Philosophical Topics, Volume 36, Issue 2, Fall 2008 - On Between Saying and Doing (Robert Brandom's John Locke Lectures Comments and Responses)

PHILOSOPHICAL TOPICS VOL. 36, NO. 2, FALL 2008 Preface Robert Brandom delivered his John Locke Lectures, “Between Sayin...

Author: Edward Minar

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PHILOSOPHICAL TOPICS VOL. 36, NO. 2, FALL 2008

Preface Robert Brandom delivered his John Locke Lectures, “Between Saying and Doing: Towards an Analytic Pragmatism,” in Oxford in May and June of 2006. In April 2007, in Prague, a conference devoted to discussing the lectures was held, organized by the Institute of Philosophy of the Academy of Sciences of the Czech Republic and the Faculty of Philosophy & Arts of the Charles XII University and with financial support from the Andrew W. Mellon Foundation. The conference began with a “School of Inferentialism,” a series of seminars by distinguished philosophers covering the background to the lectures in Brandom’s work and elsewhere. Professor Brandom then re-delivered the lectures; each of the six was followed by a critical paper and Professor Brandom’s response. The critics were John McDowell, John MacFarlane, Pirmin Stekeler-Weithofer, Huw Price, Jaroslav Peregrin, and Sebastian Rödl. This volume is made up of their (revised) papers and Professor Brandom’s responses, along with a paper by Paul Horwich summarizing the material he contributed to the “School of Inferentialism” and an introductory essay by professor Brandom himself. With the publication of the lectures in book form, it is hoped that the papers from the Prague conference will serve as a guide and stimulus to readers and recapture what Professor Brandom describes as “intense and thought-provoking conversations about this material” at the Prague conference.1 I am most grateful to the contributors to this volume and especially to Professor Brandom for his help at every stage. Edward Minar Editor, Philosophical Topics

NOTE 1. Robert Brandom, Between Saying and Doing: Towards an Analytic Pragmatism (Oxford: Oxford University Press, 2008), xx.

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PHILOSOPHICAL TOPICS VOL. 36, NO. 2, FALL 2008

Towards an Analytic Pragmatism

Robert Brandom University of Pittsburgh

Within the Anglophone tradition, pragmatism has often appeared as a current of thought that stands apart from, and indeed runs in opposition to, the mainstream of analytic philosophy. This is true whether one uses ‘pragmatist’ in a narrow sense tailored to the triumvirate of Peirce, James, and Dewey (here one might think of Russell’s dismissive responses to the latter two), or in a more capacious sense that includes the early Heidegger, the later Wittgenstein, and, more recently, neo-pragmatists such as Rorty and Putnam. There are good reasons on both sides for adopting somewhat adversarial stances, but I think that when we examine them more closely it becomes possible to see the outlines of a common project, in the service of which the two camps might find themselves joining forces. In my 2006 John Locke lectures, entitled Between Saying and Doing: Towards an Analytic Pragmatism (Oxford University Press, 2008), I explore in more detail one way of pursuing such a project. In this essay I want to offer a sketch of the basic understanding of the principal aims of the two movements that motivates that more extended discussion, and to indicate in general terms the sort of pragmatic semantic analysis (not, I will be insisting, an oxymoron) that might emerge from unifying their only apparently disparate concerns. The intended spirit is irenic, synthetic, and constructive.

I. THE CLASSICAL PROJECT OF ANALYSIS I think of analytic philosophy as having at its center a concern with semantic relations between what I will call ‘vocabularies’. Its characteristic form of question is 1

whether and in what way one can make sense of the meanings expressed by one kind of locution in terms of the meanings expressed by another kind of locution. So, for instance, two early paradigmatic projects were to show that everything expressible in the vocabulary of number-theory, and again, everything expressible using definite descriptions, is expressible already in the vocabulary of first-order quantificational logic with identity. The nature of the key kind of semantic relation between vocabularies has been variously characterized during the history of analytic philosophy: as analysis, definition, paraphrase, translation, reduction of different sorts, truth-making, and various kinds of supervenience—to name just a few contenders. In each case, however, it is characteristic of classical analytic philosophy that logical vocabulary is accorded a privileged role in specifying these semantic relations. It has always been taken at least to be licit to appeal to logical vocabulary in elaborating the relation between analysandum and analysans—target vocabulary and base vocabulary. I will refer to this aspect of the analytic project as its commitment to ‘semantic logicism’.1 If we ask which were the vocabulary-kinds whose semantic relations it was thought to be important to investigate during this period, at least two core programs of classical analytic philosophy show up: empiricism and naturalism. These venerable modern philosophical traditions in epistemology and ontology respectively were transformed in the twentieth century, first by being transposed into a semantic key, and second by the application of the newly available logical vocabulary to the self-consciously semantic programs they then became. As base vocabularies, different species of empiricism appealed to phenomenal vocabulary, expressing how things appear, or to secondary-quality vocabulary, or, less demandingly, to observational vocabulary. Typical target vocabularies include objective vocabulary formulating claims about how things actually are (as opposed to how they merely appear), primary-quality vocabulary, theoretical vocabulary, and modal, normative, and semantic vocabularies. The generic challenge is to show how what is expressed by the use of such target vocabularies can be reconstructed from what is expressed by the base vocabulary, when it is elaborated by the use of logical vocabulary. As base vocabularies, different species of naturalism appealed to the vocabulary of fundamental physics, or to the vocabulary of the natural sciences (including the special sciences) more generally, or just to objective descriptive vocabulary, even when not regimented by incorporation into explicit scientific theories. Typical targets include normative, semantic, and intentional vocabularies.

