stout mean to dispute that they are identical? I cannot tell. But if he does, I think it is clear that his only ground for doing so must be that he is assuming the truth of the peculiar doctrine as to the relation between a concrete thing and its qualities. If that peculiar doctrine of his were true, it would, I think, really follow that where, in a case like that we are considering, I perceive that A is other than B, what I am doing is to perceive with regard to some quality or set of qualities P, and some other quality or set of qualities Q, that the "complex" to which P is related in a certain way is other than the "complex" to which Q is related in the same way. My perception that A is other than B would be identical with a perception, that the complex to which P has the relation in question is other than the complex to which Q has the same relation. I should, that is to say, be perceiving, ex hypothesi, that P had the relation in question to only one complex, and that Q had it also to only one complex, and that the one to which P had it was other than that to which Q had it; and, perceiving all this, I could hardly fail to perceive also that P had not got the relation in question to the complex to which Q had it, and vice versa; which would, ex hypothesi, be the same thing as perceiving that P did not belong to B, and that Q did not belong to A. If, therefore, this peculiar doctrine of Professor Stout's were true, it would, I think, really follow that I could not perceive A to be other than B, without perceiving, with regard to some quality which I perceived to belong to A, that it did not belong to B, and vice versa. But one reason why I think that that peculiar doctrine of his cannot be true, is just that it has this consequence. It seems to me quite plain (1) that I can distinguish an A from a B, where I cannot perceive A to be in any respect qualitatively unlike B, and (2) that this means that I can do it, without perceiving with regard to any quality, which I perceive to belong to A, that it does not belong to B, or vice versa. And, since, if Professor Stout's peculiar doctrine were true, it would follow that I couldn't, I infer that his doctrine is false. If, on the other hand, all that Professor Stout means to assert in his proposition (3) is that I cannot distinguish A from B, unless some quality which I perceive A to possess, does not in fact belong to B, and vice versa, then I have to confess I see no way of proving that he is wrong. All that I then maintain is that there is no reason whatever to suppose that he is right. For, so far as I can see, the only reason for supposing so would be, if, in every such case as I have been considering, I could perceive that some quality, which I perceived to belong to A, did not belong to B. This, for the reasons I have given, I think I cannot do. It remains, therefore, a bare possibility that though I -176-

cannot perceive that any quality, which I perceive to belong to A, does not belong to B, there may nevertheless really be some quality, which I perceive to belong to A, and which

does not belong to B. It seems to me, finally, that Professor Stout is in any case mistaken in supposing that his proposition (3) follows either from (1) or (2). I am perfectly willing to admit both (1) that a concrete thing must have some qualities; which is all that I take Professor Stout to mean by saying that it is nothing apart from its qualities, since he himself holds that it is certainly other than any one of its qualities or all of them put together. And also (2) that I never do, and even never can, perceive any concrete thing without its appearing to me to have some absolutely specific quality—that to say that I perceive it is the same thing as to say that there is some such quality which it appears to me to have; and I even think it quite likely that I never can perceive any concrete thing without perceiving it to have some absolutely specific quality. But none of these admissions seems to compel me to admit any probability whatever in favour of (3). So far as I can see, they have nothing whatever to do with (3), nor, therefore, with the question we were asked to discuss. It is true that, if we grant the premiss that I cannot perceive any concrete thing without perceiving, with regard to some absolutely specific quality, that it has that quality, it will follow that I cannot distinguish two concrete things, A and B, both of which I perceive, without perceiving, with regard to some absolutely specific quality, that A has it, and with regard to some absolutely specific quality, that B has it. But how can the premiss in question possibly prove any more than this? How can it prove that it is not possible that when I distinguish A from B, every absolutely specific quality which I perceive to belong to A should also be one which I perceive to belong to B, and vice versa? Our premiss only tells us that, in the case of every concrete thing which I perceive, there must be some absolutely specific quality which I perceive to belong to it, and cannot possibly, therefore, imply anything at all, as to whether, when I perceive two, it may or may not be the case that every absolutely specific quality which I perceive to belong to the one is also perceived by me to belong to the other. My answer to our question is, then: That if (as we must do, if we are to deal with any question raised by Professor Stout) we understand the expression "is particular" in some sense which logically implies "characterizes one thing only," then, quite certainly, many characters of concrete things are not particular; and that there is no reason to suppose that absolutely specific characters are any exception to the rule. As for the question whether any characters of concrete things do characterize one thing only, that will depend upon what is meant by "characters"; and it seems to me possible that there may be some legitimate sense of the term "character," such that, in that sense, none do—that all characters of concrete things are common characters. If, however, the term "character" is used in the wide sense in which whatever is truly predicable of anything is a character of it, then, in this sense, it is quite certain that many characters of -177-

concrete things do belong, each of them, to one thing only. If we use "character" in this sense, then, it is quite certain both that many characters of concrete things are common characters, and also that many are not. And if (as Professor Stout must be doing) we use the phrase "is a universal" in a sense which logically implies "is a common character," it follows of course, that, with the same wide sense of "character," we shall have to say that many characters of concrete things are universals, and many are not. It is, however, I think, worth emphasizing that there is one well-established usage of the expression "is a universal," which is such that, in a sense, every character without exception—characters which belong to only one thing, just as much as common characters—is quite certainly a universal: that sense, namely, in which "is a universal" is simply logically equivalent to "is either predicable of something or is a relation."

Part Two by G. F. Stout What do I mean by "is particular"? The word "particular" bears for me precisely the same sense when applied to predicable characters and to the things they characterize. Concrete things are diverse from each other in a way which cannot be resolved into difference of kind. They are numerically distinct, independently of their similarity or dissimilarity. 1 In just the same way I maintain that one quality or relation may be numerically diverse from another, though both are precisely of the same sort. The roundness of one billiard-ball may

belong to the same infima species of shape as that of another, and yet there may be two shapes and not one shape. Hence I call the shapes particular, just as I call the billiard balls particular. I do not, therefore, mean by a "particular character" a character which is predicable of one thing only, though of course I maintain that a particular character, if it exists, is predicable of only one particular thing. I could not define "particular character" in this way for the very sufficient reason that I can discover no means of distinguishing two concrete things except by distinguishing their characters. Again, "particular" is for me certainly not synonymous with "concrete." What is concrete is a subject to which characters belong and which cannot itself be a character of anything else. Characters are abstract particulars which are predicable of concrete particulars. If I buy two yards of cloth, each yard is a particular length numerically distinct from the other. But the particular lengths are abstract. The corresponding concretes are the pieces of cloth, each of which is a yard long. Mr. Moore also wants to know what I mean by a character. I have through____________________ 1I do not mean to say that the difference between two things can ever be merely numerical. But there can be no difference in kind unless numerical difference is presupposed. -178-

out my original paper taken for granted that whatever is predicable of something else is a character, and that nothing is so which is not predicable of something else. So far Mr. Moore does not disagree. I must here, however, add another point, which will enable us to define precisely the main question at issue. The way in which X belongs to Y as predicate to subject and Y possesses X as a subject possesses its predicate, is radically different from other ways in which an X may belong to a Y, or a Y may possess an X. My purse belongs to me, and so does my nose; but neither my purse nor my nose are characters predicable of me. What belong to me as predicates are not the nose itself but "having a nose as part of my body" and "possessing a purse as my personal property." "Having a nose" and "possessing a purse" are adjectives like red or round. But the nose and the purse are not adjectives. Similarly, whatever in any other sense I own, I own the owning of it as a character predicable of me. Now there is a quite distinctive feature of the subject-predicate relation which is necessarily connected with its peculiar nature. If X belongs to Y as a predicable character, it follows ipso facto that Y is a member of some class. If anything is white it is ipso facto a member of the class white things. If a mountain or anything else is the highest in the world, it must be a member of the class "things in the world which rise to varying heights above sea level." If I have a nose, I am a member, not of the class noses, but of the class "things endowed with noses." In what way does the possession of a character necessarily determine that which possesses it as a member of a class? We have here to consider two alternative answers to the question—Mr. Moore's and mine. According to Mr. Moore, "to have a nose" is a single indivisible entity which belongs to me and to him, and to an indefinite multitude of other beings. It is numerically the same in all of us, whether the nose is snub or aquiline. It spreads undivided, operates unspent. It is ubiquitous without having parts or members. What alternative have I to offer? Simply this. "To have a nose" is a general term, standing not for a single character, but for a class or kind of characters. When I say that I have a nose I assert that some particular character or other which is a member of this class belongs to me. So when I say that you have a nose I assert that you have a character which is an example of the same sort or class. Whatever is a shareholder in the general class of characters "having a nose," by possessing an example of it thereby belongs to the class "things which have noses." This view necessarily presupposes that a class of characters is not ultimately constituted in the same way as a class of things. A thing belongs to a certain class only because a character of a certain kind is predicable of it. But we cannot, without moving in a vicious circle, go on

to say that characters themselves can belong to classes or kinds only because other kinds of characters are predicable of them. What I maintain, therefore, is that qualities and relations belong to classes or kinds just because they are qualities and relations. Characters as such are instances of universals, and this fact is just what makes so plausible the false statement that they are themselves universals. The con -179-

nexion between being a predicable character and being an instance of a kind of character is so immediate and fundamental that for the most part it is neither needful nor useful to take note of the distinction in ordinary thought or express it in ordinary language. Though we may say "this shape is of precisely the same shape as that," yet we are more likely to say that "this is precisely the same shape as that." The two verbal formulas have the same meaning. Similarly, we speak of the same event recurring, when what we really mean is that an event occurs which is of the same general kind as a previous event. Of course the same event cannot recur. There is no such resurrection of the body, as Mr. Bradley would say. 2 We may now pass to the crucial question. If A and B are two concrete things, in what sense can it be true both that A is round and that B is round? Let us suppose that the roundness is absolutely specific. Mr. Moore and I disagree at the outset concerning the meaning of this supposition. For me it means that the roundness of A and the roundness of B are of precisely the same kind. For Mr. Moore it means, I presume, that the roundness of A is numerically identical with the roundness of B. According to him, therefore, when we say that both A and B are round, what we assert is that this numerically identical quality belongs to both. According to me, what we assert is that some particular example of an absolute specific sort of quality belongs to A, and that a particular example of the same sort of quality belongs to B. We do not assert that it is the same instance of roundness in general which belongs to both. Similarly, when we say that A is a man and that B is a man, we assert that A is identical with some man, and that B is identical with some man; but we do [not] assert that both are identical with the same man. Let us next consider what I should call a generic kind of quality, for example, shape in general. Here again it would seem 3 that for Mr. Moore shape in general is not the name of a highly general class of qualities, but of a single quality numerically identical in round shapes and square shapes. I find this a frightfully difficult view to understand. If it is right, we ought to be able to discern in a square shape two qualities, squareness and shape. Speaking for myself, I can do nothing of the sort. The squareness is identical with the shape. There is not squareness and also—shape. But the difficulty entirely disappears if we take shape in general as the name of a class of qualities, and "squareness" as the name of a sub-class. Squareness then simply means the special sort of shape which we call square. When A and B are both said to have shape my analysis is as follows. Each of them owns some particular instance of some special sort of shape, e.g., ____________________ 2In essential agreement with Mr. Johnson, I do not regard the relation of shape in general to squareness as on the same level as that of the general class animals to the special class men. Men are distinguished from other animals inasmuch as certain class distinctive characters are predicable of them. But squareness is not thus distinguished from shape in general. Squareness just is a special sort of shape. It is not a character distinct from shape which marks off one class of shapes from others. Not only do characters of themselves fall into classes; of themselves they fall into more or less general or specific classes. 3I am not certain what Mr. Moore's exact view is. -180-

roundness or squareness; and in each the special sort of shape it has is absolutely specific. Having explained what I mean to maintain, I may now pass to Mr. Moore's criticism. Here I am bound to be so brief that I cannot hope to be adequate.

I shall state his most important argument in his own words. Admitting that in S — p propositions we assert that S has some character p of the kind P, he proceeds as follows:—"The view that 'A is red' is to be analysed in this way, so far from supporting is definitely incompatible with the view that, when I truly say, of two different concrete things, A and B, both 'A is red' and 'B is red,' what I express by 'is red' in the one sentence must be different from what I express by 'is red' in the other. On the contrary, the character for which I use 'is red' as a name is, in each case, precisely the same, namely 'has some character of the kind P.' " 4 Doubtless, I reply, "is red" does mean "has some character of the kind P." In other words, some character of the kind P is the predicate which S is asserted to possess. But the having of this character is not the character which S is asserted to have. Mr. Moore seems to be confusing the predicate of a proposition with what is asserted in the proposition. What is asserted in "A is red" is the connexion of A as subject with "red" as predicate. But for that very reason what is asserted cannot itself be the predicate. In "A is red" Mr. Moore assumes two distinct predicates (1) "red," which can be analysed into "some character of the kind, redness in general," and (2) the possession of this character by A. I deny that (2) the possession by S of the character p is a character predicable in a proposition of the form S — p. It is rather the subject-predicate relation itself. The subject-predicate relation can no more be the predicate than it can be the subject. "Red" names the predicated character; "is red" names the relation of the subject to this character. The subject-predicate relation is no more identical with the predicate, than the laying of an egg is identical with the egg which is laid. This answer is, however, incomplete. Though the relation of S to p is not itself predicable within the proposition S — p, it may be predicated in another derivative type of proposition. It is possible though unnatural to say that "I am related to having a nose as subject to predicate" or that "I possess the character of possessing a nose." The general formula for such propositions is: "S has the character of having the character p" or less awkwardly "S is related to p as subject to predicate." Here the predicate is not p but "related to p as subject to predicate." The predicate is not "possessing a nose," but possessing the possession of a nose. Now I analyse this type of proposition just as I analyse the simple S — p. It means, S has to p an instance of the same kind of relation, for which the general name is subject-predicate relation. The predicate in such propositions is a particular example of this sort of relation. The essential point is that for me the subject-predicate relation, though it may be of absolutely the same kind, is not numerically identical for diverse subjects. Just as I hold that the roundness of one billiard ball A is numerically distinct from the exactly similar roundness of another billiard ball B, so I hold that the relation of A to its ____________________ 4I hope that the reader will pay special attention to the wording of this last sentence. -181-

own roundness is numerically distinct from the relation of B to its own roundness. Mr. Moore disagrees, and just because it is Mr. Moore who disagrees I attach importance to his disagreement. But he has really done no more than indicate that he disagrees. His argument (1) applies only to one peculiar sort of predicable character, and (2) even when limited to this, it is a petitio principii. It refutes me only by presupposing that I am wrong. Mr. Moore admits that if such occurrences as a sneeze were predicable characters my position would, so far as these are concerned, be a strong one, but he denies that a sneeze is a predicate of anything else. Now I am not bound to assert that whatever can properly be called an occurrence is therefore a predicable character. It is enough if this holds for some occurrences, and especially for such as a sneeze or the flight of a bird. I hold that whatever can be truly said to be a change in something or a changeable state of something is predicable of that which changes or is in the changeable state. By a sneeze I mean a sneezing, and if the word sneeze has any other sense I am not concerned with it. Now, when I say that a man is sneezing or has just sneezed, I am certainly predicating something of him. And what can the predicate be, if it is not sneezing? The man has gone or is going through a change of a certain sort and I predicate of him a change of this sort. I affirm that some qualities at least are locally separate, just as the concrete things which possess them are locally separate. Hence I infer that such qualities are numerically distinct, however much they may resemble each other. Mr. Moore's reply is twofold. In the first

place, he questions the assumption that nothing can be locally separate from itself. He may well be right. But all that I require for my argument is the proposition that nothing in its entirety can be locally or otherwise separate from itself in its entirety. If anything is a complex unity, it may be partially present here and partially present there. I may have one foot in water and the other on dry land. The British Empire may be locally separate from itself inasmuch as Australia and Canada are locally separate. But can the roundness of one billiard ball be, in this way, locally separate from the roundness of another? I say that it cannot if the roundness is regarded as a single indivisible quality numerically the same in both balls. On the other hand, if we take roundness in general as a class of qualities, we are dealing with a complex unity which may be said to be separate from itself inasmuch as one instance of it is here and another instance of it is there. Mr. Moore also urges that qualities are locally separate only in the Pickwickian sense of belonging to separate concrete things. On this I would remark, that some qualities at least are in the same place as the things they qualify, so that local separation of the things is in the same sense local separation of the qualities. A visual sense datum has colour, brightness, extension, size and shape. All of these qualities are situated within the visual sense-field just as the sense datum is to which they belong. If we consider bodies as well as sensa I seem to catch an echo of a familiar voice crying that colour is spread over the surface of the coloured body. How, in any case, can the extension of a body be in two places and yet numerically identical in both? -182-

There remains one point more. I say that I have no means of distinguishing between two concrete things except through their qualities. Mr. Moore disagrees and wonders why I say so. In reply, I can only restate my position more precisely and appeal to the personal experience of my readers. What I mean to assert is that on reflective analysis I can find no evidence for the distinction of two things, whether this be numerical or a difference in kind, which is independent of a corresponding difference between their qualities. I do not say that in distinguishing the two things I must expressly assign the diversity of the qualities as a reason. When I assert that my purse being in my pocket and a penny in my purse, the penny must be in my pocket, I need not formulate the general principle that what is contained in a part is contained in the whole of which it is part. None the less my inference is not valid independently of this principle. Similarly the distinction between two concrete things turns out, on reflective analysis, not to be independent of a corresponding distinction between their qualities. Comparing two faces, I find them to be dissimilar in their total appearance, without formulating such propositions as "this has a slightly more pointed chin." But when I do proceed to formulate such propositions, I am specifying one by one the very differences which in their confused totality formed the indispensable evidence of the dissimilarity of the two faces. Suppose next time that so far as I can discern, the two faces are precisely similar and similarly situated—like the rectangles in Euclid's immortal book. None the less I apprehend each in its total appearance, before I begin to analyse, as numerically distinct from the other. When I proceed to analyse I formulate such propositions as "this is subnosed in precisely the same specific way as that." I am thus specifying, one by one, the several resemblances which in their confused totality formed the indispensable evidence of my original apprehension of total similarity. Now what I assert as against Mr. Moore is that the total resemblance presupposes not numerical identity but only resemblance between the several characters. If all characters predicable of the one face were numerically identical, each to each, with all the characters predicable of the other, I should have no ground, either originally or after analysis, for regarding the one face as numerically distinct from the other face. -183-

: 11 : THE RELATION OF RESEMBLANCE PANAYOT BUTCHVAROV

The Distinguishing Feature of the Resemblance Theory

The crucial question in the history of the theory of universals has not been whether the Identity Theory or the Resemblance Theory is true, but whether the thesis of the Identity Theory is intelligible. Indeed, it is only in the last few decades that the Resemblance Theory (or, for that matter, the Nominalist Theory) 1 has been understood as a distinctive theory of universals, one that does not consist merely in the rejection of the Identity Theory. Is it legitimate to speak of certain locally separated qualities as identical? Are common qualities possible? Are there entities which can exist at more than one place at the same time? This preoccupation with the intelligibility of the Identity Theory has been the natural consequence of the general assumption that there can be no serious doubt about the intelligibility of the Resemblance Theory, even if the latter is false. The assertion that the shape of one penny and the shape of another penny are one and the same shape may well seem paradoxical. For, as we have seen it, it employs criteria of identity that are different in some fundamental respects from the criteria of the identity of individuals, and it is the latter that constitutes our paradigm of identity. But it seems that the assertion that the shape of one penny and the shape of another penny are related by a certain relation, namely, resemblance, appears paradoxical to no one. For it seems to differ in no significant respect from ordinary statements asserting that a certain relation holds between certain distinct objects. Now, we can hardly assume either that the Identity Theory is unintelligible or that it is obviously true. The source of the problem of universals is the fact that situations of the recurrence of qualities are in some respects very ____________________ From Resemblance and Identity by Panayot Butchvarov. Copyright © 1966 by Indiana University Press. Reprinted by permission of the publisher and author. 1[In a previous passage, the author described these three theories as follows: "According to the Resemblance Theory of universals, the instances of a recurrent quality are distinct particular qualities related by the relation of resemblance. According to the Identity Theory, they constitute an identical quality which is present in distinct individual things at the same time. According to the Nominalist Theory, they are related only by the fact that they are objects of the applicability of one and the same general word." (pp. 7-8)—ED.]

much like situations of individual identity, but in other respects very much unlike them. They are like them in so far as, at least in the case of exact resemblance, there are no essential qualitative differences between the instances of a recurrent quality. They are unlike them in so far as the instances of a recurrent quality are locally separated at one and the same time. Thus, it seems that even if the recurrence of a quality is not a kind of identity, neither is it very unlike identity. And it is a sufficient merit of the Identity Theory to have pointed this out, just as it is a sufficient merit of the Resemblance Theory to have pointed out that there are also fundamental differences between the recurrence of a quality and the identity of an individual. But while the dispute about the Identity Theory is whether the instances of a recurrent quality are identical or nonidentical, the dispute between the Identity Theory and the Resemblance Theory is whether the instances of a recurrent quality are identical or resembling. For the rejection of the Identity Theory and acceptance of the Resemblance Theory it is not enough to show that there are good reasons for considering the instances of a recurrent quality nonidentical. It is also necessary to offer an intelligible and distinctive account of their relationship. No theory which fails to account for this relationship can be preferable to the Identity Theory. No reasons for considering the instances of a recurrent quality nonidentical would be better than the reasons for considering them identical if an intelligible account of the fact of the recurrence of the quality is not offered. Now the Resemblance Theory does offer an account of this fact. According to it, the nonidentical instances of a recurrent quality are related by the relation of resemblance. And its insistence that recurrence is a straightforward relation is, as we have seen, its distinguishing feature, that in virtue of which it is a genuine alternative to the Identity Theory. If this account is intelligible, the reasons for accepting the Resemblance Theory would be at least as good as the reasons for accepting the Identity Theory. How does one determine whether the account which the Resemblance Theory offers of the

recurrence of a quality is intelligible? Not in the way in which one may appraise the intelligibility of the account offered by the Identity Theory. The Identity Theory defends its classification of the recurrence of a quality as identity by employing with regard to the instances of a recurrent quality a set of criteria of identity which is significantly different from the set of criteria of identity employed with regard to individuals; and the identity of individuals is the paradigm of identity. Consequently, to attack the intelligibility of the Identity Theory is to claim that the former criteria are so very different from the latter, that they cannot be regarded as criteria of identity at all. But the Resemblance Theory does not attempt to change the standard criteria of resemblance. It is not as if the paradigm of resemblance were the resemblance of individuals, and the recurrence of a quality could be described as resemblance only by changing the standard criteria of resemblance. For the recurrence of qualities, i.e., qualitative resemblance, is the paradigm of resemblance. The resemblance of individuals can itself be understood only -185-

by reference to the resemblance of some of the qualities of individuals (or, according to the Identity Theory, their identity). It is self-contradictory to say that individuals a and b resemble each other and yet no quality or characteristic of a resembles (or is the same as) any quality or characteristic of b. On the other hand, it is quite legitimate to describe the resemblance of a quality of one individual and a quality of another individual without even considering whether the two individuals resemble each other. One cannot speak of the resemblance of two cats unless one is prepared to specify that the color or shape or character of the one cat resembles the color or shape or character of the other cat. But one can speak of the resemblance of the color or shape or character of the one cat and the color or shape or character of the other cat without being committed to say anything about the resemblance or nonresemblance of the two cats. The color of a certain automobile may resemble the color of the sea even if the automobile does not resemble the sea. It is useless to argue that if a quality of a resembles a quality of b, then ipso facto a resembles b. This latter use of "resembles" with regard to individuals, which incidentally is found only in philosophical discourse, is even more clearly dependent for its criteria on the resemblance (or identity) of qualities. To say, in this sense of "resembles," that a resembles is nothing more or less than to say that some quality of a resembles (or is the same as) some quality of b; and while we do have independent criteria of the resemblance of a certain quality of a and a certain quality of b, our only criterion of this philosophical resemblance of a and b is the resemblance (or identity) of some of their qualities. But if qualitative resemblance, i.e., the recurrence of qualities, is the paradigm of resemblance, then it follows that the intelligibility of the Resemblance Theory cannot be rejected with an argument, analogous to that used against the Identity Theory, that the classification of the recurrence of a quality as resemblance involves excessive deviation from the standard criteria of resemblance. How then, can one reject the Resemblance Theory as unintelligible? It would seem that this can be done in only one way. It can be argued that qualitative resemblance is distinguishable from qualitative identity only in so far as the former is classifiable in a larger class in which the latter is not classifiable, and that the classification of resemblance in that larger class is itself unintelligible, because of fundamental differences between resemblance and the remaining members of the class. If this can be shown, then it will follow that while there is still nothing wrong about regarding situations of the recurrence of qualities as situations of resemblance, situations of resemblance are no longer distinguishable from situations of qualitative identity. What is the larger class in which resemblance must be classifiable if it is to be distinguishable from qualitative identity? What is the difference between resemblance and qualitative identity? What is the difference between the statement, "a and b resemble each other," and the statement, "a and b are one and the same," a and b being qualities of distinct individuals? We have seen that their difference consists neither (1) in the fact that the one is true and -186-

the other false, nor (2) in the fact that the theory suggested by the terminology of the one is true and the theory suggested by the terminology of the other is false, nor (3) in the fact that

one represents proper usage and the other does not. It consists in the fact that while the former statement can be interpreted as classifying the recurrence of a quality as a relation, like the relations of being-to-the-left-of, giving, preceding, being-taller-than, the latter can be interpreted as classifying the recurrence of a quality as an identity, like the identity of the-man-I-am-talking-to-now and the-man-I-talked-to-yesterday or the identity of the-hatyou-saw-in-the-store and the-hat-I-am-wearing-now. The Identity Theory prefers the latter kind of classification of the recurrence of a quality because it holds that the recurrence of a quality is more like the identity of an individual man than it is like an ordinary relation of two or more distinct objects. The Resemblance Theory prefers the former kind of classification because it holds that the recurrence of a quality is more like an ordinary relation of two or more distinct objects than it is like the identity of an individual. Indeed, it would seem that any theory which presents a genuine alternative to the Identity Theory must hold that the recurrence of a quality is a relation. For such an alternative theory must at least claim that the instances of a recurrent quality are distinct, nonidentical entities. Therefore, to be at all distinguishable from the Identity Theory, the Resemblance Theory must regard resemblance as a relation. And if it is shown that resemblance cannot, in any sense, be a relation, then it will follow that the Resemblance Theory has failed to present a genuine alternative to the Identity Theory. Therefore, the problem of the intelligibility of the Resemblance Theory is not whether the classification of the recurrence of a quality as resemblance is proper; for the recurrence of qualities constitutes the paradigm of resemblance. It is the question whether the classification of resemblance as a relation is proper. And this latter question is not absurd. The paradigms of relatedness are situations such as a's being to the left of b, a's loving b, a's giving b to c, a's helping b. To ask whether resemblance is a relation is to ask whether a's resembling b is sufficiently similar to such situations in order to justify its classification as a relation. And asking this amounts to asking whether and to what extent the use of statements such as "a resembles b" is similar to the use of statements such as "a is to the left of b," "a loves b," "a gives b to c." Only thus can an attempt be made to reject the Resemblance Theory as unintelligible without at the same time making the absurd attempt to reject the terminology of resemblances as unintelligible. For if resemblance is not a relation, then it can only be qualitative identity. 2 The third alternative, which was offered by the Nominalist Theory, has already been found unacceptable. But is not identity itself a relation? And if it is, does not the above distinction between the Resemblance Theory and the Identity Theory collapse? ____________________ 2This is why one does not help the Resemblance Theory if one explains away the peculiarities of the relation of resemblance by saying that it is not an ordinary relation, or that it is very different from all other relations, or that it is a unique relation. Cf. H. H. Price, Thinking and Experience, pp. 25-26. -187-

It seems clear that either identity is not a relation or that it is a rather peculiar relation which differs in a certain fundamental respect from all other relations, including the alleged relation of resemblance. It is essential to the concept of relation that the terms of a relation be clearly and unequivocally distinct. And it is just this necessary condition of relatedness that identity must fail to satisfy. The meaning of "identity" is precisely that the entities which are said to be identical are not clearly and unequivocally distinct. Indeed, if a and b can be said to be identical, they must also be distinguishable; otherwise we can neither think nor say that they are identical. And it is because of this fact that it is at all possible to regard identity as a relation and statements asserting the identity of two objects as statements asserting that a certain transitive, symmetrical, and totally reflexive dyadic relation holds between them. At the same time, however, what is asserted of a and b in saying that they are identical is precisely that they are not, or at least not clearly and unequivocally, distinct. Therefore, assuming that the above condition of relatedness is necessary, if the assertion that a and b are identical is true then their identity is not a relation. But, even if there is a sense (to be found only in philosophical discourse) in which identity can be said to be a relation, on account of the distinguishability of the objects which are said to be identical, this sense would be very different from that in which relations whose terms are not only distinguishable but also regarded as clearly and unequivocally distinct are said to be

relations. And as we have seen, unless resemblance is a relation in this second sense, it would not be distinguishable from qualitative identity. Therefore, even if identity is a relation, the distinction between the Identity Theory and the Resemblance Theory remains clear. Henceforth I shall use the word "relation" in its second sense. Now, to consider whether resemblance is a relation is to consider whether it satisfies the standard necessary conditions of relatedness, i.e., whether the use of resemblancestatements satisfies the general necessary conditions of the use of paradigmatic relational statements, such as "a is to the left of b," "a gives b to c," "a precedes b," "a loves b." There seem to be at least three necessary conditions of relatedness. First, a relation must add a certain characteristic to the nature of each of its terms, which the term would not have if it were not related by that particular relation. Second, a relation must have clearly and unequivocally distinct terms. Third, a relation must have a definite, clearly and unequivocally determinable, number of terms. 3 The first condition is necessary in order that a group of related objects may be distinguishable from a group of arbitrarily chosen subjects. The second condition determines the most obvious essential feature of relations: a relation is necessarily a fact about more than one object; for instance, it is because of this feature that a relation is distinguishable from the fact of the possession by an individual of a quality or characteristic. The third condition is implied by the first and sec____________________ 3I.e., a relation, as a logical category, must be described as n-adic, where n is a certain definite number. -188-

ond. If a relation does not have a definite, clearly and unequivocally determinable number of terms, then (1) there would be no possibility of understanding what is the distinctive fact about the terms which constitutes their relation, and (2) there would be no possibility of determining that the terms of the relation are clearly and unequivocally distinct. Unless we know, in a definite and clear and unequivocal manner, the number of terms which the relation of giving has, we can neither understand what the relation of giving is at all nor know that its terms are clearly and unequivocally distinct. Does resemblance fail to satisfy one or more of the above conditions of relatedness? It does not seem possible to claim that it fails to satisfy the first condition. Whatever resemblance may be, there is an obvious and clear difference between a group of resembling objects and a group of arbitrarily selected objects. At least some kinds of resemblance-statements are quite obviously informative and not at all equivalent in their use to the mere listing of the objects that are said to resemble each other. Some defenders of the Identity Theory have argued that resemblance (or at least exact resemblance) does not satisfy the second condition, i.e., that it does not have clearly and unequivocally distinct terms. But they have supported their claim by merely assuming that resembling qualities are identical, and thus their defense of the Identity Theory has been circular. In general, it does not seem possible to argue plausibly that the objects which are said to be resembling are not clearly and unequivocally distinct unless one supports such a claim by appealing to the Identity Theory. But does resemblance satisfy the third necessary condition of relatedness? Does it have a definite, clearly and unequivocally determinable number of terms? I shall argue that it does not.

The Terms of a Relation of Resemblance The virtue of the Resemblance Theory is that the relation of resemblance seems to be an ordinary dyadic relation, i.e., one such that the assertion that it holds between certain two objects is logically complete, very much like relations such as preceding, loving, beingtaller-than, being-the-square-of, attracting, belonging-to, being-far-from. The typical form of a statement about resemblance is "x resembles y." Other forms of resemblance-statements, e.g., "x is like y," "there is similarity between x and y," "x is similar to y," "x and y are alike," are easily reducible to that primary form. Of course, there are singular resemblancestatements which assert the resemblance of more than two objects, such as statements of the forms "x, y, and z resemble each other" and "x resembles y and z." The relation of resemblance in such statements, however, still appears to be dyadic, each statement being

readily analyzable as a conjunction of several statements of the primary form "x resembles y." For instance, "a resembles b and c," is equivalent to "a resembles b, and a -189-

resembles c," and "a, b, and c resemble each other" is equivalent to "a resembles b, a resembles c, and b resembles c." Some dyadic relations admit of comparison in degree with another instance of the same relation. For instance, such are the relations of loving, being-far- from, helping, beinginteresting-to, perhaps also belonging-to and attracting. Let us call such relations comparative. The typical statement in which the comparative nature of a relation is made clear would have the form "xRy more than wRz," in which w would often be identical with x. The test of the comparative nature of a relation R is whether a statement of the form "xRy more than wRz" is meaningful. The relations I have just mentioned are comparative because the following statements are meaningful: "a loves b more than c loves d," "a is farther from b than c is from d," "a helps b more than c helps d," "a is more interesting to b than c is to d," perhaps also "a attracts b more than c attracts d" and "a belongs to b more than c belongs to d." On the other hand, being-the-square-of, being-taller-than, and beingthe-father-of are not comparative relations because ordinarily the following statements would not be meaningful: "a is the square of b more than c is the square of d," "a is taller than b more than c is taller than d," "a is the father of b more than c is the father of d." The distinction between comparative and noncomparative relations is analogous to the distinction between properties or states which admit of variation in degree or quantity, e.g., warm, grey, small, hard, expensive, and properties which do not, e.g., made-of-wood, rectangular, being-six-in-number, excellent. Clearly, the relation of resemblance is a comparative relation. It is possible to make statements of the form "x resembles y more than w resembles z." It has usually been taken for granted that resemblances can vary in degree, just as loves and hardnesses can. It is characteristic of almost all comparative relations that while it is logically possible for any instance of such a relation to be compared in degree with another instance of the same relation, such comparison is not logically necessary. Given such a comparative relation R, it is logically possible for its instance in situation aRb to be compared in degree with its instance in situation aRc or situation cRd; but it is not essential to it, it is not logically necessary for the correct description of aRb, that such comparison be made. The statement "aRb" is compatible with the statement "aRb more than cRd," the latter being meaningful. But "aRb" does not entail some statement such as "aRb more than cRd," i.e., a statement such as the latter is not its necessary condition. John's love for Mary can always be compared in degree with John's love for Jane or with Bill's love for Jane; but John can love Mary without loving her more or less or as much as he loves any one else or as some one else loves any one else. If you were to say "John loves Mary" and I were to ask, "More than whom does he love her?", you could either answer my question by saying, "He loves her more than he (or Bill) loves Jane" or simply point out that in saying that John loves Mary you were not committing yourself to being able to say that he loves her more than he loves some one else. -190-

