Criticism of "Are Predicates and Relational Expressions Incomplete?" Terence Parsons The Philosophical Review, Vol. 79, No. 2. (Apr., 1970), pp. 240-245. Stable URL: http://links.jstor.org/sici?sici=0031-8108%28197004%2979%3A2%3C240%3ACO%22PAR%3E2.0.CO%3B2-I The Philosophical Review is currently published by Cornell University.
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CRITICISM O F "ARE PREDICATES AND
RELATIONAL EXPRESSIONS
INCOMPLETE?"
I
S THERE a difference between predicates and names, analogous to Frege's distinction between "incomp1ete" and "complete" expressions? In a very interesting recent paper,l Peter Long says yes-albeit with very definite restrictions on the sort of incompleteness that is at issue. Frege's view is that both predicate expressions and names of particulars stand for entities, in the same sense of "stand for"; the incompleteness of predicates, as opposed to names, has to do with the nature of the entities for which they stand. Mr. Long's view is rather that predicates cannot "stand for" (or "name") things in the same sense in which proper names do. The difference is not in the sort of entities stood for, but in the sort of standingfor (or sort of naming, or designating) that it is possible for predicates and names to do. I think that Mr. Long's argument for this position fails, and most of this commentary is devoted to the minimum negative task of showing this (there is much else of value in the paper that I will not discuss). Long begins by contrasting expressing a relational proposition by means of a sign for a relation, with expressing a relational proposition by means of a relation between signs (this is only a preliminary setting of the problem; as we will see below he thinks this distinction is basically mistaken). Suppose that we initially have a language with no signs for relations at all. In this language relational propositions are expressed by means of relations between signs (signs which are names of particulars). For example, we represent the proposition that A is next to B by writing "AB"; that A is smaller than B by "AB," and so forth. Long gives only examples in which the relation between signs is used to represent a similar relation among things-for example, to symbolize smaller than we write the one name smaller than (and slightly above, and . . .) the other-but this is not central to his thesis. We could, for example, symbolize the proposition that A is heavier than B by writing "bB," a phrase in which there is very little similarity between the relation being symbolized and the symbolizing sign-relation. 1 Peter Long, "Are Predicates and Relational Expressions Incomplete?," Philosophical Review, LXXVIII ( I 969), 90-98.
240
ARE PREDICATES INCOMPLETE?
Long now points out that we can conceive of ordinary sentences in just the same way. We can conceive of the relation of being smaller than being symbolized by a relation between signs, even in the case of sentences like "A is smaller than B." Here the relation of A's being smaller than B is symbolized by a relation between a sign for A (namely, "A") and a sign for B ("B")-the relation being that the former is written before the latter, and they are separated by the further sign "is smaller than." Likewise, we can conceive of properties being expressed by means of properties of signs.2 For example, we can analyze "Socrates is bald" as expressing the proposition that Socrates is bald by means of producing a name of Socrates with the sign-property of beingfollowed by "is bald." So far I have no quarrel with Long's interesting proposal for a n alternative mode of semantic analysis of sentences. I think it is a way of analyzing language that might be as interesting and fruitful (perhaps more so) than conventional analyses. My quarrel comes only with his implicit attack on more conventional analyses. Long now introduces the notion of the index of a sign-property (or sign-relation) . He says: I shall call relational signs the indexes of sign-relations, since it is they that indicate which relation is expressed, symbolized, by the sign-relations they characterize. And I shall call predicates the indexes of sign properties, since it is they that indicate which property is expressed, symbolized, by the signproperties they characteri~e.~
I assume that this could be put into explicit definitional form as follows : x is a n index of a sign-relation (-property)y
=dz
sentences in which x occurs can be analyzed in terms of signs standing in relation y (having property y), and (ii) x indicates which relation (property) y symbolizes according to this analysis, and (iii) x characterizes y.