II. THE PRAGMATIST CHALLENGE What I want to call the “classical project of analysis,” then, aims to exhibit the meanings expressed by various target vocabularies as intelligible by means of the logical

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elaboration of the meanings expressed by base vocabularies thought to be privileged in some important respects—epistemological, ontological, or semantic— relative to those others. This enterprise is visible in its purest form in what I have called the “core programs” of empiricism and naturalism, in their various forms. In my view the most significant conceptual development in this tradition—the biggest thing that ever happened to it—is the pragmatist challenge to it that was mounted during the middle years of the twentieth century. Generically, this movement of thought amounts to a displacement from the center of philosophical attention of the notion of meaning in favor of that of use: in suitably broad senses of those terms, replacing concern with semantics by concern with pragmatics. The towering figure behind this conceptual sea change is, of course, Wittgenstein. In characterizing it, however, it will be useful to approach his radical and comprehensive critique by means of some more local, semantically corrosive argumentative appeals to the practices of deploying various vocabularies rather than the meanings they express. Wilfrid Sellars (one of my particular heroes) criticizes the empiricist core program of the classical project of analysis on the basis of what one must do in order to use various vocabularies, and so to count as saying or thinking various things. He argues that none of the various candidates for empiricist base vocabularies are practically autonomous, that is, could be deployed in a language-game one played though one played no other. For instance, no discursive practice can consist entirely of making noninferential observation reports. For such reliably differentially elicited responses qualify as conceptually contentful or cognitively significant only insofar as they can serve as premises from which it is appropriate to draw conclusions, that is, as reasons for other judgments. Drawing such conclusions is applying concepts inferentially—that is, precisely not making noninferential observational use of them.2 Quine offers an even broader pragmatist objection, not only to the empiricist program, but to essential aspects of the whole analytic semantic project. For he attacks the very notion of meaning it presupposes. Quine is what I have elsewhere called a “methodological” pragmatist.3 That is, he takes it that the whole point of a theory of meaning is to explain, codify, or illuminate features of the use of linguistic expressions. He, like Dummett, endorses the analogy: meaning is to use as theory is to observation. And he argues that postulating meanings associated with bits of vocabulary yields a bad theory of discursive practice. If there were such things as meanings that determine how it would be correct to use our expressions, then those meanings would at least have to determine the inferential roles of those expressions: what follows from applying them, what applying them rules out, what is good evidence for or against doing so. But what follows from what depends on what else is true—on laws of nature and obscure contingent facts—that is, on what claims can serve as auxiliary hypotheses or collateral premises in those inferences. If we look at what practical abilities are required to deploy various bits of vocabulary—at what one has to be able to do in order to count as saying something with them—we do not find any special set of these whose practical

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significance can be understood as pragmatically distinctive of semantically necessary or sufficient conditions.4 Quine thought one could save at least the naturalist program by retreating semantically to the level of reference and truth-conditions. James and Dewey appeal to the same sort of methodological pragmatism in support of more sweeping sorts of semantic revisionism—pursuing programs that Rorty, for instance, argues should be understood as more rejectionist than properly revisionist. And under the banner “Don’t look to the meaning, look to the use,” Wittgenstein further radicalizes the pragmatist critique of semantics. Pointing out to begin with that one cannot assume that uses of singular terms have the job of picking out objects, nor that declarative sentences are in the business of stating facts, he goes on to deny, in effect, that such uses even form a privileged center, on the basis of which one can understand more peripheral ones. (“Language,” he says, “has no downtown.”) I take it that Wittgenstein also takes the home language-game of the concept of meaning to be explanation of how expressions are correctly used. And he is profoundly skeptical about the utility or applicability of the model of postulation, explanation, and theoretical systematization in the case of discursive practices— about the possibility of systematically deriving aspects of correct use from assigned meanings. Seen from this perspective, the idea of the classical project of analysis is to codify, using logical vocabulary, the meanings expressed by one vocabulary— from which we are to derive proprieties of its use—from the meanings expressed by some other vocabulary—from which we can derive proprieties of its use. One idea, I think is that this enterprise makes sense only if we think of the uses as species of a genus—of them all being the same general kind of use, say describing, stating facts, or representing states of affairs. This may seem plausible if we focus on a very restricted set of uses—just as, in the case of tools, we might be impressed to notice that nails and hammer, screws and screwdriver, glue and brush all have the function of attaching more-or-less flat things to one another. So we can think of declarative sentences as stating empirical, physical, normative, modal, and intentional facts, making claims about such states of affairs (even if we then find ourselves metaphysically puzzled about the nature of the fact-kinds to which we have thereby committed ourselves). But if we think of the uses as very different, if we think also about the carpenter’s level, pencil, and tool belt, if we think of linguistic practice as a motley, of uses as not coming in a simple, or systematic, or even determinate variety, then the very idea that there is such a thing as meanings that permit the codification of proprieties of quite disparate kinds of use—even with liberal use of logical elaboration of the meanings—becomes contentious and in need of justification both in general and in each particular case. More specifically, Wittgenstein uses the image of “family resemblances” to urge that the kinds into which linguistic practices and the vocabularies caught up in them are functionally sorted—what belong together in boxes labeled ‘game’, ‘name’, ‘description’, ‘assertion’, ‘observation’, and so on—do not typically admit of specification in terms of underlying principles specifiable in other vocabularies, whether