And the reason for this is that John's love for Mary is a fact perfectly intelligible in abstraction from many other facts. It is logically possible that there be a world in which the only individuals existing are John and Mary. Even with regard to such a world the statement "John loves Mary" will neither be superfluous nor unintelligible nor uninformative. It makes sense to say that John loves Mary even if no one else loves any one. However, there seems to be a very small number of comparative relations for which comparison is not only logically possible but also logically necessary. This does not mean that asserting an instance of such a relation intelligibly is impossible unless a comparison of it with another instance of the same relation is also being explicitly made. What is meant is that a statement about an instance of such a relation can be made legitimately only on the

assumption that a comparison of it with another instance of the same relation constitutes the context of the statement and can be made explicit on request. Consider the relation being-far-from. Clearly a statement of the form "x is far from y" can occur alone and be perfectly intelligible. But, unless the context makes clear both that a comparison is intended and what the other term of this comparison is, the statement would be essentially incomplete; it would not be possible to determine in what cases it would be true and in what cases false. Suppose that you were to say "Washington is far from New York," and I were to ask you, "It is farther from New York than it is from where?" Clearly, in this case my question must be answered, for otherwise your statement would be vacuous. (Is Tokyo far from New York? Not in the context of space travel.) In fact, if you are unable to answer this question, the situation would be analogous to that in which someone asserts, "It is hotter here," and yet, when questioned, holds that there need not be an implicit comparison, that to be making a significant statement he need not be able to make some additional statement such as "It is hotter here than there." 4 Now it seems that the relation of resemblance belongs to this latter class of necessarily comparative relations. 5 A statement of the form "x resembles y" can be made intelligibly only if it is explicitly regarded as an elliptical version of a statement of the form "x resembles y more than w resembles z" or if the context of its use makes clear that it is such a version. At first this may seem implausible. Is it not obvious that the color of my hat resembles the color of this book? Can there be any question that we understand perfectly well what is meant by saying that the shape of one penny resembles the shape of another penny? But I believe that such rhetorical questions seem convincing only because we are already familiar with the sort of shape that a penny ordinarily has and with the sort of resemblance between the color of a hat and the color of a book which, in comparison with other usual sorts ____________________ 4"X is far from y" could be used in the sense of "x is too far from y for such and such purposes." But this is not really a different sense. It amounts to "x is farther from y than it should be if such and such purposes are to be achieved." 5Cf. D. J. O'Connor, "On Resemblance," Aristotelian Society Proceedings, 1945-46. -191-

of resemblances, would be noticeable. But suppose that we consider the assertion of the resemblance of two qualities a and b (e.g., two unusual tastes) with which we are not already familiar, and with regard to which we do not already have an established system of comparisons. Does the assertion mean that both are tastes or that both are sour or that both have the sourness of a pickle or that both have the sourness of a dill pickle or that the two are completely indistinguishable qualitatively? If a and b are colors, does the assertion of their resemblance mean that they are indistinguishable qualitatively or that both are a certain kind of pink or that both are pink or that both are red or that one is red and the other is orange or that both qualities happen to be colors? Clearly, the assertion could have any one of these meanings. And this means that it does not have any meaning at all. Consider the statement "The color of my hat and the color of this book resemble each other." Clearly, a statement of this kind can occur alone and be perfectly intelligible. It need not be followed by an explicit comparison of the degree of the resemblance with some other instance of resemblance. Nor is it necessary that the speaker or the listener should be actually conscious of such a comparison. But unless such a comparison constitutes the general context of the statement, unless the two persons are talking about the resemblance of the color of the hat and the color of the book in the general context of certain instances of color-resemblance with which both are acquainted, the statement would be essentially incomplete, it would be impossible to determine in what cases it would be true and in what cases false. Suppose that I were to say, "The color of my hat resembles the color of this book," and you were to ask, "How much does it resemble it?" or, what comes to the same thing, "It resembles it more than it resembles what other colors?" Clearly, your question must be answered if my statement is to be considered informative. If I were unable to answer it, the situation would be similar to that in which someone asserts that New York is far from Washington and yet refuses to explain, with respect to what other city New York is far from Washington. Consider a world consisting only of the color of my hat and the color of this book. Would the statement that the two colors resemble each other provide us with

any information about such a world that is not already provided by the mere listing of the two colors as its constituents? In what circumstances would we reject this statement as false and in what circumstances would we accept it as true? How would we understand the difference between the statement that the two colors resemble each other and the statement that they do not resemble each other? It may be suggested that one could consider other colors even if these other colors were not constituents of that world and that the resemblance of the color of my hat and the color of this book could be asserted in the context of the resemblances among these other colors. But, apart from the question whether in a world which consists only of two colors one can even consider other colors (the sense in which a world can be said to contain colors is obviously very different from the sense in which a world -192-

can be said to contain John and Mary, or color-patches), the suggestion still allows that the assertion of the resemblance of the two colors depends for its meaningfulness on a comparison of the degree of this resemblance with the degree of other instances of colorresemblance. 6 Does the above constitute a return to the Nominalist Theory? It does not. Indeed, the Nominalist Theory regards statements of the form "x resembles y" as uninformative because of reasons which seem similar to those I have just given. But its diagnosis is different and so is the suggested cure. According to it, there is no such fact as the recurrence of a quality at all, whether it be a qualitative identity or a resemblance, unless it is the fact of the applicability of a certain general word to certain objects. It follows from this that a mere assertion of the resemblance of two qualities is uninformative unless it can be taken to mean that a certain general word or one of a certain range of general words is applicable to both qualities. And, according to the Nominalist Theory, a resemblance-statement, though logically incomplete in itself, can be completed only by specifying the respect of the resemblance, since such a specification amounts to indicating the general word or one of a range of general words which is applicable to the terms of the resemblance. I rejected the Nominalist Theory on the grounds that the recurrence of a quality, or the resemblance of certain qualities, is distinguishable from the fact of the applicability of a certain general word. But I agree with the Nominalist Theory that isolated statements of the form "x resembles y" are logically incomplete. Yet the kind of completion of such statements which I suggest is fundamentally different from the kind of completion suggested by the Nominalist Theory. The reason why statements of the form "x resembles y" —where x and y are simple qualities—are incomplete is that the resemblance of two qualities admits of extremely wide variation of degree, and such statements do not specify the degree of the resemblance. But to speak of the degree of an instance of resemblance is necessarily to speak of its relation to the degrees of other instances of resemblance. Therefore, to know the degree of the resemblance of a and b is to know whether the resemblance of a and b ____________________ 6It has been suggested by C. J. Ducasse (in "Some Critical Comments on a Nominalistic Analysis of Resemblance," Philosophical Review, 1940) that even if a person were aware of only two hues, he might still be able to assert meaningfully that they resemble each other or that they do not, by using as evidence of their resemblance his difficulty in discriminating between them, or as evidence of their nonresemblance the lack of such a difficulty. If he frequently mistakes one of the hues for the other, then he would be able to consider them similar; if no such mistakes occur, he would consider them dissimilar. I think that Ducasse would be right if we could assume that such a person already has the concept of similarity. Then, remembering that in other cases close similarity is ordinarily accompanied by difficulty in discrimination, he would infer from the presence of such a difficulty in the case of the hues that the two hues are similar. But it cannot be supposed that he would be able to derive the concept of similarity from the concept of difficulty in discrimination. And, in any case, there is a correlation between similarity and difficulty in discrimination only if the similarity is a rather close one. -193-

is greater or lesser than the resemblance of a and c, or of b and c, or of c and d, etc. 7 But then the degree of an instance of resemblance would not need to be specified by an indication of its respect, or of the general words applicable to both of its terms. It can be so specified in a statement of the form "x resembles y more than w resembles z," which would be logically complete and yet would be a straight-forward resemblance-statement. In fact, it can be argued that this latter kind of statement is the primary kind of completion of a logically incomplete resemblance-statement of the form "x resembles y." For, what seems essential to the meaningfulness of the statement "a resembles b" is not so much the classifiability of both a and b as F, but a context in which it is clear that the statement is an elliptical version of a statement such as "a resembles b more than c." It might be argued that we can classify two colors as red only if we recognize that their resemblance is greater than, say, the resemblance of one of them and a shade of yellow. But if resemblance is a necessarily comparative relation, i.e., if the only kind of resemblancestatement which is logically complete has the form "x resembles y more than w resembles z," the question arises whether such a peculiar relation is dyadic at all. In this respect, statements of the form "x resembles y" appear to be closely analogous to what are ordinarily called, in logic, relative terms, e.g., short, bright, large. A relative term F is such that a statement of the form "x is F" is logically incomplete and its completed form contains reference to two or more objects. To say that John is short is to say that John is shorter than someone else, e.g., Peter or the average man. And this implies that being short is not a genuine property but is an elliptical way of referring to a dyadic relation. Of course, John does have a genuine property in virtue of which he is shorter than Peter, namely the particular shape and size of his body. But this property is not the property of being short. Analogously, now, we must conclude that a "relative relation," a relation whose every instance must be compared in degree with another instance of the same relation, is not a genuine dyadic relation. A statement asserting the resemblance of two objects is logically incomplete, not in the Nominalist sense (which I examined in Chapter One), that the respect of the resemblance must be stated, but in the sense that such a statement is meaningful only if regarded as an elliptical version of a statement in which reference is made to at least three objects, namely, a statement of the form "x resembles y more than w resembles z," where w can be identical with x. And to have shown that statements of the form "x resembles y" are thus logically incomplete is to have shown that resemblance is not a dyadic relation. What is meant by saying that a certain relation is dyadic is that the assertion that it holds between certain two objects is logically complete, that such an asser____________________ 7Instead of completing "x resembles y" as "x resembles y more than w resembles z," one could in some cases complete it as "x resembles y exactly." But in reality this is not a different kind of completion. If it is not to be taken to mean that x and y are one and the same color (which would be to accept the Identity Theory), the latter statement must mean simply that x resembles y either more or as much as any w can resemble any z. -194-

tion requires no other statement and no reference to any other object for its meaningfulness. Is resemblance a triadic or tetradic relation, then? It has been argued that it is. 8 For while statements of the form "x resembles y" are not logically complete, statements of the form "x resembles y more than w resembles z" are logically complete; and the former can be understood only as elliptical versions of the latter. In the same way, one can argue that the relation of being- far-from is also a triadic or tetradic relation. For while statements of the form "x is far from y" are logically incomplete, statements of the form "x is farther from y than w is from z" are not; and the former can only be understood as elliptical versions of the latter. But all such arguments are futile. They have not the slightest tendency to show that resemblance, or remoteness, is a triadic or tetradic relation. The reason is simple. It is a logical truth that resemblance cannot be the relation of difference in degree between instances of resemblance, and that remoteness cannot be the relation of difference in degree between instances of remoteness. Yet it is precisely this that they are asserted to be by the theory which holds that resemblance and remoteness are triadic or tetradic relations. To say that a resembles b more than a resembles c is precisely to say that the resemblance between a and b is greater than the resemblance between a and c. And to say that a is farther from b

than a is from c is to say that the remoteness of a from b is greater than the remoteness of a from c. Resemblance is asserted not of a, b, and c, but of a and b only, and then separately, of a and c only. The relation asserted by the statement "a is farther from b than a is from c" is intelligible only if understood as the dyadic relation of difference in degree, the terms of which are two separate instances of a dyadic relation of being-far-from, the first instance having as its terms a and b and the second instance having as its terms a and c. The relation asserted by the statement "a resembles b more than a resembles c" is also intelligible only if understood as the dyadic relation of difference in degree, the terms of which are two separate instances of a dyadic relation of resemblance, the first instance having as its terms a and b and the second instance having as its terms a and c. In a logically complete resemblance-statement the relational expression "more than" cannot refer to an aspect of the relation of resemblance; it can only refer to a second-order relation, the terms of which are two instances of a first-order relation of resemblance. Such a second-order relation can only be understood as dyadic; and the first-order relation of resemblance can only be understood as dyadic, too. But we have already seen that neither remoteness nor resemblance can be a dyadic relation. The conclusion we seem to have reached is that resemblance is not a triadic or tetradic relation. We have also seen that it is not a dyadic relation. And there can be no likelihood that it may turn out to have more than four terms. Therefore, if it is logically necessary that a relation have a definite, clearly and unequivocally determinable number of terms, then resemblance cannot ____________________ 8E.g., by D. J. O'Connor, cited. -195-

be a relation. But may we not suppose that resemblance is a unique relation, that it is quite unlike any other relation, instead of reaching the paradoxical conclusion that it is not a relation at all? A discovery of such uniqueness of the relation of resemblance would not be an ordinary discovery. For the peculiarities of resemblance because of which it would be considered unique are not the kind of peculiarities that other relations might have. They are basic, categorial peculiarities. And recognizing these peculiarities is not recognizing that resemblance is a very peculiar relation. A relation which is neither clearly dyadic, nor clearly triadic or tetradic or n-adic, is not just a peculiar relation. It is not a relation at all and statements in which reference is made to it are not relational statements. But the distinguishing characteristic of the Resemblance Theory, as we have seen, is its claim that the situations of the recurrence of qualities are very much like ordinary situations of the relatedness of distinct objects. To reach the conclusion that resemblance is not a relation is to reach the conclusion that the Resemblance Theory is false.

The Meaning of Resemblance-Statements A conclusion such as the one we have reached cannot be just happily proclaimed and then seized upon as a basis of philosophical theorizing. Even if we have reached it without making mistakes about the nature of relations and the use of relational statements, its significance must be assessed carefully and with restraint. For the theory of universals it is not enough to say that necessarily comparative statements such as resemblance-statements differ from relational statements in such fundamental respects that they should not be considered relational at all. Perhaps this would be enough for the rejection of the Resemblance Theory, since, as we have seen, it is essential to the distinctive character of the latter that resemblance be considered a relation. But it would not be enough for the purposes of presenting an adequate theory of universals. The peculiar features of resemblance-statements must be explained. If resemblance-statements are not relational, then what does their meaning consist in? Why are there such statements at all, and not merely statements of qualitative identity? Philosophy is the one cognitive discipline in which there is no place for mysteries. And the use of such a familiar and commonplace kind of statement as resemblance-statements can even less be a mystery. Let us begin with an explanation of the analogous case of the relation of being-far-from. Perhaps it will provide us with the clues for an adequate account of resemblance.

There is no dyadic relation of being-far-from. Nor is being-far-from a triadic or tetradic relation. And it makes no sense to suppose that it has more than four terms. Does this mean that statements of the form "x is far from y" and even statements of the form "x is farther from y than it is from z" are meaningless? It would be absurd to reach such a conclusion. It would also be -196-

unnecessary. For we all know quite well what is meant by a statement such as "a is farther from b than it is from c." Clearly, it is synonymous with the statement "The distance between a and b is greater than the distance between a and c." And in the latter the word "distance," though denoting a spatial relation which may be problematic in its own way, is not the name of the relation being-far-from. "The distance between x and y" is synonymous with "the length of the straight line connecting x and y" or "the length of the route connecting x and y" or even "the time needed for travelling between x and y." Thus it is seen that while there is not a dyadic relation such as being-far - from, nor a triadic or tetradic relation such as the one suggested by the structure of the form "x is farther from y than w is from z," statements of this form are not at all meaningless and merely constitute variants of statements of the form "The distance between x and y is greater than the distance between w and z." The latter are relational statements, the relation being that of difference in length. And statements of the form "x is farther from y than w is from z" (as well as their elliptical versions of the form "x is far from y") are also relational, but the relation they really assert is not, as one would ordinarily have supposed, the relation of being-far-from or even the relation of difference in degree between two instances of the relation of being-far-from, but, again, simply the relation of difference in length between two distances. The above explanation of the meaning of statements of the form "x is far from y" is analogous to the explanation of the meaning of statements containing relative terms. To say that John is short is to say that he is shorter than, say, Peter. Only the latter, expanded statement is logically complete. But this does not mean that John still has a quality of being short, though it is essential that this quality be related to Peter's corresponding quality by the relation of shorter than. It is not John's shortness that is shorter than Peter's shortness. The quality of being short has been shown to be spurious and reference to it in this case has been shown to be simply a misleading way of asserting that John and Peter are related by the relation of being-shorter- than. The terms of this relation are not shortnesses. If they are not John and Peter, they are the height of John and the height of Peter. Now, what would be the corresponding explanation of the meaning of statements of the form "x resembles y more than w resembles z"? It would seem that the key requirement which such an explanation must meet is that an expression be found whose function in the explanation of the meaning of such statements would be analogous to the function of the phrase "the distance between x and y" in the explanation of the meaning of statements of the form "x is farther from y than w is from z," or to the function of the phrase "the height of x" in the explanation of the meaning of statements of the form "x is shorter than y." Such an expression must satisfy two conditions. First, it must not refer to a relation of resemblance. (Just as "the distance between x and y" refers not to the relation of beingfar-from, but, if to a relation at all, only to that of being-spatially-separated-from; and just as "the height of x" does not refer to x's property of being short.) Second, it -197-

must be such that it can occur in statements which, though not containing reference to a relation of resemblance, express faithfully the meaning of statements of the form "x resembles y more than w resembles z." (Just as "the distance between x and y" can occur in statements of the form "The distance between x and y is greater than the distance between w and z," which do not contain reference to a relation of being-far-from and yet express faithfully the meaning of statements of the form "x is farther from y than w is from z"; and just as "the height of x" can occur in statements of the form "The height of x is shorter [i.e., less] than the height of y," which do not contain reference to the shortness of x and yet

express faithfully the meaning of statements of the form "x is shorter than y.") Clearly, the required expression cannot be "the resemblance between x and y." While this expression does satisfy the second condition, it fails to satisfy the first condition. Indeed, the statement "The resemblance between a and b is greater than the resemblance between a and c" would seem to express faithfully the meaning of the statement "a resembles b more than a resembles c." But it contains reference to what may only be interpreted as a relation of resemblance. Thus, instead of elucidating the meaning of the latter statement, the former statement is comprehensible only because the latter statement is comprehensible. Such an explanation of the meaning of resemblance-statements would be like explaining the meaning of "a is farther from b than it is from c" by translating it as "The remoteness of a from b is greater than the remoteness of a from c," or explaining the meaning of "a is shorter than b" by translating it as "a's shortness is greater than b's." But what other expression is there? What expression would satisfy the above two conditions? It would seem that the only other expression that could be suggested with any plausibility is "the common quality (i.e., the universal) whose instances are x and y." It satisfies the first condition. If the common quality is a specific universal, then its instances can be regarded as specifically identical. If it is a generic universal, then its instances can be regarded as generically identical. In neither case is there a possibility of confusing the identity of the instances with a relation of resemblance. For, as we have seen, what is meant by "identity," be the latter specific or only generic, is essentially incompatible with what is meant by "relation." The expression "the common quality whose instances are x and y" meets also the second condition. Common qualities, i.e., universals, can be compared in respect to degree of generality. A specific universal, such as a shade of pink, has the lowest possible generality; it cannot have instances which are qualitatively distinguishable. The several kinds of pink are already generic universals, though of very low generality; the instances of such a universal may have qualitative differences, though not pronounced ones. Pink has higher generality. The generality of the universal red is even higher; its instances may have considerable qualitative differences; one of them may instantiate a specific shade of pink while the other may instantiate a specific shade of crimson. Now, clearly, such levels of generality correspond to the degrees of resemblance that a logically complete resemblance-statement compares. Consequently, a statement of the -198-

form "The universal of least generality instantiated in x and in y is of lower generality than the universal of least generality instantiated in w and in z" would seem to express faithfully the meaning of a statement of the form "x resembles y more than w resembles z," assuming that both statements are about simple qualities. 9 ____________________ 9The qualifying phrase "of least generality" in the above translation of a resemblancestatement is needed because, in addition to the universal of least generality instantiated in both of two qualities, all of its superordinate universals are also instantiated in these qualities. An instance of pink is also an instance of red and of color. -199-

: 12 : QUALITIES NICHOLAS WOLTERSTORFF 1. POINTING is a kind of drawing attention to. Supposing then, I point at the tail of a dog. How does this differ from pointing at a dog? That it does differ is clear. For if someone asks me, "Are you pointing at a dog?" I can say, "No, I am pointing at the tail of a dog." And if, pointing, I say, "This would not be so short, but it became gangrenous and we had to cut it off," I cannot be viewed as pointing at a dog. But then, how do these pointings differ? Someone might venture that, since pointing usually involves an aiming of the finger, perhaps one aims one's finger differently in the two cases. This will not do at all, however, for it takes only a moment's reflection to see that the same aiming may be used either to point at a dog or to point at the tail of a dog. So knowing what someone is pointing at involves

knowing more than the rule: when someone points, follow the aim of his finger in order to know what he is pointing at. But what else does it involve? Well, suppose you point at a dog, and as the direct result of your pointing my attention is drawn to the dog's tail and not to the dog. In this case something has gone wrong; I failed to know what you were pointing at. And, it would seem, the cause of the failure was that my attention was not drawn to what you intended it to be drawn to. You intended to draw my attention to the dog, and instead it was drawn to the dog's tail. So pointing seems to be an intentional action, an intentional drawing attention to something; and knowing what you are pointing at involves knowing your intention. Hydras can and do aim their limbs in certain directions, and their aiming of limbs may well draw our attention to things, but they cannot point. Yet this seems clearly wrong, for we do say that the weather vane is pointing to the west, and that the spinner is pointing to the 7. But how does the weathervane's pointing to the west differ from its pointing to the large oak? And how does the spinner's pointing to the 7 differ from its pointing to the red background? It seems to me it does not. We can say, indifferently, that the spinner points to the 7 or to the background, though gamblers seem by and large to be interested in the numbers and not in the colored backgrounds. But when a man points at a number he is not pointing at a colored background. ____________________ Reprinted from The Philosophical Review, LXIX (1960) by permission of the editor and the author.

So what we should have said above is that one kind of pointing involves a reference to intention, and that this is the kind which is relevant when we say that a man is pointing at the tail of the dog and not at the dog. But how can you know what I intend to call your attention to? The simplest method is, of course, for me to accompany my pointing with the words "this dog" or "the tail of this dog." But such verbalization is not essential; indeed, it is clearly subsidiary. For we call attention to things not only by means of words, but in order to teach words; the words "dog" and "tail," for example, are customarily taught children by pointing. So imagine that these words are not available; how then can I let you know that I am pointing at the dog and not at his tail? The most straightforward way is probably to point again, this time aiming my finger at the dog's head and not at his tail. But just this is certainly not enough. For how are you to know that I am pointing twice at the same dog and not once at his tail and once at his head? The answer to this is simple enough: I accompany my second pointing with the words "This is the same as that," or words to this effect. Of course, I do not first point at the dog's tail and then at his head, and say "This is the same as that"; for a dog's tail is not the same as a dog's head. Rather I aim my finger first at the dog's tail, then at his head, and, by then affirming the identity of the object pointed at, I show it to be something bigger than and different from either the dog's tail or his head. 1 It is, in short, a dog. And to make my intention more and more unambiguous, I point more and more times at the dog, each time affirming the identity of the object pointed at. So for you to know what I am pointing at, you must know the circumstances under which I would be willing to say that I am pointing at the same thing as that at which I pointed previously. I shall call this knowing the identity criteria for the thing pointed at. The utility of using terms like "dog" and "tail of a dog" to accompany our pointings may then be viewed as due to the fact that singular terms like these are, in a sense, ossified identity criteria. Telling you that I am pointing at a dog is a way of informing you of the circumstances under which I would be willing to say that I am pointing at the same thing as that at which I pointed previously. Now I wish to suggest, as preliminary to what I shall argue in this paper, that the difference between qualities and particulars is to be explicated in essentially the same way in which I have explicated the difference between a dog and a tail of a dog. Suppose, for instance, that I point and say, "This is green." What then am I pointing at; that is, does "this" refer to a particular or to a quality? I suggest that it may be either, and that the way to find out is to determine the identity criteria of the entity referred to. Suppose I say, "This is green and that

is green, only this is a tree and that is a carpet, so this is not identical with that"; here it is clear that I am pointing at two distinct particulars and not at one identical quality. But if I say "This is green" while pointing in the direction of a tree, and then, pointing in the direction of my ____________________ 1Cf. W. V. Quine, "Identity, Ostension, and Hypostasis," in From a Logical Point of View (Cambridge, Mass., 1953), pp. 65-79. -201-

carpet, say "And this is green, and this is identical with that," then I would be pointing at a quality. And so would a father who in teaching his child says, "Here's green, and here's green, and here's green again." (And incidentally, if we do say these things, it disposes of the traditional prejudice that qualities and universals cannot be pointed at.) But what I have shown does not quite prove what I have concluded; for how do I know that, when you are apparently pointing at a quality, you are not rather pointing at a larger and scattered particular? The difference lies, I suggest, in the reason that you give for asserting the identity. Though every case of pointing at a certain quality might also be viewed as pointing at a scattered particular, the difference lies in the criteria used for asserting identity. Now what I wish to discuss in this paper are the identity criteria for qualities. And my fundamental thesis will be that there are two distinct interpretations of these criteria, each being perfectly intelligible and consistent in itself, but that our ordinary language about qualities gives us no ground for saying that either is the correct, or even preferable, interpretation. In the tradition one of these interpretations has been preferred by nominalists and the other by realists—meaning by "nominalist" one who holds that qualities are to be interpreted in terms of particulars and classes of particulars, or quality-classes as I shall call them; and meaning by "realist" one who holds that qualities are universals. Hence I can also put my thesis thus: the dispute between nominalists and realists is a pointless dispute, incapable of solution except by arbitrary fiat. But in spite of this it is not a meaningless dispute, for the position of each disputant can be given an intelligible and consistent, yet distinct, formulation. 2. For the issue which I wish to discuss a consideration of predicates is irrelevant. Indeed, if the case for the existence of qualities or universals rested on an analysis of such terms, I should regard it as a very shaky case. For to hold that, in "Socrates is wise," "Socrates" refers to a particular and "wise" to a universal, is certainly to confuse names with predicates. 2 And to hold that the repeated applicability of predicates like "red" can be explained only by saying that each of the entities to which it is applicable possesses redness, is to utter something uninformative at best and tautologous at worst. 3 But then I do not think that the case for the existence of qualities and universals rests on an analysis of such terms. Rather the issue first joins, I think, when we consider expressions like "the color of his hat," "the wisdom of Socrates," and "the pitch of St. Mary's bell." Each of these is a description in which the word preceding the "of" ordinarily names or refers to a quality, and the word succeeding the "of" ordinarily names or refers to a particular. I shall henceforth call these quality-descriptions, without implying anything as to their analysis. Now the offhand inclination of the nominalist is to take these expressions as referring to aspects of ____________________ 2Cf. M. Lazerowitz, "The Existence of Universals," Mind, LV (1946), 1-24. 3Cf. D. F. Pears, "Universals" in Logic and Language, II, ed. by A. Flew (Oxford, 1955), pp. 51-64. -202-

particulars, to "abstract particulars" if you will, whereas the offhand inclination of the realist is to take them as referring to qualities. I shall eventually show that neither the realist nor the nominalist need stake his case on his ability or inability to follow out this original inclination; but it will be important first to consider who is right on this issue.

The realist would hold that, if the color of my coat is in fact green, then "the color of my coat" refers to the same entity as does "greenness." Is there anything in our use of qualitydescriptions to show that this view is mistaken? One fact which seems to show its incorrectness is that we say such things as, "What was the color of your coat?" (when the coat is destroyed) and "What was the pitch of St. Mary's bell" (when the bell is broken). The use of the past tense here would seem to indicate that we are referring to something which was destroyed when the coat or the bell was destroyed; and what could this be but a certain aspect of the coat or the bell? For colors are not destroyed by burning coats, nor pitches by breaking bells. But this argument is inconclusive. For one might also say, while pointing in the direction of a color sample, "This is the color that my coat was," and while playing a note on the piano, "This is the pitch that St. Mary's bell had." And this seems to indicate that tenses here are determined by the fact that the coat which formerly possessed the indicated color no longer exists, rather than by the fact that the color of the coat is an aspect of the coat which is destroyed along with the destruction of the coat. And second, we sometimes even tense the verb in statements which refer unambiguously to qualities. We would not say, of course, that "green was a color"; but we might say, "What was the pitch you just gave?" and "The cloying sweetness you smelled was insect repellent." But there is another class of cases which conclusively shows that the realist cannot be wholly right. For suppose a painter friend of mine comes to me one day and says, "I want you to see the wonderful green on my latest canvas." So I pull a color chart from my pocket and ask him to point to the color he has in mind. He may then point to one and say, "This is it." But he may also summarily wave the chart aside and say, "No, that won't do, you'll have to see my canvas in order to see what I'm referring to." In this latter case "the green on my canvas" is used to refer not to a certain color but to a particular qualitative aspect of my friend's canvas; for the friend might admit that the color of my sample was just like that on his canvas, but still deny that they are identical, since after all his canvas is not in the same place as my sample. Thus it is clear that quality-descriptions are not always used to refer to qualities. So is the nominalist then right, or are there also cases in which quality - descriptions must be viewed as referring to qualities and not to aspects? The sort of case one naturally thinks of here is "The color of this hat is the same as the color of this blotter"; and "The pitch of this chorale is the same as the pitch of St. Mary's bell." In these cases it seems that we are asserting the existence of a quality shared by two different particulars. But these examples raise a new issue which is central to the whole debate over universals. For -203-

"the same" is an ambiguous expression, meaning either "identical" or "similar." Thus if two children have the same father, they have the identical father and not two similar ones; and if two college boys wear the same tuxedo so that they cannot go to dances together they wear the identical tuxedo. 4 But on the other hand, though every soldier wears the same uniform, all soldiers can appear on parade clothed. The difference between these two senses of "the same" is also clear from our use of qualifying adverbs. One speaks of two things as being almost the same, or nearly the same, or not at all the same. And here we clearly mean "similar," for identity does not hold in degrees. Now with this distinction in hand the nominalist can easily show that statements like "The color of his coat is the same as the color of this blotter" do not refute his position. For "is the same as" can here be construed to mean "is exactly or closely similar to"; hence the statement does not say that this quality is identical with that but that this aspect is similar to that. The realist obviously has a way of blocking this answer, however; for one might also say, "The color of this blotter is identical with the color of his coat." And though this is a rather stiff way of speaking, and though the nominalist may wish to hold that, in some sense, no information is conveyed by this sentence which is not conveyed by "The color of this blotter is exactly similar to the color of his coat," yet the two sentences are not synonymous. There is also another class of statements which gives the nominalist trouble. Examples are, "This is the color of his coat," said while pointing in the direction of a blotter; "This is the

pitch of Nun ist das Heil," said while playing a note on the piano; and "You too can have the wisdom of Socrates," proclaimed by an encyclopedia advertisement. Here we seem unambiguously to be asserting that one quality is shared by two distinct particulars; and the nominalist cannot now escape by distinguishing senses of "the same." Of course, on the analogy of "He has his father's hands," he might attempt to reformulate these and say that "This is the color of his coat" really means "This is exactly similar to the color of his coat." But I see no defense that could be given for such a reformulation. In summary, then, quality-descriptions may be used to refer either to aspects or to qualities; and in ordinary speech we usually do not make it clear how we are using them. The reference can, however, be made clear by asking for the circumstances under which the speaker would be willing to say that he was referring or pointing again to the same entity, with "the same" understood now as meaning "identical" and not "similar." Having done this, it turns out that neither the realist's inclination to regard these expressions as referring to qualities, nor the nominalist's inclination to regard them as referring to aspects, can be wholly correct. This, however, need give the realist no anxiety, since all he has to show is that, whatever else there be, there are universals. The nominalist, however, contends that there are only particulars ____________________ 4This example is from D. C. Williams, "On the Elements of Being," The Review of Metaphysics, VII (1953), 6. -204-

and classes of particulars; so unless he can find a nominalistic interpretation of these references to qualities, an analysis of quality-descriptions will show already that nominalism is not a possible view. But before considering the two alternative analyses of qualities, I think it worth remarking that a good many confusions in the history of philosophy have been caused by a failure to see that quality-descriptions may refer either to particulars or universals. For example, I think this failure is responsible for the extreme ambivalence in all classical modern philosophy on whether we really perceive only particulars or only universals. And it is clearly responsible for the views of G. F. Stout 5 and D. C. Williams, 6 and for G. E. Moore's total failure to understand Stout. 7 Stout says, for instance, that "of two billiard balls, each has its own particular roundness separate and distinct from that of the other, just as the billiard balls themselves are distinct and separate. As Jones is separate and distinct from Robinson, so the particular happiness of Jones is separate and distinct from that of Robinson." Of course, Stout is wrong in holding that "the roundness of this ball" can refer only to a particular; but Moore is equally wrong in holding that it can refer only to a universal. 3. In addition to quality-descriptions referring to qualities, the terms we must now consider are ones like "greenness," "circularity," and "stickiness." I shall give these the traditional name of abstract singular terms. And what I wish to see is whether, at this stage, either realism or nominalism can be shown to be mistaken. In analyzing abstract singular terms, the nominalist seems in general to have two courses open: he can say that all statements using such terms can be translated into synonymous statements whose singular terms refer only to concrete particulars; or, failing this, he can say that abstract singular terms refer not to universals but to certain classes of particulars, quality-classes. According to the first suggestion, a statement like "Greenness is a color" is to be paraphrased as "For every entity, if it is green, then it is colored." Now is this paraphrase really synonymous with the original? It is not, I think. For the analysis assumes that "is a color" is synonymous with "is colored." But this is surely false, if for no other reason than that the ranges of meaningful application of these two terms are different. Green is a color but is not colored; and a blotter is colored but is not a color. There are also other flaws in the paraphrase; for certainly the connection between being green and being a color is in some sense a necessary connection, as well as being in some sense a relation of subsumption. But neither of these features is brought out by the proposed analysis. Thus the

only plausible interpretation of nominalism seems to be that which regards hues, pitches, virtues, and so forth as classes of particulars. ____________________ 5"The Nature of Universals and Propositions," Hertz Lecture, Proceedings of the British Academy, X (1921-1923), 157-172. 6Op. cit. 7"Are the Characteristics of Particular Things Universal or Particular," symposium in Proceedings of the Aristotelian Society, Supp. vol. III (1923), 95-113. [Reprinted as chapter 10 of this book.] -205-

Now the strongest objections to the class theory are based on the belief that the classes which nominalism proposes to identify with qualities cannot actually be defined. I think, however, that they can be; and so I shall take it as my main task to show that this objection is invalid. Classes, according to the usual conception, are identical if and only if they have the same members. Hence the first thing we must do is decide when quality-classes do and when they do not have the same members; and for this we shall first have to know what criterion is used in determining the membership of such classes. Well, what criterion do we use? Suppose I come into a paint store with a sample of the color of my living room wall, and ask for some paint of the same (identical) color. How do I go about deciding whether the color of the paint handed to me is or is not identical with that on my wall? The answer seems clear: I bring a sample of the paint and a sample of the wall-color close together, and if they resemble each other I say they have the same (identical) color. Similarly, to find out whether St. Mary's bell has a pitch identical with that of St. Thomas' bell, I listen carefully to a peal from each and compare. In short, similarity is the criterion for membership in qualityclasses; and our chief task is therefore this: given particulars and the relation of similarity holding among pairs of particulars, how can qualities be defined as certain kinds of classes? But before describing what sort of class a quality actually is, we must deal with several complexities in the ordinary concept of similarity. In ordinary language things are not merely similar but are more or less similar, and, to make the situation worse, they are more or less similar in two quite different ways. For by saying that x is more similar to y than to z I may mean either that x is similar to y in more respects than it is to z, or that, whatever the respect in which they are similar, x is more closely similar to y in that respect than to z. For example, a nickel resembles a dime in both color and shape, while resembling a penny only in shape; and the color of a dime is more like that of a quarter than like that of a nickel. Now both the fact that things are similar in different respects, and the fact that things are similar in varying intensities, give trouble to the nominalist. Consider first the difficulties arising from the varying intensities of similarity. The problem is just this: what degree of similarity is necessary for identity of qualities? That it is less than exact similarity seems to be implied by the fact that green things are by no means all exactly similar in color. Sage, lakes, blotters, grass, lamps, flower pots, bruises—all are green, but all are not exactly similar in color. On the other hand, if I ask for paint of the same color as that already on my wall, I would not be satisfied with just a green, or even an olive-green. And if a psychologist tells me to adjust a second light until it has the same brightness as the first, he clearly means exactly the same. Indeed, it always makes sense to say of qualities that they are almost the same but still not identical. So it is not clear what degree of similarity is necessary for identity of qualities. I am inclined to think, however, that it is exact similarity, and that the difference in shades of green can be given another -206-

explanation. But whether I am right or wrong on this point will make no difference. For I shall show later that precisely the same difficulties arise for the realist; and hence the difficulties arising from varying intensities of similarity cannot be used as a ground for preferring realism. I shall, in what I say further, mean by "similarity" always exact similarity;

but this will in no way prejudge my central thesis. The difficulties arising from the fact that things are similar in various respects are more troublesome. A quality-class would seem, quite clearly, to be a class of all and only those things which are similar in a certain respect. Or, to put it more precisely, a quality-class is a class which fulfills these two requirements: (i) of the members of the class, each is similar to every other; (ii) no thing outside the class is similar to every member of the class. But it would seem that, unless we introduce more conditions, this definition by no means yields only those classes which can plausibly be identified with qualities. One of the difficulties which arises is called by Goodman the difficulty of imperfect community. 8 Suppose the universe included a class of things of the following description: one is green and hard, another is hard and square, and a third is square and green— symbolized as gh, hs, and sg. Now this class fulfills our requirements for a quality-class, since each member is similar to every other, and we are to suppose that there is nothing outside the class which is similar to every member of the class. Yet there is no quality common to the three members, and consequently the class cannot be identified with a quality. A second difficulty Goodman calls the companionship difficulty. Suppose that everything green is sticky, and everything sticky is green. In this case the class of green entities would be identical with the class of sticky entities. But then the qualities greenness and stickiness cannot be identified with this class; for greenness is not identical with stickiness. Now it would seem that, to prevent these difficulties, we must somehow get at the inside of particulars and distinguish the different respects in which they resemble each other. Thus we might try taking similarity as a triadic relation, saying always that x is similar to y in respect to z, and then defining a quality- class as a class of particulars similar to each other in only one respect, and that the same respect throughout. But this would be to give up the game immediately. For suppose we do regard similarity as a triadic relation, always saying, for instance, that the blotter is similar to the coat in respect to its color. What then does "color" refer to? A class of particulars? If so, we have precisely the same difficulty that we were trying to escape. So apparently it refers to a universal, with the usage of "the same respect" determined according to the criteria recommended by the realist. But this was just what the nominalist wanted to avoid. Thus, since respects in this context are universals, the nominalist can make no use of them. But there is a way of avoiding the difficulties of companionship and imperfect community, and this is just to keep in mind that the class of particulars includes not only concrete physical objects and events but also what I have ____________________ 8N. Goodman, The Structure of Appearance (Cambridge, Mass., 1951), pp. 124 ff. -207-

called the aspects of these. The color of the Taj Mahal (on one interpretation of this phrase), as well as the Taj Mahal, is a particular; and a color patch as well as a tree is an instance of greenness. Furthermore, there are aspects of aspects, for instance, the hue of the color of the Taj Mahal. We are, then, to remember that the relation of similarity holds among aspects as well as among concrete particulars. Now no doubt an apprehension will arise over using qualitative aspects of things in order to define qualities. I do not think, however, that such a procedure is circular. For I may very well recognize the shape of Eisenhower's face without having an independent recognition of that shape itself—without knowing what kind of shape it is, without being able to say in what way this shape differs from other shapes, without being able to sketch it, and so forth. The inclusion of aspects in our quality-classes immediately eliminates the companionship difficulty. This arose, it will be remembered, whenever we had a class of things of this schematic form: gs, gs, gs. But now we also have the two particulars g and s. According to our rules then, gs, gs, gs, g will form one quality-class; and gs, gs, gs, s will form another. The two classes have different memberships and are therefore not identical because s and g do

not resemble each other. The difficulty of imperfect community is likewise solved. Our example illustrating this was, schematically, gh, hs, sg. We are now directed to allow also the three aspects g, h, and s. This gives us the three classes gh, sg, g; gh, hs, h; and hs, sg, s; and the difficulty is resolved. In summary then, a quality, according to a nominalist, is a class of all and only those particulars which bear a certain resemblance to each other. Hence qualities A and B are identical if and only if they have the same instances (members); and we determine whether they do or do not have the same instances by observing the relations of similarity and dissimilarity among the instances. 4. Now the realist regards all this as wrong, and insists that qualities are not classes of particulars but are instead universals. Such classes may, in some way, be associated with qualities, but they are not to be identified with them. What then does the realist propose as the identity criterion for qualities? Consider again the example of my coming into the paint store and asking for some paint of the same color as that on my wall. How do I decide whether the color of the paint is identical with the color of my wall? Obviously what I do is compare the colors. And if I find that they resemble each other exactly, I say that this color is identical with that. Similarly, to find out whether the pitch of St. Mary's bell is identical with the pitch of St. Paul's, I listen carefully to see whether I can discern any difference in pitch. And to find out whether the flavor of this cheap Scotch is really identical with the flavor of this expensive Scotch, I taste each carefully and compare the flavors. Thus the relation of similarity constitutes the identity criterion for universals. The contrast between nominalism and realism is often drawn by saying that the former makes use of the relation of similarity holding between particulars, whereas the latter makes use of the notion of universals shared by -208-

particulars. 9 But it can now be seen that this contrast between resemblance - theorists and universals-theorists is improperly drawn. Both theories make use of the relation of resemblance, the only difference being that they use it in different ways. The nominalist uses resemblance as the criterion for membership in quality-classes, whereas the realist uses resemblance as the criterion for identity of universals. And it is because both theories use the relation of resemblance that any vagueness which appears in the one theory as a result of vagueness in the notion of resemblance will make a parallel appearance in the other. Now the usual objections to the realistic interpretation of qualities are made, not on the ground that it involves a program impossible of being carried out, but rather on the ground that it involves a commitment to queer and weird entities, things best shunned. This seems to me a baseless prejudice, and I shall concentrate my attention on showing why the objection is not applicable. There is, for instance, a long and by no means dead tradition to the effect that only particulars can be perceived, that universals may be objects of reason but not of perception. But this is certainly mistaken. For we can play a pitch on a violin, relish a sweetness on our tongues, feel annoyed by an acridity, and watch admiringly an old man's tenacity. The usual doctrine is that we can play sounds but not pitches, taste stuffs but not sweetness, be annoyed by smells but not by acridity, and observe an old man but not tenacity. But once we see that the reference of terms and of pointings is fixed by the identity criteria of the entity referred to, and once we see that there are identity criteria for universals as well as for particulars, there seems no reason at all to defend the dictum that only instances of universals can be perceived but not universals themselves. Psychologists, in speaking of brightness and loudness scales, have had the correct intuition. Immediately associated with the view just considered is the belief, present in Western philosophy almost since its inception, that universals are indifferent to the buzz of space and time, composing a still and immutable world of their own. But this is equally mistaken; for if we can point to and perceive universals, then universals must be locatable. The basis

of the traditional doctrine is, I suppose, a vague intuition of the fact that places and times play no role in determining the identity of universals. But of course it does not follow from this that universals are outside of space and time. Greenness does appear at certain times and places; the father in teaching his child says, "Here's green, and here's green, and here's green again." And though we would probably never ask, "Where is green?" men have asked "Where is virtue to be found?" and conductors have no doubt inquired "Where is that F-sharp coming from?" So the usual dread of admitting the existence of universals is quite unfounded. They are quite as humdrum and quite as circumambient as particulars, differing just in the fact that the criteria for saying "This is the same universal as that" are different from those for saying "This is the same physical object as that." ____________________ 9Cf. H. H. Price, Thinking and Experience (London, 1953), ch. I. -209-

5. We have seen, then, that both realism and nominalism can be given consistent and plausible interpretations. According to the nominalist, similarity is a relation holding among particulars, and we use it as the criterion for membership in quality-classes. According to the realist, similarity is a relation holding among qualities as well, and we use it as the criterion for the identity of universals. Which theory, then, is correct? What statements do we make about qualities which show that the one interpretation is right and the other wrong? i. We might consider, first, the statements which gave the nominalist trouble previously—for example, "The color of this table is identical with the color of that table." Now the realist interprets this to mean that there is here one entity, a universal, shared by two particulars; and he holds that we establish the identity of this entity by comparing the color of this table with the color of that. And this is certainly a plausible interpretation. Unfortunately, however, the nominalist's interpretation is equally plausible. For he interprets the sentence to mean that there is here one entity, a class, of which these two particulars are members; and he holds that we establish the fact that they are members of the same class by comparing the two tables. So this sort of statement—statements asserting an identity of qualities—can be handled easily by both theories. ii. But there is another kind of statement which, prima facie at least, offers more promise. According to the nominalist, similarity holds only among particulars. Apparently all we need do then to refute nominalism is find statements asserting similarity among qualities. And such are immediately at hand; for instance, "Yellow is more like orange than like purple." But will this really turn the trick; is it impossible to give a nominalistic interpretation of this sentence? One paraphrase which the nominalist might suggest is this: take anything yellow, anything orange, and anything purple; then the yellow thing is more like the orange thing than like the purple thing. But there is no assurance that this statement is even true; for though, in respect to color, yellow things are more like orange things than like purple things, this may well not be true in general. The way around this objection, however, is just to make the paraphrase refer to aspects and not to concrete things, thus: for anything yellow and anything orange and anything purple, the color of the yellow thing is more similar to the color of the orange thing than to the color of the purple thing. And though this is by no means as straightforward an interpretation of our original statement as that which the realist can give, there seems to be no consideration which would show it to be actually mistaken. So apparently there is no way of showing either theory to be incorrect. But it might still be felt that there are grounds for preferring one theory to the other. So let us consider various suggestions to this effect. i. Is there any way, for instance, of showing the one theory to be simpler than the other? I think not. For the realist assumes the existence of universals, whereas the nominalist assumes the existence of quality-classes. Consequently on this level they are precisely comparable. Furthermore, the definition of -210-

ii.

quality-classes does not seem to me significantly more or less complicated than that of universals. So the test of simplicity yields inconclusive results. It has sometimes been argued that the criteria for the identity of classes are clearer than those for universals; and if this were true, it would certainly be a reason for preferring nominalism. But whether or not universals are in general vaguer entities than classes (and I suppose they are), they are certainly no more vague than quality-classes. For as we have already seen, both the realist and the nominalist make use of the notion of similarity; consequently any vagueness in the one theory will find its parallel in the other. So the criterion of clarity also gives no ground for preference.