(2)
Long does not define what he means by "indicates" or by "characterizes," but it is clear enough from his discussion what he means 2 Strictly speaking, this should read "We can conceive of property-object propositions being expressed by the fact that certain signs have certain properties." In general, according to this view, it is no longer signs that express propositions, it is facts (e.g., that certain signs have certain properties). Long, op. cit., pp. 93-94.
TERENCE PARSONS
(at least for the cases we will deal with). Somewhat vaguely put, a sign, s, characterizes a sign-relation (-property) if that relation (property) is analyzable in terms of syntactical relations to s; and a sign s indicates which relation (property) is symbolized by the sign-relation (-property) it characterizes if the presence of s gives us the information needed to know which relation is being expressed.4 It now turns out, of course, that all predicates and relational signs are indexes, because we can always analyze them as characterizing sign-properties or sign-relations, in terms of which we can in turn analyze sentences as sketched above. And this brings us to the meat of the argument for the appropriate asymmetry between predicates and names-an asymmetry which will justify us in calling the former incomplete and the latter complete, and will justify us in concluding that predicates cannot standfor things in the same sense in which names can. The argument goes: Here we are attacking only a "false" conception of what it is for an expression, an element of language, to stand for, designate, a relation. We are not saying that it is wrong to speak of an expression as standing for, designating, a relation. T o say that "next to" stands for, is a sign for, a relation is to say no more than that it is a relational sign, and we are not denying that the sign or expression "next to" is a relational one. But it is only as an index of a signrelation that it is a sign for a relation. If we call "symbols" only those signs that are not indexes, we can say: No expression can be the symbol for a relation. What expresses, symbolizes, a relation is not an expres~ion.~
Here we have both a proposed explanation and a proposed justification for saying that predicates and relational signs do not stand for properties or relations in the way in which names do, but only in some indirect manner. Using "stands for," for the relation in which names stand to what they name, we could define the "only" appropriate sense for indexes as:
i stands for, z =,f i characterizes a sign-relation (-property) y which symbolizes z6 4
I t may be that these two accounts collapse into one another, i.e., that s
characterizesx if and only if s indicates which relation (property) x symbolizes. Long, op. cit., p. 95. Perhaps this should read i stands for, z = df i characterizes some sign-relation (-property) y which stands for, z. I t is not clear whether Long believes that sign-properties stand for, things, or whether he denies this as well. 6
ARE PREDICATES INCOMPLETE?
Now let me turn from exposition to criticism. This mode of argument is unconvincing, for at least two reasons. First, to argue that predicates and relational expressions are indexes, and so stand for, relations, is not to deny that they stand for, relations. Sentences can be analyzed in many ways, no one analysis necessarily precluding any other. What Long has done is to focus our attention on one mode of analysis to the point where we have lost sight of another. But the other, the analysis which claims that relational expressions stand for, relations, has not thereby been shown to be incorrect. Secondly, such a line of argument cannot possibly produce the requisite asymmetry between names and predicates, for precisely the same inference can be drawn concerning names. The crucial point is that names, also, are indexes. If this can be shown, then the rest of Long's arguments must break down, since they all depend on predicates and relational expressions being indexes, and names not being indexes. The argument that predicates were indexes rested upon the possibility of analyzing sentences solely in terms of names and their properties and relations. The corresponding argument for names will then rest upon the possibility of analyzing sentences in terms of predicates and their properties and relations. This is quite straightforward. For example, we analyze the relational sentence "A is smaller than B" as expressing the proposition that A is smaller than B by the presence of a sign for the relation7 being smaller than, having the sign-property that it is preceded by "A" andfollowed by "B." Likewise we can analyze "Socrates is bald" as expressing the proposition that Socrates is bald by the presence of a sign for the property being bald, having the sign-property
I t might be held that I am begging questions by assuming that we could have signs for relations. I am not because: (i) I am only attacking Mr. Long's arguments, not demonstrating the falsity of his conclusions. If I can undermine his arguments by assuming for names what he assumes for predicates, this is sufficient. (ii) I n any case I need not assume that we have signs which stand for, relations -it suffices to have signs which stand for, relations. Cf. the examples at the end of the paper.