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by genus and differentia(e) or any other kind of explicit rule or definition. It is easy to understand this line of thought as entailing a straightforward denial of the possibility of semantic analysis in the classical sense. One thought underlying these observations about the unsystematic, unsurveyable variety of kinds of uses of expressions and about the uncodifiable character of those kinds concerns the essentially dynamic character of linguistic practice. I think Wittgenstein thinks that an absolutely fundamental discursive phenomenon is the way in which the abilities required to deploy one vocabulary can be practically extended, elaborated, or developed so as to constitute the ability to deploy some further vocabulary, or to deploy the old vocabulary in quite different ways. Many of his thought-experiments concern this sort of process of pragmatic projection of one practice into another. We are asked to imagine a community that uses proper names only for people, but then extends the practice to include rivers. There is no guarantee that interlocutors can master the extended practice, building on what they can already do. But if they can, then they will have changed the only sessences proper-name usage could be taken to have had.5 In the old practice it always made sense to ask for the identity of the mother and father of the named item; in the new practice, that question is often senseless. Again, we are asked to imagine a community that talked about having gold or silver in one’s teeth, and extends that practice to talk about having pain in one’s teeth. If as a matter of contingent fact the practitioners can learn to use the expression ‘in’ in the new way, building on but adapting the old, they will have fundamentally changed the smeanings of ‘in’. In the old practice it made sense to ask where the gold was before it was in one’s tooth; in the new practice asking where the pain was before it was in the tooth can lead only to a distinctively philosophical kind of puzzlement.6 At every stage, what practical extensions of a given practice are possible for the practitioners can turn on features of their embodiment, lives, environment, and history that are contingent and wholly particular to them. And which of those developments actually took place, and in what order, can turn on any obscure fact. The reason vocabulary-kinds resist specification by rules, principles, definitions, or meanings expressed in other vocabularies is that they are the current time-slices of processes of development of practices that have this dynamic character—and that is why the collection of uses that is the current cumulative and collective result of such developments-by-practical-projection is a motley.7 If that is right, then any codification or theoretical systematization of the uses of those vocabulary-kinds by associating with them meanings that determine which uses are correct will, if at all successful, be successful only contingently, locally, and temporarily. Semantics on this view is an inherently Procrustean enterprise, which can proceed only by theoretically privileging some aspects of the use of a vocabulary that are not at all practically privileged, and spawning philosophical puzzlement about the intelligibility of the rest.8 On this conception, the classical project of analysis is disease that rests on a fundamental, if perennial, misunderstanding—one that can be removed or ameliorated only by heeding the advice to replace concern with meaning by concern

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with use. The recommended philosophical attitude to discursive practice is accordingly descriptive particularism, theoretical quietism, and semantic pessimism.