6. My conclusion to this whole discussion, therefore, is that there is no ground whatever for preferring either realism or nominalism. Now in such a situation, the intuitive response of the contemporary philosopher is to suspect that the dispute is meaningless. But it is clear that this is not the case. For if the color of two tables is indistinguishable, the realist says the color of the one is therefore identical with the color of the other, whereas the nominalist says they are exactly similar and therefore belong to the same quality-class. But "is similar to" is not synonymous with "is identical with"; and regarding entities as identical if and only if they have the same members is not the same as regarding entities as identical if and only if they are exactly similar. Hence we find that we have here the anomalous situation of a meaningful but pointless dispute. To see more clearly the source of this anomaly, consider a hypothetical case in which the distinction between similarity and identity cannot, as a matter of fact, be drawn. Suppose, for instance, that identity of persons were determined by identity of memories; and imagine that I find a person with memories the same as mine in all respects. Are his memories then identical with mine, or are they merely exactly similar? I think it is easily seen that such a question cannot be answered. The distinction between the two senses of "the same" is here inoperative; for there is no defense which one could give of the contention that they are similar but not identical, but there is also no defense which one could give of the contention that they are not only similar but identical. The distinction between qualitative and numerical sameness is vacuous. But the situation with respect to qualities is not quite like this, for the nominalist can point to something which will distinguish similarity from identity, namely, difference of place; and his contention is that, though x and y may be qualitatively similar, this does not prove that they are identical. So the issue here is not whether similarity can be distinguished from identity, but whether difference of place shall establish nonidentity. Now in the case of physical objects it does; all 1959 Fords may be qualitatively alike, but they are not identical. And if this were the only permissible criterion for the identity of entities, realism would be an impossible view; indeed, one could not even distinguish between the meaning and the criteria of identity. But suppose on the other hand that all our singular terms referred to universals. In this case -211-

nominalism would be an impossible view, and again there would be no way of distinguishing between the meaning and the criteria of identity. As a matter of fact, however, identity can be determined according to different criteria; and so the issue is joined. But it cannot be settled. For though the nominalist may insist on diversity of places as implying nonidentity, he can give no justification for his insistence; and though the realist may insist that nonidentity of places does not always determine nonidentity of entities, he too can give no reason for his insistence. The debate is thus clear enough, and it may seem surprising that our language fails to reflect it. Still, it may not be so surprising. For in the first place, both theories regard similarity as, directly or indirectly, determining the identity of qualities. And secondly, in our existing language the reference of quality-descriptions is ambiguous, and it is this ambiguity which is fundamental to the whole issue. For though there are indeed some cases in which qualitydescriptions cannot be interpreted as referring to particulars, we saw that the nominalist can, by using the notion of classes, still interpret them as referring in a roundabout way to particulars. Hence we end where we began.

Whatever be the reasons, though, it is clear that, given our actual language, there is no point is distinguishing senses of "this is the same as that" when dealing with qualities. For whatever our theory, we would all agree that a person knew what colors were if, upon being asked to bring something of the same color as the green thing I have, he always brought something green. 10 ____________________ 10I have profited a great deal in writing this paper from conversations with Mr. Noel Fleming. [Later, more fully developed, and somewhat revised thoughts on the issues discussed in this article will be found in the author's book, On Universals: An Essay in Ontology (Chicago: University of Chicago Press, 1970)—ED.] -212-

PART THREE Abstract Entities, Meaning, and Language

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: 13 : ON WHAT THERE IS 1 W. V. QUINE A curious thing about the ontological problem is its simplicity. It can be put in three Anglo-Saxon monosyllables: "What is there?" It can be answered, moreover, in a word—"Everything"—and everyone will accept this answer as true. However, this is merely to say that there is what there is. There remains room for disagreement over cases; and so the issue had stayed alive down the centuries. Suppose now that two philosophers, McX and I, differ over ontology. Suppose McX maintains there is something which I maintain there is not. McX can, quite consistently with his own point of view, describe our difference of opinion by saying that I refuse to recognize certain entities. I should protest of course that he is wrong in his formulation of our disagreement, for I maintain that there are no entities, of the kind which he alleges, for me to recognize; but my finding him wrong in his formulation of our disagreement is unimportant, for I am committed to considering him wrong in his ontology anyway. When I try to formulate our difference of opinion, on the other hand, I seem to be in a predicament. I cannot admit that there are some things which McX countenances and I do not, for in admitting that there are such things I should be contradicting my own rejection of them. It would appear, if this reasoning were sound, that in any ontological dispute the proponent of the negative side suffers the disadvantage of not being able to admit that his opponent disagrees with him. This is the old Platonic riddle of non-being. Non-being must in some sense be, otherwise what is it that there is not? This tangled doctrine might be nicknamed Plato's beard; historically it has proved tough, frequently dulling the edge of Occam's razor. It is some such line of thought that leads philosophers like McX to impute being where they might otherwise be quite content to recognize that there is nothing. Thus, take Pegasus. If

Pegasus were not, McX argues, we should ____________________ Reprinted from The Review of Metaphysics, II (1948) by permission of the editor and the author. 1This is a revised version of a paper which was presented before the Graduate Philosophy Club of Yale University on May 7, 1948. The latter paper, in turn, was a revised version of one which was presented before the Graduate Philosophical Seminar of Princeton University on March 15.

not be talking about anything when we use the word; therefore it would be nonsense to say even that Pegasus is not. Thinking to show thus that the denial of Pegasus cannot be coherently maintained, he concludes that Pegasus is. McX cannot, indeed, quite persuade himself that any region of space-time, near or remote, contains a flying horse of flesh and blood. Pressed for further details on Pegasus, then, he says that Pegasus is an idea in men's minds. Here, however, a confusion begins to be apparent. We may for the sake of argument concede that there is an entity, and even a unique entity (though this is rather implausible), which is the mental Pegasus-idea; but this mental entity is not what people are talking about when they deny Pegasus. McX never confuses the Parthenon with the Parthenon-idea. The Parthenon is physical; the Parthenon-idea is mental (according any way to McX's version of ideas, and I have no better to offer). The Parthenon is visible; the Parthenon-idea is invisible. We cannot easily imagine two things more unlike, and less liable to confusion, than the Parthenon and the Parthenon-idea. But when we shift from the Parthenon to Pegasus, the confusion sets in—for no other reason than that McX would sooner be deceived by the crudest and most flagrant counterfeit than grant the non-being of Pegasus. The notion that Pegasus must be, because it would otherwise be nonsense to say even that Pegasus is not, has been seen to lead McX into an elementary confusion. Subtler minds, taking the same precept as their starting point, come out with theories of Pegasus which are less patently misguided than McX's, and correspondingly more difficult to eradicate. One of these subtler minds is named, let us say, Wyman. Pegasus, Wyman maintains, has his being as an unactualized possible. When we say of Pegasus that there is no such thing, we are saying, more precisely, that Pegasus does not have the special attribute of actuality. Saying that Pegasus is not actual is on a par, logically, with saying that the Parthenon is not red; in either case we are saying something about an entity whose being is unquestioned. Wyman, by the way, is one of those philosophers who have united in ruining the good old word "exist." Despite his espousal of unactualized possibles, he limits the word "existence" to actuality—thus preserving an illusion of ontological agreement between himself and us who repudiate the rest of his bloated universe. We have all been prone to say, in our common-sense usage of "exist," that Pegasus does not exist, meaning simply that there is no such entity at all. If Pegasus existed he would indeed be in space and time, but only because the word "Pegasus" has spatio-temporal connotations, and not because "exists" has spatiotemporal connotations. If spatio-temporal reference is lacking when we affirm the existence of the cube root of 27, this is simply because a cube root is not a spatio-temporal kind of thing, and not because we are being ambiguous in our use of "exist." However, Wyman, in an ill-conceived effort to appear agreeable, genially grants us the non - existence of Pegasus and then, contrary to what we meant by non-existence of Pegasus, insists that Pegasus is. Existence is one thing, he says, and sub -216-

sistence is another. The only way I know of coping with this obfuscation of issues is to give Wyman the word "exist." I'll try not to use it again; I still have "is." So much for lexicography; let's get back to Wyman's ontology. Wyman's overpopulated universe is in many ways unlovely. It offends the aesthetic sense of us who have a taste for desert landscapes, but this is not the worst of it. Wyman's slum of

possibles is a breeding ground for disorderly elements. Take, for instance, the possible fat man in that doorway; and, again, the possible bald man in that doorway. Are they the same possible man, or two possible men? How do we decide? How many possible men are there in that doorway? Are there more possible thin ones than fat ones? How many of them are alike? Or would their being alike make them one? Are no two possible things alike? Is this the same as saying that it is impossible for two things to be alike? Or, finally, is the concept of identity simply inapplicable to unactualized possibilities? But what sense can be found in talking of entities which cannot meaningfully be said to be identical with themselves and distinct from one another? These elements are well nigh incorrigible. By a Fregean therapy of individual concepts, some effort might be made at rehabilitation; but I feel we'd do better simply to clear Wyman's slum and be done with it. Possibility, along with the other modalities of necessity and impossibility and contingency, raises problems upon which I do not mean to imply that we should turn our backs. But we can at least limit modalities to whole statements. We may impose the adverb "possibly" upon a statement as a whole, and we may well worry about the semantical analysis of such usage; but little real advance in such analysis is to be hoped for in expanding our universe to include so-called possible entities. I suspect that the main motive for this expansion is simply the old notion that Pegasus, e.g., must be because it would otherwise be nonsense to say even that he is not. Still, all the rank luxuriance of Wyman's universe of possibles would seem to come to naught when we make a slight change in the example and speak not of Pegasus but of the round square cupola on Berkeley College. If, unless Pegasus were, it would be nonsense to say that he is not, then by the same token, unless the round square cupola on Berkeley College were, it would be nonsense to say that it is not. But, unlike Pegasus, the round square cupola on Berkeley College cannot be admitted even as an unactualized possible. Can we drive Wyman now to admitting also a realm of unactualizable impossibles ? If so, a good many embarrassing questions could be asked about them. We might hope even to trap Wyman in contradictions, by getting him to admit that certain of these entities are at once round and square. But the wily Wyman chooses the other horn of the dilemma and concedes that it is nonsense to say that the round square cupola on Berkeley College is not. He says that the phrase "round square cupola" is meaningless. Wyman was not the first to embrace this alternative. The doctrine of the meaninglessness of contradictions runs [way] back. The tradition survives, moreover, in writers such as Wittgenstein who seem to share none of Wyman's -217-

motivations. Still I wonder whether the first temptation to such a doctrine may not have been substantially the motivation which we have observed in Wyman. Certainly the doctrine has no intrinsic appeal; and it has led its devotees to such quixotic extremes as that of challenging the method of proof by reductio ad absurdum—a challenge in which I seem to detect a quite striking reductio ad absurdum eius ipsius. Moreover, the doctrine of meaninglessness of contradictions has the severe methodological drawback that it makes it impossible, in principle, ever to devise an effective test of what is meaningful and what is not. It would be forever impossible for us to devise systematic ways of deciding whether a string of signs made sense—even to us individually, let alone other people—or not. For, it follows from a discovery in mathematical logic, due to Church, that there can be no generally applicable test of contradictoriness. I have spoken disparagingly of Plato's beard, and hinted that it is tangled. I have dwelt at length on the inconveniences of putting up with it. It is time to think about taking steps. Russell, in his theory of so-called singular descriptions, showed clearly how we might meaningfully use seeming names without supposing that the entities allegedly named be. The names to which Russell's theory directly applies are complex descriptive names such as "the author of Waverly," "the present King of France," "the round square cupola on Berkeley College." Russell analyzes such phrases systematically as fragments of the whole sentences in which they occur. The sentence "The author of Waverly was a poet," e.g., is explained as

a whole as meaning "Someone (better: something) wrote Waverly and was a poet, and nothing else wrote Waverly." (The point of this added clause is to affirm the uniqueness which is implicit in the word "the," in "the author of Waverly.") The sentence "The round square cupola on Berkeley College is pink" is explained as "Something is round and square and is a cupola on Berkeley College and is pink, and nothing else is round and square and a cupola on Berkeley College." The virtue of this analysis is that the seeming name, a descriptive phrase, is paraphrased in context as a so-called incomplete symbol. No unified expression is offered as an analysis of the descriptive phrase, but the statement as a whole which was the context of that phrase still gets its full quota of meaning—whether true or false. The unanalyzed statement "The author of Waverly was a poet" contains a part, "the author of Waverly," which is wrongly supposed by McX and Wyman to demand objective reference in order to be meaningful at all. But in Russell's translation, "Something wrote Waverly and was a poet and nothing else wrote Waverly," the burden of objective reference which had been put upon the descriptive phrase is now taken over by words of the kind that logicians call bound variables, variables of quantification: namely, words like "something," "nothing," "everything." These words, far from purporting to be names specifically of the author of Waverly, do not purport to be names at all; -218-

they refer to entities generally, with a kind of studied ambiguity peculiar to themselves. These quantificational words or bound variables are of course a basic part of language, and their meaningfulness, at least in context, is not to be challenged. But their meaingfulness in no way presupposes there being either the author of Waverly or the round square cupola on Berkeley College or any other specifically preassigned objects. Where descriptions are concerned, there is no longer any difficulty in affirming or denying being. "There is the author of Waverly" is explained by Russell as meaning "Someone (or, more strictly, something) wrote Waverly and nothing else wrote Waverly." "The author of Waverly is not" is explained, correspondingly, as the alternation "Either each thing failed to write Waverly or two or more things wrote Waverly." This alternation is false, but meaningful ; and it contains no expression purporting to designate the author of Waverly. The statement "The round square cupola on Berkeley College is not" is analyzed in similar fashion. So the old notion that statements of non-being defeat themselves goes by the board. When a statement of being or non-being is analyzed by Russell's theory of descriptions, it ceases to contain any expression which even purports to name the alleged entity whose being is in question, so that the meaningfulness of the statement no longer can be thought to presuppose that there be such an entity. Now what of "Pegasus"? This being a word rather than a descriptive phrase, Russell's argument does not immediately apply to it. However, it can easily be made to apply. We have only to rephrase "Pegasus" as a description, in any way that seems adequately to single out our idea: say "the winged horse that was captured by Bellerophon." Substituting such a phrase for "Pegasus," we can then proceed to analyze the statement "Pegasus is," or "Pegasus is not," precisely on the analogy of Russell's analysis of "The author of Waverly is" and "The author of Waverly is not." In order thus to subsume a one-word name or alleged name such as "Pegasus" under Russell's theory of description, we must of course be able first to translate the word into a description. But this is no real restriction. If the notion of Pegasus had been so obscure or so basic a one that no pat translation into a descriptive phrase had offered itself along familiar lines, we could still have availed ourselves of the following artificial and trivialseeming device: we could have appealed to the ex hypothesi unanalyzable, irreducible attribute of being Pegasus, adopting, for its expression, the verb "is-Pegasus," or "pegasizes." The noun "Pegasus" itself could then be treated as derivative, and identified after all with a description: "the thing that is-Pegasus," "the thing that pegasizes." If the importing of such a predicate as "pegasizes" seems to commit us to recognizing that there is a corresponding attribute, pegasizing, in Plato's heaven or in the mind of men, well

and good. Neither we nor Wyman nor McX have been contending, thus far, about the being or non-being of universals, but rather about that of Pegasus. If in terms of pegasizing we can -219-

interpret the noun "Pegasus" as a description subject to Russell's theory of descriptions, then we have disposed of the old notion that Pegasus cannot be said not to be without presupposing that in some sense Pegasus is. Our argument is now quite general. McX and Wyman supposed that we could not meaningfully affirm a statement of the form "So-and-so is not," with a simple or descriptive singular noun in place of "so-and-so," unless so-and-so be. This supposition is now seen to be quite generally groundless, since the singular noun in question can always be expanded into a singular description, trivially or otherwise, and then analyzed out a la Russell. We cannot conclude, however, that man is henceforth free of all ontological commitments. We commit ourselves outright to an ontology containing numbers when we say there are prime numbers between 1000 and 1010; we commit ourselves to an ontology containing centaurs when we say there are centaurs; and we commit ourselves to an ontology containing Pegasus when we say Pegasus is. But we do not commit ourselves to an ontology containing Pegasus or the author of Waverly or the round square cupola on Berkeley College when we say that Pegasus or the author of Waverly or the cupola in question is not. We need no longer labor under the delusion that the meaningfulness of a statement containing a singular term presupposes an entity named by the term. A singular term need not name to be significant. An inkling of this might have dawned on Wyman and McX even without benefit of Russell if they had only noticed—as so few of us do—that there is a gulf between meaning and naming even in the case of a singular term which is genuinely a name of an object. Frege's example will serve: the phrase "Evening Star" names a certain large physical object of spherical form, which is hurtling through space some scores of millions of miles from here. The phrase "Morning Star" names the same thing, as was probably first established by some observant Babylonian. But the two phrases cannot be regarded as having the same meaning; otherwise that Babylonian could have dispensed with his observations and contented himself with reflecting on the meanings of his words. The meanings, then, being different from one another, must be other than the named object, which is one and the same in both cases. Confusion of meaning with naming not only made McX think he could not meaningfully repudiate Pegasus; a continuing confusion of meaning with naming no doubt helped engender his absurd notion that Pegasus is an idea, a mental entity. The structure of his confusion is as follows. He confused the alleged named object Pegasus with the meaning of the word "Pegasus," therefore concluding that Pegasus must be in order that the word have meaning. But what sorts of things are meanings? This is a moot point; however, one might quite plausibly explain meanings as ideas in the mind, supposing we can make clear sense in turn of the idea of ideas in the mind. Therefore Pegasus, initially confused with a meaning, ends up as an idea in the mind. It is the more remarkable that Wyman, subject to the same initial motivation as McX, should have avoided this particular blunder and wound up with unactualized possibles instead. -220-

Now let us turn to the ontological problem of universals: the question whether there are such entities as attributes, relations, classes, numbers, functions. McX, characteristically enough, thinks there are. Speaking of attributes, he says: "There are red houses, red roses, red sunsets; this much is pre-philosophical common-sense in which we must all agree. These houses, roses, and sunsets, then, have something in common; and this which they have in common is all I mean by the attribute of redness." For McX, thus, there being attributes is even more obvious and trivial than the obvious and trivial fact of there being red houses, roses, and sunsets. This, I think, is characteristic of metaphysics, or at least of that part of metaphysics called ontology: one who regards a statement on this subject as true at all must

regard it as trivially true. One's ontology is basic to the conceptual scheme by which he interprets all experiences, even the most commonplace ones. Judged within some particular conceptual scheme—and how else is judgment possible?—an ontological statement goes without saying, standing in need of no separate justification at all. Ontological statements follow immediately from all manner of casual statements of commonplace fact, just as—from the point of view, anyway, of McX's conceptual scheme—"There is an attribute" follows from "There are red houses, red roses, red sunsets." Judged in another conceptual scheme, an ontological statement which is axiomatic to McX's mind may, with equal immediacy and triviality, be adjudged false. One may admit that there are red houses, roses, and sunsets, but deny, except as a popular and misleading manner of speaking, that they have anything in common. The words "houses," "roses," and "sunsets" denote each of sundry individual entities which are houses and roses and sunsets, and the word "red" or "red object" denotes each of sundry individual entities which are red houses, red roses, red sunsets; but there is not, in addition, any entity whatever, individual or otherwise, which is named by the word "redness," nor, for that matter, by the word "househood," "rosehood," sunsethood." That the houses and roses and sunsets are all of them red may be taken as ultimate and irreducible, and it may be held that McX is no better off, in point of real explanatory power, for all the occult entities which he posits under such names as "redness." One means by which McX might naturally have tried to impose his ontology of universals on us was already removed before we turned to the problem of universals. McX cannot argue that predicates such as "red" or "is-red," which we all concur in using, must be regarded as names each of a single universal entity in order that they be meaningful at all. For, we have seen that being a name of something is a much more special feature than being meaningful. He cannot even charge us—at least not by that argument—with having posited an attribute of pegasizing by our adoption of the predicate "pegasizes." However, McX hits upon a different stratagem. "Let us grant," he says, "this distinction between meaning and naming of which you make so much. Let us even grant that "is red," "pegasizes," etc., are not names of attributes. Still, you admit they have meanings. But these meanings, whether they are -221-

named or not, are still universals, and I venture to say that some of them might even be the very things that I call attributes, or something to much the same purpose in the end." For McX, this is an unusually penetrating speech; and the only way I know to counter it is by refusing to admit meanings. However, I feel no reluctance toward refusing to admit meanings, for I do not thereby deny that words and statements are meaningful. McX and I may agree to the letter in our classification of linguistic forms into the meaningful and the meaningless, even though McX construes meaningfulness as the having (in some sense of "having") of some abstract entity which he calls a meaning, whereas I do not. I remain free to maintain that the fact that a given linguistic utterance is meaningful (or significant, as I prefer to say so as not to invite hypostasis of meanings as entities) is an ultimate and irreducible matter of fact; or, I may undertake to analyze it in terms directly of what people do in the presence of the linguistic utterance in question and other utterances similar to it. The useful ways in which people ordinarily talk or seem to talk about meanings boil down to two: the having of meanings, which is significance, and sameness of meaning, or synonymy. What is called giving the meaning of an utterance is simply the uttering of a synonym, couched, ordinarily, in clearer language than the original. If we are allergic to meanings as such, we can speak directly of utterances as significant or insignificant, and as synonymous or heteronymous one with another. The problem of explaining these adjectives "significant" and "synonymous" with some degree of clarity and rigor—preferably, as I see it, in terms of behavior—is as difficult as it is important. But the explanatory value of special and irreducible intermediary entities called meanings is surely illusory. Up to now I have argued that we can use singular terms significantly in sentences without presupposing that there be the entities which those terms purport to name. I have argued

further that we can use general terms, e.g., predicates, without conceding them to be names of abstract entities. I have argued further that we can view utterances as significant, and as synonymous or heteronymous with one another, without countenancing a realm of entities called meanings. At this point McX begins to wonder whether there is any limit at all to our ontological immunity. Does nothing we may say commit us to the assumption of universals or other entities which we may find unwelcome ? I have already suggested a negative answer to this question, in speaking of bound variables, or variables of quantification, in connection with Russell's theory of descriptions. We can very easily involve ourselves in ontological commitments, by saying, e.g., that there is something (bound variable) which red houses and sunsets have in common; or that there is something which is a prime number between 1000 and 1010. But this is, essentially, the only way we can involve ourselves in ontological commitments: by our use of bound variables. The use of alleged names is no criterion, for we can repudiate their -222-

namehood at the drop of a hat unless the assumption of a corresponding entity can be spotted in the things we affirm in terms of bound variables. Names are in fact altogether immaterial to the ontological issue, for I have shown, in connection with "Pegasus" and "pegasize," that names can be converted to descriptions, and Russell has shown that descriptions can be eliminated. Whatever we say with help of names can be said in a language which shuns names altogether. To be is, purely and simply, to be the value of a variable. In terms of the categories of traditional grammar, this amounts roughly to saying that to be is to be in the range of reference of a pronoun. Pronouns are the basic media of reference; nouns might better have been named pro-pronouns. The variables of quantification, "something," "nothing," "everything," range over our whole ontology, whatever it may be; and we are convicted of a particular ontological presupposition if, and only if, the alleged presuppositum has to be reckoned among the entities over which our variables range in order to render one of our affirmations true. We may say, e.g., that some dogs are white, and not thereby commit ourselves to recognizing either doghood or whiteness as entities. "Some dogs are white" says that some things that are dogs are white; and, in order that this statement be true, the things over which the bound variable "something" ranges must include some white dogs, but need not include doghood or whiteness. On the other hand, when we say that some zoölogical species are cross - fertile, we are committing ourselves to recognizing as entities the several species themselves, abstract though they be. We remain so committed at least until we devise some way of so paraphrasing the statement as to show that the seeming reference to species on the part of our bound variable was an avoidable manner of speaking. If I have been seeming to minimize the degree to which in our philosophical and unphilosophical discourse we involve ourselves in ontological commitments, let me then emphasize that classical mathematics, as the example of primes between 1000 and 1010 clearly illustrates, is up to its neck in commitments to an ontology of abstract entities. Thus it is that the great mediaeval controversy over universals has flared up anew in the modern philosophy of mathematics. The issue is clearer now than of old, because we now have a more explicit standard whereby to decide what ontology a given theory or form of discourse is committed to: a theory is committed to those and only those entities to which the bound variables of the theory must be capable of referring in order that the affirmations made in the theory be true. Because this standard of ontological presupposition did not emerge clearly in the philosophical tradition, the modern philosophical mathematicians have not on the whole recognized that they were debating the same old problem of universals in a newly clarified form. But the fundamental cleavages among modem points of view on foundations of mathematics do come down pretty explicitly to disagreements as to the range of entities to which the bound variables should be permitted to refer. The three main mediaeval points of view regarding universals are designated -223-

by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism. Realism, as the word is used in connection with the mediaeval controversy over universals, is the Platonic doctrine that universals or abstract entities have being independently of the mind; the mind may discover them but cannot create them. Logicism, represented by such latter-day Platonists as Frege, Russell, Whitehead, Church, and Carnap, condones the use of bound variables to refer to abstract entities known and unknown, specifiable and unspecifiable, indiscriminately. Conceptualism holds that there are universals but they are mind-made. Intuitionism, espoused in modern times in one form or another by Poincaré, Brouwer, Weyl, and others, countenances the use of bound variables to refer to abstract entities only when those entities are capable of being cooked up individually from ingredients specified in advance. As Fraenkel has put it, logicism holds that classes are discovered while intuitionism holds that

they are invented—a fair statement indeed of the old opposition between realism and conceptualism. This opposition is no mere quibble; it makes an essential difference in the amount of classical mathematics to which one is willing to subscribe. Logicists, or realists, are able on their assumptions to get Cantor's ascending orders of infinity; intuitionists are compelled to stop with the lowest order of infinity, and, as an indirect consequence, to abandon even some of the classical laws of real numbers. The modern controversy between logicism and intuitionism arose, in fact, from disagreements over infinity. Formalism, associated with the name of Hilbert, echoes intuitionism in deploring the logicist's unbridled recourse to universals. But formalism also finds intuitionism unsatisfactory. This could happen for either of two opposite reasons. The formalist might, like the logicist, object to the crippling of classical mathematics; or he might, like the nominalists of old, object to admitting abstract entities at all, even in the restrained sense of mind-made entities. The upshot is the same: the formalist keeps classical mathematics as a play of insignificant notations. This play of notations can still be of utility—whatever utility it has already shown itself to have as a crutch for physicists and technologists. But utility need not imply significance, in any literal linguistic sense. Nor need the marked success of mathematicians in spinning out theorems, and in finding objective bases for agreement with one another's results, imply significance. For, an adequate basis for agreement among mathematicians can be found simply in the rules which govern the manipulation of the notations— these syntactical rules being, unlike the notations themselves, quite significant and intelligible. 2 I have argued that the sort of ontology we adopt can be consequential— notably in connection with mathematics, although this is only an example. Now how are we to adjudicate among rival ontologies? Certainly the answer is ____________________ 2See Goodman and Quine, "Steps toward a constructive nominalism," Journal of Symbolic Logic, vol. 12 (1947), pp. 97-122. -224-

not provided by the semantical formula "To be is to be the value of a variable" ; this formula serves rather, conversely, in testing the conformity of a given remark or doctrine to a prior ontological standard. We look to bound variables in connection with ontology not in order to know what there is, but in order to know what a given remark or doctrine, ours or someone else's, says there is; and this much is quite properly a problem involving language. But what there is is another question. In debating over what there is, there are still reasons for operating on a semantical plane. One reason is to escape from the predicament noted at the beginning of the paper: the predicament of my not being able to admit that there are things which McX countenances and I do not. So long as I adhere to my ontology, as opposed to McX's, I cannot allow my bound variables to refer to entities which belong to McX's ontology and not to mine. I can, however, consistently describe our disagreement by characterizing the statements which McX affirms. Provided merely that my ontology countenances linguistic forms, or at least concrete inscriptions and utterances, I can talk about McX's sentences. Another reason for withdrawing to a semantical plane is to find common ground on which to argue. Disagreement in ontology involves basic disagreement in conceptual schemes; yet McX and I, despite these basic disagreements, find that our conceptual schemes converge sufficiently in their intermediate and upper ramifications to enable us to communicate successfully on such topics as politics, weather, and, in particular, language. In so far as our basic controversy over ontology can be translated upward into a semantical controversy about words and what to do with them, the collapse of the controversy into questionbegging may be delayed. It is no wonder, then, that ontological controversy should tend into controversy over language. But we must not jump to the conclusion that what there is depends on words. Translatability of a question into semantical terms is no indication that the question is linguistic. To see Naples is to bear a name which, when prefixed to the words "sees Naples,"

yields a true sentence; still there is nothing linguistic about seeing Naples. Our acceptance of an ontology is, I think, similar in principle to our acceptance of a scientific theory, say a system of physics: we adopt, at least insofar as we are reasonable, the simplest conceptual scheme into which the disordered fragments of raw experience can be fitted and arranged. Our ontology is determined once we have fixed upon the over-all conceptual scheme which is to accommodate science in the broadest sense; and the considerations which determine a reasonable construction of any part of that conceptual scheme, e.g. the biological or the physical part, are not different in kind from the considerations which determine a reasonable construction of the whole. To whatever extent the adoption of any system of scientific theory may be said to be a matter of language, the same—but no more— may be said of the adoption of an ontology. But simplicity, as a guiding principle in constructing conceptual schemes, -225-

is not a clear and unambiguous idea; and it is quite capable of presenting a double or multiple standard. Imagine, e.g., that we have devised the most economical set of concepts adequate to the play-by-play reporting of immediate experience. The entities under this scheme—the values of bound variables—are, let us suppose, individual subjective events of sensation or reflection. We should still find, no doubt, that a physicalistic conceptual scheme, purporting to talk about external objects, offers great advantages in simplifying our over-all reports. By bringing together scattered sense events and treating them as perceptions of one object, we reduce the complexity of our stream of experience to a manageable conceptual simplicity. The rule of simplicity is indeed our guiding maxim in assigning sense data to objects: we associate an earlier and a later round sensum with the same so-called penny, or with two different so-called pennies, in obedience to the demands of maximum simplicity in our total world-picture. Here we have two competing conceptual schemes, a phenomenalistic one and a physicalistic one. Which should prevail? Each has its advantages; each has its special simplicity in its own way. Each, I suggest, deserves to be developed. Each may be said, indeed, to be the more fundamental, though in different senses: the one is epistemologically, the other physically, fundamental. The physical conceptual scheme simplifies our account of experience because of the way myriad scattered sense events come to be associated with single so-called objects; still there is no likelihood that each sentence about physical objects can actually be translated, however deviously and complexly, into the phenomenalistic language. Physical objects are postulated entities which round out and simplify our account of the flux of experience, just as the introduction of irrational numbers simplifies laws of arithmetic. From the point of view of the conceptual scheme of the elementary arithmetic of rational numbers alone, the broader arithmetic of rational and irrational numbers would have the status of a convenient myth, simpler than the literal truth (namely the arithmetic of rationals) and yet containing that literal truth as a scattered part. Similarly, from a phenomenalistic point of view, the conceptual scheme of physical objects is a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part. Now what of classes or attributes of physical objects, in turn? A platonistic ontology of this sort is, from the point of view of a strictly physicalistic conceptual scheme, as much of a myth as that physicalistic conceptual scheme itself was for phenomenalism. This higher myth is a good and useful one, in turn, in so far as it simplifies our account of physics. Since mathematics is an integral part of this higher myth, the utility of this myth for physical science is evident enough. In speaking of it nevertheless as a myth, I echo that philosophy of mathematics to which I alluded earlier under the name of formalism. But my present suggestion is that an attitude of formalism may with equal justice be adopted toward the physical conceptual scheme, in turn, by the pure aesthete or phenomenalist. -226-

The analogy between the myth of mathematics and the myth of physics is, in some additional and perhaps fortuitous ways, strikingly close. Consider, for example, the crisis which was precipitated in the foundations of mathematics, at the turn of the century, by the discovery of Russell's paradox and other antinomies of set theory. These contradictions had to be obviated by unintuitive, ad hoc devices; our mathematical myth-making became deliberate and evident to all. But what of physics? An antinomy arose between the undular and the corpuscular accounts of light; and if this was not as out-and- out a contradiction as Russell's paradox, I suspect that the reason is merely that physics is not as out-and-out as mathematics. Again, the second great modem crisis in the foundations of mathematics —precipitated in 1931 by Godel's proof that there are bound to be undecidable statements in arithmetic —has its companion-piece in physics in Heisenberg's indeterminacy principle. In earlier pages I undertook to show that some common arguments in favor of certain ontologies are fallacious. Further, I advanced an explicit standard whereby to decide what the ontological commitments of a theory are. But the question of what ontology actually to adopt still stands open, and the obvious counsel is tolerance and an experimental spirit. Let us by all means see how much of the physicalistic conceptual scheme can be reduced to a phenomenalistic one; still physics also naturally demands pursuing, irreducible in toto though it be. Let us see how, or to what degree, natural science may be rendered independent of platonistic mathematics; but let us also pursue mathematics and delve into its platonistic foundations. From among the various conceptual schemes best suited to these various pursuits, one—the phenomenalistic—claims epistemological priority. Viewed from within the phenomenalistic conceptual scheme, the ontologies of physical objects and mathematical objects are myths. The quality of myth, however, is relative; relative, in this case, to the epistemological point of view. This point of view is one among various, corresponding to one among our various interests and purposes. -227-

: 14 : EMPIRICISM, SEMANTICS, AND ONTOLOGY 1 RUDOLF CARNAP

The Problem of Abstract Entities Empiricists are in general rather suspicious with respect to any kind of abstract entities like properties, classes, relations, numbers, propositions, etc. They usually feel much more in sympathy with nominalists than with realists (in the medieval sense). As far as possible they try to avoid any reference to abstract entities and to restrict themselves to what is sometimes called a nominalistic language, i.e., one not containing such references. However, within certain scientific contexts it seems hardly possible to avoid them. In the case of mathematics, some empiricists try to find a way out by treating the whole of mathematics as a mere calculus, a formal system for which no interpretation is given or can be given. Accordingly, the mathematician is said to speak not about numbers, functions, and infinite classes, but merely about meaningless symbols and formulas manipulated according to given formal rules. In physics it is more difficult to shun the suspected entities, because the language of physics serves for the communication of reports and predictions and hence cannot be taken as a mere calculus. A physicist who is suspicious of abstract entities may perhaps try to declare a certain part of the language of physics as uninterpreted and uninterpretable, that part which refers to real numbers as space-time coordinates or as values of physical magnitudes, to functions, limits, etc. More probably he will just speak about all these things like anybody else but with an uneasy conscience, like a man who in his everyday life does with qualms many things which are not in accord with the high moral principles he professes on Sundays. Recently the problem of abstract entities has arisen again in connection with semantics, the theory of meaning and truth. Some semanticists say that certain expressions designate certain entities, and among these designated entities they

include not only concrete material things ____________________ Reprinted from Rudolf Camap, Meaning and Necessity, 2nd. ed., suppl. A (Chicago : University of Chicago Press, 1956) by permission of the author and the publisher. Copyright © 1956 by the University of Chicago Press. 1I have made here some minor changes in the formulations to the effect that the term "framework" is now used only for the system of linguistic expressions, and not for the system of the entities in question.

but also abstract entities e.g., properties as designated by predicates and propositions as designated by sentences. 2 Others object strongly to this procedure as violating the basic principles of empiricism and leading back to a metaphysical ontology of the Platonic kind. It is the purpose of this article to clarify this controversial issue. The nature and implications of the acceptance of a language referring to abstract entities will first be discussed in general; it will be shown that using such a language does not imply embracing a Platonic ontology but is perfectly compatible with empiricism and strictly scientific thinking. Then the special question of the role of abstract entities in semantics will be discussed. It is hoped that the clarification of the issue will be useful to those who would like to accept abstract entities in their work in mathematics, physics, semantics, or any other field; it may help them to overcome nominalistic scruples.