TERENCE PARSONS
that it is preceded by the sign "Socrates." These analyses are exactly symmetrical to long'^,^ and showjust as much or just as little as his.9 I conclude that Long's discussion does not give us a relevant sense of incompleteness in which predicates are incomplete while names are not. This conclusion should be stated very tentatively, because there is much in Long's paper that I have not touched on. My belief is that his discussions of the incompleteness of predicates all rest upon the argument criticized here. Let me point out that I have not attempted to answer some of the questions raised in his paper (for example, "what is the difference between a complex sign and a complex of signs?"), nor many interesting and closely related questions (for example, Frege's "What makes the parts of a thought hold together ?").lo 8 This may not be completely apparent due to the informal wording (which I have adopted in parallel with Long's). The symmetry can be brought out by comparing : "The fact that in 'Socrates is bald' a sign for the man, Socrates, has a sign-property which symbolizes being bald expresses the proposition that Socrates is bald." with: "The fact that in 'Socrates is bald' a sign for the property, being bald, has a sign-property which symbolizes Socrates expresses the proposition that Socrates is bald." Both theories can be restated in terms of classes rather than properties, and both present equal difficulties in extending them to a theory of truth for sentences containing connectives and quantifiers. 9 It might be thought that all of this is not particularly important-that there still remains an asymmetry, between names and predicates, which is that we could imagine a symbolism totally without the latter, but not one without the former. But this also is incorrect. Consider the following notation: we use English predicates to symbolize properties and relations, but replace the use of names with the style of writing the predicates (i.e., with properties of the predicates). E.g., let us symbolize "Socrates is wise" by writing "Wise" with its initial letter 3 mm. high. We can symbolize "Socrates is cleverer than Aristotle" by writing "clevereR," where the "C" is 3 mm. high and the final "R" is 5 mm. high. The names "Socrates" and "Aristotle" are here being replaced by 3 - mm. and 5 - mm. letter heights, respectively (i.e., by certain properties of predicates articulable in terms of letter heights). Conversely, "Aristotle is cleverer than Socrates" is written "Clevere~." Note that one cannot insist that we still have names here-namely, letter heights-without correspondingly insisting that we still have predicates in Long's symbolism-namely, letter arrangements. Both symbolisms are equally impractical in use, owing to our limited ability to discriminate shapes, arrangements, and sizes. lo Gottlob Frege, "On Concept and Object," Philosophical Writings o f GottlobFrege, ed. by Geach and Black (Oxford, 1960), p. 54.
ARE PREDICATES INCOMPLETE?
One last point. I t might be maintained that although Long has not shown that predicates are incomplete, as opposed to names, he has shown that in any analysis of a propositional sign something must be incomplete and something else complete-that is, that in any sentential analysis there must be some asymmetry in the roles of the various signs. In other words, any analysis must construe some signs as indexes while construing others as non-indexes-although different modes of analysis may cut up the pie in different but equally legitimate ways.11 I think even this is incorrect. For, first of all, I see no real need ever to construe any sign as an index. ( I do not deny that there may be various sorts of inadequacies in the "conventional" semantics. But I do not see how any of them are removed by moving to the index theory.) Secondly, even if we do employ indexes, there may still be no asymmetry among the sentential constituents. For example, we could construe both predicates and names as indexes, each of them characterizing signproperties of the period at the end of the sentence (or of the entire complex propositional sign). In all cases, the move to indexes does not give us an appropriate sense of incompleteness.
TERENCE PARSONS University of Illinois at Chicago Circle
l1 Frege himself my have held this; cf. Begr~sschri (selections)in Geach and Black, op. cit., bottom of p. I 5.
245