III. EXTENDING THE PROJECT OF ANALYSIS: PRAGMATICALLY MEDIATED SEMANTIC RELATIONS On this account Wittgenstein is putting in place a picture of discursive meaningfulness or significance that is very different from that on which the classical project of analysis is predicated. In place of semantics, we are encouraged to do pragmatics—not in the sense of Kaplan and Stalnaker, which is really the semantics of token-reflexive expressions, nor again in the sense of Grice, which addresses conversational heuristics in terms that presuppose a prior, independent, classical semantics—but ‘pragmatics’ in the sense of the study of the use of expressions in virtue of which they are meaningful at all. To the formal, mathematically inspired tradition of Frege, Russell, Carnap, and Tarski, culminating in model-theoretic and possible-worlds semantics, is opposed an anthropological, natural-historical, socialpractical inquiry aimed both at demystifying our discursive doings, and at deflating philosophers’ systematic and theoretical ambitions regarding them. I think that contemporary philosophers of language have tended to draw this opposition in the starkest possible terms, treating these approaches as mutually exclusive, hence as requiring that a choice be made between them, thereby marking out a substantial sociological faultline in the discipline. Those who are moved by the pragmatist picture generally accept the particularist, quietist conclusions Wittgenstein seems to have drawn from it. And those committed to some version of the project of semantic analysis have felt obliged to deny the significance of pragmatics in this sense, or at the least to dismiss it as irrelevant to properly semantic concerns. In the most extreme cases, the attitudes of anti-pragmatist philosophers of language to Wittgenstein’s picture verges on that of the Victorian lady to Darwin’s theory: One hopes that it is not true, and that if it is true, at least that it not become generally known. But I do not think we are obliged to choose between these approaches. They should be seen as complementing rather than competing with one another. Semantics and pragmatics, concern with meaning and concern with use, ought surely to be understood as aspects of one, more comprehensive, picture of the discursive. Pragmatist considerations do not oblige us to focus on pragmatics to the exclusion of semantics; we can deepen our semantics by the addition of pragmatics. If we extract consequences from the pragmatists’ observations somewhat more modestly and construe the analytic project somewhat more broadly, the two will be seen not only as compatible, but as mutually illuminating. If we approach the pragmatists’ observations in an analytic spirit, we can understand pragmatics as providing special resources for extending and expanding the analytic semantic project, from exclu-

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sive concern with relations among meanings to encompass also relations between meaning and use. In its most ambitious form, as in the present project, such an enterprise would aspire to articulate something like a logic of the relations between meaning and use. If we leave open the possibility that the use of some vocabulary may be illuminated by taking it to express some sort of meaning or content—that is, if we do not from the beginning embrace theoretical semantic nihilism—then the most important positive pragmatist insight will be one complementary to the methodological pragmatism I have already identified. The thought underlying the pragmatist line of thought is that what makes some bit of vocabulary mean what it does is how it is used. What we could call semantic pragmatism is the view that the only explanation there could be for how a given meaning gets associated with a vocabulary is to be found in the use of that vocabulary: the practices by which that meaning is conferred or the abilities whose exercise constitutes deploying a vocabulary with that meaning. To broaden the classical project of analysis in the light of the pragmatists’ insistence on the centrality of pragmatics, we can focus on this fundamental relation between use and meaning, between practices or practical abilities and vocabularies. We must look at what it is to use locutions as expressing meanings—that is, at what one must do in order to count as saying what the vocabulary lets practitioners express. I am going to call this kind of relation “practice-vocabulary sufficiency”— or usually, “PV-sufficiency,” for short. It obtains when engaging in a specified set of practices or exercising a specified set of abilities9 is sufficient for someone to count as deploying a specified vocabulary. Of course it matters a lot how we think about these content-conferring, vocabulary-deploying practices or abilities. The semantic pragmatist’s claim that use confers meaning (so talk of practices or the exercise of abilities as deploying vocabularies) reverts to triviality if we are allowed to talk about “using the tilde to express negation,” “the ability to mean red by the word ‘red’,” or “the capacity to refer to electrons by the word ‘electron’” (or, I think, even intentions so to refer). And that is to say that the interest of the PV-sufficiency of some set of practices or abilities for the deploying of a vocabulary is quite sensitive to the vocabulary in which we specify those practices-or-abilities. Talk of practices-or-abilities has a definite sense only insofar as it is relativized to the vocabulary in which those practicesor-abilities are specified. And that means that besides PV-sufficiency, we should consider a second basic meaning-use relation: “vocabulary-practice sufficiency,” or just “VP-sufficiency,” is the relation that holds between a vocabulary and a set of practices-or-abilities when that vocabulary is sufficient to specify those practicesor-abilities.10 VP-sufficient vocabularies that specify PV-sufficient practices let one say what it is one must do to count as engaging in those practices or exercising those abilities, and so to deploy a vocabulary to say something. PV-sufficiency and VP-sufficiency are two basic meaning-use relations (MURs). In terms of those basic relations, we can define a more complex relation: the relation that holds between vocabulary V’ and vocabulary V when V’ is VP-sufficient to

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specify practices-or-abilities P that are PV-sufficient to deploy vocabulary V. This VV-relation is the composition of the two basic MURs. When it obtains I will say that V’ is a pragmatic metavocabulary for V. It allows one to say what one must do in order to count as saying the things expressed by vocabulary V. We can present this relation graphically in a meaning-use diagram (MUD): The conventions of this diagram are:

Meaning-Use Diagram #1: Pragmatic Metavocabulary

V Res: VV-1,2

V'