Linguistic Frameworks Are there properties, classes, numbers, propositions? In order to understand more clearly the nature of these and related problems, it is above all necessary to recognize a fundamental distinction between two kinds of questions concerning the existence or reality of entities. If someone wishes to speak in his language about a new kind of entities, he has to introduce a system of new ways of speaking, subject to new rules; we shall call this procedure the construction of a linguistic framework for the new entities in question. And now we must distinguish two kinds of questions of existence: first, questions of the existence of certain entities of the new kind within the framework; we call them internal questions; and second, questions concerning the existence or reality of the system of entities as a whole, called external questions. Internal questions and possible answers to them are formulated with the help of the new forms of expressions. The answers may be found either by purely logical methods or by empirical methods, depending upon whether the framework is a logical or a factual one. An external question is of a problematic character which is in need of closer examination. The world of things. Let us consider as an example the simplest kind of entities dealt with in the everyday language: the spatio-temporally ordered system of observable things and events. Once we have accepted the thing language with its framework for things, we can raise and answer internal questions; e.g., "Is there a white piece of paper on my desk?," "Did King Arthur actually live?," "Are unicorns and centaurs real or merely imaginary?," and the like. These questions are to be answered by empirical investigations. Results of observations are evaluated according to certain rules as confirming or disconfirming evidence for possible answers. (This evaluation ____________________ 2The terms "sentence" and "statement" are here used synonymously for declarative (indicative, propositional) sentences. -229-

is usually carried out, of course, as a matter of habit rather than a deliberate, rational procedure. But it is possible, in a rational reconstruction, to lay down explicit rules for the evaluation. This is one of the main tasks of a pure, as distinguished from a psychological, epistemology.) The concept of reality occurring in these internal questions is an empirical, scientific, non-metaphysical concept. To recognize something as a real thing or event means

to succeed in incorporating it into the system of things at a particular space - time position so that it fits together with the other things recognized as real, according to the rules of the framework. From these questions we must distinguish the external question of the reality of the thing world itself. In contrast to the former questions, this question is raised neither by the man in the street nor by scientists, but only by philosophers. Realists give an affirmative answer, subjective idealists a negative one, and the controversy goes on for centuries without ever being solved. And it cannot be solved because it is framed in a wrong way. To be real in the scientific sense means to be an element of the system; hence this concept cannot be meaningfully applied to the system itself. Those who raise the question of the reality of the thing world itself have perhaps in mind not a theoretical question as their formulation seems to suggest, but rather a practical question, a matter of a practical decision concerning the structure of our language. We have to make the choice whether or not to accept and use the forms of expression in the framework in question. In the case of this particular example, there is usually no deliberate choice because we all have accepted the thing language early in our lives as a matter of course. Nevertheless, we may regard it as a matter of decision in this sense: we are free to choose to continue using the thing language or not; in the latter case we could restrict ourselves to a language of sense-data and other "phenomenal" entities, or construct an alternative to the customary thing language with another structure, or, finally, we could refrain from speaking. If someone decides to accept the thing language, there is no objection against saying that he has accepted the world of things. But this must not be interpreted as if it meant his acceptance of a belief in the reality of the thing world; there is no such belief or assertion or assumption, because it is not a theoretical question. To accept the thing world means nothing more than to accept a certain form of language, in other words, to accept rules for forming statements and for testing, accepting, or rejecting them. The acceptance of the thing language leads, on the basis of observations made, also to the acceptance belief, and assertion of certain statements. But the thesis of the reality of the thing world cannot be among these statements, because it cannot be formulated in the thing language, or it seems, in any other theoretical language. The decision of accepting the thing language, although itself not of a cognitive nature, will nevertheless usually be influenced by theoretical knowledge, just like any other deliberate decision concerning the acceptance of linguistic or other rules. The purposes for which the language is intended to -230-

be used, for instance, the purpose of communicating factual knowledge, will determine which factors are relevant for the decision. The efficiency, fruitfulness, and simplicity of the use of the thing language may be among the decisive factors. And the questions concerning these qualities are indeed of a theoretical nature. But these questions cannot be identified with the question of realism. They are not yes-no questions but questions of degree. The thing language in the customary form works indeed with a high degree of efficiency for most purposes of everyday life. This is a matter of fact, based upon the content of our experiences. However, it would be wrong to describe this situation by saying: "The fact of the efficiency of the thing language is confirming evidence for the reality of the thing world"; we should rather say instead: "This fact makes it advisable to accept the thing language." The system of numbers. As an example of a system which is of a logical rather than a factual nature let us take the system of natural numbers. The framework for this system is constructed by introducing into the language new expressions with suitable rules: (1) numerals like "five" and sentence forms like "there are five books on the table"; (2) the general term "number" for the new entities, and sentence forms like "five is a number"; (3) expressions for properties of numbers (e.g., "odd," "prime"), relations (e.g., "greater than"), and functions (e.g., "plus"), and sentence forms like "two plus three is five"; (4) numerical variables ( "m," "n," etc.) and quantifiers for universal sentences ("for every n, ..." and existential sentences "there is an n such that ...") with the customary deductive rules. Here again there are internal questions, e.g., "Is there a prime number greater than a

hundred?" Here, however, the answers are found, not by empirical investigation based on observations, but by logical analysis based on the rules for the new expressions. Therefore the answers are here analytic, i.e., logically true. What is now the nature of the philosophical question concerning the existence or reality of numbers? To begin with, there is the internal question which, together with the affirmative answer, can be formulated in the new terms, say by "There are numbers" or, more explicitly, "There is an n such that n is a number." This statement follows from the analytic statement "five is a number" and is therefore itself analytic. Moreover, it is rather trivial (in contradistinction to a statement like "There is a prime number greater than a million," which is likewise analytic but far from trivial), because it does not say more than that the new system is not empty; but this is immediately seen from the rule which states that words like "five" are substitutable for the new variables. Therefore nobody who meant the question "Are there numbers?" in the internal sense would either assert or even seriously consider a negative answer. This makes it plausible to assume that those philosophers who treat the question of the existence of numbers as a serious philosophical problem and offer lengthy arguments on either side, do not have in mind the internal question. And, indeed, if we were to ask them: "Do you mean the question as to whether the framework of numbers, if we were to accept it, would be -231-

found to be empty or not?," they would probably reply: "Not at all; we mean a question prior to the acceptance of the new framework." They might try to explain what they mean by saying that it is a question of the ontological status of numbers; the question whether or not numbers have a certain metaphysical characteristic called reality (but a kind of ideal reality, different from the material reality of the thing world) or subsistence or status of "independent entities." Unfortunately, these philosophers have so far not given a formulation of their question in terms of the common scientific language. Therefore our judgment must be that they have not succeeded in giving to the external question and to the possible answers any cognitive content. Unless and until they supply a clear cognitive interpretation, we are justified in our suspicion that their question is a pseudo-question, that is, one disguised in the form of a theoretical question while in fact it is non-theoretical; in the present case it is the practical problem whether or not to incorporate into the language the new linguistic forms which constitute the framework of numbers. The system of propositions. New variables, "p," "q," etc., are introduced with a rule to the effect that any (declarative) sentence may be substituted for a variable of this kind; this includes, in addition to the sentences of the original thing language, also all general sentences with variables of any kind which may have been introduced into the language. Further, the general term "proposition" is introduced. "p is a proposition" may be defined by "p or not p" (or by any other sentence form yielding only analytic sentences). Therefore, every sentence of the form "... is a proposition" (where any sentence may stand in the place of the dots) is analytic. This holds, for example, for the sentence: a. "Chicago is large is a proposition."

b. c. d.

(We disregard here the fact that the rules of English grammar require not a sentence but a that-clause as the subject of another sentence; accordingly, instead of (a) we should have to say "That Chicago is large is a proposition.") Predicates may be admitted whose argument expressions are sentences; these predicates may be either extensional (e.g., the customary truth-functional connectives) or not (e.g., modal predicates like "possible," "necessary," etc.). With the help of the new variables, general sentences may be formed, e.g., "For every p, either p or not-p." "There is a p such that p is not necessary and not-p is not necessary." "There is a p such that p is a proposition."

(c) and (d) are internal assertions of existence. The statement "There are propositions" may be meant in the sense of (d); in this case it is analytic [since it follows from (a)] and even trivial. If, however, the statement is meant in an external sense, then it is non-cognitive. -232-

It is important to notice that the system of rules for the linguistic expressions of the propositional framework (of which only a few rules have here been briefly indicated) is sufficient for the introduction of the framework. Any further explanations as to the nature of the propositions (i.e., the elements of the system indicated, the values of the variables "p," "q," etc.) are theoretically unnecessary because, if correct, they follow from the rules. For example, are propositions mental events (as in Russell's theory)? A look at the rules shows us that they are not, because otherwise existential statements would be of the form: "If the mental state of the person in question fulfils such and such conditions, then there is a p such that...." The fact that no references to mental conditions occur in existential statements (like (c), (d), etc.) shows that propositions are not mental entities. Further, a statement of the existence of linguistic entities (e.g., expressions, classes of expressions, etc.) must contain a reference to a language. The fact that no such reference occurs in the existential statements here, shows that propositions are not linguistic entities. The fact that in these statements no reference to a subject (an observer or knower) occurs (nothing like: "There is a p which is necessary for Mr. X"), shows that the propositions (and their properties, like necessity, etc.) are not subjective. Although characterizations of these or similar kinds are, strictly speaking, unnecessary, they may nevertheless be practically useful. If they are given, they should be understood, not as ingredient parts of the system, but merely as marginal notes with the purpose of supplying to the reader helpful hints or convenient pictorial associations which may make his learning of the use of the expressions easier than the bare system of the rules would do. Such a characterization is analogous to an extra-systematic explanation which a physicist sometimes gives to the beginner. He might, for example, tell him to imagine the atoms of a gas as small balls rushing around with great speed, or the electromagnetic field and its oscillations as quasi- elastic tensions and vibrations in an ether. In fact, however, all that can accurately be said about atoms or the field is implicitly contained in the physical laws of the theories in question. 3 ____________________ 3In my book Meaning and Necessity (Chicago, 1947) I have developed a semantical method which takes propositions as entities designated by sentences (more specifically, as intensions of sentences). In order to facilitate the understanding of the systematic development, I added some informal, extra-systematic explanations concerning the nature of propositions. I said that the term "proposition" "is used neither for a linguistic expression nor for a subjective, mental occurrence, but rather for something objective that may or may not be exemplified in nature.... We apply the term 'proposition' to any entities of a certain logical type, namely, those that may be expressed by (declarative) sentences in a language" (p. 27). After some more detailed discussions concerning the relation between propositions and facts, and the nature of false propositions, I added: "It has been the purpose of the preceding remarks to facilitate the understanding of our conception of propositions. If, however, a reader should find these explanations more puzzling than clarifying, or even unacceptable, he may disregard them" (p. 31) (that is, disregard these extra-systematic explanations, not the whole theory of the propositions as intensions of sentences, as one reviewer understood). In spite of this warning, it seems that some of those readers who were puzzled by the explanations, did not disregard them but thought that by raising objections -233-

The system of thing properties. The thing language contains words like "red," "hard," "stone," "house," etc., which are used for describing what things are like. Now we may introduce new variables, say "f," "g," etc., for which those words are substitutable and furthermore the general term "property." New rules are laid down which admit sentences like "Red is a property," "Red is a color," "These two pieces of paper have at least one color in common" (i.e., "There is an f such that f is a color, and ..."). The last sentence is an internal assertion. It is of an empirical, factual nature. However, the external statement, the philosophical statement of the reality of properties—a special case of the thesis of the reality of universals—is devoid of cognitive content. The systems of integers and rational numbers. Into a language containing the framework of natural numbers we may introduce first the (positive and negative) integers as relations among natural numbers and then the rational numbers as relations among integers. This

involves introducing new types of variables, expressions substitutable for them, and the general terms "integer" and "rational number." The system of real numbers. On the basis of the rational numbers, the real numbers may be introduced as classes of a special kind (segments) of rational numbers (according to the method developed by Dedekind and Frege). Here again a new type of variables is introduced, expressions substitutable for them (e.g., number."

), and the general term "real

The spatio-temporal coordinate system for physics. The new entities are the space-time points. Each is an ordered quadruple of four real numbers, called its coordinates, consisting of three spatial and one temporal coordinate. The physical state of a spatio-temporal point or region is described either with the help of qualitative predicates (e.g., "hot") or by ascribing numbers as values of a physical magnitude (e.g., mass, temperature, and the like). The step from the system of things (which does not contain space-time points but only extended objects with spatial and temporal relations between them) to the physical coordinate system is again a matter of decision. Our choice of certain features, although itself not theoretical, is suggested by theoretical knowledge, either logical or factual. For example, the choice of real numbers rather than rational numbers or integers as coordinates is not much influenced by the facts of experience but mainly due to considerations of mathematical simplicity. The restriction to rational coordinates would not be in conflict with any experimental knowledge we have, because the result of any measurement is a rational number. However, it would prevent the use of ordinary geometry (which says, e.g., that the diagonal of a square with the side 1 has the irra ____________________ against them they could refute the theory. This is analogous to the procedure of some laymen who by (correctly) criticizing the ether picture or other visualizations of physical theories, thought they had refuted those theories. Perhaps the discussions in the present paper will help in clarifying the role of the system of linguistic rules for the introduction of a framework for entities on the one hand, and that of extra-systematic explanations concerning the nature of the entities on the other. -234-

tional value √2) and thus lead to great complications. On the other hand, the decision to use three rather than two or four spatial coordinates is strongly suggested, but still not forced upon us, by the result of common observations. If certain events allegedly observed in spiritualistic séances, e.g., a ball moving out of a sealed box, were confirmed beyond any reasonable doubt, it might seem advisable to use four spatial coordinates. Internal questions are here, in general, empirical questions to be answered by empirical investigations. On the other hand, the external questions of the reality of physical space and physical time are pseudo-questions. A question like "Are there (really) space- time points?" is ambiguous. It may be meant as an internal question; then the affirmative answer is, of course, analytic and trivial. Or it may be meant in the external sense: "Shall we introduce such and such forms into our language?" ; in this case it is not a theoretical but a practical question, a matter of decision rather than assertion, and hence the proposed formulation would be misleading. Or finally, it may be meant in the following sense: "Are our experiences such that the use of the linguistic forms in question will be expedient and fruitful?" This is a theoretical question of a factual, empirical nature. But it concerns a matter of degree; therefore a formulation in the form "real or not?" would be inadequate.

What Does Acceptance of a Kind of Entities Mean? Let us now summarize the essential characteristics of situations involving the introduction of a new kind of entities, characteristics which are common to the various examples outlined above. The acceptance of a new kind of entities is represented in the language by the introduction of a framework of new forms of expressions to be used according to a new set of rules.

There may be new names for particular entities of the kind in question; but some such names may already occur in the language before the introduction of the new framework. (Thus, for example, the thing language contains certainly words of the type of "blue" and "house" before the framework of properties is introduced; and it may contain words like "ten" in sentences of the form "I have ten fingers" before the framework of numbers is introduced.) The latter fact shows that the occurrence of constants of the type in question —regarded as names of entities of the new kind after the new framework is introduced—is not a sure sign of the acceptance of the new kind of entities. Therefore the introduction of such constants is not to be regarded as an essential step in the introduction of the framework. The two essential steps are rather the following. First, the introduction of a general term, a predicate of higher level, for the new kind of entities, permitting us to say of any particular entity that it belongs to this kind (e.g., "Red is a property," "Five is a number"). Second, the introduction of variables of the new type. The new entities are values of these variables; -235-

the constants (and the closed compound expressions, if any) are substitutable for the variables. 4 With the help of the variables, general sentences concerning the new entities can be formulated. After the new forms are introduced into the language, it is possible to formulate with their help internal questions and possible answers to them. A question of this kind may be either empirical or logical; accordingly a true answer is either factually true or analytic. From the internal questions we must clearly distinguish external questions, i.e., philosophical questions concerning the existence or reality of the total system of the new entities. Many philosophers regard a question of this kind as an ontological question which must be raised and answered before the introduction of the new language forms. The latter introduction, they believe, is legitimate only if it can be justified by an ontological insight supplying an affirmative answer to the question of reality. In contrast to this view, we take the position that the introduction of the new ways of speaking does not need any theoretical justification because it does not imply any assertion of reality. We may still speak (and have done so) of "the acceptance of the new entities" since this form of speech is customary; but one must keep in mind that this phrase does not mean for us anything more than acceptance of the new framework, i.e., of the new linguistic forms. Above all, it must not be interpreted as referring to an assumption, belief, or assertion of "the reality of the entities." There is no such assertion. An alleged statement of the reality of the system of entities is a pseudostatement without cognitive content. To be sure, we have to face at this point an important question; but it is a practical, not a theoretical question; it is the question of whether or not to accept the new linguistic forms. The acceptance cannot be judged as being either true or false because it is not an assertion. It can only be judged as being more or less expedient, fruitful, conducive to the aim for which the language is intended. Judgments of this kind supply the motivation for the decision of accepting or rejecting the kind of entities. 5 Thus it is clear that the acceptance of a linguistic framework must not be regarded as implying a metaphysical doctrine concerning the reality of the entities in question. It seems to me due to a neglect of this important distinction that some contemporary nominalists label the admission of variables of abstract types as "Platonism." 6 This is, to say the least, an extremely misleading terminology. It leads to the absurd consequence, that the ____________________ 4W. V. Quine was the first to recognize the importance of the introduction of variables as indicating the acceptance of entities. "The ontology to which one's use of language commits him comprises simply the objects that he treats as falling ... within the range of values of his variables ["Notes on Existence and Necessity," Journal of Philosophy, 40, 1943, p. 118; compare also his "Designation and Existence," Journal of Philosophy, 36 (1939), and "On Universals," Journal of Symbolic Logic, 12 (1947).] 5For a closely related point of view on these questions see the detailed discussions in Herbert Feigl, "Existential Hypotheses," Philosophy of Science, 17 (1950), 35-62. 6Paul Bernays, "Sur le platonisme dans les mathématiques" (L'Enseignement math., 34 (1935), 52-69). W. V. Quine, see previous footnote and a recent paper, "On What There Is"

[reprinted in this volume]. Quine does not acknowledge the distinction which -236-

position of everybody who accepts the language of physics with its real number variables (as a language of communication, not merely as a calculus) would be called Platonistic, even if he is a strict empiricist who rejects Platonic metaphysics. A brief historical remark may here be inserted. The non-cognitive character of the questions which we have called here external questions was recognized and emphasized already by the Vienna Circle under the leadership of Moritz Schlick, the group from which the movement of logical empiricism originated. Influenced by ideas of Ludwig Wittgenstein, the Circle rejected both the thesis of the reality of the external world and the thesis of its irreality as pseudo- statements ; 7 the same was the case for both the thesis of the reality of universals (abstract entities, in our present terminology) and the nominalistic thesis that they are not real and that their alleged names are not names of anything but merely flatus vocis. ( It is obvious that the apparent negation of a pseudo-statement must also be a pseudo-statement.) It is therefore not correct to classify the members of the Vienna Circle as nominalists, as is sometimes done. However, if we look at the basic anti-metaphysical and pro-scientific attitude of most nominalists (and the same holds for many materialists and realists in the modern sense), disregarding their occasional pseudo-theoretical formulations, then it is, of course, true to say that the Vienna Circle was much closer to those philosophers than to their opponents.

Abstract Entities in Semantics The problem of the legitimacy and the status of abstract entities has recently again led to controversial discussions in connection with semantics. In a semantical meaning analysis certain expressions in a language are often said to designate (or name or denote or signify or refer to) certain extra- linguistic entities. 8 As long as physical things or events (e.g., Chicago or ____________________ I emphasize above, because according to his general conception there are no sharp boundary lines between logical and factual truth, between questions of meaning and questions of fact, between the acceptance of a language structure and the acceptance of an assertion formulated in the language. This conception, which seems to deviate considerably from customary ways of thinking, will be explained in his article ["Semantics and Abstract Objects," Proceedings of the American Academy of Arts and Sciences, 80 (1951)]. When Quine in the article ["On What There Is"] classifies my logicistic conception of mathematics (derived from Frege and Russell) as "platonic realism" (p. 224), this is meant (according to a personal communication from him) not as ascribing to me agreement with Plato's metaphysical doctrine of universals, but merely as referring to the fact that I accept a language of mathematics containing variables of higher levels. With respect to the basic attitude to take in choosing a language form (an "ontology" in Quine's terminology, which seems to me misleading), there appears now to be agreement between us: "the obvious counsel is tolerance and an experimental spirit" ["On What There Is," p. 227.] 7See Carnap, Scheinprobleme in der Philosophie; das Fremdpsychische und der Realismusstreit, Berlin, 1928. Moritz Schlick, Positivismus und Realismus, reprinted in Gesammelte Aufsätze, Wien, 1938. 8See Introduction to Semantics (1943); Meaning and Necessity (Chicago, 1947). -237-

Caesar's death) are taken as designata (entities designated), no serious doubts arise. But strong objections have been raised, especially by some empiricists, against abstract entities as designata, e.g., against semantical statements of the following kind: 1. "The word 'red' designates a property of things"; 2. "The word 'color' designates a property of properties of things";

3. 4. 5.

"The word 'five' designates a number"; "The word 'odd' designates a property of numbers"; "The sentence 'Chicago is large' designates a proposition."

Those who criticize these statements do not, of course, reject the use of the expressions in question, like "red" or "five"; nor would they deny that these expressions are meaningful. But to be meaningful, they would say, is not the same as having a meaning in the sense of an entity designated. They reject the belief, which they regard as implicitly presupposed by those semantical statements, that to each expression of the types in question (adjectives like "red," numerals like "five," etc.) there is a particular real entity to which the expression stands in the relation of designation. This belief is rejected as incompatible with the basic principles of empiricism or of scientific thinking. Derogatory labels like "Platonic realism," "hypostatization," or " 'Fido'- Fido principle" are attached to it. The latter is the name given by Gilbert Ryle to the criticized belief, which, in his view, arises by a naive inference of analogy : just as there is an entity well known to me, viz. my dog Fido, which is designated by the name "Fido," thus there must be for every meaningful expression a particular entity to which it stands in the relation of designation or naming, i.e., the relation exemplified by "Fido"-Fido. The belief criticized is thus a case of hypostatization, i.e., of treating as names expressions which are not names. While "Fido" is a name, expressions like "red," "five," etc., are said not to be names, not to designate anything. Our previous discussion concerning the acceptance of frameworks enables us now to clarify the situation with respect to abstract entities as designata. Let us take as an example the statement: (a) " 'Five' designates a number." The formulation of this statement presupposes that our language L contains the forms of expressions which we have called the framework of numbers, in particular, numerical variables and the general term "number." If L contains these forms, the following is an analytic statement in L: ( b) "Five is a number." Further, to make the statement (a) possible, L must contain an expression like "designates" or "is a name of" for the semantical relation of designa ____________________ The distinction I have drawn in the latter book between the method of the name - relation and the method of intension and extension is not essential for our present discussion. The term "designation" is used in the present article in a neutral way; it may be understood as referring to the name-relation or to the intension-relation or to the extension-relation or to any similar relations used in other semantical methods. -238-

tion. If suitable rules for this term are laid down, the following is likewise analytic: (c) " 'Five' designates five." (Generally speaking, any expression of the form " '...' designates ..." is an analytic statement provided the term "..." is a constant in an accepted framework. If the latter condition is not fulfilled, the expression is not a statement.) Since (a) follows from (c) and (b), (a) is likewise analytic. Thus it is clear that if someone accepts the framework of numbers, then he must acknowledge (c) and (b) and hence (a) as true statements. Generally speaking, if someone accepts a framework for a certain kind of entities, then he is bound to admit the entities as possible designata. Thus the question of the admissibility of entities of a certain type or of abstract entities in general as designata is reduced to the question of the acceptability of the linguistic framework for those entities. Both the nominalistic critics, who refuse the status of designators or names to expressions like "red," "five," etc., because they deny the existence

of abstract entities, and the skeptics, who express doubts concerning the existence and demand evidence for it, treat the question of existence as a theoretical question. They do, of course, not mean the internal question; the affirmative answer to this question is analytic and trivial and too obvious for doubt or denial, as we have seen. Their doubts refer rather to the system of entities itself; hence they mean the external question. They believe that only after making sure that there really is a system of entities of the kind in question are we justified in accepting the framework by incorporating the linguistic forms into our language. However, we have seen that the external question is not a theoretical question but rather the practical question whether or not to accept those linguistic forms. This acceptance is not in need of a theoretical justification (except with respect to expediency and fruitfulness), because it does not imply a belief or assertion. Ryle says that the "Fido"-Fido principle is "a grotesque theory." Grotesque or not, Ryle is wrong in calling it a theory. It is rather the practical decision to accept certain frameworks. Maybe Ryle is historically right with respect to those whom he mentions as previous representatives of the principle, viz. John Stuart Mill, Frege, and Russell. If these philosophers regarded the acceptance of a system of entities as a theory, an assertion, they were victims of the same old, metaphysical confusion. But it is certainly wrong to regard my semantical method as involving a belief in the reality of abstract entities, since I reject a thesis of this kind as a metaphysical pseudo-statement. The critics of the use of abstract entities in semantics overlook the fundamental difference between the acceptance of a system of entities and an internal assertion, e.g., an assertion that there are elephants or electrons or prime numbers greater than a million. Whoever makes an internal assertion is certainly obliged to justify it by providing evidence, empirical evidence in the case of electrons, logical proof in the case of the prime numbers. The demand for a theoretical justification, correct in the case of internal assertions, -239-

is sometimes wrongly applied to the acceptance of a system of entities. Thus, for example, Ernest Nagel asks for "evidence relevant for affirming with warrant that there are such entities as infinitesimals or propositions." He characterizes the evidence required in these cases—in distinction to the empirical evidence in the case of electrons—as "in the broad sense logical and dialectical." Beyond this no hint is given as to what might be regarded as relevant evidence. Some nominalists regard the acceptance of abstract entities as a kind of superstition or myth, populating the world with fictitious or at least dubious entities, analogous to the belief in centaurs or demons. This shows again the confusion mentioned, because a superstition or myth is a false (or dubious) internal statement. Let us take as example the natural numbers as cardinal numbers, i.e., in contexts like "Here are three books." The linguistic forms of the framework of numbers, including variables and the general term "number," are generally used in our common language of communication; and it is easy to formulate explicit rules for their use. Thus the logical characteristics of this framework are sufficiently clear (while many internal questions, i.e., arithmetical questions, are, of course, still open). In spite of this, the controversy concerning the external question of the ontological reality of the system of numbers continues. Suppose that one philosopher says: "I believe that there are numbers as real entities. This gives me the right to use the linguistic forms of the numerical framework and to make semantical statements about numbers as designata of numerals." His nominalistic opponent replies: "You are wrong: there are no numbers. The numeral may still be used as meaningful expressions. But they are not names, there are no entities designated by them. Therefore the word "number" and numerical variables must not be used (unless a way were found to introduce them as merely abbreviating devices, a way of translating them into the nominalistic thing language)." I cannot think of any possible evidence that would be regarded as relevant by both philosophers, and therefore, if actually found, would decide the controversy or at least make one of the opposite theses more probable than the other. (To construe the numbers as classes or properties of the second level, according to the Frege-Russell method, does, of course, not solve the controversy, because the first philosopher would affirm and the second deny the existence of the system of classes or properties of the second level.) Therefore I feel compelled to regard the external question as a pseudo-question, until both parties to the controversy offer a common interpretation of the question as a cognitive question; this would involve an indication of possible evidence regarded as relevant by both sides.

There is a particular kind of misinterpretation of the acceptance of abstract entities in various fields of science and in semantics, that needs to be cleared up. Certain early British empiricists (e.g., Berkeley and Hume) denied the existence of abstract entities on the ground that immediate experience presents us only with particulars, not with universals, e.g., with this red patch, but not with Redness or Color-in-General; with this scalene triangle, but not -240-

with Scalene Triangularity or Triangularity-in-General. Only entities belonging to a type of which examples were to be found within immediate experience could be accepted as ultimate constituents of reality. Thus, according to this way of thinking, the existence of abstract entities could be asserted only if one could show either that some abstract entities fall within the given, or that abstract entities can be defined in terms of the types of entity which are given. Since these empiricists found no abstract entities within the realm of sense-data, they either denied their existence, or else made a futile attempt to define universals in terms of particulars. Some contemporary philosophers, especially English philosophers following Bertrand Russell, think in basically similar terms. They emphasize a distinction between the data (that which is immediately given in consciousness, e.g., sense-data, immediately past experiences, etc.) and the constructs based on the data. Existence or reality is ascribed only to the data; the constructs are not real entities; the corresponding linguistic expressions are merely ways of speech not actually designating anything (reminiscent of the nominalists' flatus vocis). We shall not criticize here this general conception. (As far as it is a principle of accepting certain entities and not accepting others, leaving aside any ontological, phenomenalistic and nominalistic pseudo-statements, there cannot be any theoretical objection to it.) But if this conception leads to the view that other philosophers or scientists who accept abstract entities thereby assert or imply their occurrence as immediate data, then such a view must be rejected as a misinterpretation. References to space-time points, the electromagnetic field, or electrons in physics, to real or complex numbers and their functions in mathematics, to the excitatory potential or unconscious complexes in psychology, to an inflationary trend in economics, and the like, do not imply the assertion that entities of these kinds occur as immediate data. And the same holds for references to abstract entities as designata in semantics. Some of the criticisms by English philosophers against such references give the impression that, probably due to the misinterpretation just indicated, they accuse the semanticist not so much of bad metaphysics (as some nominalists would do) but of bad psychology. The fact that they regard a semantical method involving abstract entities not merely as doubtful and perhaps wrong, but as manifestly absurd, preposterous and grotesque, and that they show a deep horror and indignation against this method, is perhaps to be explained by a misinterpretation of the kind described. In fact, of course, the semanticist does not in the least assert or imply that the abstract entities to which he refers can be experienced as immediately given either by sensation or by a kind of rational intuition. An assertion of this kind would indeed be very dubious psychology. The psychological question as to which kinds of entities do and which do not occur as immediate data is entirely irrelevant for semantics, just as it is for physics, mathematics, economics, etc., with respect to the examples mentioned above. 9 ____________________ 9Wilfrid Sellars ("Acquaintance and Description Again," in Journal of Philosophy, 46 [1949], 496-504; see pp. 502ff.) analyzes clearly the roots of the mistake "of tak-241-

Conclusion For those who want to develop or use semantical methods, the decisive question is not the alleged ontological question of the existence of abstract entities but rather the question whether the use of abstract linguistic forms or, in technical terms, the use of variables beyond those for things (or phenomenal data), is expedient and fruitful for the purposes for which semantical analyses are made, viz. the analysis, interpretation, clarification, or

construction of languages of communication, especially languages of science. This question is here neither decided nor even discussed. It is not a question simply of yes or no, but a matter of degree. Among those philosophers who have carried out semantical analyses and thought about suitable tools for this work, beginning with Plato and Aristotle and, in a more technical way on the basis of modern logic, with C. S. Peirce and Frege, a great majority accepted abstract entities. This does, of course, not prove the case. After all, semantics in the technical sense is still in the initial phases of its development, and we must be prepared for possible fundamental changes in methods. Let us therefore admit that the nominalistic critics may possibly be right. But if so, they will have to offer better arguments than they have so far. Appeal to ontological insight will not carry much weight. The critics will have to show that it is possible to construct a semantical method which avoids all references to abstract entities and achieves by simpler means essentially the same results as the other methods. The acceptance or rejection of abstract linguistic forms, just as the acceptance or rejection of any other linguistic forms in any branch of science, will finally be decided by their efficiency as instruments, the ratio of the results achieved to the amount and complexity of the efforts required. To decree dogmatic prohibitions of certain linguistic forms instead of testing them by their success or failure in practical use, is worse than futile; it is positively harmful because it may obstruct scientific progress. The history of science shows examples of such prohibitions based on prejudices deriving from religious, mythological, metaphysical, or other irrational sources, which slowed up the developments for shorter or longer periods of time. Let us learn from the lessons of history. Let us grant to those who work in any special field of investigation the freedom to use any form of expression which seems useful to them; the work in the field will sooner or later lead to the elimination of those forms which have no useful function. Let us be cautious in making assertions and critical in examining them, but tolerant in permitting linguistic forms. ____________________ ing the designation relation of semantic theory to be a reconstruction of being present to an experience." -242-

: 15 : THE LANGUAGES OF REALISM AND NOMINALISM RICHARD B. BRANDT THE most difficult problem of all those which arise in the course of constructing a theory about universals is that of finding a satisfactory formulation of what exactly the problem is. And, one might add, perhaps the most baffling problem for the student of the history of controversies about this topic is that of finding what various writers have thought on this matter. 1 Therefore it is no mean virtue of proposals by some recent writers including Quine, Carnap, Goodman, and Church, if it is true of them, as I think it is, that they have provided at least in outline an adequate formulation of the problem. Their proposal has consisted of two parts: (1) the definition of a "nominalist" language and of a "realist" language, and (2) an inquiry—considered tantamount to raising the old question "Are there universals?"—whether use of the latter, essentially richer, language is necessary or convenient for science or philosophy. 2 The following remarks, while touching on the first of these issues, will concentrate on three questions, two of which may be construed as aspects of the second of these matters. These latter two are as follows. (They will be raised, however, in the reverse order.) (a) Are distinctively realist locutions meaningful, and if so, in what sense (e.g., in the sense in which statements whose only non-logical terms are observation predicates or terms ____________________ Reprinted from Philosophy and Phenomenological Research, XVII (1957), by permission

of the editor and the author. Morris Lazerowitz's proposal that "theories" here consist of conflicting recommendations about classifications, e.g., recommendations about whether predicates should be classified as proper names. "The Existence of Universals," Mind, Vol. LV (1946), pp. 1-25. 2It is a mistake and misleading, however, to suppose that a purely syntactical criterion can be given for a nominalist system, so that, e.g., an uninterpreted language could be identified as nominalist or realist. Thus the specification of a nominalist language as one that contains no names for entities other than individuals is not helpful except in the context of further information how to identify what is an individual. (Of course, this is helpful as a specification of the author's own decision about how to use "nominalist," but not as a clarification of the author's stand in respect of the historic controversy between realists and nominalists.) And it is confusing if it turns out that something which traditionally would have been identified as a universal turns out to be capable of serving as an "individual." 1Witness

explicitly definable in terms of these are meaningful, or, say, in the sense in which statements are meaningful which contain theoretical constructs like "electron")? In what sense can instructions for their use be given, compatibly with their remaining distinctively realist locutions? 3 (b) Are certain forms of nominalist language—in particular, the one corresponding to the resemblance theory of the type currently popular especially in England—adequate for the statement of facts, or definitions, which scientists and/or philosophers will want language to be rich enough to provide ? (The question whether realist language is necessary or convenient for the construction of semantical systems is a part of this issue, and one with which I shall not deal.) Actually, in this context I shall also be arguing that there is no point in the resemblance theory, as compared with more liberal forms of nominalism. (c) There is a third question, which I shall not argue separately but which I shall have in mind throughout. This is: Does this "linguistic" formulation of the problem of universals do justice to historical controversies about universals, in respect of their point and in respect of the arguments used? A good many philosophers today hold that the primary issue is whether there are universals, and think that the question is one of analytic ontology. Language, they think, is a secondary matter; if there are universals, then of course we need a language capable of talking about them. 4 How will this charge be answered by one who, like the writer, is convinced that the historical problem ought to be stated in the linguistic form? Of course, one will agree that the matter is one of analytic ontology, and that the main question is whether there are universals. But this agreement leaves open the problem of the correct analysis of the claim that there are universals; and it leaves open the question of what analytic ontology is and how one decides questions in this territory. The new formulation may be construed ____________________ 3It may be said that this is not a very helpful question. It may be said that we can have no criterion for meaningfulness beyond translatability into an ideal language; and, it may be said, when we are engaged in deciding what kind of ideal language is adequate, we do not need to raise as a separate question the issue of meaningfulness, since we are in process of formulating the very criterion of meaningfulness. But this objection, I believe, overlooks essential points. For one of the criteria on which many will insist, for the formulation of a satisfactory ideal language, is that its non-logical vocabulary include only terms which can function essentially in a system of statements which can be confirmed or disconfirmed by possible experience. And it is a serious point whether one must discard this criterion if one adopts a realist form of ideal language. Again, it is surely clarifying to inquire whether realist terms can be construed as functioning like the observation predicates in a nominalist language, or rather more like theoretical constructs. 4I do not suppose these philosophers would deny that the talk of realist and nominalist languages has a function, i.e., that of clarifying the use of abstract nouns in actual speech, as well as the use of terms like "property," "attribute," and "class"—by considering how

they may be construed as related to predicates like "blue" and "human," and their function, dispensability, and definability. These questions, it would probably be allowed, are worth while discussing, even if they have no bearing on the traditional problem of universals. In this case the ideal language could be viewed as a model to which actual use more or less approximates, and which therefore illuminates actual usage. -244-

as precisely a proposal on these matters. But how can one make out that a particular formulation is adequate to the historic controversy, and clarifying of the issues without by-passing them? There seems no alternative to trying it out in the following ways. One can try out and see whether the linguistic theory can state all that is clear in the "abstract particular" theory as held (not, of course, in quite the same form in each case) by writers such as G. F. Stout, J. R. Jones, and Donald Williams, as contrasted with the more "orthodox" view supported by writers like G. E. Moore, W. E. Johnson, and Bertrand Russell. (One will do this by construing the former theory as a proposal for a language in which there are names for abstract particulars, with predicates and abstract nouns defined in terms of these.) And one can then see whether all that was clear in the arguments can be translated into this form without loss of point. And much the same can be done for the resemblance theory. Again, one can try out the formulation and see if it makes clear why many philosophers have not been convinced by such arguments for realism as the one that scientific knowledge is knowledge of the interrelations of specifiable characters, 5 or the one purporting to prove that things have qualities in common by appeal to the fact that at least two things are colored. 6 (The formulation makes clear that it is one thing to accept the laws of physics, quite another thing to say they are about "specifiable characters" ; that it is one thing to say that two things are both colored, but quite another to consent to the meaningfulness and helpfulness of an expression such as "common quality.") And so on. Of course, everyone has to make up his own mind whether everything clear and forceful in the older discussions is saved, and whether the issues gain in clarity when translated into the linguistic formulation; there can be no demonstrations here. Without discussing this third issue separately, I shall bear it in mind, and accent it where I can. Writers who advocate the new formulation often proceed as if the past did not exist; whereas it seems important to get clear the continuity between their proposals and historically important theories and arguments. I shall begin with nominalist languages, raising primarily the second question stated above; I shall then proceed to realist languages, raising primarily the first question stated above. ____________________ 5For instance, C. A. Baylis, "Universals, Communicable Knowledge, and Metaphysics," Journal of Philosophy, Vol. XLVIII, 636-44. 6See Pap, Elements of Analytic Philosophy, New York (Macmillan, 1949), p. 78. The point, p. 79, to the effect that "univocal predicate" cannot be defined without realist language is a serious difficulty for a nominalist account of language. -245-

I. Nominalist Languages Let us begin, then, with a definition of "nominalist language" in general. First, nominalist language will contain the customary logical notations, including the notation for the relation of identity. Next, it will contain an indefinitely large number of names of individuals, and also variables with the specification that only individual names can be substituted for them. Third, there may or may not be predicate-names; but if so, they must be predicate - names which can be meaningfully used in connection with individual names, and it is understood that the predicate-name will not itself be used as a subject for predications. It is also convenient for our purpose to refuse to accept as a predicate any expression which either explicitly contains the name of an individual, or the meaning of which could be explained only by expressions containing the names of particular individuals (thus eliminating from

our discussion expressions like "is a descendant of Napoleon"). Finally, our language may contain any further expressions which are introduced by definition in terms of the foregoing. (It may be proposed that proper names can be dispensed with altogether, in favor of variables and predicates; but since an individual cannot be uniquely identified by reference to its properties alone, it seems to me to conduce to clarity not to make this move.) The foregoing statement does not explain what is meant by the expressions "name of an individual" and "predicate-name." Such explanations need to be provided, if we are to avoid misunderstanding, and if we hope to throw some light on traditional controversies by the concept of a nominalist language. Moreover, there is the question whether a nominalist might find it necessary to use the term "universal" in his metalanguage, in order to explain what he means by a "nominalist language." Let us first look at the term "individual name." Although one cannot claim that there is a generally accepted nominalist definition of this term, it is not implausible to propose that a term is an individual name if it names (or purports to name) something which has a date or which endures through a stretch of time. As an alternative we might consider a recent suggestion, offered as a necessary condition for being a concrete individual, that a concrete individual cannot be referred to by a description, a unique reference for which is determined by the meaning alone of the words making up the describing expression; 7 this proposal, however, does not pretend to give a sufficient condition. In any case, however, we may expect less disagreement about the extension of "individual name" than we may have about its definition—the extension being confined to events, things, persons but not numbers, facts, or qualities. So that in practice, if we know how the terms of a language work in speech, there will not be much if any disagreement whether a given ____________________ 7P. F. Strawson, "Particular and General," Proceedings, The Aristotelian Society (1953-54), pp. 256-57. -246-

term is properly called an individual-name; and a nominalist might with reason hold that this is all he needs, to decide whether a language is a nominalist language. (It is enough if we know how to use this term, even if we cannot define it.) Can we define in a similar way the term "first-order predicate"? W. E. Johnson proposed that a general term is one which can be significantly used in the plural, and is one to which any article—like "the," or "an"—can be significantly prefixed. This definition, however, is too closely bound to the peculiarities of the English language. But, following Russell, we may propose this: we shall say a symbol is a first-order predicate if, in the most elementary expressions in which neither logical constants nor variables appear, it can be used to make a meaningful assertion if and only if it is combined with some characteristic number of names of individuals, and if its meaning can be explained without reference to particular individuals. I propose to assume, on this basis, that we can identify a predicate term in a functioning language. Let us now note that a nominalist language, so defined, is one that could not contain the term "universal" or "property" or "relation" (although it can contain "universal-word" etc.); indeed it will be without abstract terms like "humanity" so that it cannot talk about a particular universal. It does not permit raising any of the questions about qualities or relations which have traditionally puzzled philosophers. A person who holds that such a language is adequate to what can or should be said, is obviously not a realist in the traditional sense. Now let us consider some nominalist theories, construing them all as proposals that a certain type of nominalist language is adequate for science and philosophy. I shall consider three types, each differing from the other in only one respect: the predicates admitted. The first, the most extreme type, admits no predicates at all. The second, the resemblance theory (on which I shall concentrate my remarks, since it is still widely held), admits one relational predicate, "resembles." The third, moderate nominalism, permits any number of predicates

of individuals. (This is the view for which Quine hankers on occasion.) 1. Extreme nominalism. The first view is interesting as an ideal type with attractions, more than as a view that has actually been held (and perhaps it has never been held). It is attractive because many arguments for realist language (with the undeniable complex ties of realism) take their start from the fact of predicates: from raising questions about the meaning or signification of predicates, about why it is that the same predicate is applicable to two things, and so on. It would seem that an effective way to banish the ghost of realism would be to deny the necessity of predicates in an ideal language. Unfortunately, such a language cannot serve the purposes of science. For no synthetic empirical statement, or at least no very interesting one, can be framed in such a language. For instance, in such a language we could not give information such as we actually give in a sentence like "My marble is red." For consider how we should have to introduce an expression like "is red" -247-

into the language. We should have to treat it as definitionally identical with "is identical with A or B or ..." and so on, letting our letters be the names of all the red things in the universe. We could then say truly "A is red," using our newly defined predicate. But this statement would either be false or analytically true. And the same would be the case for any empirical predicate we might want to use. As philosophers have long known, it is impossible to construct a language that will say what we want to say, if its non-logical terms are proper names only. 2. The Resemblance Theory. We come now to the popular theory which, in accordance with our formulation of the basic question about universals, we construe as the theory that a language is adequate for science and philosophy if it is a nominalist language which admits only one relational predicate in addition to logical notions and names of individuals: "resembles" or some more complex but closely related term. Now unquestionably this type of language is much richer than the first one, and not obviously inadequate. For perhaps all the predicates we need can be introduced as defined terms: for instance, roughly and initially, "is red" being defined as "resembles A and B" where "A" and "B" are names of individuals. If so, these so introducible predicates may be regarded as theoretically eliminable; we then could get along just with "resembles" alone. In order to assess this theory, let us consider two questions. The first is whether there is any advantage in the resemblance theory as compared with the more liberal moderate nominalism. The second is the question whether the familiar "in respect" objection is a fatal objection to it. (1) Let us begin our consideration of the question whether the resemblance theory has any advantages over the more liberal moderate nominalism, by reverting to an objection, raised by Russell long ago. 8 Russell criticized the theory on the ground that it admits one universal, Resemblance, and having done so there is no particular point in refusing to admit more. Now Russell's objection, as stated, is unacceptable. For the resemblance theory does not "admit" one universal; all it does is admit one relational predicate into the language. But the theory is still nominalist in the general sense of not permitting even the naming of particular universals, much less explicit talk of universals. So, if it is a language adequate for science and philosophy, then a realist theory is incorrect. Yet Russell's argument is relevant for the issue we are here raising, and we may rephrase it as follows. We may say: "The resemblance theory differs from moderate nominalism only in the number of predicates regarded as necessary for science. But surely this is not an important difference. And if so, why all the fuss about resemblance? It is true that the resemblance language, if cumbersome, is in a sense more economical, in making do with fewer predicates; but the moderate nominalist has the advantage that, with his wealth of predicates, he can dispense with proper names, or at least with all but one." This reformulation of Russell's objection must, I believe, be accepted. At least, we can say that the resem____________________ 8The Problems of Philosophy (Home University Library), pp. 150-51.

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blance theory is no gain over the theory of the moderate nominalist unless it can be shown that admission of the one predicate "resembles" is somehow less vulnerable to the arguments that may be advanced by realists, than is the admission of more predicates, as in moderate realism. But can any such advantage be shown? Well, at least we can say it has not yet been shown. Professor Price, in defending the resemblance theory against objections of the Russell type, argues that the use of general words like "resembles" does not commit us to any "general something (universals) which they mean." 9 But this defense applies to the use of any general term, just as well as to "resembles." Price goes on to argue that a philosopher ought not to feel inclined to say that "resembles" names a universal, for "what we ordinarily call 'relations' (as well as what we call 'qualities') are themselves founded upon or analyzable into resemblances." 10 But is it true that to call resemblance a relation is to sin against the rules of ordinary language? Moreover, it appears inconsistent for Price to use this argument, since he holds that "resembles" itself can be defined or analyzed in terms of higher-order senses of "resembles," and so far is no different from other relational predicates. Somewhat similar arguments have been posed by D. J. O'Connor. 11 O'Connor first argues that the term "resembles" could not reasonably be regarded as designating any one universal, because, in his words, "there are ever so many different senses of the word resemblance." The correct reply to this argument would seem to be that, then perhaps there are ever so many different universals designated by "resembles" in its many different senses. This argument at least hardly secures a fundamental difference between the status of "resembles" and other relation words. O'Connor goes on to offer a second argument, to the effect that "resembles" is "essentially vague" like "useful" or "important." The words are vague because the borderline of their use is ill-defined and, in the nature of the case, is bound to be so. There cannot, for this reason alone, be any common nature or universal that is instantiated in all the recurring cases that we are prepared to call "similar." To my mind what this argument suggests is that "resembles" is perhaps not a very good term for selection as the basic non-logical predicate of an ideal language; something like "exactly matches," if we could make do with it, or something like it, might be much better. If "resembles" is really so vague as this, one will wonder whether we can have even moderate success with it, in the introduction of other terms by definition. But furthermore, most predicates, if not all, are vague to some degree; and it is by no means clear why the vagueness of "resembles" frees the use of this term from any implications in the direction of realism that may adhere to the use of other terms. ____________________ 10Ibid., p. 25. 11In a symposium, "Abstract Ideas and Images," Supplementary Volume 27, The Aristotelian Society (1953), pp. 149-52. 9H. H. Price, Thinking and Experience (Hutchinson's University Library, 1953), p. 24. See A. C. Lloyd, "On Arguments for Real Universals," Analysis, Vol. II (1951), p. 104. -249-

In summary, it does not seem that good reasons have been given for thinking that any realistic commitments involved in allowing any number of predicates of first order, in a language, are avoided by the expedient of using the one predicate "resembles." And if this is correct, the resemblance theory so far has no advantage over moderate nominalism. A resemblance theorist might object to the foregoing remarks, on the ground that the resemblance theory has been misconstrued. For I have here taken this theory to maintain that an ideal language, adequate for science, can get on with only one non-logical predicate, the predicate "resembles." It may be urged that this construction does injustice to the theory. I do not propose to argue this point beyond taking note of one particular alternative construction of the theory, as follows. The resemblance theorist might say that what he is

doing is proposing a program for analyzing any general term you please by means of "resembles" (in some sense or other) and the names of individuals. And according to this program, he may say, it is claimed that no predicate in particular is the basic uneliminable predicate, not even "resembles" itself. Indeed, he may say, any particular use of "resembles" can itself be defined, along the lines of his program; there is no term or concept which is indispensable. About this particular proposal, it may properly be remarked that it certainly does not show that all predicates can be dispensed with from an ideal language; any such view runs into the difficulty that infects extreme nominalism. The most that could be shown is that no particular predicate is indispensable. But if some—one or more—predicates must always be used for any synthetic statement, it remains to be shown how there is some advantage to nominalism in holding that no particular predicate is indispensable; if the use of predicates at all is giving hostages to realism, it is not obvious what is the gain of giving only one or some unspecified one, as opposed to giving several. The mere number seems no point of theoretical import. (2) Let us now turn to a familiar objection to the resemblance theory, the so-called "in respect" argument. Formulated with reference to the resemblance theory as I have defined it, the objection comes essentially to this. "You claim," the objector says, "that a language consisting of names of individuals, logical constants and variables, and 'resembles' is rich enough to enable us to define all observation predicates, for instance 'red-106' [when using 'red-106' to refer to some perfectly specific kind of red]. But this is not true. For, to take 'red-106' as an example, something is not red-106 if and only if it just resembles some standard particulars, A and B. It has to resemble them in a particular respect, viz., in color. And you cannot state what this respect is, without in the end bringing in other general terms besides 'resembles.' So your proposed set of primitives is after all too poor." In order to assess the weight of this objection, let us first consider the sense in which "resembles" is used by the resemblance theory. Sometimes, we may note, this word is used so as to apply to predicates or classes, as when we say "This color closely resembles the color of my dog's nose," or "Cambridge blue resembles the blue of an American flag." This sense of -250-

"resembles" is inapplicable for purposes of the resemblance theory, which wants a sense of this term for correct application to pairs of individuals. Are there such senses? Three such senses, I think, will readily occur to us. 12 (1) The first we may call total resemblance—the sense of the term in use, for example, when we say that Mr. X's face resembles Mr. Y's face, without meaning to imply that there is some particular quality of X's face which is exactly or nearly like some quality of Mr. Y's face. Or (2), we may mean exact part resemblance, A resembling B in the sense that A has some quality which exactly matches (is indistinguishable from) some quality of B. Finally (3), we may use "A resembles B" in the sense of inexact partial resemblance, viz., as meaning "A has some quality which is similar to, but does not exactly match, some quality of B." Now, for a reason to be explained, the resemblance theorist will probably work with the first sense if he can. But will this first sense do? Let us consider how he will define "x is red-106." First he will pick as standard individuals objects colored exactly the desired kind of red. (We may note the problem would be more complex if he wanted to define "red" in the determinable sense, for reds can vary along three different dimensions.) Now, obviously he cannot say anything quite as simple as "x is red-106" means "x total-resembles A and B." At the least he will say something like this: "x is red-106" means the same as "x totalresembles A and B at least as closely as A and B total-resemble each other." But will this work? It will not, and for several reasons. (1) Suppose an object, to be tested for redness, is in fact blue, round, and smooth. And suppose that standard-object A is red, round, and rough; whereas standard-object B is red, square, and smooth. In this case, the object will resemble both A and B in respect of one quality, and A and B resemble one another in respect of just one quality. Thus it is not clear why we should not say that the object resembles both A and B at least as closely as they resemble each other. Hence we must classify it as red-106 although in fact it is blue. Or, if A and B happen to resemble each other in some other respect besides color, a red object will fail to be classified as red unless it happens to resemble both of them in other ways as well. 13 Is there any way of removing

this difficulty in principle? An obvious move is to increase the number and diversity of the standard particulars. Thus one might say that "x is red-106" means the same as "x totalresembles all of A, B, C ... as closely as the two least similar of these resemble each other." (And one might also add, "and has less total-resemblance to M, N ... than the two most similar of these have to each other.") Will this work? (2) This leads us to a second difficulty: how are we to estimate comparative degree of resemblance. If we assume that objects have very many, perhaps infinite points of resemblance and difference, it is not clear how we are to decide questions ____________________ 12At least they will after reading Professor D. J. O'Connor's discussion of the kinds of resemblance, in Proceedings, The Aristotelian Society, for 1945-46. 13For a statement of difficulties in Carnap's proposals about the definition of qualityclasses in terms of "resembles," see Goodman, The Structure of Appearance (Cambridge: Harvard University Press, 1951), ch. V. -251-

about relative total-resemblance. Indeed, it is not even clear how we should proceed if we used the notion of inexact partial resemblance (as defined above) rather than totalresemblance, for in this case such an estimate would presumably involve making a count of the points of resemblance and the points of difference, a count which however cannot be made if the number of such points is infinite. (And what would be the alternative to such counting ?) Possibly this difficulty will not arise for phenomenal objects, if it can be shown that the number of their points of similarity and difference is very small. But very likely phenomenal objects are more complex than philosophers are apt to think them—having numerous properties such as looking as if so- and-so were the case—and they appear to have many relational qualities. If so, then phenomenal objects are not clearly more satisfactory, than are physical objects, for application of the type of definition we are considering. (3) But suppose we can make the comparisons of degree of similarity which are needed. Then we are still not out of the woods. For we still have to ask ourselves, for any proposed definition put forward, whether it is complex enough. How many standard particulars must we have, in order to be sure in advance, that no object can possibly turn up which would be classified as red-106 by our definition, although in fact it is some other color? It looks as if we cannot know this in advance, for any proposed definition, unless we examine all objects. And this shows that our definition, however extensionally equivalent with the definiendum is not really identical in meaning with it. And so, if what the resemblance-theory is purporting to give us is a way of rendering the meaning of predicates like "is red-106" by means of "resembles" and names of individuals it has not succeeded. I conclude that the program of the resemblance theory cannot be carried through, by means of the notion of total-resemblance. In my opinion the program would be equally unsuccessful, and for almost exactly the same reasons, if pursued in terms of one of the other senses of "resembles": exact resemblance in some quality or partial resemblance in some quality. And in any case there is a further objection, from the nominalist point of view, to these other tacks. For use of them means that the definition of the desired predicates makes use of "resembles" in a sense which can be applied to observed particulars only by a person who has the concept "has some quality such that ..." In other words, this form of the theory avoids realistic language at the expense of using "resembles" in a way which assumes realistic concepts. Now we must not exaggerate the difficulty. Our suggestion that the theory assumes that a person "has the concept" of such-and-such is itself vague talk. Moreover, there is no formal objection to the theory here; for the theory proposed to carry out definitions of observation predicates in terms of "resembles" and names of individuals, with no restrictions on the particular meaning to be adopted for "resembles." All we can claim is this: It will be awkward for a resemblance theorist positively to object to realist locutions, as meaningless or leading to paradox, if these locutions are merely ways of -252-

putting into words explicitly the very concepts a person must have in order to use

"resembles" in the sense necessary for the resemblance theory program. These difficulties are enough. They are not necessarily all the difficulties to be found in the resemblance theory. Indeed, any problems that turn up in the moderate nominalist theory will a fortiori be problems for the resemblance theory. But these difficulties are enough to show that, if we want to be nominalists, we had better be moderate nominalists. 3. Moderate Nominalism. The moderate nominalist, we recall, is a person who makes rather less far-reaching claims than do nominalists of the extremer sorts. He differs from extremer nominalisms in allowing in his ideal language an unrestricted set of predicates which are applicable to individuals. Moreover, this view in no sense attempts to reduce predicates to individual names, or to regard the functioning of predicates as similar to the functioning of names of individuals. As Quine has remarked, it is just accepted that the fact that "houses and roses and sunsets are all of them red may be taken as ultimate and irreducible." 14 Of course, this admission of predicates does not lead to realist locutions provided one refuses to talk of entities designated or meant by terms like "human"—what such nominalists suppose need not be done in order to explain their use satisfactorily. Let us be clear that according to the definition I have proposed, this view is a clear case of nominalism. But having said this, we should take note of the fact that some writers who call themselves "realists" or at least are critical of some forms of nominalism, hold a view indistinguishable from moderate nominalism. And there is a certain justification in this, just on account of the way this view distinguishes the status of predicates by refusing to allow them ever to occur in the subject place in a sentence, and on account of its refusal to suppose that predicates can be reduced or analyzed in any way. And, conceivably, this is as far as we ought to go toward realism. The moderate nominalist can also introduce a good many traditional realistic expressions in his language—can do so, on account of the fact that his language admits any linguistic expression, providing it is used simply as a synonym for some expression in the standard form of the nominalist language. For instance, the moderate nominalist may use the realist-sounding expression, "Redness has an instance" but meaning by it simply "Something is red." Or he may say, "Redness is a property common to many objects," meaning by it simply, "Many objects are red." But the moderate nominalist is not a realist: according to our definition he is not a realist unless he advocates a language essentially richer than moderate nominalism, one the expressions of which cannot be translated without loss of meaning into expressions in the standard forms of the nominalist language, and using only the standard vocabulary of nominalism. I shall have a comment on the adequacy of moderate nominalism for science ____________________ 14From a Logical Point of View (Cambridge: Harvard University Press, 1935), p. 10. -253-

and philosophy at the end; but first let us turn to our second main question, whether realist language can be recommended to an empiricist as being at least meaningful.

II. The Languages of Realism There are many possible realist languages, and if one decides that nominalist languages are not enough, he still has the job of deciding among realist languages. The choice between these possible realist languages presumably has to be made on the basis of simplicity, adequacy for the purposes of what we want to say, the avoidance of paradox, and the possibility of stating the semantic rules for such a language in a language the clarity of which cannot seriously be questioned. But there are certain properties all realist languages will share—characters which distinguish them from nominalist languages. First, all realist languages will relax the restriction permitting only names of individuals as subjects of a sentence, and permitting variables to range only over individuals. Second, in order for the first change to be effected the realist language requires an enriched vocabulary; in particular, it requires some predicates which are meaningfully applicable to non-individuals; and it is convenient to add names of

non-individuals, to function in the subject places of sentences. Among the predicates applicable to non-individuals which will be added in such a language will presumably be ones including: "is similar to," "is a color," "designates," "is an instance of," "is a universal." Since English is a realist language, we are already actually using many predicates of this sort. In order to discuss the question whether realist language is meaningful, it is necessary to specify further at least one type of realist language. We may note that one might introduce as one's non-individual names, the names of classes; or one might introduce the names of so-called "abstract particulars." 15 I ____________________ 15As Donald Williams does, in "On the Elements of Being," Review of Metaphysics, Vol. VII, Nos. 1 and 2. It may be questioned whether his language should not be regarded as a nominalist language. I think it is inconvenient to regard it as such, since his "abstract particulars" are not parts of concrete individuals in any ordinary sense. It is worthwhile to consider how this alternative realist language compares with the language of attributes in respect of simplicity, etc. (1) Moore (in supplementary volume III of the Aristotelian Society) was puzzled about what the names of these abstract particulars are supposed to name. I should prefer to make two points. First, an explanation of the reference of one of them is surely not provided for another person with more ease than the reference of attribute names. For instance, the reference of "the redness of this" (or of some arbitrarily chosen corresponding proper name) would have to be introduced by some expression like, "that about this which makes it correct to call it 'red.' " Second, following suggestions by Dawes Hicks in the above symposium, we may note that the number of numerically different abstract particulars one finds in a given object seems a rather arbitrary matter. One might distinguish a very large number of color-particulars in any object. At least this does not look like a gain in economy. (2) It is sometimes urged that this theory avoids a substratum view of particulars. Just what this difficulty of the attribute theory is supposed to be, I do -254-

prefer, however, to introduce as names of non-individuals, the names of attributes (properties or qualities) and relations. So let us introduce a set of new names into our language (and, if we wish, a correspondingly distinct set of variable letters); and let us specify that each name is to be the name of the signification of a predicate already in the language. (I shall consider later the meaning of "signification.") Perhaps the simplest thing is to form such names simply by writing the predicates already admitted with an initial capital letter (so "Red," "Human"). It is worth noting that we could make various limitations, restricting the number of names to be introduced. For instance, we might decide to admit such names only in the case of observation predicates, or phenomenal predicates. Or, as Aristotelians, we might admit names corresponding only to those predicates which have instances, instead of making the Platonic move of admitting a name for every predicate. There are two special predicates of non-individuals which we shall want in our language, of course among many others. The first of these is the relational predicate "is an instance of." This predicate is indefinable in nominalist language, but we can define it implicitly, by laying down that "x is an instance of F-ness" is true just in case that x is F. The second predicate is "is a universal," or better, "has universalness." This predicate is not necessary if we have a special variable notation for quantifying specifically over the designata of our new non-individual names. In other words, it is not essential for a realist language to contain the word "universal." ____________________ not know. But I cannot see why, if two exactly similar abstract particulars can be numerically distinct just through being in different space-times, an attribute theorist should be required to postulate a mysterious substratum to explain how two concrete particulars, although instances of the same qualitative universals, can be numerically different if they are in different space-times. (3) It is advocated (Williams, p. 11) as a virtue of this theory that it makes possible a definition of the relation of predication in

terms of the notion of a member of a set (of similars constituting a class) being included in the "concurrence sum" which constitutes a concrete individual (viewed as a sum of abstract particulars). But is it doubtful how much has been gained when we consider that these abstract particulars are not parts in any ordinary sense and when, it appears, a "concurrence sum" must be explained as the "peculiar interpenetration, the unique congress in the same volume, which we call 'belonging to (or inhering in, or characterizing) the same thing' " (p. 8). (4) More serious are the difficulties of Williams' view (essentially involved in the foregoing proposal about the definition of "predication"), that abstract terms like "Humanity" can be defined as the set of abstract particulars exactly resembling any specific abstract particular of the "human" sort. For the set is to consist of all those abstract particulars which resemble one particular. Now is this supposed to be one and the same relation that they all have? If so, the notion of an abstract universal is presupposed. If in consistency this is denied, then we are left with abstract particulars each standing in a numerically different relation of similarity to something; and it is not clear that there is any mark belonging to all and only those which are to belong to the class Humanity. (5) If there are difficulties in defining the general expression, "is a universal," one would like to ask if there are not more difficulties in defining "is an abstract particular." Universalhood may be regarded as a property of universals; being an abstract particular, we may conjecture, is itself a similarity-set like Humanity, but one of which all abstract particulars (excluding itself, since presumably we shall need different types of such particulars) are members—but we should like to know more about the definition. -255-

However, it is convenient, and if one wishes a language rich enough to talk about languages with names designating universals, it is necessary. We may propose the following as a preliminary definition of this expression. "Has universalness," then, means the same as, "could be signified by a predicate." (This definition, again, is not helpful unless we are clear what we mean by "signified." I shall return to this point later.)The foregoing remarks are, of course, only the merest beginning of a description of a realist language. For one thing, I have spoken only of proper names of universals. But we shall probably want other expressions designating universals. For instance, we shall want, corresponding with the universalname "garnetness," the expression, "the color of this marble" or "the color of transparent almandite." Thus we shall have expressions with different meanings, all designating the same universal. We may incidentally note that, if our language is thus rich, we must distinguish between the meaning or sense of some expressions, and the universals which they designate.Let us now turn to the question whether synthetic statements in our realist language can be regarded as empirically meaningful. We can, of course, give semantic rules for them, provided that we use a metalanguage which is itself realist. But I should suppose that a skeptic about the meaningfulness of these locutions would want to be shown precisely that a metalanguage was itself meaningful, insofar as it contained such expressions. For the benefit of skeptics let us now consider the following points. 1. The skeptic is apt to be ready to concede that any type of statement actually used seriously by empirical scientists will have empirical meaningfulness. If so, it is then relevant for him to note that scientists do appear to use realist expressions. As Carnap has pointed out, 16 the physicist is apt to say something like, "These two bodies have the same chemical properties, but there are certain physical properties in which they differ." 2. We may note that there are some demands for definition which cannot consistently be made by a nominalist. In particular, the nominalist cannot demand a definition of all realist terms in nominalist language, a definition it is logically impossible to give. Further, there is some doubt whether there is any satisfactory definition of "concrete individual"; and we could point to difficulties in explaining what is the sufficient condition for two individual names naming the same thing, or, in other words, in explaining the definition of "identity" or "numerical difference" as applied to concrete individuals. Indeed, we may note that the most frequently offered definition of "identity" of individuals is one that actually makes use of realist language, by the notion of all properties of the one being also properties of the other (or the notion of the same matrices being applicable to both); and this definition is hardly satisfactory if realist locutions are not meaningful.

3.

Let us consider realist language as an extension of nominalist language, and compare it, as such, with the language of theoretical constructs in physics as an extension of observation language. Now it is well ____________________ 16Meaning and Necessity (Chicago: University of Chicago Press, 1947), p. 22. -256-

known that not all the terms in the vocabulary of theoretical physics can be explicitly defined—or even defined by means of the counter-factual-in observation terms. Indeed, not every statement in such a system can be said to be meaningful in the sense that it can be said to be true if and only if some some statement in the observation language is true. Now the language of realism appears to be at least as tightly linked to observation statements in nominalist language as are the statements of physical theory to observation statements. For instance, the realist statement "Red is a color" is true if and only if anything that is red is colored. Or the realist statement, "Red is more similar to orange than it is to green" is true just in case anything that is red is more color-similar to anything orange than it is color-similar to anything that is green. Obviously there are enormously many statements formulable in realist language which are true if and only if some statement in nominalist language is true. Indeed, one might argue that the more serious problem is the question whether realist statements are not so closely linked that we ought rather to deny the autonomy of realist language altogether, claiming that no important statements can be formulated in it which cannot be regarded as just a picturesque idiom which is precisely synonymous with some nominalist statement. However, there are some statements formulable in some realist languages which cannot be viewed in this way, for instance, some statements quantifying over classes (which are important for mathematics). Moreover, we need to ask by what criterion of synonymy it might be proposed to show that these realist expressions are just picturesque synonyms of nominalist ones. "Achilles is an instance of tallness" at least does not look like a statement just synonymous with "Achilles is tall," since the former, among other things, contains the relational predicate "is an instance of," whereas the latter does not. The outcome of these considerations is, I believe, that realistic language is a distinct extension of nominalist language but that, as used, truth- conditions of many or most realist statements can be formulated in a nominalist language. This situation appears closely parallel to the relation between theoretical constructions in physics and the language of observation. If the language of such constructs, then, is regarded as meaningful, why not realist language? It is possible that there is one point of difference: that realist language is not as indispensable for empirical science, particularly for the formulation of laws and for prediction, as is the language of theoretical constructs in physics. 17 ____________________ 17I am here considering realist language as an extension of nominalist language. It is not obvious why a person should not take the opposite view, regarding realist language as primary, and viewing nominalist locutions, e.g., "Churchill is no longer prime minister," as an extension of the vocabulary and forms which must be given meaning in terms of realist language. This is what is done by Goodman in The Structure of Appearance. Thus the concession to nominalism that I am here making, that nominalist language is an acceptable way of talking and that realist language is what has to be justified, is a concession that might be questioned. Since ordinary English includes realist locutions, the nominalist might well be asked to explain why he regards realist language as less clear and demanding of justification. Quine's various criticisms of criteria -257-

4.

Nevertheless it would strike us as odd if anyone proposed that we can show the meaningfulness of realist vocabulary only by a piece-meal specification of the points of contact between particular realist statements and particular nominalist statements. Surely there is some more general account possible, of what realist terms refer to. I wish to make an attempt in this direction, to explain to the moderate nominalist how to use

realist terms for observable properties. In doing so, I shall assume that he knows ordinary English, but not technical terms used by realist philosophers. I should also like to keep to the nominalist segment of English, but it is no mean task to decide whether a given expression can appropriately be said to be nominalist (since it might qualify as a picturesque locution identical in meaning with some expression in the standard form of nominalism); so I shall merely confine myself to ordinary expressions it is reasonable to suppose the moderate nominalist will concede he understands. Let us consider as an example the color-predicate "garnet," assuming that this is perfectly specific in the sense that any two objects properly called garnet will exactly match in color. What we are interested in is giving instructions for the use of "garnetness," of such a general sort that they can be applied in the case of any observable quality. Our instructions will consist in giving our novice facts about what "garnetness" refers to, so that, by elimination, he can pick out, select as an object of attention, something of which he can say without fear of error, "This is garnetness." ("This" is ordinarily used to refer to a single entity; and the case will be true here, although some of the tests of a "single entity"—such as continuity of space-time occupied—appropriate for some entities will not apply here.) We assume, now, that our novice knows how to classify all possible objects as garnet or not-garnet; ability to do this is part of what is meant by saying a person knows how to use this predicate. But, how does he do this? It will be agreed that he cannot justifiably so classify, say, a marble, unless he has looked at it. Moreover, when he looks he must notice something in particular about it; he must notice its color. (If you are wanting to classify something with respect to color, you must notice the particular kind of color it is; and so on.) Now, if he has noticed its particular color, and the marble is garnet, and he has recognized that it is garnet, then our novice has been aware of what it is proper to call garnetness. (This is what Cook Wilson called the "characteristic being" of this universal.) But now we must remind our pupil that "garnetness" is not being used to name just some part of this marble, certainly not in any ordinary sense of "part of"; it is not even something that is a "part of this marble in any sense which excludes the possibility of becoming aware of garnetness by observing any other object which is garnet. (This ____________________ for identity of attributes (e.g., in Mind, Vol. LXIV, p. 159) here have point. (Incidentally, why not say that ϕ = ψ if and only if all the properties of ϕ are properties of ψ, and conversely?) -258-

instruction gives our pupil a clue to what it means to say that "garnet" names a type, not a part of a particular individual. Of course, he will be under no temptation to think it names a part in any ordinary sense of "part"; for any part of an object ordinarily has several qualities at once, for instance, in the case of the surface, it will have, say, smoothness, shininess, garnetness, and so on.) Indeed—although in this case perhaps the explanatory phrase is obviously in the "realist" branch of ordinary English—what "garnetness" names is the very same as we should be talking about if we said, "This color is the very same as the color of transparent almandite." Now, can our novice pick out something, as an object for attention, which fits this prescription, or can he not? I suggest that it is only reasonable to concede that he can, and that he can pick out only one thing that fits. (And, having done so, he can see how to confirm statements like, "Garnetness is very similar to crimson, but darker.") Moreover, there is no reason why the name of any observable quality (or relation) cannot be introduced in this same general way. Indeed, we might even define "is a universal," at least for the class of observables, as "can be made the referent of an abstract term, introduced in the way described." We may notice, incidentally, that we began our instruction for use of garnetness" by supposing that the pupil knew whether or not to apply "is garnet" to all possible objects. It would not have been enough to assume that he applied this expression correctly to all actual

objects. For this more limited ability is compatible with his not understanding "is garnet" correctly at all; he might be confusing this expression with some other one which happens to have the same extension as "is garnet." (Would we be sure that a person knew the difference between "centaur" and "unicorn" just because he said, correctly, that there are no objects of either kind in the world?) In order to be able to say correctly that a person understands a predicate term, he must be able to pick out, attend to, the property which makes it applicable, which is what it means to "know the intension" or "signification" of a term. 18 So far we have said nothing about the case of non-observable qualities or relations. Can we explain in a similar way what is meant by speaking of the "signification" of non-observation predicates? We may observe that, if we are only asking to be assured of the meaningfulness of some statements in realist language, we do not have to concern ourselves with this. Further, we must concede that the signification of such terms, say for instance "malleable," is not capable of sensuous presentation in the sense in which this is true of "garnet." But, if we know how to test for the applicability of a predicate term, it seems we can say that there is a sense in which thought can grasp the meaning of the corresponding abstract term. At least this is true in the sense that we shall know how to confirm some statements containing such an abstract term. Doubtless there is a great deal more which needs to be said; ____________________ 18See the discussion in Carnap, "Meaning and Synonymy in Natural Languages," Philosophical Studies, Vol. VI (1955), pp. 33-47. -259-

but these observations perhaps suggest a line one might take to defend the view that a language with names for non-observable properties would not necessarily be meaningless. One might concede that realist languages are meaningful, but question whether there is any conclusive reason for using them, in preference to moderate nominalism. Recent discussions about the reconstruction of mathematics, or the formulation of a semantical system, without realist locutions bear upon this and are well known. A question that has not been sufficiently considered is whether realist locutions are necessary for empirical sciences like psychology or linguistics. I conclude with two remarks on this. First, if it turns out that realist language is required only for discussing the reference of linguistic forms, there is something to be said for calling one's theory a form of Conceptualism. Second, it may well be that realist language is less important in the empirical sciences themselves, than in the philosophical enterprise of providing definitions, particularly of basic terms like "law," "cause," "probable," etc. For instance, it seems to me that the use of any determinable terms is puzzling, and that a philosophical theory is better if it can offer a definition of all determinable terms by means of names of specific qualities. Consider, for instance, the predicate "is colored." The realist can define this term. For he can pick out specific colors at the extremes of the color cone, say F, G, H, and say "This marble is colored" means "There is some quality Q, such that this marble is an instance of it, and such that Q resembles 19 F, G, and H at least as closely as the two least resembling of these that resemble each other." Goodman has shown a different and more elegant way of doing this. The nominalist cannot do as well. Of course, not all words need be defined ; it is enough if we can teach people to use them consistently, in one way or another. But it is an advantage of realist languages if they have a superior capacity to provide definitions. ____________________ 19It might be objected that use of this term is unfortunate because it is itself a determinable. If so, we can remove it and substitute a more complex definition in terms of least discriminable difference, matching, or indistinguishability, in the manner of Goodman. -260-

: 16 : GRAMMAR AND EXISTENCE: A PREFACE TO ONTOLOGY WILFRID SELLARS

I My purpose in this paper is to examine the current dogma that to sanction the move from (1) S is white to (2) (Ef) S is f or from (3) S is a man to (4) (EK) S is a K or from (5) Tom is clever or Tom is tall to (6) (Ep) p or Tom is tall is to commit onself to the existence of entities of a higher order than perceptible individuals. I shall begin by assuming that if these moves, each of which is a form of what is called "existential quantification," do involve a commitment to such entities, the entities in question are such straightforward abstract entities as Triangularity, Mankind and the proposition that Tom is clever. I shall subsequently turn my attention to the idea, recently elaborated by Peter Geach, but which stems from the work of Gottlob Frege, that what one is committed to by these moves, or their ordinary language counterparts, is not abstract individuals, entities which ape the individuality of perceptible things, but rather what, for the moment, I shall simply refer to as non-individual entities, entities which have no names, but are, somehow, stood for by parts of speech other than names. I shall begin by exploring the move from (1) to (2), taking as my point of departure the fact that the latter is often "informally" rendered by (21) There is an f such that S is f. ____________________ Reprinted from Mind, 69 (1960) by permission of the editor and the author.

For, I believe, a careful examination of this "reading" will enable us to put our finger on the source of the dogma in its first or orthodox form. Now a first glance at (21) may well lead one to think that the expression "an f" in "There is an f ..." has the form of the particle "an" followed by a variable which takes common nouns, or expressions having the force of common nouns, as its values. Another glance, however, raises the question, "If the first 'f' is a common noun variable, must not the same be true of the second?" One sees immediately, however, that if the second "f" were a common noun variable, the "white" from which the quantification began would have to be a common noun. We should accordingly expect (1) to read,

(11) S is a white and even if we hastily transform (1 1) into (12) S is a white thing we are startled to think that "quantification over predicate variables" involves the questionable idea that "S is white" has the form "S is a white thing," or must be transformed into the latter as a condition of the quantification. We also notice that this line of thought carries with it the implication that (2 1) should read (22) There is an f such that S is an f Now it is perfectly clear that something has gone wrong; a conviction which is conclusively reinforced by the reflection that if we "read" (7) (Ex) x is white as (71) There is an x such that x is white parity of reasoning would require us to interpret the second "x" as a common noun variable, which it simply cannot be. What, then, are we to make of the expressions "an x" in (7 1) and "an f" in (21)? Since we cannot dodge the fact that in their ordinary use the context "a(n)—" calls for a common noun to fill the gap, is there any other way than the above in which these expressions can be construed in terms of common nouns? The answer, of course, is obvious to one who knows the literature of the problem, for one immediately thinks of those curious common nouns "individual" and "quality," and of the locutions, "There is an individual ..." and "There is a quality...." Surely, then, it is the category words, "individual" and "quality," which belong after the "There is a ..." in the "informal readings" of (2) and (7). If we follow up this line of thought, we end up with something like (23) There is a quality, f, such that S is f. and -262-

(72) There is an individual, x, such that x is white and with the idea that the "f" which occurs in the context "f" of the original "informal reading" is playing a dual role: (a) the role of the category word (constant) "quality"; (b) the role of a variable which reappears at the end of the sentence. But is (2 3) a well-formed sentence? Here is the rub; for notice that "There is a quality, f, ..." commits us to the form (8) f is a quality and, if "white" is to be a value of "f," to (9) White is a quality. But if so, this means that just as "quality" plays in (9) a role analogous to that of "man" in "Tom is a man," so "white" is playing a role analogous to that of "Tom." We have, it appears, avoided the Scylla of turning "white" into a common noun, only to whirl into the Charybdis of the idea that "quantification over a predicate variable" involves turning it into a proper name, with a consequent commitment to Platonism. And this fact stands out even more clearly if we replace our original sentence (1) by

(10) S is triangular. For whereas "white" can play both the adjective and noun roles, so that (9) is a proper English sentence, we must actually transform "triangular" into "triangularity" to get the statement which corresponds to (9), namely (11) Triangularity is a quality.