2: VP-suff

1: PV-suff

P

• Vocabularies are shown as ovals, practices-or-abilities as (rounded) rectangles. • Basic meaning-use relations are indicated by solid arrows, numbered, and labeled as to kind of relation. • Resultant meaning-use relations are indicated by dotted arrows, numbered, and labeled as to kind and the basic MURs from which they result. The idea is that a resultant MUR is the relation that obtains when all of the basic MURs listed on its label obtain. Being a pragmatic metavocabulary is the simplest species of the genus I want to introduce here. It is a pragmatically mediated semantic relation between vocabularies. It is pragmatically mediated by the practices-or-abilities that are specified by one of the vocabularies (which say what counts as doing that) and that deploy or are the use of the other vocabulary (what one says by doing that). The semantic relation that is established thereby between the two vocabularies is of a distinctive sort, quite different from, for instance, definability, translatability, reducibility, and supervenience. My basic suggestion for extending the classical project of analysis so as to incorporate as essential positive elements the insights that animate the pragmatist critique of that project is that, alongside the classical semantic relations between vocabularies that project has traditionally appealed to, we con-

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sider also pragmatically mediated ones—of which the relation of being a pragmatic metavocabulary is a paradigm. Under what circumstances would this simplest pragmatically mediated semantic relation be philosophically interesting, when considered in connection with the sorts of vocabularies that have traditionally been of most interest to classical analysis? At least one sort of result that could be of considerable potential significance, I think, is if it turned out that in some cases pragmatic metavocabularies exist that differ significantly in their expressive power from the vocabularies for the deployment of which they specify sufficient practices-or-abilities. I will call that phenomenon “pragmatic expressive bootstrapping.” If one vocabulary is strictly weaker in expressive power than the other, I will call that relations—though of course it is not expressed in terms of the machinery I have been introducing—is Huw Price’s pragmatic normative naturalism.11 He argues, in effect, that although normative vocabulary is not reducible to naturalistic vocabulary, it might still be possible to say in wholly naturalistic vocabulary what one must do in order to be using normative vocabulary. If such a claim about the existence of an expressively bootstrapping naturalistic pragmatic metavocabulary for normative vocabulary could be made out, it would evidently be an important chapter in the development of the naturalist core program of the classical project of philosophical analysis. It would be a paradigm of the sort of payoff we could expect from extending that analytic project by including pragmatically mediated semantic relations. (Later on I’ll discuss briefly a claim of this shape concerning indexical vocabulary.) The meaning-use diagram of the pragmatically mediated semantic relation of being a pragmatic metavocabulary illustrates a distinctive kind of analysis of that relation. It exhibits that relation as the resultant, by composition, of the two basic meaning-use relations of PV-sufficiency and VP-sufficiency. A complex MUR is analyzed as the product of operations applied to basic MURs. This is meaning-use analysis. The same analytic apparatus applies also to more complex pragmatically mediated semantic relations. Consider one of the pragmatist criticisms that Sellars addresses to the empiricist core program of the classical analytic project. It turns on the assertion of the pragmatic dependence of one set of vocabulary-deploying practices-or-abilities on another. Because he thinks part of what one is doing in saying how things merely appear is withholding a commitment to their actually being that way, and because one cannot be understood as withholding a commitment that one cannot undertake, Sellars concludes that one cannot have the ability to say or think how things seem or appear unless one also has the ability to make claims about how things actually are. In effect, this Sellarsian pragmatist critique of the phenomenalist form of empiricism consists in the claim that the practices that are PV-sufficient for ‘is’-j talk are PP-necessary for the practices that are PV-sufficient for ‘looks’-j talk.12 That pragmatic dependence of practices-or-abilities then induces a resultant pragmatically mediated semantic relation between the vocabularies. The meaning-use diagram for this claim is:

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Meaning-Use Diagram #2: Pragmatically Mediated Semantic Presupposition

Vlooks- f

Res1:VV 1,2,3

3:PV-suff

Plooks- f

Vis- f 1:PV-suff

2:PP-nec

Pis- f

The resultant MUR here is a kind of complex, pragmatically mediated, VV-necessity, or semantic presupposition. In fact, although Sellars’s argument for the crucial PP-necessity relation of pragmatic dependence of one set of vocabulary-deploying practices-or-abilities on another is different, his argument against the observational version of empiricism—the claim that purely noninferential, observational uses do not form an autonomous discursive practice, but presuppose inferential uses—has exactly the same form:

Meaning-Use Diagram #3: Pragmatically Mediated Semantic Presupposition

Vobservational

Res1:VV 1,2,3

3:PV-suff

Pobservational

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Vinferential 1:PV-suff

2:PP-nec

Pinferential

For these cases, we can say something further about the nature of the pragmatically mediated semantic relation that is analyzed as the resultant MUR in these diagrams. For instead of jumping directly to this VV resultant MUR, we could have put in the composition of the PP-necessity and second PV-sufficiency relation, yielding a kind of complex pragmatic presupposition: Meaning-Use Diagram #4: Composition

Vlooks- f

Vis- f Res2:PV 2,3

3:PV-suff

Plooks- f

2:PP-nec

1:PV-suff

Pis- f

If this diagram were completed by an arrow from Vis-f to Vlooks-f such that the same diagonal resultant arrow could represent both the composition of relations 2 and 3 and the composition of relation 1 and the newly supplied one, then category theorists would say that the diagram commutes. And the arrow that needs to be supplied to make the diagram commute they call the retraction of relation 1 through the composition Res2:

Meaning-Use Diagram #5: Composition and Retraction

Vlooks- f 3:PV-suff

Plooks- f

Retraction of 1 throughRes2

Res2:PV 2,3

2:PP-nec

Vis- f 1:PV-suff

Pis- f

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After composition, then, the next most complex form of resultant MUR is retraction. Analyzing the structure of Sellars’s pragmatist arguments against empiricism requires recognizing the pragmatically mediated semantic relation he claims holds between phenomenal and objective vocabulary as the retraction of a constellation of more basic meaning-use relations.

IV. AUTOMATA: SYNTACTIC PV-SUFFICIENCY AND VP-SUFFICIENCY Now this is all extremely abstract. To make it more definite, we need to fill in (at least) the notions of vocabulary, practice-or-ability, PV-sufficiency, and VP-sufficiency, which are the fundamental elements that articulate what I am calling the “meaning-use analysis” of resultant meaning-use relations—in particular, the pragmatically mediated semantic relations between vocabularies that I am claiming we must acknowledge in order to pursue the classical project of philosophical analysis in the light of what is right about the pragmatist critique of it. We can begin to do that by looking at a special case in which it is possible to be unusually clear and precise about the things and relations that play these metatheoretic roles. This is the case where ‘vocabulary’ takes a purely syntactic sense. Of course, the cases we eventually care about involve vocabularies understood in a sense that includes their semantic significance. But besides the advantages of clarity and simplicity, we will find that some important lessons carry over from the syntactic to the semantic case. The restriction to vocabularies understood in a spare syntactic sense leads to correspondingly restricted notions of what it is to deploy such a vocabulary, and what it is to specify practices-or-abilities sufficient to deploy one. Suppose we are given an alphabet, which is a finite set of primitive sign types—for instance, the letters of the English alphabet. The universe generated by that alphabet then consists of all the finite strings that can be formed by concatenating elements drawn from the alphabet. A vocabulary over such an alphabet—in the syntactic sense I am now after—is then any subset of the universe of strings that alphabet generates. If the generating alphabet is the English alphabet, then the vocabulary might consist of all English sentences, all possible English texts, or all and only the sentences of Making It Explicit.13 What can we say about the abilities that count as deploying a vocabulary in this spare syntactic sense?14 The abilities in question are the capacity to read and write the vocabulary. In this purely syntactic sense, ‘reading’ it means being able practically to distinguish within the universe generated by the alphabet, strings that do, from those that do not, belong to the specified vocabulary. And ‘writing’ it means practically being able to produce all and only the strings in the alphabetic universe that do belong to the vocabulary. We assume as primitive abilities the capacities to read and write, in this sense, the alphabet from whose universe the vocabulary is drawn—that is, the capacity to

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respond differentially to alphabetic tokens according to their type, and to produce tokens of antecedently specified alphabetic types. Then the abilities that are PV-sufficient to deploy some vocabularies can be specified in a particularly simple form. They are finite-state automata (FSAs). As an example, suppose we begin with the alphabet {a, h, o, !}. Then we can consider the laughing Santa vocabulary, which consists of strings such as ‘hahaha!’, ‘hohoho!’, ‘hahahoho!’, ‘hohoha!’, and so on.15 Here is a graphical representation of a laughing Santa finite-state automaton, which can read and write the laughing Santa vocabulary: The Laughing Santa Automaton

a 1

h

2

o

3

!

4

h The numbered nodes represent the states of the automaton, and the alphabetically labeled arcs represent state-transitions. By convention, the starting state is represented by a square (State 1), and the final state by a circle with a thick border (State 4). As a reader of the laughing Santa vocabulary, the task of this automaton is to process a finite string, and determine whether or not it is a licit string of the vocabulary. It processes the string one alphabetic character at a time, beginning in State 1. It recognizes the string if and only if (when and only when) it arrives at its final state, State 4. If the first character of the string is not an ‘h’, it remains stuck in State 1, and rejects the string. If the first character is an ‘h’, it moves to State 2, and processes the next character. If that character is not an ‘a’ or an ‘o’, it remains stuck in State 2, and rejects the string. If the character is an ‘a’ or an ‘o’, it moves to State 3. If the next character is an exclamation point, it moves to State 4, and recognizes the string ‘ha!’ or ‘ho!’—the shortest ones in the laughing Santa vocabulary. If instead the next character is an ‘h’, it goes back to State 2, and repeats itself in loops of ‘ha’s and ‘ho’s any number of times until an exclamation point is finally reached, or it is fed a discordant character. As a writer of the laughing Santa vocabulary, the task of the automaton is to produce only licit strings of that vocabulary, by a process that can produce any and all such strings. It begins in its initial state, State 1, and emits an ‘h’ (its only available move), changing to State 2. In this state, it can produce either an ‘a’ or an ‘o’— it selects one at random16—and goes into State 3. In this state, it can either tack on an exclamation point, and move into its final state, State 4, finishing the process, or