II I asked a moment ago if (23) is a well-formed sentence, and we now have serious grounds for doubt. For while, as we have just seen, the first "f" in (2 3) must be a variable which takes such singular terms as "white(ness)" and "triangularity" for its values, the second "f" is required by its context, namely "S is—," to take adjectives. If, therefore, "f" is to be the same variable throughout the sentence, the concluding context must be reformulated to admit of a variable which also takes singular terms. How this might be done is no mystery. We simply construct our variable with the aid of the most convenient of the suffixes which are used to form abstract nouns from adjectives, thus "f-ness," and rewrite (2 3) to read (24) There is a quality, f-ness, such that S has f-ness and discover that what our "informal reading" of (2) has given us is an existential statement which stands to (11) S has whiteness -263-

as "There is a man, x, such that S loves x" stands to "S loves Socrates." Well, then, to go from (1) to a quantified statement in which "the predicate is quantified," must we first, in effect, transform it into (1 1)—in which, after all, the predicate is no longer "(is) white" but "exemplifies whiteness"? Does all quantification presuppose a point of departure in which the constants to be replaced by variables are singular terms? The answer, surely, is a categorical No. The contrary supposition is generated not by reflecting on the logic of quantification as such, but by reflecting, as we have been doing, on an "informal reading" of quantified statements, a reading which may have much to recommend it in the way of making certain logical relationships intuitive, but is far from giving us the ordinary language equivalent of these quantified statements. The "informal reading" is a contrived reading which generates puzzles as soon as its auxiliary role is overlooked, and it is made the focal point of philosophical reflection on quantification and existence.

III But what, then, it may well be asked, is the correct reading of (2), if it is neither "There is an f such that S is f" (21) nor "There is a quality, f-ness, such that S has f-ness" (2 4)? In other words, how would we ordinarily say what the logistician says by means of (2)? Now it is easy enough, if I may be permitted a paradox, to invent an "ordinary language equivalent" of (2). One simply begins by noting that the force in the case of quantification over variables of type 0, the force of "(Ex) is white" (7) captured by (73) Something is white and proceeds to represent (2) by (25) S is something. The latter both preserves the form is ..." (as contrasted with "... has (or exemplifies) ...") and, by avoiding the reading "There is an f ... " bypasses the stream of thought explored in sections I and II above.

Now, if we could convince ourselves that (2 5) would be a reasonable invention—or, better, that it isn't really an invention at all—we would have gained an important vantage point in the battle over abstract entities. The above suggestion, however, in the absence of an elaborate interpretation and defence, is scarcely more than a promissory note. And there is no dodging the fact that most if not all of the general statements we make which correspond to logistically formulated statements in which there is quantification over variables which take adjectives, common nouns, verbs and sentences for their values, do involve the use of category words. And since the use of category words involves a prima facie commitment to abstract singular terms -264-

such as "Triangularity"—and others which we shall be exploring in a moment—the question naturally arises, "Does the use of these singular terms involve a commitment to Platonism?" But before we begin to explore the significance of the fact that we do make use of category words and abstract singular terms, it is important to dwell for a moment on the claim which is implicit in the argument up to this point. This claim—which it is my purpose to defend—can be summed up by saying that one no more has to construe "(Ef) S is f" (2) as saying "There is a quality, f-ness, such that S has f-ness" (2 4) than we have to construe "S is white" (1) as really saying "S has whiteness" (1 1). 1 Another way of making this claim is by saying that the widespread view that the introduction of predicate variables carries with it the use of such category words as "quality," "attribute," or "property" is simply a mistake. Indeed, from this point of view, not only is the "introduction of the category word 'quality' " a distinct step in "committing oneself to a framework of qualities," this "commitment" involves the introduction of a new set of variables ("f-ness" as opposed to "f") and a set of singular terms (e.g. "whiteness," "triangularity") to be their values. According to this claim, it is a mistake to suppose that a predicate variable belongs in the context "... is a C" where "C" is a category word. Thus "f is a quality" (8) would be ill formed, the proper expression being. (12) f-ness is a quality. For while the singular term "Socrates" belongs in both the ordinary context "Socrates is a man" and the categorizing context (13) Socrates is a particular and the singular term variable "x" belongs in both the context "—is white" and the context "—is an individual," "triangular" must be turned into "tri____________________ 1It might be thought illuminating to replace the original statement (1), by (12) S: Whiteness and the statement (9) White is a quality by (91) Whiteness: Qualitykind and to say that in (1 2) "Whiteness" is the "predicate," whereas in (9 1) it is the "subject." It must be pointed out, however, that one has not shown that (1 2) is not simply a rewriting of the categorial counterpart of (1), namely (11) S has whiteness [that "whiteness" is juxtaposed to "S" says that S has whiteness] or, indeed, a rewriting of (1) itself [that "whiteness" is juxtaposed to "S" says that S is white]—in which case the

singular term "whiteness" would be a sham—unless one sketches the modus operandi of a new form of language which breaks away from our ordinary categories of "singular term," "common noun," "adjective," etc., and which cannot in any straight- forward sense be translated into the language we actually use. That (1 1)—or (1)— could be rewritten as (12), and that (9) could be rewritten as (91) has not the slightest tendency to show that they have a common logical form to be represented by "———: ...." Compare Peter Strawson's contribution to the symposium on "Logical Subjects and Physical Objects," Philosophy and Phenomenological Research, xvii (1957), and my criticisms thereof. -265-

angularity" and "f" to "f-ness" as one moves from "S is—" to "—is a quality." The reason, of course, is that "Socrates" is a singular term, and "x" a singular term variable to begin with, while "triangular" and "f" are not. (It should not be assumed that "Socrates" is unambiguously the same singular term in both cases).

IV Before taking the next step in the argument, it will be useful to develop the parallel claim—which I also wish to defend—in connection with the move from "S is a man" (3) to "(EK) S is a K" (4). To read (4) as (41) There is a K such that S is a K and to take the context "There is a K ..." seriously leads one to (42) There is a class, 2 K-kind, such that S is a member of K-kind just as "There is an f such that S is f" (2 1) led us to "There is a quality, f-ness, such that S has f-ness" (24) . Furthermore, just as "S has whiteness" (11) is the categorial counterpart of (1), so (31) S is a member of mankind is the categorial counterpart of (3). And, it seems to me, "man" is no more functioning as the name of a class in (3) than "white" is functioning as the name of a quality in (1). Furthermore, just as the "is" in the latter is not "has" or "exemplifies" in disguise, so the "is a" in the former is not "is a member of" in disguise. It is surely as incorrect to regard "S is a man" as a class-membership statement, as it is to regard "S is triangular" as a qualityexemplification statement. The "introduction of classes" as extensional entities takes its point of departure from common nouns (and expressions having the force of common nouns) which are applied to a certain domain of logical subjects—where a logical subject is, roughly, an item referred to by a singular term. 3 If we limit our attention to classes pertaining to physical things, the point I wish to make can best be put by saying that once one has made the move from statements of the forms ____________________ 2By no means all common nouns and common noun expressions stand for kinds of thing. Kinds are a distinctive subset of classes, and we speak of the instances rather than the members of kinds. Since I am not concerned in this paper with the distinctive character of kinds, I shall refer to kinds simply as classes and speak of their members rather than their instances. 3The term "individual" is often used in the sense of "logical subject" as characterized above. In this broad use, "individual" is to be contrasted with "particular," for particulars are, roughly, those individuals which are referred to by the singular terms which occur in observation statements. -266-

(14) S is a K and (15) S is an f-thing 4 to their categorial counterparts (141) S is a member of K-kind and (151) S is a member of the class of f-things it is an additional step to introduce classes as extension of entities in terms of co-extensive classes. For it is simply not true that in non-technical contexts classes are identical if their memberships coincide. To resume, just as the transition from (1) to (2) does not involve treating "f" as a variable for which singular terms ("names of properties") are values, so, I wish to argue, the transition from "S is a man" (3) to "(EK) S is a K" (4) and from "S is a white-thing" (12) to (18) (E f-thing) S is an f-thing do not involve treating "K" or "f-thing" as variables for which singular terms ("names of kinds") are values. Again, just as it is I believe clarifying to read "(Ex) x is white" as "Something is white," rather than "There is an individual, x, such that x is white," and "(Ef) S is f" as "S is something" rather than "There is a property, f-ness, such that S has f-ness," so I believe it to be clarifying to read "(EK) S is a K" (4) as (43) S is a something rather than as "There is a class, K-kind, such that S is a member of K- kind" (42). Finally, to mobilize the force of these considerations, note that the statement ____________________ 4It is important to note that while we can form the expression "white-thing" from the adjective "white" and the category word "thing" in accordance with the formula (16) S is a white-thing = D f S is a thing. S is white it would be a serious mistake to suppose that all common nouns pertaining to physical objects are built from adjectives and the category word "thing" in accordance with the formula (17) S is an N = D f (S is a thing) and S is A 1 ... A n (where "N" is a common noun and the "A 1 "s adjectives). To suppose that "thing" is the sole primitive common name is (a) to overlook the fact that the category word "thing" has a use only because there are statements of the form "S is an N"; (b) to expose oneself to all the classical puzzles about substrata. (This point is elaborated in my "Substance and Form in Aristotle: an Exploration," Journal of Philosophy liv [1957], pp. 688-699.) Reflection on the first of these points makes it clear, incidentally, that it is a mistake to view the category of substance or thinghood as a summum genus. -267-

does not say "There is a class ... ," though what it does say can be put categorizingly by saying "There is a class which has a member and another member, and all its members are identical with e ither of these."

V Similar considerations apply, mutatis mutandis, to the move from "Tom is clever or Tom is tall" (5) to "(Ep) p or Tom is tall" (6). The variable "p" is no more to be construed as taking singular terms for its values, than is "f" or "K." On the other hand, the statement (51) (The proposition) that Tom is clever is a disjunct of (the proposition) that Tom is tall is the categorial counterpart of (5) just as "S has (the quality) whiteness" is the categorial counterpart of (1) "S is white." It will be convenient to use the expression "that-p" as the variable which corresponds to "p" as "f-ness" to "f," "K-kind" to "K." And to conclude the drawing of parallels, I believe it to be clarifying to read "(Ep) p or Tom is tall" (6) as (61) Something or Tom is tall. Note, by the way, that if, as it seems reasonable to suppose, "that it is raining" is functioning as a singular term in (20) Jones believes that it is raining, the quantified statement corresponding to (20) as (6) corresponds to (5) would be not (21) (Ep) Jones believes p but rather (211) (E that-p) Jones believes (the proposition) that-p. But we shall have something more to say on this topic in our concluding remarks.

VI Let us suppose, for the moment, that the above line of thought can be carried through and defended. And let us ask what light it throws on the idea that the "existentially quantified" formulae of the logistician are the counterparts -268-

of the statements in everyday discourse in which, to use Quine's phrase, we make ontological commitments, i.e. say that there are objects or entities of such and such kinds? Just this, that they are not the counterparts. Or, more precisely, that there is no general correspondence between existentially quantified formulae and existence statements. Only in those cases where the variable which is quantified is a variable of which the values are singular terms will a quantified formula be the counterpart of an existence statement. Nor is this all; not even all (so-called) existential quantification over singular term variables has the force of an existence statement. For the latter involve common nouns or expressions having the force of common nouns. Thus, (22) There are tame tigers involves the context (23) x is a tame tiger. Failure to see that common nouns or expressions having the force of common nouns are essentially involved in existence statements is due, in part, to the mistaken idea that such a

statement as "S is white" (1), in which occurs the adjective "white," differs only, so to speak, graphologically from "S is a white thing" (1 2), in which occurs the common noun expression "white-thing." For if this were so, then "Something is white" would differ only graphologically from "Something is a white thing" and we could use indifferently the formulae "(Ex) x is white" (7) and "(Ex) x is a white thing" (7 4). It is important to see that it is just as incorrect to read "(Ex) x is white" as "There is a thing which ..." as to read "(Ef) S is f" as "There is a property...." For unless one sees that not even quantification over singular term variables of type 0 makes, as such, an existence commitment involving an ontological category, i.e., says "There are particulars," one is likely to think that "There are particulars" is unavoidable in a way in which "There are qualities" might not be. For while we can scarcely hope to dispense with quantification over variables of type 0, able philosophers have found it possible to hope that quantification over variables of higher types can (in principle) be dispensed with, or at least reduced to the status of a bookkeeping device for dealing with cash in which it does not appear. We have already had something to say about the force of "thing" in the noun expression "white thing," and we shall have more to say about the category words "individual" and "particular" at the end of the argument. The point I am concerned to press at the moment, however, is that among the forms by the use of which one most clearly and explicitly asserts the existence of objects of a certain sort—I am not concerned with singular existence statements, which raise their own problems—are the forms "There is an N," "Something is an N" and "There are Ns," and that the logistical counterpart of these forms is (24) (Ei) i is an N -269-

where "i" is a variable taking singular terms of a given type as its values, and "N" is an appropriate common noun. We can sum this up by saying that only where the so-called "existential quantification" is a quantification over a context of the form "i is an N" is a quantified statement the counterpart of a statement asserting the existence of objects of a certain sort—and this, after all, is analytic. 5 Put thus positively, the thesis seems to ring true. If, however, we make the same point negatively, by saying that to quantify over an adjective-, common noun- or sentence variable is not to make the PMese equivalent of a statement asserting the existence of attributes, kinds or propositions, it becomes clear that we have much more work to do. For, to take but the case of quantification over an adjective variable, our claim that it is illuminating to parallel the reading of "(Ex) x is white" (7) as "Something is white" (7 3), by a reading of "(Ef) S is f" (2) as "S is something" (25) stand in urgent need of expansion and clarification. Perhaps the best way of accomplishing this is by examining the constructive views advanced in Peter Geach's contribution to the Aristotelian Society symposium 6 on "What there is" which takes its point of departure from Quine's provoking essay of this name. Geach sees that Quine's account won't do. He sees, to put the matter in terms of our examples, that the statement "S is white" (1) entails the general statement (26) There is something which S is (i.e. white) and insists, correctly, that the latter is not to be confused with (27) There is something which S has (i.e. whiteness). To take another example, he sees that (25) Jack and Jill are both tall entails the general statement (26) There is something which Jack and Jill both are

and that the latter statement is not to be confused with (261) There is something which Jack and Jill have in common. It would be incorrect to attach the rider "i.e. tallness" to the former. The proper rider would be "i.e. tall," thus (262) There is something (i.e. tall) which Jack and Jill both are. Now Geach's "There is something which S is" corresponds to our "S is something." And his insistence that the something which S is is white and not ____________________ 5It follows that the phrase "existential quantification" should be dropped and replaced by (rather than abbreviated into) one of its logistical equivalents, e.g. ∑-quantification. 6Supplementary volume xxv (1951). -270-

whiteness corresponds to our distinction between "S is something" and "S has (i.e. exemplifies) something." Thus, in the terms of our analysis, Geach's "There is something which S is" (2 6) is the counterpart of "(Ef) S is f" (2) and he has correctly seen that the latter does not involve a commitment to the use of such abstract singular terms as "whiteness" or "tallness." But while he is on the right track up to this point, he builds the above insight into a larger mistake. For he is misled by his own formulation into supposing that (262) There is something (i.e. tall) which both Jack and Jill are. Although it does not commit us to the "abstract or universal entity" tallness, it does commit us to the "property" tall. Thus he tells us that while the predicate "red" is not to be construed as a name, it does "stand for" something, and he proposes "property" as a "general term for what predicates stand for." He continues "This way of speaking [saying that what a predicate stands for is a property] has its dangers, but can be given a harmless interpretation; 'property' may here be taken to be just short for 'something that an object is or is not.' " 7 Now Geach's properties are essentially the same sort of thing as Frege's concepts. Indeed, it is clear from other statements of his that Geach would have used Frege's term were it not for its conceptualistic connotations. I shall shortly be discussing a difficulty which is present in Frege's account of concepts. It will, however, be convenient to lay the groundwork by exploring what Geach has to say about properties. Now it is important to realize that Geach gives two accounts of the term "property"; one of which, though cautious, is based on a simple grammatical mistake, while the other is derived from Frege's account, and is more difficult to expose. The cautious account is contained in the passage quoted above, in which he stipulates that "property" is to be equivalent to "something that an object is or is not." The Fregean account is the one in which properties are introduced as what predicates stand for. We shall return at a later stage in the argument to the dangers involved in the idea that predicates stand for properties. Our present concern is with the force of the statement "There is something which Jack and Jill both are" (26). Let me begin by noting that in our illustration, "There is something which Jack and Jill both are" (26) was a generalization from "Jack and Jill are both tall" (25). Now to move from the latter to (27) Jack and Jill are both something 8 is to avoid at least the appearance of an existence statement. For the hypothesis with which we are working is that only those "something-" statements which are of the form "Something is an N," where "N" is a common noun, ____________________

7Op.

cit., p. 133. the reading of "(Ef) S is f'' as "S is something" would require the use of indices to draw distinctions which become relevant when it is a question of reading such statements as (27). For if Jack were tall and Jill were short, it would follow that Jack and Jill were both something, though they would not be "the same something."

8Clearly

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have the force of existence statement—thus of the statement "There are Ns." But Geach's formulation, beginning, as it does, with "There is ... ," though it is equally legitimate and equally involves no commitment to abstract singular terms, has the prima facie appearance of an existence statement. And, I am sorry to say, Geach has been taken in by it. And if the entities he introduces are what things are rather than what they exemplify, they are abstract entities, none the less, as Quine has noted in his reply, 9 and Geach's denial that these entities are individually referred to by such singular terms as "Tallness" is open, as we shall see, to the reply that he has avoided the abstract individual tallness only at the expense of treating the adjective "tall" as a peculiar kind of singular term, and hence introducing the abstract individual tall. The key point to notice is that unlike existence statements proper, the statement (26) There is something which Jack and Jill both are begins not with "There is a ... ," not with "There is a something... ," but simply with "There is something...." If it began with "There is a something ... ," thus using "something" as a common noun, one might well look for a common noun, such as "property," to pinpoint just what sort of "something" "there is" which Jack and Jill both are. We could then have (263) There is a property which Jack and Jill both are. But all this, as by now should be obvious, is logical nonsense. "Something" is not a common noun, and it is incorrect, therefore, to introduce "property" as equivalent to "something which an object is or is not." The term "property" has, as a common noun, the form "—is a property" whereas, unless "something" is to be construed as a common noun, the supposed equivalent has the form "—is something which an object is or is not," thus (28) Tall is something which an object is or is not and not "—is a something which an object is or is not." Only if the expression "something which an object is or is not" were a common noun expression (which it is not) would it be correct to introduce the common noun "property" as its stipulated equivalent. In short, this way of introducing the term "property" is simply a mistake.

VII It is important to remember that I have not criticized Geach's claim that there is something which Jack and Jill both are. It is what he proceeded to make of this claim that I took exception. I want now to examine this claim in ____________________ 9Op. cit., pp. 149 ff. -272-

closer detail, for I think that once we get the hang of Geach's formulation we will be less tempted to make his mistake. Suppose we had begun with an example which involved the common noun "man," instead of the adjective "tall," say (29) Tom is a man.

The corresponding generalization, as we have represented it, would be, (30) Tom is a something where the fact that the "something" comes after the indefinite article makes it clear that "something" is, so to speak, quantifying over a common noun variable. How would we express this generalization in the manner of Geach? Certainly we can say ( 301) There is something which Tom is But this doesn't distinguish the result of generalizing from (29) on the one hand, and from (31) Tom is tall on the other. While to say "There is a something which Tom is" is to court disaster. The answer suggests itself when we note that the "There is something which ..." manner of expressing quantification rests on a rhetorical device which I shall call "question-echoing counterparts." The point is simply that such a statement as (10) S is triangular can serve as the answer to either of the following questions, (32) What is triangular? and (33) S is what? Now to the original statement there correspond the following pair of question - echoing counterparts, (101) S is what is triangular: Triangular is what S is. It is important to note that although the adjective "triangular" is serving as the grammatical subject of the second of these statements, the "rôle" it is playing is a unique one, and is, indeed, rhetorical in character. It would surely be a howler to suppose that because it is functioning in this context as a grammatical subject, it is in any more profound sense functioning as a subject. Its rôle is rhetorically derivative from its adjectival rôle in the original, or non-question-echoing statement. Other examples of question-echoing counter -273-

parts would be "Tom is who is a man": "A man is what Tom is" and "Tall is what Jack and Jill both are": "It is Jack and Jill who are both tall. " Now the question-word "what?" plays a number of rôles in English which might well be split up among a number of interrogatives. In particular, we might introduce the interrogative "quale?" to indicate that the answer is to be in terms of an adjective, and the interrogative "quid?" to indicate that the answer is to be in terms of a common noun. Then we would have the question- echoing counterparts (311) Tall is quale Tom is: Tom is who is tall, (292) A man is quid Tom is: Tom is who is a man. To the first of each of these pairs there would correspond a general statement which would bear the mark of its origin, thus, (34) There is something which is quale Tom is (i.e. tall). (35) There is something which is quid Tom is (i.e. a man)

or, more concisely, (341) There is somequale which Tom is (i.e. tall). (351) There is somequid which Tom is (i.e. a man).

VIII I pointed out above that Geach gives two accounts of how the general term "property" might be introduced. Of these two accounts we have so far considered only one—the "cautious" one, we have called it—and found it to be a mistake. The second account, as we noted, derives from Frege, and our discussion of it will be usefully prepared by a theme from Frege's "On Concept and Object." 10 It will be remembered that Frege distinguishes between concepts and objects and is faced by the problem "How can one say of anything that it is a concept?" For the term "concept" being, presumably, a common noun, we should be able to make statements of the form (36)—is a concept. Frege, however, proceeds to rule out such statements as (37) The concept square root of four is a concept on the ground that the expression "the concept square root of four," being a singular term, refers to an object rather than a concept. The same objection would, presumably, hold against ____________________ 10First published in the Vierteljahrschrift fuer Wissenschaftliche Philosophie xvi (1892), pp. 192-205; translated by Peter Geach and published in Translations from the Philosophical Writings of Gottlob Frege by Peter Geach and Max Black (New York, Philosophical Library, 1952). [Reprinted in this volume—ED.] -274-

(38) The concept man is a concept and (39) The concept triangular is a concept and, even more obviously, against (381) Man-kind is a concept and (391) Triangularity is a concept. Since, presumably, something can fill the blank in "—is a concept," we seem to be left with (381) Man is a concept and (392) Triangular is a concept. These sentences, however, are puzzling, to say the least, for it is difficult to repress the feeling that since "concept" is a common noun, the context "—is a concept" requires a singular term rather than an adjective or a common noun to complete it.

Now our discussion of Geach has made it clear that we can form sentences in which something other than a singular term is the grammatical subject. Consider, for example, (40) Triangular is what (quale) the table is and (41) Men is what (quid) Tom and Dick are or, as we can also put it, (401) Triangular is something which the table is (411) Men is something which Tom and Dick are but, as we emphasized at that time, there is nothing in these contexts which authorizes the introduction of a common noun, whether "concept" or "property." There is, however, another context which tempts one to introduce such a common noun, namely, (42)—is what "triangular" stands for (43)—is what "man" stands for. For, one is tempted to expostulate with Geach, surely adjectives and common nouns stand for something—though, of course, they are not names. Surely we can say (44) "Triangular" stands for something -275-

or (441) There is something which "triangular" stands for. And can we not therefore legitimately introduce the common noun "concept" as having the force of "something which a predicate stands for?" The answer is, as before, No; not however, because it is incorrect to say that there is something which "triangular" stands for (or bedeutet), but because the expression "something which a predicate stands for" like the expression "something which an object is or is not" does not play the sort of rôle which would make it proper to introduce a common noun as its stipulated equivalent. This time, however, the matter is not quite so simple, for there is a related line of thought which does seem to authorize without grammatical absurdity the introduction of a common noun having the force of Frege's "concept" or Geach's "property." This line of thought rests on the idea that "means" 11 —which I shall now use in place of "stands for" because its simpler grammatical form will make the point more intuitive—has at least the appearance of being a transitive verb. That this appearance is misleading will be the burden of a subsequent stage in my argument. But accepting, for the moment, this appearance at its face value, and taking as our standing point, without comment, the sentence (45) "Triangular" means triangular, the following moves all seem in good order; first to (451) Triangular is meant by "triangular" then, on the analogy of the move from "x is victimized by y" to "x is the victim of y," to (452) Triangular is the meaning of "triangular," which involves the common noun "meaning." It is then a simple step to stipulate that "concept," "property," "nature" and "form" are to be general terms for the meaning of adjectives and common nouns.

I shall be subjecting this line of thought to a severe critique in a moment. For the time being, however, I shall simply postulate that this mode of introducing such sentences as "Triangular is a meaning," "Triangular is a concept" and "Triangular is a property" is in some sense misguided. For I want to go on to the question, Would this mean that Frege's notion of a concept is misguided? The answer is No rather than Yes. Frege did have something ____________________ 11There is a family of semantical concepts each of which might be (and has been) conceived of as a "mode of meaning." Thus we might say that in our language "triangular" connotes triangularity, denotes 1 triangular things, and denotes 2 the class of triangular things. Each of these is a legitimate concept and a proper subject for logical investigation. But none of them, obviously, is what Geach has in mind when he speaks of "triangular" as standing for something. The sense of "meaning" which I have in mind is that in which it is an informative statement for us to say that "dreieckig" (in German) means triangular, whereas " 'triangular' (in our language) means triangular" is as "trifling" as "White horses are white." -276-

important in mind which he builds into his notion of a concept, and which does not require the use of adjectives, common nouns or verbs as the grammatical subjects of sentences. For the significant core of Frege's doctrine is compatible with the idea that the common noun context "—is a concept" requires something like a singular term for its subject, and hence with the rejection of a simple concept-object dichotomy. The clue to the correct formulation of this core theme is found in his characterization of concepts as "unsaturated" (ungesaettigte). For, in effect, this means that we may be able to get somewhere with "unsaturated" singular terms—if we can find such—as the subject of statements of the form "—is a concept." And once we have hit upon this suggestion, the next move follows of itself. For among the singular terms available to us from the previous discussion are singular terms of the form "that-p," and we know what an "unsaturated" singular term of this form would look like. In short, we hit upon, for example, (393) That x is triangular is a concept. On this analysis, concepts would be "unsaturated" propositions. And if, as Frege seems to do, we use the term "object" in such a manner that anything referred to by a singular term is an object, we would have to say that concepts differ from objects not by being non-objects, but by being "unsaturated" or "incomplete" objects. Thus, when Frege says that to "assert something about a concept ... it must first be converted into an object, or, speaking more precisely, represented by an object" (p. 46), his thought was undoubtedly guided by the fact that (393) comes as close as it does to having the adjective "triangular" as its subject, by having the unsaturated singular term "that x is triangular" as its subject instead. Now if the above line of thought is sound, we would no longer be precluded from saying that triangularity is a concept (391) by the fact that "triangularity" is a singular term. The fundamental difference between "triangularity" and "that x is triangular" would be that the latter makes explicit a gappiness or incompleteness which is perhaps implicit in the former. Indeed, it is tempting to suppose that the abstract singular term "triangularity" simply has the force of the unsaturated singular term "that x is triangular." We shall subsequently see that this is not the case, but if we permit ourselves this supposition for the moment, then we would interpret the statement "Triangularity is a quality" (11) as, so to speak, a rewriting of (111) That x is triangular is a quality and, consequently, regard a quality as a specific form of concept, the latter being a more inclusive notion, including as it does multiply as well as singly unsaturated propositions, and a variety of each. Now it must be admitted that the idea that there are abstract entities such as triangularity, mankind, etc., takes a most interesting, if disturbing, turn if these entities are to be equated

with gappy or unsaturated propositions. The notion of a gappy entity is a puzzling one, even if it is softened into the idea of -277-

an incomplete entity. On the other hand, it appears to illuminate contrasting historical positions. For if one accepts the idea that "Triangularity" is simply, so to speak, a rewriting of "That x is triangular," one is tempted to say that the difference between the Platonic and the Aristotelian conceptions of universals is that Plato takes the abstract singular term "triangularity" to be a name which conceals no gaps, whereas Aristotle, by denying the apartness of the universal, is, in effect, recognizing the unsaturated, incomplete or gappy status which is made explicit by the unsaturated abstract singular term "that x is triangular." There is, I believe, some truth to this suggestion—though I do not think that it does justice to the radical character of Aristotle's rejection of Plato's Ideas. But that is a story for another occasion.

IX Let us suppose, for the time being, then, that the abstract singular term "triangularity" simply has the force of "that x is triangular." Then in addition to its intrinsic interest, the above discussion has shown us a way of saying something about triangularity without using the singular term "triangularity." Thus, instead of saying (46) Triangularity implies having three sides we can say (461) That anything is triangular implies that it has three sides. The latter preserves—indeed, highlights—the adjectival role of "triangular." No sooner have we said this, however, than we see how little we have said, if our aim is to avoid Platonistic anxieties. For if we put aside the complications introduced by the generality of (461) and turn our attention, instead, to (47) That S is triangular implies that S has three sides it becomes manifest that we have avoided the singular term "triangularity" only to embrace the singular term "that S is triangular," and that we have escaped universals only to accept propositions. Actually, however, this new turn of events has brought us to the very heart of the matter. Statement (47) is, indeed, of the form (48) that-p implies that-q and does involve two singular terms. But not all logical connectives play a predicate role, and while those which do connect singular terms of the form "that-p," those which do not connect statements and statement expressions, and statements are not singular terms, having, as they do, the form "p" rather than "that-p." Both predicative and non-predicative connectives have their legitimate place in the grammar of our language, but unless these places are -278-

carefully distinguished and correctly understood, philosophical perplexities of the most pervasive sort will be endemic. The story is, in essence, a familiar one. Truth-functional connectives do not require that the connected expressions function as singular terms. Thus, as we saw above, while "Tom is clever or Tom is tall" (5) and "(Ep) p or Tom is tall" (6) have categorial counterparts which are built around the singular terms "that Tom is clever," "that Tom is tall" and the singular term

variable "that-p," neither (5) nor (6) itself contains any other singular term than "Tom." Can we, then, say what is said by "That S is triangular implies that S has three sides" (47) and "That anything is triangular implies that it has three sides" (46 1) without committing ourselves to singular terms formed from statements? Surely it will be said, all we need to do is to make use of the familiar symbol " ⊃" which was specifically designed to be the non-predicative core of the predicative term "implies." We would then have

(471) S is triangular ⊃ S has three sides and

(462) (x) x is triangular ⊃ x has three sides and if this move is successful, we should have freed ourselves (temporarily, at least) not only from expressions of the form "that-p," but also, unless we find other reasons for re-introducing them, from unsaturated singular terms of the forms "that x is f" and "that x is a K"; and hence from "f-ness" and "K-kind." We would indeed have extricated ourselves from Plato's beard.

X It is well to pause for a moment to let the fact sink in that our argument has brought the problem of abstract entities face to face with the problem of necessary connection; and to note that it is but a short step to the problem of "causal connection" or "natural implication," and to the realization that "causally implies" like "logically implies" is a predicative connective and requires the use of abstract singular terms as in (49) That it has just lightninged (causally) implies that it will shortly thunder and (50) That x is released (causally) implies that x will fall. -279-

XI Even if we could take it as established that to quantify over adjective-common noun- and statement-variables is not to assert the existence of qualities, kinds or propositions, we would sooner or later have to face the fact that ordinary language does involve the use of the singular terms and the common nouns which raise the spectre of Platonism—and, indeed, that we do make the existence statements which the Platonist hails as the substance of his position. For we do make such statements as "There is a quality (thus trangularity) which ... ," "There is a class (thus, dog-kind—or the class of white things) which ... ," and "There is a proposition (thus, that Caesar crossed the Rubicon) which...." These statements, genuinely existential in character, make forthright ontological commitments. Or are these commitments, perhaps, less forthright than they seem? Can they, perhaps, be "reduced" to statements which make no reference, explicit or implicit, to ontological categories? We asked above "Is there any way of saying something about triangularity without actually

using the abstract singular term 'triangularity'?" This question led us first to the idea of the predicative implication-statement "That anything is triangular implies that it has three sides," which avoids "triangularity" but at the expense of using the unsaturated abstract singular term "that x is triangular." The effort to avoid even these abstract singular terms led us then to the notion of a general truth-functional statement to be represented as

(462) (x) x is triangular ⊃ x has three sides. Without questioning the soundness of this notion, I shall now ask instead, "Is there any statement of which the subject is 'f-ness' which cannot be reformulated as a statement in which 'f-ness' is replaced by the sentential function 'x is f' (N.B.: not 'that x is f')"? To this question correspond a number of others of which two are more directly germane to our argument, namely, "Is there any statement of which the subject is 'K-kind' which cannot be reformulated as a statement in which 'K-kind' is replaced by 'x is a K' (not 'that x is a K')?" and "Is there any statement of which the subject is 'that-p' which cannot be reformulated as a statement in which 'that-p' is replaced by 'p'?" And to these questions the direct annd simple answer is Yes. For neither (51) f-ness is a quality nor (52) K-ness is a class nor (53) That p is a proposition can be so reformulated. -280-

But if these contexts (which we have called categorizing contexts) do not admit of the desired reformulation, and consequently revive our Platonistic anxieties, it is equally true that these anxieties can be at least temporarily stilled by a relatively simple and straightforward therapy. This relief is provided by pointing out that whereas the truth or falsity of statements to the effect that a physical object belongs to an empirical kind is ascertained by observing or inferring that it satisfies certain empirical criteria, the truth or falsity of such categorizing statements as (11) Triangularity is a quality, (54) Dog-kind is a class, (55) That Chicago is large is a proposition, is ascertained not by "examining" triangularity, betweenness, dog-kind or that Chicago is large, but by reflecting on the rôle in discourse of the corresponding expressions. This is the insight contained in Carnap's contention (in The Logical Syntax of Language) that the above statements are in the "material mode of speech" and are the "quasi-syntactical" counterparts (roughly—for I am following the general spirit, rather than the letter of Carnap's account) of (112) "Triangular" (N.B.: not "triangularity") is an adjective (in English), 12 (541) "Dog" (N.B.: not "dog-kind") is a common noun (in English), (551) "Chicago is large" (N.B.: not "that Chicago is large") is a sentence (in English). But surely, it will be said, the word "triangular" is just as abstract an entity as triangularity.

Where is the "nominalistic" gain? Is not the term " 'triangular' " as much a singular term as "triangularity," and "adjective" as much a common noun as "quality"? The answer is simple and straightforward. " 'Triangular' " is not a singular term, but a common noun, and the gain arises in that we can hope to equate (11 3) with something like

(113) (x) is a "triangular" ⊃ x is an adjective where " 'triangular' " is a common noun referring to items playing a certain linguistic role, as "bishop" is a common noun referring to items playing a certain chess role. "A 'triangular' is an adjective" would be the counterpart of "A bishop is a diagonal-mover." Unfortunately, no sooner is one relaxed by this therapy, and considering the possibility of extending it to some other contexts in which "abstract entities are acknowledged," than a number of more serious objections arise which threaten a relapse. ____________________ 12This Carnapian interpretation of categorizing statements would carry with it a reinterpretation of the categorial counterparts of such statements as (1). Thus, "S exemplifies f-ness" would be the equivalent in the material mode, a quasi-semantical equivalent of " 'f is true of S." The relation of the latter to " 'S is f is true" would remain to be explored. Again, "S is a member of K-kind" would be the quasi-semantical equivalent of " 'K' is true of S." The latter, however, would seem to be as closely related to "S satisfies the criteria of 'K' " as to " 'S is a K' is true." -281-

The first of these objections grants that if the only contexts involving such expressions as "triangularity," "betweenness," "dog-kind," and "that Chicago is large" which could not be reformulated in the object language without the use of abstract singular terms were categorizing statements such as (11), (54), and (55) above, or such other statements as might be capable of straightforward treatment under the more general notion of "quasi-syntactical statements in the material mode of speech," then the Carnapian therapy— vintage 1932—would be successful. After granting this, however, it proceeds to argue that there are contexts in which abstract singular terms occur, which neither can be reformulated in the object language, to avoid them, nor respond to this syntactical treatment. Consequently, it continues, there are reasons which cannot be dispelled by any therapy yet mentioned for thinking that we are committed to the straightforward existence of qualities, relations, kinds, propositions, etc. And if, it concludes, by way of counter attack, there are such entities, then even the idea that such a categorizing statement as (11) Triangularity is a quality is really about the adjective "triangular" instead of, as it purports to be, about triangularity, must be simply a mistake.

XII Now the task of examining all contexts in which abstract singular terms occur to see if they admit of an interpretation free of Platonistic implications, is an intricate and demanding one which, even if I were prepared to undertake it, would require a larger canvas than is at hand. I shall therefore limit myself to a few manageable points which, as I see it, lay the groundwork for a successful use of a therapy essentially the same as the one proposed by Carnap (but which, of course, has a much longer—and indeed, venerable—history). The first point I wish to make arises from the fact that if we press the above critic to specify the contexts he has in mind, the chances are that he will come up with examples from discourse in which we are either explaining what a word means or characterizing the thoughts and beliefs of intelligent beings.

It goes without saying that one of the oldest and strongest roots of conceptual realism is the conviction that we cannot make sense of thinking in its various modes unless we interpret it as involving something like an "intellectual perception" of abstract entities. Thus the road we are travelling leads sooner or later to the problem of problems, the Mind-Body problem, the Gordian knot which has been cut so often, but never untied. I do not propose to untie it on this occasion. I shall therefore turn my attention to discourse about the meanings of words to see if it involves a commitment to abstract entities. -282-

Let us consider, therefore, such a context as the following: (56) "Dreieckig" (in German) means.... And let us ask what we should place at the end of this context to make a well formed sentence. A number of answers suggest themselves, of which the first, and most obviously unsatisfactory, is that what we should place there is the quoted expression " 'triangular.' " This clearly won't do, at least as it stands, for the simple reason that if we were looking for the beginning of a sentence which has as its ending (57) ... (in German) means "triangular" we would find the answer—assuming that Germans form the names of expressions, as we do, by means of the quoting device—in (58) " 'Triangular' " (in German) means "triangular." Now we might try to put this informally by saying that the German word 'dreieckig' means a quality and not a word, and that if any German expression means the word "triangular" it is the German expression " 'triangular.' " But so to put the matter raises more puzzles than it resolves, for when we say that the German word "dreieckig" means a quality, we imply that the proper way to complete the original context, (56), is by the use of the abstract singular term "triangularity," which would give us (59) "Dreieckig" (in German) means (the quality) triangularity, and a moment's reflection tells us that this won't do at all. For surely the German word which means triangularity is "Dreieckigkeit" and not "dreieckig," thus (60) "Dreieckigkeit" (in German) means triangularity. 13 Now the source of our trouble is that we have been taking for granted that what belongs in the place of the dots in (56) is a singular term. But, then, it will be said, is not "means" a transitive verb? and does it not, therefore, require to be followed by an expression which refers to an object, as do the concluding expressions in (61) Tom hit Harry, (62) Tom hit a man, (63) Tom hit the man next door. It is this reasoning which confronts us with our dilemma, for if the context takes a singular term, and if, as we have seen, it doesn't take "triangularity," what else is there for it to take but " 'triangular.' " We must apparently choose between (64) "Dreieckig" (in German) means "triangular" which is false, and, ____________________ 13See footnote 11.

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(65) "Dreieckig" (in German) means triangular which because it uses the adjective "triangular" rather than a singular term is, apparently, ill-formed. Now the way out of this labyrinth consists in recognizing that it is incorrect to say that "dreieckig" means a word, and equally incorrect to say that it means a non-word, for the simple reason that "means" is not a transitive verb. Not that it is an intransitive verb, for it is neither, and the attempt to fit it under one of the other of these headings, on the supposition that they are not only mutually exclusive but jointly exhaustive, is the cause of the puzzle. Once this point has been made, however, it can be granted that even though (64) "Dreieckig" (in German) means "triangular" is false, there is a sense in which the true statement (65) "Dreieckig" (in German) means triangular is about the English word "triangular." For by making statements of this form we bring people to understand the German word "dreieckig," for example, by leading them to reflect on their use of its English counterpart. It is because the understanding of (53) involves an imaginative rehearsal of the use of "triangular" that (53) differs from a simple statement to the effect that "dreieckig" is the German counterpart of the English word "triangular." The latter statement could be fully understood, as the former could not, by someone who did not have the English word "triangular" in his active vocabulary. Now the prime result of all this logic chopping is that the context (66) '—' (in L) means... does not require a singular term to fill the right hand blank. Thus, to use other relevant examples, (67) "Homme" (in French) means man [not mankind] and (68) "Paris est belle" (in French) means Paris is beautiful [not that Paris is beautiful]. It follows that the existentially quantified counterparts of (65), (67), and (68) are (69) (Ef) "dreieckig" (in German) means f, (70) (EK) "Homme" (in French) means K, (7 1) (Ep) "Paris est belle" (in French) means p, and that it would be as incorrect to read these as "There is a quality ... ," "There is a class ..." and "There is a property ... ," as we found it to be to make the corresponding readings in the case of (2), (4) and (6). We are now in a position to grant that we do speak of the "meaning" of a -284-

word while insisting that the common noun "meaning" (or its sophisticated counterparts, "concept" (Frege) and "property" (Geach)—far from embodying a fundamental logical category—arises from contexts of the form " '—' means ..." (66), by treating "means" as of a piece with ordinary transitive verbs. Thus, by analogy, we have (651) Triangular is meant (in German) by "dreieckig," (652) Triangular is what "dreieckig" (in German) means, (691) There is something (i.e. triangular) which "dreieckig" (in German) means and while none of these involves a commitment to a common noun expression having the force of "meaning," the fact that one of the principles of linguistic development is analogy, easily generates the common noun "meaning" and permits us to say (653) Triangular is the meaning of "dreieckig" (in German) and to make the statement properly existential in form, (692) There is a meaning which "dreieckig" (in German) means or, with Geach, (693) There is a property which "dreieckig" (in German) stands for. In other words, while it would be incorrect simply to say that there are no such things as meanings, or Frege's concepts, or Geach's properties, to trace the common noun "meaning" to its source in the translation rubric " '—' (in L) means ..." (66) is to make what amounts to this point in a less misleading and dogmatic way. The upshot of the foregoing discussion of meaning with respect to the primary theme of this article can be summed up by saying that the translation context (66), does not properly take a singular term on the right hand side unless the expression of L which is placed in the single quotes of the left hand side is itself a singular term. In other words, this context does not of itself originate a commitment to abstract entities. This point might be obscured by a failure, where the quoted expression of L is a sentence, to distinguish between the context (72) '—' (in L) means p and the context (73) X—by uttering "..." (in L)—asserts that-p where X is a person. The former context abstracts from the many specific ways in which the English sentence represented by "p" and the corresponding sentence of L function in discourse. That the context. (74) X asserts that-p -285-

unlike context (72) above does involve the use of the abstract singular term "that-p" is a point to which we shall return at the close of the argument.

XIII Perhaps the most interesting consequence of the above analysis is the fact that it frees the "semantical definition of truth" from the commitment to propositions which it has often been taken to involve. Thus, the definiens of Carnap's definition of "true sentence of L" developed on pages 49 ff. of his Introduction to Semantics, namely,

(75) S is a true sentence of L = Df (Ep) S designates p (in L) · p is incorrectly read as "there is a proposition, p, such that S designates p (in L) and p." It can readily be seen that this reading exhibits inconsistencies which are the counterpart of those explored in the opening section of this paper in connection with the "informal reading" of "(Ef) S is f" as "there is an f such that S is f." Thus, whereas "S designates p" requires that "p" be a sentential variable and not a singular term variable, the context "there is a proposition, p, ..." requires that "p" be a singular term variable of the form "that-p." And if we revise the definition to avoid the inconsistency by taking "S" to be the name of a that-clause (in L) rather than the name of a sentence, thus obtaining (76) S is a true that-clause (in L) = Df There is a proposition, that-p, such that S designates that-p (in L) and that-p we see at once that we have an ill-formed expression on our hands, for the concluding conjunct "p" of the original definiens has been turned into the singular term variable "that-p," and to patch this up we must turn "and that-p" into "and that-p is the case," where "that-p is the case" is the categorized counterpart of "p," as "S has f-ness" is of "S is f." The "propositional" reading of Carnap's definition becomes, under the pressure of the demand for consistency, (77) T is a true that-clause (in L) = Df there is a proposition, that-p, such that T designates that-p (in L) and that-p is the case, and while I do not wish to impugn the consistency of the notion, thus introduced, of the truth of a that-clause, I do wish to insist that this notion is philosophically unsound in so far as it rests on the mistaken idea that the truth must be defined in terms of propositions, and leads to the mistaken idea that the truth of statements is derivative from that of that-clauses. -286-

XIV Our success in showing that the context " '—' (in L) means ..." does not originate a commitment to the use of abstract singular terms (though it accepts them with grace if they are already in use) raises the hope that all other uses of abstract singular terms stem from their use in "quasi-syntactical statements in the material mode of speech." In other words, the hope is revived that what we have called the syntactical therapy will work. If, however, as a result of this optimism we take a closer look at this therapy, we find that it is not without its own difficulties. Indeed, it is apparently open to a simple and devastating objection. How can "Triangularity is a quality" (11) have something like the force of "'Triangular' (in English) is an adjective" (112) in view of the fact that (11) makes no reference to the English language? The objection is no mere question begging, for it presents an argument to prove that (11) makes no reference to the English language in general nor to the English word "triangular" in particular. It points out that the German translation of ( 11) is (11g) Dreieckigkeit ist eine qualitaet and argues that there is just as much reason to say that (11g) is about the German word "dreieckig" as to say that (11) is about the English word "triangular." Since (11g) presumably makes the same statement as its English counterpart (11), the objection concludes that neither of these statements is about either word. Again, how can the truth of (11) be ascertained by reflecting on the use of the word "triangular" if, were a German to say (78) Dreieckigkeit ist eine qualitaet, aber es gibt keine Englische Sprache, his colleagues would recognize that his statement was only contingently false? For if his statement is only contingently false, it might have been true, and if it had been true, he could have made a true statement, namely (11g) above even though there was no English language

in general, nor, in particular, such an English word as "triangular." And if there is only a contingent connection between the truth of (11g) and the existence of the English language, how could we English users ascertain the truth of (11) simply by reflecting on the syntax of the English word "triangular"? The answer to his puzzle involves two steps, the first of which we have already taken, for it consists in reminding ourselves that (79) "Dreieckigkeit ist eine qualitaet" (in German) means triangularity is a quality does not involve the singular term "that triangularity is a quality." Consequently, the fact that (11g) "has the meaning it does" does not commit us to -287-

the existence of a non-linguistic abstract entity (a proposition) of which (11g) is the German name; nor, a fortiori, does the fact that (11) and (11g) "have the same meaning" commit us to the existence of a non-linguistic abstract entity which stands over and against both languages and has a name in each. That there is a linguistic abstract entity, a rôle which is played in German by one group of vocables and in English by another and of which "that triangularity is a quality" is the English name is indeed the case. It has been pointed out above, however, that statements about linguistic rôles are reducible to statements involving no abstract singular terms. Now if we take seriously the fact that the inter-translatability of (11) and (11g), their existence as counterparts of one another in the two languages, does not involve the existence of a proposition which they both name, we are in a position to approach the question "By virtue of what are these two sentences counterparts?" without being tangled ab initio in a commitment to Platonic entities. In other words, we can look for a rôle which (11) might play in English and for a rôle which (11g) might play in German which would make (11) and (11g) counterparts and appropriately inter-translatable, unhampered by the mistaken idea that two inter-translatable expressions must be different names of one entity. And once we undertake this unhampered search, the result is surely a foregone conclusion. Thus the second step consists in noting that while (80) Triangularity is a quality, but "triangular" is not an adjective in the language I speak is not in any simple sense self-contradictory, as is shown by the fact that one of its German counterparts, (80g) Dreieckigkeit ist eine qualitaet aber "triangular" ist nicht ein Adjectiv in seine (Sellars 1) Sprache is only contingently false, it is nevertheless "logically odd" in a way which requires its falsity. Notice that not only (83g) but both (801) Triangularity is a quality, but "triangular" was not an adjective in the language I spoke yesterday and (802) Triangularity is a quality, but "triangular" will not be an adjective in the language I will speak tomorrow are contingently false. The logical oddity of (80) consequently hinges on the fact that I cannot—and this is a matter of strict logic—simultaneously make understanding use of "triangularity is a quality" while understandingly denying that "triangular" is an adjective. And the reason for this is simply that to know how to use singular terms ending in "-ity" is to know that they are formed from adjectives; while to know how to use the common noun "quality" is (roughly) to know that its well-formed singular sentences are of the form

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"—is a quality" where the blank is appropriately filled by an abstract noun. (That the parallel points about "-keit" and "qualitaet" in German are genuine parallels is clear.) Thus a more penetrating examination (80) shows it to be self-contradictory in spite of the fact that one of its German counterparts is not. Thus, while my ability to use "triangular" understandably involves an ability to use sentences of the form "—is triangular" in reporting and describing matters of physical, extralinguistic fact, my ability to use "triangularity" understandingly involves no new dimension of the reporting and describing of extra-linguistic fact—no scrutiny of abstract entities—but constitutes, rather, my grasp of the adjectival role of "triangular." Is this all there is to it? Is the story really so simple? Of course not. Philosophy moves along asymptotes, and to move along one, it must move along many. Progress is dialectical, and comes from raising and answering objections. This time the objection is that the above account makes unintelligible the plain fact that we have the two sentences "Triangularity is a quality" (11) and " 'Triangular' (in English) is an adjective" (112). Why should our "grasp of the adjectival role of 'triangular' " be embodied in the former, when the latter does exactly this job in such a straightforward and successful way? The answer to this question is best approached by noting an important difference between the two abstract singular-term expressions "triangularity" and "that x is triangular," which we have hitherto taken to have the same force. The existence of such a difference is made clear by the fact that there is something odd about the statement " That x is triangular is a quality" (111) and even odder about (81) That Socrates is a K is a particular. To begin with, it is, surely, triangularity which is the quality just as it is Socrates which is the particular. If so, a distinction is called for between "Triangularity is a quality" (11) and what we might represent as (82) That x is triangular is a particular-gappy proposition and, correspondingly, between (83) Socrates is a particular and (84) That Socrates is a K is a kind-gappy proposition. Thus, if we assume for the moment that ontological categories are the material mode of speech for syntactical categories, then the syntactical counterpart of "Triangularity is a quality" (11) would not be (114) "x is triangular" is a singular-term gappy attributive sentence but simply " 'Triangular' (in English) is an adjective" (112) and the syntactical counterpart of "Socrates is a particular" (83) not -289-

(841) "Socrates is a K" is a common-noun gappy classifying sentence but simply (831) "Socrates" is a singular term (of type 0).

The non-self-sufficiency, then, of universals and individuals is not a matter of gappiness, but rather a reflection of the fact that adjectives, common nouns and singular terms alike are what they are because of their different contribution to the statement-making rôle performed by the sentence. It is often said that "one place predicate" is a more penetrating syntactical concept than that of an adjective—even when the latter is expanded to include adjectival expressions as well as simple adjectives. And there is certainly an element of truth in this contention which we might try to put by saying that "one place predicate" makes explicit reference to the way in which adjectives are incomplete. But once we try to spell this out, we see that the point is not that "adjective" obscures the fact that adjectives are incomplete—for it doesn't—but rather that it does not give us, so to speak, an intuitive picture of this incompleteness. Indeed, we are only half-way to this intuitive picture if we replace (11 2) by (115) "Triangular" (in English) is a one place predicate. To get it we must say (116) "—is triangular" (in English) is a singular-term-gappy-attributive sentence. Consider, now, the statement (821) That—is triangular is a particular-gappy state of affairs (which is a candid reading of what might also be rendered by (822) That x is triangular is a propositional (N.B.: not sentential) function. What can we make of it? Are we not tempted to think that (82 1) is simply a rewriting of (116)? For, we might argue, how could (821) be true if it were not a rewriting of (11 6)? Can it be a complete sentence if it contains a gap instead of mentioning it? And where can an appropriate gap be found if not in the gappy sentence "—is triangular"? Why, then, would we hesitate? What is there about the "feel" of (82 1) which militates against the idea that it could be a rewriting of (11 6) ? I think I can put my finger on it by calling attention to the fact that a foreigner who was learning English and had made substantial progress, but had not yet added the word "triangular" to his vocabulary, could fully understand (116) whereas (821) cannot be fully understood unless one not only knows that "triangular" is an English word, but actually has it in one's active vocabulary. But if this is the source of our hesitation, we are in a position to answer our -290-

original question. For we have now located a difference between the "material" and the "formal" modes of speech which enables us to see how they can "have the same force" without one being a simple rewriting of the other. For while it would be incorrect to say that "That—is triangular is a particular- gappy state of affairs" (821) is a mere rewriting of " '—is triangular' (in English) is a singular-term-gappy attributive sentence" (116), it is at least a reasonable next step in the direction of the truth to interpret it as a rewriting which presupposes that "writer" and "reader" are able to use as well as mention sentences of the form "—is triangular." It should be noted, in this connection, that a similar point can be made about the difference between " 'Dreieckig' (in German) means triangular" (65) and (654) "Dreieckig" (in German) is the counterpart of the English word "triangular." For the former presupposes, as the latter does not, that the English-speaking person to

whom it is addressed not only recognizes that "triangular" is an English word, but enjoys its presence in his active vocabulary. It is, as we have seen, by leading those to whom it is addressed to rehearse in imagination the role of "triangular" that (65) is an explanation of the German word "dreieckig." Thus (65) has essentially the force of " 'dreieckig' (in German), plays the same rôle as 'triangular' in our language." The abstract singular term "triangularity" can be construed as the English name of this rôle. And this is the place to pick up a topic which was raised towards the end of our first bout with the rubric " '—' means ..." only to be dropped like the hot potato it is. I there pointed out that the context " '—' (in L) means p" (72), where '—' is a sentence of L, must not be confused with "X, by uttering '—' (in L), asserts that-p" (73). The latter does, whereas the former does not, involve the use of the singular term "that-p." What then are we to do about this apparent commitment to Platonic entities? The clue is contained in (73) itself. I am not however, suggesting that "X asserts that-p" (74) is a simple rewriting of (85) X utters "—" (in L) which won't do at all for the obvious reason that one can assert, for example, that it is raining without using any given language, L. Shall we, then, accept the equation. (86) X asserted that-p = Df There is a language, L, and a sentence S, such that S is a sentence of L and S (in L) means p and X, speaking L, uttered S? This might be the beginning of an analysis, for our discussion of the material mode of speech has shown us that "X asserts that-p" (74) might mention a sentence (in this case a sentence in an unspecified language) even though it does not appear to do so, and that "that-p" can be construed as the name of -291-

a rôle which is played in different languages by different vocables and in the unspecified language by unspecified vocables. On the other hand, that (86) can't be the end of the analysis is clear

XV I began by arguing that "existential quantification over predicate or sentential variables" does not assert the existence of abstract entities. I then suggested that if the only contexts involving abstract singular terms of the forms "f-ness," "K-kind," and "that-p" which could not be reformulated in terms of expressions of the forms "x is f," "x is a K," and "p" were categorizing statements such as "f-ness is a quality," "K-kind is a class," "p is a proposition," then we might well hope to relieve platonistic anxieties by the use of syntactical therapy. I then examined a context which has been thought to correlate words with extra-linguistic abstract entities, namely the context " '—' (in L) means ... ," and found that it does not do so. Encouraged by this, I proceeded to examine the distinction between the material and the formal modes of speech to see if the idea that such categorizing statements as "Triangularity is a quality" have the force of syntactical statements such as " 'triangular' is an adjective" can run the gauntlet of familiar objections, with what I believe to be hopeful results. Yet if I stand off and scrutinize the argument, my enthusiasm cannot but be sobered by a consciousness of how much remains to be done before something like a nominalistic position is secure. For I cannot overlook the fact that two of the most puzzling contexts in which abstract singular terms occur have been noted only to be passed over in search of simpler game. I refer, of course, in the first place to mentalistic contexts such as (87) Jones inferred that S is f and, in the second, to such "nomological" contexts as (88) That it has just lightninged implies that it will shortly thunder. Then there are such evaluative contexts as

(89) That he was late is better than that he not have come at all. The task of clarifying the force of contexts such as these is as large as philosophy itself. And to this task the foregoing is but a prolegomenon. -292-

: 17 : A WORLD OF INDIVIDUALS NELSON GOODMAN

Individuals and Classes For me, as a nominalist, the world is a world of individuals. But this simple statement, I have learned from bitter experience, can be misunderstood in numberless ways. Some misunderstandings have arisen from inadequacies in my own explanations. Other misunderstandings have arisen from inadequate attention to those explanations. Conflicting arguments in bewildering variety have been brought forward to show that nominalism is bad. This paper is one more attempt to make clear what I mean by nominalism and why I think nominalism is good. A certain amount of trouble can be blamed on emotions attaching to the word "individual." One writer 1 calls it an "honorific" word; and I am often criticized for applying the term "individual" to something or other that is unworthy of it. Use of a different word, even a coined one, might have been advisable in order to forestall such complaints. Nevertheless, I am prepared to defend the choice of the term "individual" as entirely in accord with a common practice of adapting ordinary language to technical purposes. In some cases, what I take as an individual may indeed lack many characteristics usually associated with the term "individual," and may not count as an individual according to common usage. But the situation with respect to the term "class" is exactly parallel. According to the layman's prelogical usage, children in a schoolroom make up a class, and so do people at a given social level, but Plato and this sheet of paper and the Taj Mahal do not. The term "set" in ordinary usage is perhaps even more restricted than the term "class." Yet by the logician's usage any things whatever make up a class or set. The contention that a genuine whole or individual cannot consist of widely scattered and very unlike parts misses the point as completely as would the contention that a genuine class cannot consist of widely scattered and very unlike members. In the case of "individuals" as in the case of "class," a technical usage is explicated with the help of a calculus, and the divergence ____________________ Reprinted from The Problem of Universals (Notre Dame, Indiana: University of Notre Dame Press, 1956) by permission of the publisher. 1Victor Lowe on p. 125 of "Professor Goodman's Concept of an Individual" in the Philosophical Review, vol. 62 (1953), pp. 117-26.

from ordinary usage is expressly noted. A class for Boole need not have social cohesion; and an individual for me need not have personal integration. Confusion of another kind has resulted from the incautious opening sentence of my joint article 2 with Quine. Although the statement "We do not believe in abstract entities" was intended more as a headline than as final doctrine, and although some reservations concerning it were almost immediately indicated 3 it has been fair game for critics ever since. Neither of us would write that sentence today, but neither of us would so change it as to affect anything beyond the first paragraph of the article in question. Quine has recently written that he would "now prefer to treat that sentence as a hypothetical statement of conditions for the construction in hand." 4 My own change would be not from the categorical to the hypothetical, but from the vaguely general to the more specific. I do not look upon abstractness as either a necessary or a sufficient test of incomprehensibility; and

indeed the line between what is ordinarily called "abstract" and what is ordinarily called "concrete" seems to me vague and capricious. Nominalism for me consists specifically in the refusal to recognize classes. What has not always been noticed is that essentially this revision is made in my book, 5 published four years later than the joint article. A key principle in this later formulation is that the nominalist rejects classes as incomprehensible, but may take anything whatever as an individual. Some misguided criticism would have been obviated had enough attention been paid to this statement; but I suspect that some of my critics feel they do me a kindness by not taking it seriously. Further explanation may help. Nominalism as I conceive it (and I am not here speaking for Quine) does not involve excluding abstract entities, spirits, intimations of immortality, or anything of the sort; but requires only that whatever is admitted as an entity at all be construed as an individual. A given philosopher, nominalist or not, may impose very stringent requirements upon what he will admit as an entity; but these requirements, however sound they may be and however intimately associated with traditional nominalism, are quite independent of nominalism in my sense. The nominalism I have described demands only that all entities admitted, no matter what they are, be treated as individuals. Just what this means, I shall explain in the following sections; but for the moment we may suppose that to treat entities as individuals for a system is to take them as values of the variables of lowest type in the system. Incidentally, several of my critics have confused themselves by lumping together, without due attention to context, passages from different parts of my ____________________ 2"Steps Towards a Constructive Nominalism," Journal of Symbolic Logic, vol. 12 (1947), pp. 105-22. 3See the third paragraph and the second footnote of the joint article. 4From a Logical Point of View, Harvard University Press, 1953, pp. 173-4. 5The Structure of Appearance, Harvard University Press, 1951, see especially p. 35. Incidentally (as explained in the book and later in the present article) since any nominalistic system is readily translated into a platonistic one, acceptance of most of the book by no means depends upon an acceptance of nominalism. This has been explicitly acknowledged by most of my critics. -294-

book. In Chapter VI, I discuss the choice of elements for a certain constructional system; but this does not turn upon the propriety of construing certain entities as individuals. Whatever we are willing to recognize as an entity at all may be construed as an individual. But in building a system, we must consider carefully what entities we are willing to recognize at all—or better, what terms we are willing to interpret as denoting and what terms we want to interpret syncategorematically. Important as the question is, nominalism does not decide it. I have never suggested that nominalism is enough to make a system acceptable. I have suggested only that platonism is enough to make it inacceptable. But more of this later. Now, however, is nominalism consequential at all? If the nominalist is free to construe anything he pleases as an individual, can't he even construe a class as an individual? Whatever can be construed as a class can indeed be construed as an individual, and yet a class cannot be construed as an individual. If this seems paradoxical, it can perhaps be clarified by means of an analogy. Suppose that in a certain game a player is to begin by dealing each card from his hand onto the table at either his left or his right; he may put any card on either side and may move a card from side to side if he likes. Then while it is quite true that he is free to put any card on either side, he can never get a left-hand card on the right-hand side; for a card is a left-hand card or a right-hand card according as it lies on his left or his right. Similarly, a table is an individual, or the class of its legs and top, or the class of its molecule-classes of atoms, according to the way it is construed in a system. And whether the Great Dipper is an individual or a class of stars depends upon the system we are using. We can construe anything as an individual (and aside from nominalistic scruples we can construe anything as a class); but we can no more construe a class as an individual than

we can get a left-hand card on the right-hand side.

The Principle of Nominalism In brief, while the nominalist may construe anything as an individual, he refuses to construe anything as a class. But just what is the principle of this refusal? In my book I said that, roughly speaking, the nominalist sticks at a distinction of entities without a distinction of content; and some of my critics have overlooked the more explicit formulation that soon followed. The nominalist denies that two different entities can be made up of the same entities. Let us suppose, for example, that a nominalist and a platonist start with the same minimal, atomic elements 6 for their systems; merely for comparative purposes take the number of these atoms as 5. The nominalist ____________________ 6An atomic element—or atom—of a system is simply an element of the system that contains no lesser elements for the system. Depending on the system, an electron or a molecule or a planet might be taken as an atom. -295-

admits also all wholes or individual sums comprised of these, and so has a universe of 2 5 — 1, or 31, entities. He cannot concoct any more; for whatever individuals among the 31 are added together, the result is another individual among those 31. Our platonist, we may suppose, admits no sums of atoms but admits all classes of them. This, not counting the null and unit classes, gives him also 31 entities. But he further admits all classes of classes of atoms; and by this single step he welcomes into his universe 2 31 — 1, or over two billion, additional entities. And he has no thought of stopping there. He also admits all classes of classes of classes of atoms, and so on ad infinitum, climbing up through an explosively expanding universe towards a prodigiously teeming Platonic Heaven. He gets all these extra entities out of his original five by a magical process that enables him to make two or more distinct entities from exactly the same entities. And it is just here that the nominalist draws the line. In the nominalist's world, if we start from any two distinct entities and break each of them down as far as we like (by taking parts, parts of parts, and so on), we always arrive at some entity that is contained in one but not the other of our two original entities. In the platonist's world, on the contrary, there are at least two different entities that we can so break down (by taking members, members of members, and so on) as to arrive at exactly the same entities. For instance, suppose K has two members: the class of a and b, and the class of c and d; and suppose L has two members: the class of a and c, and the class of b and d. Then although K and L are different classes, they alike break down into a, b, c, and d. Again K breaks down into the same entities as does the class having K and L as its members. These are clear cases of what the nominalist objects to as a distinction of entities without distinction of content. This discloses the relationship between nominalism and extensionalism, which springs from a common aversion to the unwonted multiplication of entities. Extensionalism precludes the composition of more than one entity out of exactly the same entities by membership; nominalism goes further, precluding the composition of more than one entity out of the same entities by any chains of membership. For the extensionalist, two entities are identical if they break down into the same members; for the nominalist, two entities are identical if they break down in any way into the same entities. The extensionalist's restriction upon the generation of entities is a special case of the nominalist's more thoroughgoing restriction. Nominalism describes the world as composed of individuals. To explain nominalism we need to explain not what individuals are but rather what constitutes describing the world as composed of them. So to describe the world is to describe it as made up of entities no two of which break down into exactly the same entities. What this means I have just explained, but a somewhat more technical formulation may be helpful. Suppose we have two constructional systems, having one or more (but not necessarily the same or even the same number of) atoms. Entities other

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than atoms are generated in system I as classes, and in system II as sum- individuals. Let us now obliterate all purely notational differences between the two systems. We may suppose from the start that each system uses but one style of variable. 7 Then let us remove all remaining tell-tale signs from system I other than "∊" by expansion in terms of "∊," and

similarly let us remove all peculiar signs of system II other than "≪" by expansion in terms

of "≪." Finally, let us put "R" in for every occurrence of "∊," "∊/∊," "∊/∊/∊," etc in

system I, and for every occurrence of "≪" in system II. No purely notational distinction between the two systems remains; and "R" in each is irreflexive, asymmetric, and transitive. Will anything now reveal which system is which? For each system, x is an atom if and only if nothing stands in the relation R to x; 8 and x is an atom of y (symbol: "Axy") if and only if x is an atom and is identical with or bears the relation R to y. Now in a nominalistic but not in a platonistic system, entities are the same if their atoms are the same. Thus the disguised systems will be distinguishable from each other by the fact that the nominalistic system satisfies, while the platonistic system violates, the principle:

(x) (Axy ≡ Axz) ⊃ y = z. 9 Obviously the disguised I will violate this principle if the system acknowledges more than 2n — 1 entities, where n is the number of its atoms; or again, if I acknowledges any unit-classes, since the unit-class and its member will have the same atoms. But even if I is a platonistic system so restricted as to be distinguished on neither of these two scores, it will still be detectable in its disguised version through violation of the stated principle. And if I admits no two such classes, then indeed it is not platonistic at all, regardless of its notation. This, I think, disposes of the charge that the distinction between nominalism and platonism is a mere matter of notation, 10 and also clarifies the nominalist's dictum: "No distinction of entities without distinction of content." For a nominalistic system, no two distinct things have the same atoms; only from different atoms can different things be generated; all non-identities between things are reducible to non-identities between their atoms. The further question must be raised whether the distinction between nominalism and platonism can be made purely formal? In the case we have just considered, the problem was how to determine whether a given system is nominalistic or platonistic when we know that a given one of its relations ____________________ 10E.g., by Wang on p. 416 of "What is an Individual?" in Philosophical Review, vol. 62 (1953), pp. 413-20.

7The

aim is to take systems as nearly alike as possible, in order to isolate the critical

difference. In the following text, " ∊" is to be read "is a member of," "∊/∊" is to be read "is a member of a member of," etc.; and "≪" is to be read "is a proper part of." 8Any

null class of system I will thus appear simply as one of the atoms of the disguised version of I, and thus leave no revealing trace. 9Both systems will satisfy the converse principle; under nominalism and platonism alike, if x and y are identical they have the same atoms. -297-

is either ∊* or ≪. Suppose now that we are confronted with a system without knowing anything about the interpretation of its predicates; or better, suppose we are given only the arrow-diagrams of the relations of the system. Can we determine whether the system is nominalistic or platonistic? The answer is no. We need to know either which elements are atoms of the system or—what amounts to the same thing—which relation is the "generating" relation 11 of the system. Take, for example, the following diagram for a system

with a single relation: If we know that a, b, and c are the atoms of the system, or that the relation mapped is a generating one, then we know that the system is platonistic— since the distinct elements d and f then have exactly the same atoms. On the other hand, if we know that a, b, c, d, and f are all atoms of the system, then we know that the system is nominalistic. But if we do not know what the atoms are or whether the relation is a generating relation, we cannot tell whether the system is platonistic or nominalistic. Notice, though, that without such knowledge, neither can we tell whether a system is extensional or not. The system diagrammed is extensional if the relation is that of child to parent but surely not extensional if the relation is that of member to class. 12 Lest anyone gleefully welcome the apparent opportunity to dismiss both "nominalistic" and "extensional" as not purely formal characterizations of systems, I hasten to point out that no characterization of systems is purely formal in the sense implied. For if we are given just an arrow-diagram, without any interpretative information whatever, then we do not even know that the arrows represents relationships or that the letters represent elements. We can tell nothing at all about the system in question or even that there is a system in question; the diagram might be a hex sign or a complex character serving as the proper name of a single element. A classification of symbolic systems becomes significant only when at least some restrictions are imposed upon the interpretation of the symbols. The criterion for nominalism is formal to the same rather high degree as the usual criterion for extensionality. ____________________ 11Given the atoms of the system, a generating relation is one such that if and only if x is a non-atomic element of the system will there be some element y that stands in that relation to x. The generating relation G of a system is the relation that obtains between two elements x and y of the system if and only if x and y are connected by a chain in which

each linked pair belongs to a generating relation of the system. (Note that this does not enable us to determine whether a given relation is "a" or "the" generating relation of a system unless we are told what the atoms are.) 12The system diagrammed, in fact, is extensional only if it is nominalistic, although obviously this is not true of all systems. Every system, of course, is nominalistic only if it is extensional. -298-

What I have tried to do so far is to explain my version of nominalism. In outline, I have said that the nominalist insists on the world being described as composed of individuals, that to describe the world as composed of individuals is to describe it as made up of entities no two of which have the same content, and that this in turn is to describe it by means of a system for which no two distinct entities have exactly the same atoms. Now, by way of justifying and defending the nominalism thus explained, I want to consider a number of objections to it.

Answers to Objections (i) Objection: The nominalism described is not really nominalism in the traditional sense. Answer: Doubtless a good many different theses are equally legitimate descendants of earlier nominalism. I claim no more than that the principle I have set forth is one reasonable formulation of the traditional injunction against undue multiplication of entities. And I willingly submit this claim to Father Bochenski for adjudication. If he rules against me, he deprives me of nothing but a label that incites opposition. (ii) Objection: The principle of nominalism set forth is false as a statement, and groundless as a stipulation; for we know from everyday experience that different things often are made out of the same material, or the same particles, at different times. Answer: The catch here is the phrase "at different times." Of course, different figures are often made out of the same lump of clay at different times; and of course, the same atoms often combine into different articles at different times. Likewise, different rooms are, so to speak, often made out of the same building at different places; and the same roads sometimes make up different crossings at different places. Admittedly, it is (spatially) different parts of the building or or the roads that are comprised in the two different rooms or the two different crossings; but so likewise, it is (temporally) different parts of the clay or the atoms that are comprised in the different figures or the different articles. We are at liberty to disregard the temporal or any other dimension we please; but if we were to rule out the spatial divisibility of buildings, or of roads, then we could not very consistently speak of the building, or a road, at different places. Similarly, if we rule out temporal divisibility, then we cannot very consistently speak of the clay, or of the atoms, at different times. The common experience of (different temporal parts of) the same clay making up different figures no more discredits the principle of nominalism than does the common experience of (different spatial parts of) the same building making up different rooms. A variation on this objection points to ordered pairs like Washington, Lincoln and Lincoln, Washington as clearly illustrating the composition of -299-

different entities out of the same individuals. 13 To be pertinent, of course, this objection must not rest on any appeal to the logician's usual manner of defining these ordered pairs as distinct classes of classes; for the legitimacy of such multiple generation of classes out of the same individuals is just what is in question. Rather the argument must be that, regardless of how ordered pairs are defined in any formal system, we have here an everyday instance of distinct things being composed of the same things. But surely this claim is not true. Normally we no more conclude that we describe different composite entities when we name two people in different order than we conclude that a house from top to bottom and the

house from bottom to top are different entities, or that the capital of Massachusetts and the largest city in New England are different things. We do not take the varied histories of the Battle of Bull Run as recounting different occurrences. In daily life a multiplicity of descriptions is no evidence for a corresponding multiplicity of things described. Thus I find in common experience nothing discordant with the principle of nominalism. (iii) Objection: Observance of the stated principle of nominalism is no sufficient guarantee of soundness or sense in a philosophical system; for trash of almost any kind can still be brought in on the ground floor as admitted atoms of the system. Answer: Granted. Nominalism no more guarantees philosophical soundness than the refusal to eat poison guarantees physical well-being. Many additional rules must be observed if we are to achieve either philosophical or physical health. Indeed, in some cases a moderately platonistic system with a wholesome atomic ontology may be a lesser evil than a nominalistic system that takes monstrous vacuities as its atoms—just as a very tiny dose of poison may be less harmful than a bullet in the head. Nominalism is a necessary rather than a sufficient condition for an acceptable philosophic system. To build well we must also exercise the most scrupulous care in choosing our raw materials. A given philosopher's choice of atoms may very likely be guided by attitudes or principles that are associated with nominalism by temperament or tradition; but such associated principles are independent of nominalism as I have defined it. Nominalism does not protect us from starting with ridiculous atoms. It does protect us from manufacturing gimcracks out of sound atoms by the popular devices of platonism. Nominalism, in other words, is a restrictive rule of processing that won't select our raw materials or help us make good things out of bad materials but will help keep us from making bad things out of good materials. (iv) Objection: To keep the rule of nominalism by generating wholes, rather than classes, of individuals costs as much as it pays; for it often means forcing the imagination to accept as individuals some scattered or hetero____________________ 13Cf. p. 110 of C. G. Hempel's article "Reflections on Nelson Goodman's The Structure of Appearance," in the Philosophical Review, vol. 62 (1953), pp. 108-16. -300-

geneous conglomerations that are never in practice recognized as single units and are surely incomprehensible if classes are. 14 Answer: This is perhaps the most chronic complaint against nominalism: that a progessively and in the end hopelessly strained analogy is involved in extending the application of such terms as "part," "whole," and "individual" beyond the realm of well-demarcated spatiotemporally continuous lumps. Yet as I have suggested earlier, I think this objection can be flatly and finally answered. The terminology of a system is irrelevant to the classification of the system as nominalistic or platonistic by the criterion I have explained. So long as a system admits no two distinct entities having exactly the same atoms, it is nominalistic no matter whether its generating relation is called "∊*" or "≪" or just "R," and no matter whether the values of its variables are called "classes" or "individuals" or just "entities." The words and symbols used in a system do not make it platonistic; it becomes platonistic only when it admits different entities having just the same atoms. Thus a nominalistic system cannot put any burden on the imagination that a platonistic system does not. For the nominalist's apparatus is simply part of the platonist's apparatus. A nominalistic system can be mapped into a platonistic one. A nominalistic system is a platonistic system curtailed in a specific way.

Whatever new charges may be brought against nominalism, this best-loved of all objections now deserves to be laid to rest. (v) Objection: Nominalism is trivial for a finitist and pointless for a non- finitist, since any system with a finite ontology can easily be made nominalistic while a system with an infinite ontology is repugnant to any nominalist. Answer: Take the last point first. The nominalist is unlikely to be a non-finitist only in much the way a bricklayer is unlikely to be a ballet dancer. The two things are at most incongruous, not incompatible. Obviously, by the stated criterion for nominalism, some systems with infinite ontologies are nominalistic, and some systems with finite ontologies are platonistic. But now, Hao Wang argues, 15 any finitistic platonistic system can be easily nominalized. He does not suppose that this can be done by any immediately obvious method, but refers to an ingenious device invented by Quine, 16 Now for the moment let us suppose that this device is entirely successful. Does this mean that the nominalistic program is thereby rendered pointless and trivial? On the contrary it means that an important part of the nominalistic program has been accomplished. The nominalist, after all, is looking for a nominalistic translation of everything that seems to him worth saving. The more he succeeds in finding ways of supplanting platonistic constructions by nominalistic ones, the fewer will be the cases where platonistic apparatus need ____________________ 14This objection is urged, for example, by Lowe in the article cited in footnote 1 above; and is also put forth by Quine on p. 559 of his review of The Structure of Appearance, in the Journal of Philosophy, vol. 48 (1951), pp. 556-63. 15See the article cited in footnote 10 above. 16In Quine's article "On Universals" in the Journal of Symbolic Logic, vol. 12 (1947), pp. 78-84. -301-

be eschewed; for we can use without qualms whatever we know how to eliminate. When Wang in effect says: "So you see these occurrences of platonism are harmless after all," he completely discounts the fact that only the nominalist's efforts removed the sting. One might as well say that the program for eradicating smallpox in the United States is trivial because there is no smallpox around. In one sense, of course, any completed program is trivial— in just the sense that the goal of any program is to trivialize itself. Unfortunately, however, the nominalistic program has not been so fully accomplished for all finite systems. Quine, after presenting his device, explicitly points out its fatal defects. The device can never be used in a system with an ontology embracing the entire universe; for more inscriptions will be needed to write out even a single universally quantified statement than there are things in the universe. Quine offers his device as an interesting but unsuccessful attempt, and drops it forthwith. Thus Wang is wrong about the facts concerning Quine's device; and even if the facts were as Wang supposes, they would not support the conclusion he tries to draw. (vi) Objection: Nominalism is impossible. Answer: This neatly complements the charge of triviality just discussed. Call a program impossible until it is completed, and call it trivial afterwards, and you have a well-rounded defense against it. In the formal sciences we have proofs that certain problems cannot be solved—for example, the trisection of angles with straight-edge and compass alone. But nothing even resembling proof is available for the impossibility of nominalism. And parts of the program that were once confidently cited as impossible have recently been accomplished; in particular the nominalistic and even finitistic treatment of most of classical mathematics, including general definitions for "proof" and "theorem." 17 Even if full realization of the nominalistic program ultimately does turn out to be

impossible, the efforts expended on it may not be unfruitful. The impossibility of trisecting the angle with straight-edge and compass hardly detracts from the value of Euclidean geometry, or leads us to conclude that Euclid was too frugal in his choice of tools. In the end, the nominalist may not be quite able to live within his means, but he is going to keep on trying as long as he can. Before he resorts to larceny he wants to make very sure that, and how much, he needs to steal. (vii) Objection: Nominalism would hamper the development of mathematics and the other sciences by depriving them of methods they have used and are using to achieve some of their most important results. 18 Answer: Not at all. The nominalist does not presume to restrict the scientist. The scientist may use platonistic class constructions, complex num____________________ 17In the joint article "Steps Towards a Constructive Nominalism," cited in footnote 2 above. 18E.g., see p. 40 of Carnap's "Empiricism, Semantics and Ontology" in the Revue Internationale de Philosophie, vol. 4 (1950), pp. 20-40. (Reprinted in Semantics and the Philosophy of Language, ed. Linsky, University of Illinois Press, 1952, pp. 208-28). -302-

bers, divination by inspection of entrails, or any claptrappery that he thinks may help him get the results he wants. But what he produces then becomes raw material for the philosopher, whose task is to make sense of all this: to clarify, simplify, explain, interpret in understandable terms. The practical scientist does the business but the philosopher keeps the books. Nominalism is a restraint that a philosopher imposes upon himself, just because he feels he cannot otherwise make real sense of what is put before him. He must digest what is fed him before he can assimilate it; but he does not expect it all to be pre-digested. All the same, the advantages to the scientist of abundant and intricate apparatus are easily overestimated. Paucity of means often conduces to clarity and progress in science as well as in philosophy. Some scientists indeed—for example, certain workers in structural linguistics 19 —have even imposed the full restriction of nominalism upon themselves in order to avoid confusion and self-deception. The policy of "no holds barred" may be exhilarating, but it can sometimes result in a terrible tangle. (viii) Objection: Nominalism is bigoted. In adopting or rejecting systematic apparatus or a system-form, we ought to be governed not by a supposed insight into its intrinsic merits and defects but solely by the results we are enabled to achieve. Languages and system-forms are instruments, and instruments are to be judged by how well they work. The philosopher must not handicap himself by prejudiced or dogmatic repudiations of anything that will serve his purpose. Answer: This point is strongly urged by Carnap 20 and seems also to have been responsible for Quine's somewhat tentative defection from nominalism. But surely the nominalist does not want to exclude anything that will serve the purpose of philosophy. His critics seem to conceive of that purpose as consisting of correct prediction and the control of nature. These are certainly among the major concerns of daily life, technology, and science; but they do not constitute the primary goal of philosophy—nor, I think, of science in its more philosophical aspects. Obviously a system that predicted future events correctly but reported past events erroneously would be quickly dropped by any theoretical scientist or philosopher in his right mind. But even a true and detailed account of facts past, present, and future will leave the philosopher's work undone. As I suggested a moment ago, his task is to interrelate, systematize, interpret, explain. He is driven not by practical needs but by an impractical desire to understand. He, too, will judge a system by how well it works; but a system works for him only to the extent that it clarifies. The nominalist shuns platonistic devices precisely because he feels, that their use would defeat rather than serve the purpose of philosophy. A clear story cannot be told in unintelligible language. ____________________

19In

particular, Zellig Harris and Noam Chomsky. See, for instance, the latter's "Systems of Syntactic Analysis" in the Journal of Symbolic Logic, vol. 18 (1953), pp. 242-56. the article cited in footnote 18 above.