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emit another ‘h’ and return to State 2 to repeat the process. In any case, whenever it reaches State 4 and halts, the string it has constructed will be a member of the laughing Santa vocabulary. I hope this brief rehearsal makes it clear how the constellation of nodes and arrows that makes up this directed graph represents the abilities to read and write (recognize and produce arbitrary strings of) the laughing Santa vocabulary.17 What it represents is abilities that are PV-sufficient to deploy that vocabulary—that is, read and write it, in the attenuated sense appropriate to this purely syntactic case. And the digraph representation is itself a vocabulary that is VP-sufficient to specify those vocabulary-deploying abilities. That is, the digraph representation of this finitestate automaton is a pragmatic metavocabulary for the laughing Santa vocabulary. The relation between the digraph vocabulary and the laughing Santa vocabulary is, then, a pragmatically mediated—not now semantic, but syntactic—relation between vocabularies. It may seem that I am stretching things by calling the digraph form of representation a ‘vocabulary’. It will be useful, as a way of introducing my final point in the vicinity, to consider a different form of pragmatic metavocabulary for the laughing Santa vocabulary. Besides the digraph representation of a finite-state automaton, we can also use a state-table representation. For the laughing Santa automaton this is: State 1 State 2 State 3 a Halt 3 Halt h 2 Halt 2 o Halt 3 Halt ! Halt Halt 4 In read mode, the automaton starts in State 1. To see what it will do if fed a particular character, we look at the row labeled with that character. The LSA will Halt if the input string starts with anything other than an ‘h’, in which case it will change to State 2. In that state, the automaton specified by the table will halt unless the next character is an ‘a’ or an ‘o’, in which case it changes to State 3, and so on. (There is no column for State 4, since it is the final state, and accepts/produces no further characters.) Clearly there is a tabular representation corresponding to any digraph representation of an FSA, and vice versa. Notice further that we need not use a twodimensional table to convey this information. We could put the rows one after another, in the form: aHalt3Halth2Halt2oHalt3Halt!HaltHalt4. This is just a string, drawn from a universe generated by the alphabet of the LSA, together with ‘Halt’ and the designations of the states of that automaton. The strings that specify finite-state automata that deploy vocabularies defined over the same basic alphabet as the LSA then form a vocabulary in the technical syntactic sense we have been considering. And that means we can ask about the automata

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that can read and write those state-table encoding vocabularies. The meaning-use diagram for this situation is then:

Meaning-Use Diagram #6: Specifying the Automaton that Deploys the Laughing Santa Vocabulary

VLaughing Santa Res: VV-1,2 1: PV-suff

VLSA StateTable

2: VP-suff

PLaughing Santa Automaton

3: PV-suff

PLSA State-Table Automaton

V. THE CHOMSKY HIERARCHY AND A SYNTACTIC EXAMPLE OF PRAGMATIC EXPRESSIVE BOOTSTRAPPING Restricting ourselves to a purely syntactic notion of a vocabulary yields a clear sense of ‘pragmatic metavocabulary’: both the digraph and the state-table vocabularies are VP-sufficient to specify practical abilities articulated as a finite-state automaton that is PV-sufficient to deploy—in the sense of recognizing and producing—the laughing Santa vocabulary, as well as many others. (Of course, it does that only against the background of a set of abilities PV-sufficient to deploy those vocabularies.) Perhaps surprisingly, it also offers a prime example of strict pragmatic expressive bootstrapping. For in this setting we can prove that one vocabulary that is expressively weaker than another can nonetheless serve as an adequate pragmatic metavocabulary for that stronger vocabulary. That is, even though one cannot say in the weaker vocabulary everything that can be said in the stronger one, one can still say in the weaker one everything that one needs to be able to do in order to deploy the stronger one. Here the relevant notion of the relative expressive power of vocabularies is also a purely syntactic one. Already in the 1950s, Chomsky offered mathematical characterizations of the different sets of strings of characters that could be generated by

15

different classes of grammars (that is, in my terms, characterized by different kinds of syntactic metavocabularies) and computed by different kinds of automata. The kinds of vocabulary, grammar, and automata lined up with one another, and could be arranged in a strict expressive hierarchy: the Chomsky hierarchy. It is summarized in the following table: Vocabulary Regular Context-Free

Grammar AÆaB AÆa AÆ

Context-Sensitive

c1Ac2Æc1c2

Recursively Enumerable

No Restrictions on Rules

Automaton Finite State Automaton Push-Down Automaton Linear Bounded Automaton Turing Machine (= 2 Stack PDA)