20In

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The nominalist cannot demonstrate the need for the restrictions he imposes upon himself. He adopts the principle of nominalism in much the same spirit that he and others adopt the principle of extensionality or that logical philosophers in general adopt the law of contradiction. None of these is amenable to proof; all are stipulated as prerequisites of soundness in a philosophic system. They are usually adopted because a philosopher's conscience gives him no choice in the matter. This does not mean that he need deny that he might some time change his mind. If the neopragmatist pushes me hard enough, I will even concede that I might some day give up the law of contradiction in the interests of getting better results—although if I should give up the law I am puzzled about what the difference would then be between getting results and not getting results. But I make this concession only if the pragmatist concedes in return that we might some day even give up his Law of Getting Results. Or does he want to exempt this as constituting the essence of the human mind? Carnap protests eloquently against what he considers narrowmindedness in philosophy, concluding with the exhortation: "Let us be cautious in making assertions and critical in examining them but tolerant in permitting linguistic forms"; and Quine agrees that "the obvious counsel is tolerance and an experimental spirit." 21 Reluctant as I am to cast a shadow on all this sweetness and light, there are limits to my tolerance of tolerance. I admire the statesman tolerant of divergent political opinions, and the person tolerant of racial and educational differences; but I do not admire the accountant who is tolerant about his addition, the logician who is tolerant about his proofs, or the musician who is tolerant about his tone. In every activity, satisfactory performance requires meticulous care in some matters; and in philosophy, one of these matters is the choice of systematic apparatus or "linguistic form." Thus in place of Carnap's exhortation, I propose another: "Let us, as philosophers, be utterly fastidious in choosing linguistic forms." What choices fastidiousness will dictate varies with the individual philosopher. But if that were good reason for indifference, then variations in taste and belief would be good reason for indifference about quality in art and about truth in science.

Au Revoir I have explained my version of nominalism, and dealt with objections to the effect that it is not nominalism at all, that it is false or groundless, that it is too weak, that it is too strong, that it is trivial, that it is impossible, that it cripples the sciences, and that it is bigoted. Yet I by no means suppose that I have answered all the criticisms that will be or even all that have been made. Nominalism generates few entities but it arouses endless objections. The ____________________ 21From a Logical Point of View (see footnote 4 above), p. 19. -304-

nominalist is looked upon as an intellectual vandal; and all the good neighbors rush to protect the family heirlooms against him. But the nominalist can go about his business undismayed; for his position is virtually unassailable. Every device he uses, every step he takes, is acceptable to his opponents; he makes no move that is not entirely legitimate by platonistic standards. When the nominalist and the platonist say au revoir, only the nominalist can be counted on to comply with the familiar parting admonition they may exchange : "Don't do anything I wouldn't do." -305-

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Bibliographical Notes THE following notes are intended as a selective guide to the contemporary literature on the problem of universals. Bertrand Russell. Russell's views are scattered throughout his numerous writings. An especially clear exposition of a Platonic version of realism is contained in chapters 9 and 10 of The Problems of Philosophy (New York: Oxford University Press, 1912). His view that particulars are bundles of coexisting qualities is presented in chapter 6 of An Inquiry into Meaning and Truth (London: Allen and Unwin 1940); he provides an important commentary on his view on pp. 685-686 of his "Reply to Criticisms" in The Philosophy of Bertrand Russell, edited by P. A. Schilpp (New York: Tudor Publishing Co., 1951); Gustav Bergmann provides an interesting criticism in "Russell on Particulars," reprinted in his The Metaphysics of Logical Positivism (London: Longmans, Green and Co., Ltd., 1954). A number of important papers by Russell are reprinted in Logic and Knowledge, Essays 1901-1950, edited by Robert C. Marsh (New York: The Macmillan Company, 1956). Gottlob Frege. The volume Translations from the Philosophical Writings of Gottlob Frege, edited by Peter Geach and Max Black (Oxford: Basil Blackwell, 1952) contains several relevant papers including "Function and Concept," What is a Function?" and "On Sense and Reference." Frege's paper "The Thought: A Logical Inquiry" was published in Mind (1956). A number of papers on Frege's ontology and semantics are collected in Essays on Frege, edited by E. D. Klemke (Urbana: University of Illinois Press, 1968). Gustav Bergmann. Bergmann's ontology is developed in two volumes of papers— Meaning and Existence (1960) and Logic and Reality (1964)—and in his recent Realism, A Critique of Brentano and Meinong (1967), all published by the University of Wisconsin Press. A number of papers on ontology by some of Bergmann's former students and critics are collected in Edwin B. Allaire et al., Essays in Ontology (The Hague: M. Nijhoff, 1963). Ludwig Wittgenstein. Wittgenstein's early ontology of logical atomism is developed in his Tractatus Logico-Philosophicus (1921), translated by D. F. Pears and B. F. McGuiness (London: Routledge and Kegan Paul, 1961); a number of papers on Wittgenstein's ontology are collected in Essays on Wittgenstein's Tractatus, edited by Irving M. Copi and Robert Beard (New York: The Macmillan Co., 1966). His subsequent repudiation of this ontology and his theory of family resemblances is contained in Philosophical Investigations (Oxford: Basil Blackwell, 1953); a collection of papers on this period is Wittgenstein, The Philosophical Investigations, edited by George Pitcher (New York: Doubleday & Co., 1966). P. F. Strawson. The second part of Strawson's Individuals, an Essay in Descriptive Metaphysics (London: Methuen & Co., 1959) contains his theory of predication. For a briefer presentation see his "Singular Terms and Predicates," Journal of Philosophy (1961). The Theory of Abstract Particulars. A view just like Stout's is developed by Donald C. Williams in "The Elements of Being," The Review of Metaphysics (1953), reprinted in his Principles of Empirical Realism (Springfield, Illinois: Charles C. Thomas, 1966). In a series of papers, J. R. Jones has defended Stout against his critics: "Are the Qualities of Particular Things Universal or Particular," Philosophical Review (1949); "Simple Particulars," Philosophical Studies (1950); "Characters and Resemblances," Philosophical Review (1951). In a series of three articles, "The Nature of Universals," Mind (1927), Norman Kemp Smith ends up with a view resembling Stout's. A criticism of the theory is contained in R. I. Aaron, "Two Senses of the Word 'Universal,' '' Mind (1939). W. V. Quine. His collection From a Logical Point of View (Cambridge: Harvard University Press, second edition, 1961), in addition to "On What There Is," also contains other relevant papers such as "Two Dogmas of Empiricism," "Identity, Ostension,

and Hypostasis," and "Logic and the Reification of Universals." Related papers are "Designation and Existence," Journal of Philosophy (1939); and "On Universals," Journal of Symbolic Logic (1947). All of his Word and Object (Cambridge: The M.I.T. Press, 1960) is relevant, especially chapters 6 and 7. His critique of Carnap is contained in "On Carnap's Views on Ontology" in The Ways of Paradox and Other Essays (New York: Random House, 1966). There have been a number of critical analyses of Quine's criterion of ontological commitment; among the best are Alonzo Church, "Ontological Commitment," Journal of Philosophy (1958), and Charles Chihara, "Our Ontological Commitment to Universals," Nous (1968). Rudolf Carnap. Carnap's semantics is contained in his Meaning and Necessity (Chicago : University of Chicago Press, 1956). Recent discussions of the metaphysical implications of semantics are contained in his "Intellectual Autobiography" and "Replies and Systematic Expositions" in The Philosophy of Rudolf Carnap, edited by P. A. Schilpp (La Salle: The Open Court Publishing Co., 1963), pp. 60-67, 871-873. In the same volume is contained Wilfrid Sellars, "Empiricism and Abstract Entities," together with a number of other articles on Carnap's semantics; Carnap's reply to Sellars, pp. 923-927, is interesting. His early views are contained in The Logical Syntax of Language (London: Routledge and Kegan Paul, 1937), Part 5. Wilfrid Sellars. Sellars's ontology is developed in Science, Perception and Reality (London: Routledge and Kegan Paul, 1963) and Science and Metaphysics, Variations on Kantian Themes (London: Routledge and Kegan Paul, 1968). Several of his papers especially relevant to the problem of universals, such as "Abstract Entities," are reprinted in Philosophical Perspectives (Springfield, Illinois: Charles C. Thomas, 1967). Nelson Goodman. Goodman's views on the problem of universals are developed in The Structure of Appearance (Indianapolis: The Bobbs-Merrill Company, second edition, 1966), chapters 2, 4, and 6. In chapter 2, part 4, he presents a version of the calculus of individuals which he had earlier developed with Henry S. Leonard in "The Calculus of Individuals and its Uses," Journal of Symbolic Logic (1940). See also an article he wrote with Quine, "Steps Toward a Constructive Nominalism," Journal of Symbolic Logic (1947). Skeptical Essays. There have been numerous attempts to debunk the problem of universals, to show that it is merely a pseudoproblem. Among the best are D. F. Pears, "Universals," Philosophical Quarterly (1951); Morris Lazerowitz, "The Existence of Universals," Mind (1946); and J. L. Austin, "Are There A Priori Concepts?" and "The Meaning of a Word," in Philosophical Papers (New York: Oxford University Press, 1961). Foundations of Mathematics. The problem of universals is today often approached from the perspective of logic and mathematics. The question of the existence of classes and of numbers is incorporated into the problem. Two recent surveys of the problem from this perspective are George Berry, "Logic with Platonism," Synthese (December, 1968), and Guido Kung, Ontology and the Logistic Analysis of Language, an Enquiry into the Contemporary Views on Universals (Dordrecht, Holland: D. Reidel, 1967). The Philosophy of Mathematics, Selected Readings, edited by Paul Benacerraf and Hilary Putnam, contains selections from the major sources in this field, together with a useful bibliography. Two recent papers which try to dispense with mathematical objects are G. D. Duthie, "Notes on the Logic of Natural Numbers," Philosophical Quarterly (1959), and Paul Benacerraf, "What Numbers Could Not Be," Philosophical Review (1965). A semantical theory following Frege is developed in Alonzo Church, Introduction to Mathematical Logic (Princeton: Princeton University Press, 1956), Introduction. Miscellaneous. R. I. Aaron, The Theory of Universals (New York: Oxford University Press, 1952) contains some useful historical discussion in the first part, together with a systematic analysis of the problem in the second. Brand Blanshard, who writes in the tradition of F. H. Bradley and Bernard Bosanquet, presents very interesting discussions of the problem of universals in The Nature of Thought (London: Allen and Unwin, 1939), volume 1, chapters 16 and 17, and in Reason and Analysis (La Salle: The Open Court Publishing Co., 1962), chapter 9. Two articles well worth reading are Anthony Quinton, "Properties and Classes," Proceedings of the Aristotelian Society (1957-1958); and Arthur Pap, "Nominalism, Empiricism, and Universals," Philosophical Quarterly, I (1959), II (1960). -308-

INDEX

abstract entities, 228 -229, 237 -241, 242 abstract ideas, 26 abstract singular terms, 205 -206, 282 , 286 , 287,289,292 acquaintance, principle of, 102 , 103 , 158 - 159, 165 adjectives, 85 , 90 , 92 , 93 -95, 154 -155, 159, 161 , 162 -163; Aristotelian, 81 -82, 84 Allaire, Edwin B., 17 n Anscombe, G. E. M., 111 , 121 n Aquinas, Thomas, 108 , 116 Aristotle, 8 , 15 , 81 , 108 , 111 , 116 , 119 , 242,255,278 article, 247 ; definite vs. indefinite, 58 -59, 62, 65 , 80 , 136 , 155 , 273 atomic fact, 94 , 96 , 97 Ayer, A. J., 72 , 123 , 125 , 131 , 132 Austin, J. L., 104 Bambrough, Renford, 119 -130 Baylis, C. A., 245 n behavior problem, 7 Bergmann, Gustav, 13 n, 14 , 17 n, 67 -83, 98 Berkeley, George, 21 , 26 , 34 , 100 , 118 , 119, 155 , 166 , 240 Bernays, Paul, 236 n Black, Max, 102 n, 274 n Blue and Brown Books (Wittgenstein), 119, 122 , 123 Bochensky, Father, 299 Bosanquet, Bernard, 153 , 159 bound variables, 219 , 222 -223, 224 Bradleyan regress, 71 , 86 , 106 n Bradley, F. H., 153 , 158 , 159 Brandt, Richard B., 243 -260 Brouwer, Luitzen Egbertus Jan, 224 Buck, Roger C., 118 n Butchvarov, Panayot, 184 -199 calculus, meromorphic, 82 Cantor, Georg, 224 Carnap, Rudolf, 10 n, 224 , 228 -242, 251n, 256 , 259 , 281 , 282 , 286 , 302 n, 303, 304 Cassirer, Ernst, 10 n categorizing contexts, 281 category statement, 282 category, ultimate, 8 , 9 category words, 262 , 263 , 264 , 265 , 282 causal connections, 279 causal explanation, 8 causality, 38 change, 38 Chomsky, Noam, 303 n Christian Platonism, 45 n Church, Alonzo, 16 n, 69 , 79 , 218 , 224 clarity, rule of, 211 classes, as existential entities, 266 cognition, 16 , 37 , 38 , 41 , 54 common names, 80 -83, 95 , 96 , 97 common qualities, 4 , 6 -7 commonsense, 7 , 8 , 10 , 24 , 26 , 28 , 34 , 37 community, imperfect, 207 -208 companionship, 207 -208 comparative, and noncomparative relations, 189 -193 complex, concrete vs. inclusive, 160 concept correlates, 78 -79, 80 concepts, 41 ; complex, 124 ; first and second level, 63 , 75 n; and object, 57 , 59 , 61, 62 , 64 , 65 ; and percept, 21 -22, 33 , 34, 84 , 85 ; as predicative, 57 , 59 , 60 , 62-63, 65 -66; vs. properties, 271 , 272 , 274, 275 , 276 , 285 ; property vs. mark, 63-64; saturated

vs. unsaturated, 65 , 66 , 70-71, 72 , 73 , 74 , 76 , 78 , 277 , 278 , 279; sense and reference, 60 , 64 ; subordination of, 58 , 61 ; vs. things, 23 n; truth value, 60 ; usage of term, 56 conceptualism, 44 , 45 , 48 , 53 , 260 ; defined, 224 conceptual realism, 282 contradiction, law of, 304 ; meaninglessness of, 218

Descartes, René, 119 determinable vs. determinate terms, 51 -53, 154, 161 , 162 , 163 , 260 Donagan, Alan, 98 -118 Ducasse, C. J., 193 n Dummet, Michael, 131 n dyadic relations, 189 -190, 195 -196, 197 empiricism, 256 ; abstract entities, 228 -229, 240-241; logical, 237 ; vs. particularism, 16 entities: abstract, 228 -229, 237 -241, 242 , 264; concrete, 4 ; vs. existents, 67 , 68 - 69 ; linguistic abstract, 288 ; multiplication of, 69 , 74 , 75 , 296 , 299 ; necessary connections, 279 ; nonindividual, 261 , 282; Platonic, 278 , 288 , 291 ; and time, 33 epistemic, 161 epistemology, 230 ; and conceptualism, 44 , 45, 48 epistemonic, 161 n, 162 Eskimos, snow words, 10 Euclidean geometry, 302 exemplars, 46 -48 exemplification, 14 , 15 , 70 , 71 , 74 , 80 ; first and second order, 106 ; as a relation, 105 -106; and universals, 102 -103, 104, 105 , 115 , 116 existence claims, 7 , 8 existential entities, 266 existentialism, quantification, 261 , 263 , 268, 270 n, 284 existential statements, 280 existents, 67 , 68 -69, 70 , 71 , 74 , 79 , 81 explanation, category, 6 , 15 ; causal, 8 ; commonsense, 10 ; metaphysical, 8 , 9 ; motive, 8 extensionalism vs. nominalism, 296 , 298 extensionality, 304 external vs. internal questions, 229 , 230 , 236,237 family resemblance, 119 -122, 123 , 124 Feigl, Herbert, 236 n Fido-Fido principle, 238 , 239 finitism, 301 flatus vocis, 237 , 241 Fleming, Noel, 212 n formalism, 224 , 226 formal logic, 40 , 144 Fraenkel, 224 Frege, Gottlob, 13 n, 15 , 56 -66, 67 -83, 101, 115 , 217 , 220 , 224 , 236 n, 239 , 240, 242 , 261 , 271 , 274 , 276 , 277 , 285 fundamentum divisionis, 160 , 162 fundamentum relationis, 156 games, 120 , 122 -126 Geach, P. T., 121 n, 261 , 270 , 271 , 272 , 273, 274 , 275 , 276 , 285 general names, 128 , 132 , 133 God, 25 , 45 n, 116 Gödel, Kurt, 227 Goodman, Nelson, 17 n, 98 , 109 , 113 , 207 , 224n,251n,257n,260,293-305 Grice, H. P., 131 n, 147 n Grossman, Reinhardt, 67 n, 118 n Grundlagen der Arithmetik (Frege), 56 , 58, 59 n, 60 , 61 n, 63 happening words, 143 Harris, Zellig, 303 n Heisenberg, Werner, 227 Hempel, C. G., 300 n

Heracleitus, 38 Hicks, G. Dawes, 85 n, 254 Hilbert, David, 224 Hockberg, Herbert, 118 n Hume, David, 21 , 26 , 34 , 100 , 118 , 119 , 240 hylomorphism, 82 hypostatization, 83 , 238 idea, abstract, 26 idealism, subjective, 230 ; and time, 22 idealist error, 117 -118 identity, 204 , 256 ; criteria of, 201 -202, 208, 209 , 210 ; numerical sameness, 211 ; qualitative, 186 ; as a relation, 187 -188; vs. resemblance, 184 -189, 193 , 198 ; theory of, 4n imagism, 48 Individuals (Strawson), 123 individuation, problem of, 17 infinite regress, 14 -15 Inquiry into Meaning and Truth (Russell), 111 instances, of universals, 25 , 27 , 29 , 50 , 124, 133 , 134 , 135 , 136 , 137 -138, 149 , 179, 254 , 255 instantiation, degrees of, 45 , 52 integers, 234 internal vs. external questions, 229 , 230 , 236, 237 intertranslatability and counterparts, 287 , 288 -310-

Introduction to Semantics (Carnap), 286 intuition, 38 intuitionism, 224 Johnson, W. E., 84 , 85 , 86 , 87 , 89 , 90 , 92, 94 , 126 , 153 , 154 , 156 , 161 , 162 , 163, 169 , 171 , 180 n, 245 , 247 Jones, J. R., 245 Kerry, Benno, 56 , 57 , 58 , 59 , 61 , 63 , 64 , 65 language, 24 , 49 , 53 , 55 , 57 , 58 , 62 , 66 , 107, 120 , 122 , 123 , 128 , 129 , 133 , 212 , 303; abstract entities, 228 -229, 238 - 239 ; classes of nouns, 134 -135, 141 ; featureplacing sentences, 139 -142, 143 , 146; happening words, 143 ; ideal, 244 , 247, 249 ; integers and rational numbers, 234 ; natural number system, 231 - 232 ; nominalist, 243 , 244 , 246 -254, 256-257; and ontology, 225 ; property- location, 139 ; propositional system, 232 ; realist, 243 , 254 -260; real numbers, 234 , 238, 240 ; spatio-temporal coordinates, 234-235; thing properties, 234 ; of things, 230 ; universal-particular problem, 87 ; and universals, 111 -112; see also linguistic framework Lazerowitz, Morris, 202 n, 243 n Leibniz, G. W., 42 , 74 n, 82 linguistic abstract entities, 288 linguistic framework, internal vs. external questions, 229 , 230 , 236 , 237 ; space- time system, 229 -230 linguistics, 13 , 243 , 244 ; of resemblance, 49; structural, 303 Lloyd, A. C., 249 n Logic (Johnson), 92 , 161 logic, 77 ; Aristotelian, 81 ; formal, 40 , 144 ; mathematical, 14 n, 90 , 95 ; Russellian, 115 "Logical Atomism" (Russell), 102 logical atomism, 85 Logical Syntax of Language (Carnap), 281 logicism, 224 Lowe, Victor, 293 n, 301 n McTaggart, John, 84 , 153 , 156 , 157 , 159 , 160, 169 mapping, 71 -72, 73 , 75 , 77 , 80 materialism, 237 mathematical logic, 14 n, 90 , 95 , 97

mathematics, 257 , 260 , 302 , 303 ; and ontology, 223 -225, 226 -227, 228 ; and universals, 223 -224 meaning, 221 , 222 , 238 , 283 -286; vs. naming, 109 , 220 -221 Meiland, Jack, 17 n mental illness, 7 metaphysics, 3 , 4 n; vs. science, 12 Mill, John Stuart, 239 mind-body problem, 282 Moore, G. E., 21 n, 85 n, 98 , 99 , 100 , 101 , 104, 105 , 106 , 115 , 116 , 117 , 118 , 158 , 167-178,178-183,205,245,254n Nagel, Ernest, 240 names, 68 ; common, 80 -83, 95 , 96 , 97 ; individual, 246 ; general, 128 , 132 , 133 ; predicate, 246 naming, 148 ; vs. meaning, 109 , 220 -221 natural kinds, 36 Nature of Existence (McTaggart), 84 , 156, 159 neo-Platonists, 116 neopragmatism, 304 nexus, 70 , 71 , 74 nominalism, 4 n, 48 , 68 , 123 , 125 -130, 202, 236 , 239 , 242 , 281 ; abstract entities, 240 ; abstract singular terms, 205 - 206 ; characters and functions, 73 -74; common names, 80 -83; concept correlates, 78 -79, 80 ; concepts as existents, 79; concepts and functions, 75 ; definite vs. indefinite article, 58 -59, 62 , 65 , 80 ; vs. existentialism, 296 , 298 ; expressions, 101; extreme, 247 -248; as false and groundless, 299 -300, 304 ; vs. finitism, 301; generation of wholes, 300 -301; as hampering mathematics and the sciences, 303 , 304 ; identity of qualities, 210; as impossible, 302 , 304 ; individuals and classes, 293 -295; language of, 243 , 244, 246 -254, 256 -257; and linguistic recurrence, 11 ; mapping, 73 , 75 , 77 , 80 ; moderate, 248 , 250 , 253 -254, 258 , 260 ; multiplication of entities, 296 , 299 ; vs. particularism, 11 ; vs. Platonism, 295 - 299, 300 , 301 , 302 , 303 , 305 ; quality classes, 205 -208, 210 -211; quality-descriptions, 202 -205; reference and sense, 74; reification of classes, 77 -78; resemblance, 11 -12, 155 -156; vs. resemblance and identity theories, 184 , 187 , 193 ; vs. resemblance theory, 247 , 248 -253; rule of clarity, 211 ; rule of simplicity, 209 - 210 ; saturated vs. unsaturated expres -311-

nominalism cont'd sions, 73 , 74 , 76 , 78 ; as trivial and pointless, 301 -302, 304 ; truth value, 73 , 78 , 79; Vienna Circle, 237 ; as weak, 300 , 304 nouns, 134 -135, 141 , 155 , 262 , 263 numbers, rational, 234 ; real, 234 , 238 , 240 number system, natural, 231 -232 Occam's razor, 15 , 108 -109, 215 Ockham, 82 O'Connor, D. J., 191 n, 195 n, 249 , 251 n one-place predicate, 290 ontology, 6 , 38 , 39 , 41 , 54 , 72 , 81 , 82 , 215, 220 , 221 , 223 ; analytic, 244 ; and abstract entities, 229 ; entity vs. existent, 67, 68 -69; individual vs. character, 68 , 82; and language, 225 ; and mathematics, 223-225, 226 -227, 228 ; name, 68 ; object and function, 67 ; philosophy of resemblances, 45 , 48 ; rule of simplicity, 225-226; truth values, 68 Owens, Joseph, 108 n Pap, Arthur, 245 n paradox, Russell's, 227 Parmenides (Plato), 4 , 5 , 6 , 8 , 15 , 82 , 105 particulars, 25 -26; bare, 17 ; and characters, 167 -170, 178 -183; distinctness and identity, 136 -137, 139 , 145 -146; expressions, 91 ; as subjects of predicates, 35 ; as substantive, 90 particularism, 4 ; Berkeley and Hume, 26 ; and empiricism, 16 ; and nominalism, 11 ; vs. realism, 10 , 12 -17; resemblance theory, 11 -12; spatial plurality, 27 -28, 29; spatiotemporal relations, 22 , 34 ; theory of abstract particulars, 11 ; theory of bare particulars, 17 ; two-place problem, 27 -33

Pears, D. F., 8 -9, 98 , 113 , 114 , 122 n, 202 n Pegasus, 215 , 216 , 217 , 219 , 220 , 223 Peirce, C. S., 242 percepts/concepts, 21 -22, 33 , 34 , 84 , 85 Philebus (Plato), 104 Philosophical Investigations (Wittgenstein), 120, 122 , 123 Philosophy of Bertrand Russell (Schilpp), 117 physics, and abstract entities, 228 ; and realist vs. nominalist language, 256 -257 Plato, 4 -5, 8 , 15 , 16 , 38 , 82 , 87 , 89 , 92 , 104, 105 , 107 , 108 , 109 , 112 , 161 , 219 , 224, 236 n, 242 , 255 , 278 , 293 Platonism, 4 n, 114 , 229 , 236 , 237 , 263 , 265, 278 , 280 , 281 , 282 , 288 , 291 , 292 , 294n, 295 -299, 300 , 301 , 302 , 303 , 305 ; Christian, 45 n Plato's beard, 98 , 215 , 218 , 279 plenitude, principle of, 103 Poincaré, J. H., 224 pointing, 200 -201 pragmatism, 304 predicate, 35 , 57 , 59 , 60 , 62 -63, 65 -66, 70, 202 ; first-order, 247 , 250 ; one-place, 290; primitive, 101 , 110 , 113 , 115 , 116 , 117, 118 predicate-name, 246 Price, H. H., 11 n, 12 n, 36 -55, 140 n, 187 n, 209n, 249 Principia Mathematica (Russell), 72 , 85 , 93, 95 Problem of Knowledge (Ayre), 123 Problems of Philosophy (Russell), 84 , 99 , 102 properties vs. concept, 271 , 272 , 274 , 275 , 276, 285 ; vs. mark, 63 -64 propositions, 232 ; atomic, 89 , 90 , 91 , 94 , 95, 97 ; and universals, 163 -165; truth of, 286 psychology, and abstract entities, 241 qualities, common, 4 , 6 -7; identity criteria, 201 -202, 208 ; nonobservable, 259 ; and particulars, 201 ; and relations, 37 , 38, 55 , 131 , 153 , 156 , 157 , 159 , 165 , 179, 180 , 182 , 183 , 249 quality classes, 202 , 205 -208, 210 -211; imperfect community and companionship difficulty, 207 -208 quality descriptions, 202 -205 quantification, existential, 261 , 263 , 268 , 270n, 284 ; over variables, 109 -111, 218 219, 222 , 223 , 262 , 263 , 264 , 270 , 273 , 280, 292 question-echoing statements, 273 Quine, W. V., 11 n, 16 , 80 , 81 , 82 , 83 , 98, 109 , 110 , 111 , 113 , 201 n, 215 -227, 224n, 236 n, 247 , 253 , 257 n, 269 , 270 , 272, 301 , 302 , 303 , 304 Ramsey, F. P., 84 -97, 126 , 131 , 132 , 133 n, 134 Ramsey's maxim, 126 rationalism, 16 realism, 4 , 5 -6, 7 , 48 , 68 , 69 , 123 , 125 , 127, 129 , 130 , 202 , 230 , 231 , 237 , 247 , 249, 250 ; abstract singular terms, 205 -312-

206; as circular and uninformative, 113 - 114 ; classical difficulty with, 103 , 104 - 107 ; conceptual, 282 ; defined, 224 ; exemplification, 70 , 71 , 74 , 80 ; existents, 69, 70 , 71 , 74 ; functions, 72 , 73 ; hypostatized characters, 83 ; identity of qualities, 210 ; individuals and characters, 69-70, 71 , 72 ; instance of, 254 , 255 ; language of, 243 , 254 -260; and linguistic recurrence, 13 ; mapping, 71 -72; mathematics, 257 ; moderate, 108 -113; nexus, 70 , 71 , 74 ; vs. particularism, 10 , 12-17; particulars, 25 -26; Platonic, 45 n, 236n, 238 ; predication, 70 ; qualities as universals, 10 -11; quality-descriptions, 202-205; quantified variables, 109 -111; and rationalism, 16 ; reality of relations, 99 -100, 101 ; rule of clarity, 211 ; rule of simplicity, 209 -210, 254 ; saturated vs. unsaturated expressions, 70 -71, 72; and time, 22 ; truth-function, 100 , 101 realist principle, 101 , 107 , 109 , 110 , 111 , 115, 116 , 117 recurrence, 38 -39, 40 , 41 ; causality, 38 ; and characteristics, 38 , 40 , 43 ; and conceptual cognition, 37 , 38 , 41 , 54 ; conjoint, 36 ; identity vs. resemblance, 184 187, 193 ; linguistic, 11 , 13 ; natural, 3 - 4, 6 , 9 , 36 ; quality and relation, 37 , 38; as a

relation, 187 ; resemblance, 55 ; of sets, 36 reductionism, 9 regress, Bradleyan, 71 , 86 , 106 n; infinite, 14-15; Ryle's, 107 regularity theory, 38 reification, of classes, 77 -78 relational properties, 37 relations, 50 ; dyadic, 189 -190, 195 -196, 197; and exemplification, 105 -107; first and second order, 195 ; and identity, 187-188; vs. non-relation, 23 ; and qualities, 37 , 38 , 55 , 131 , 153 , 156 , 157 , 159, 165 , 179 , 180 , 182 , 183 , 249 ; reality of, 99 -100, 101 ; and recurrence, 187 ; and resemblance, 187 , 188 -189, 196 ; and space, 42 ; triadic, 207 resemblance, 7 , 49 , 162 ; and characteristics, 44 ; close, 43 , 44 ; comparative vs. noncomparative relations, 189 -193; different, 45 -46; exact vs. complete, 42 ; exemplars, 46 -48; family, 119 -122, 123 , 124; first and second order, 50 , 51 ; higher order, 249 ; vs. identity, 184 -189, 193, 198 ; inexact, 53 -54; in-respect argument, 250 ; intensity of, 42 -43, 44 ; and nominalism, 11 -12, 155 -156, 184 , 187, 193 , 247 , 248 -253; vs. particularism, 11 -12; philosophy of, vs. philosophy of universals, 40 -41, 43 -44, 45 - 46, 48 , 49 -55; vs. properties, 130 ; qualitative, 186 ; recurrence, 55 ; as a relation, 187, 188 -189, 196 ; theory of, 244 ; total, exact part, and inexact partial, 251 253 ; as triadic or tetradic relation, 195 - 196, 197 ; and universals, 48 -51, 208 - 209 Russell, Bertrand, 16 n, 21 -35, 68 , 72 , 73 n, 76, 77 , 84 , 85 , 86 , 87 , 89 , 90 , 91 , 94 , 95, 96 , 98 , 99 -118, 126 , 148 , 153 , 158 , 165, 218 , 219 , 220 , 222 , 223 , 224 , 233 , 236n, 239 , 240 , 245 , 248 , 249 Russellian logic, 115 Russell's paradox, 227 Ryle, Gilbert, 105 , 238 , 239 Ryle's regress, 107 saturated vs. unsaturated concepts, 65 , 66 , 70-71, 72 , 73 , 74 , 76 , 78 , 277 , 278 , 279 Schilpp, P. A., 117 Schlick, Moritz, 236 Schroeder, E., 57 n science, 37 , 302 , 303 ; vs. metaphysics, 8 -9, 12,25 Scotus, Duns, 82 Sellars, Wilfrid, 109 , 241 n, 261 -292 semantics, and abstract entities, 228 -229, 237-241, 242 sense, and reference, 60 , 64 sentences, feature placing, 139 -142, 143 , 146 Separate Substances, 116 sets, 36 simplicity, rule of, 209 -210, 225 -226, 254 skepticism, 3 , 7 , 8 -9, 10 , 12 Socrates, 4 , 45 , 86 , 87 , 89 , 90 , 91 , 92 , 94 , 96, 108 , 109 , 142 , 202 , 204 , 264 , 265 , 289 Some Main Problems of Philosophy (Moore), 99, 115 space, real vs. perceived, 28 -33; relational theory of, 42 ; and time, 5 , 6 , 16 , 84 , 216, 229 -230, 234 -235; two-place problem, 27 -33, 173 -174 spatial plurality, 27 -28, 29 Spinoza, B., 119 statements, categorizing, 282 ; existential, 280 -313-

Stout, G. F., 11 , 85 , 136 , 153 -166, 167 - 178,178-183,205,245 Strawson, P. F., 14 n, 123 , 131 -149, 246 n, 265n structural linguistics, 303 structure, and internal complexity, 37 subjective idealism, 230 subject/predicate propositions, 13 , 14 , 23 - 24, 26 , 34 , 35 , 60 , 86 -87, 88 , 89 , 94 , 111, 112 , 133 , 179 , 181 subordination, of concepts, 58 , 61 substances, and adjectives, 85 , 92 , 93 -95; as complex unity, 159 , 160 , 182 ; vs. occurrence, 169 , 173 ; and qualities, 157 - 158,159,174-177

substantives, 23 , 33 , 34 , 90 substitutivity, law of, 13 , 14 symbols, incomplete, 91 , 93 , 95 , 97 , 218 terms, abstract singular, 282 , 286 , 287 , 289,292 tetradic relation, 195 -196, 197 thing-language, 230 , 234 things vs. concepts, 23 n Three Philosophers (Anscombe), 111 time, 22 , 84 ; entities in, 33 Tractatus Logico-Philosophicus (Wittgenstein), 119 triadic relation, 195 -196, 197 , 207 truth-function, 100 , 101 , 279 truth-value, 60 , 68 , 73 , 78 , 79 two-place problem, 27 -33, 173 -174 ultimate category, 8 , 9 universalia ante rem, 39 , 45 , 53 , 54 n, 127 universalia in rebus, 38 , 39 , 40 , 48 , 49 , 52 , 54, 127 universals, 10 -11, 87 , 111 -112; abstract, 153; abstract nouns, 155 ; acquaintance, 158-159, 165 ; adjectives, 90 , 154 -155, 159, 161 , 162 -163; characters, 154 , 156 , 157, 170 , 177 -178; characters as particulars, 167 -170, 178 -183; as common qualities, 4 ; complex, 87 -88, 89 ; degrees of generality, 198 ; determinable and determinate characteristics, 51 -53, 154 , 161, 162 , 163 ; distributive unity, 154 , 155, 156 , 161 ; exemplified vs. unexemplified, 102 -103, 104 , 105 , 115 , 116 ; expressions, 91 ; as family resemblance, 119-122, 123 , 124 ; games analogy, 120 , 122-126; identity criteria, 209 , 210 ; instances of, 25 , 27 , 29 , 124 , 133 , 134 , 135, 136 , 137 -138, 149 , 179 ; linguistic formulation, 243 , 244 ; and mathematics, 223-224; as predicates, 35 ; proposition as alternative, 163 -165; qualities and relations, 55 , 131 , 153 , 156 , 157 , 159 , 165 , 179, 180 , 182 , 183 ; vs. quality classes, 202; as recurrent characteristics, 38 -39, 40, 41 ; and resemblance, 40 -41, 43 -44, 45-46, 48 , 49 -55, 208 -209; spatiotemporal location, 5 , 6 , 16 ; substances and adjectives, 85 , 92 , 93 -95; substance vs. occurrence, 169 , 173 ; substances and qualities, 157 -158, 159 , 174 -177; theory of, 4 , 6 , 7 , 9 ; theory of abstract particulars, 11 variables, bound, 219 , 222 -223, 224 ; common noun, 262 , 263 ; quantification over, 218-219, 222 , 223 , 262 , 263 , 264 , 270 , 273,280,292 Veatch, Henry B., 108 n, 118 n verbs, and substantives, 23 , 33 , 34 Vienna Circle, 237 Waisman, Friedrich, 98 Wang, Hao, 297 n, 301 , 302 Walters, S. M., 121 n Wells, R., 67 n, 68 n, 77 , 78 , 79 Weyl, Hermann, 224 Whitehead, A. N., 84 , 93 , 224 wholes, generation of, 300 -301 Whorf, Benjamin, 10 n Williams, Donald C., 204 n, 205 , 245 , 254 n Wilson, Cook, 162 , 258 Wisdom, Arthur J., 122 n, 124 Wittgenstein, Ludwig, 89 , 90 , 91 , 94 , 96 , 97, 101 , 116 , 119 -130, 217 , 237 Wolterstorff, Nicholas, 200 -212 words, category, 262 , 263 , 264 , 265 , 282 ; for snow, 10 ; general, 128 , 132 , 133 ; happening, 143 -314-