The point I want to make fortunately does not require us to delve very deeply into the information summarized in this table. A few basic points will suffice. The first thing to realize is that not all vocabularies in the syntactic sense we have been pursuing can be read and written by finite-state automata. For instance, it can be shown that no finite-state automaton is PV-sufficient to deploy the vocabulary anbn, defined over the alphabet {a,b}, which consists of all strings of any arbitrary number of ‘a’s followed by the same number of ‘b’s. The idea behind the proof is that in order to tell whether the right number of ‘b’s follow the ‘a’s (when reading) or to produce the right number of ‘b’s (when writing), the automaton must somehow keep track of how many ‘a’s have been processed (read or written). The only way an FSA can store information is by being in one state rather than another. So, it could be in one state—or in one of a class of states—if one ‘a’ has been processed, another if two have, and so on. But by definition, a finite-state automaton only has a finite number of states, and that number is fixed in advance of receiving its input or producing its output. Whatever that number of states is, and whatever system it uses to code numbers into states (it need not be one-to-one—it could use a decimal coding, for instance), there will be some number of ‘a’s that is so large that the automaton runs out of states before it finishes counting. But the vocabulary in question consists of arbitrarily long strings of ‘a’s and ‘b’s. In fact, it is possible to say exactly which vocabularies finite-state automata (specifiable by digraphs and state-tables of the sort illustrated above) are capable of deploying. These are called the ‘regular’ vocabularies (or languages). The next point is that slightly more complex automata are capable of deploying vocabularies, such as anbn, that are not regular, and hence cannot be read or written by finite-state automata. As our brief discussion indicated, intuitively the problem FSAs have with languages like anbn is that they lack memory. If we give them a memory, we get a new class of machines: (nondeterministic18) push-down

16

automata (PDAs). In addition to being able to respond differentially to and produce tokenings of the alphabetic types, and being able to change state, PDAs can push alphabetic values to the top of a memory-stack, and pull such values from the top of that stack. PDAs can do everything that finite-state automata can do, but they can also read and write many vocabularies, such as anbn, that are not regular, and so cannot be read and written by FSAs. The vocabularies they can deploy are called “context-free.” All regular vocabularies are context-free, but not vice versa. This proper containment of classes of vocabularies provides a clear sense, suitable to this purely syntactic setting, in which one vocabulary can be thought of as “expressively more powerful” than another: the different kinds of grammar can specify, and the different kinds of automata can compute, ever larger classes of vocabularies. Context-free vocabularies that are not regular require more powerful grammars to specify them, as well as more powerful automata to deploy them. FSAs are special kinds of PDAs, and all the automata are special kinds of Turing machines. Recursively enumerable vocabularies are not in general syntactically reducible to context-sensitive, context-free, or regular ones. And the less capable automata cannot read and write all the vocabularies that can be read and written by Turing machines. Nonetheless, if we look at pragmatically mediated relations between these syntactically characterized vocabularies, we find that they make possible a kind of strict expressive bootstrapping that permits us in a certain sense to evade the restrictions on expressive power enforced for purely syntactic relations between vocabularies. The hierarchy dictates that only the abilities codified in Turing machines—twostack push-down automata—are PV-sufficient to deploy recursively enumerable vocabularies in general. But now we can ask: what class of languages is VP-sufficient to specify Turing machines, and hence to serve as sufficient pragmatic metavocabularies for recursively enumerable vocabularies in general? The surprising fact is that the abilities codified in Turing machines—the abilities to recognize and produce arbitrary recursively enumerable vocabularies—can quite generally be specified in context-free vocabularies. It is demonstrable that context-free vocabularies are strictly weaker in syntactic expressive resources than recursively enumerable vocabularies. The push-down automata that can read and write only context-free vocabularies cannot read and write recursively enumerable vocabularies in general. But it is possible to say in a context-free vocabulary what one needs to be able to do in order to deploy recursively enumerable vocabularies in general. The proof of this claim is tedious, but not difficult, and the claim itself is not at all controversial—though computational linguists make nothing of it, having theoretical concerns very different from those that lead me to underline this fact. (My introductory textbook leaves the proof as an exercise to the reader.19) Generalpurpose computer languages such as Pascal and C++ can specify the algorithms a Turing machine, or any other universal computer, uses to compute any recursively enumerable function, hence to recognize or produce any recursively enumerable vocabulary. And they are invariably context-free languages20—in no small part just

17

because the simplicity of this type of grammar makes it easy to write parsers for them. Yet they suffice to specify the state-table, contents of the tape (or of the dual stacks), and primitive operations of any and every Turing machine. Here is the MUD characterizing this pragmatically mediated relation between syntactically characterized vocabularies: Meaning-Use Diagram #7: Syntactic Pragmatic Expressive Bootstrapping

VRecursively Enumerable Res1: VV-1,2 1: PV-suff

VContextFree

2: VP-suff

PTuring Machine

3: PV-suff

PPush-Down Automaton

I called the fact that context-free vocabularies can be adequate pragmatic metavocabularies for recursively enumerable vocabularies in general ‘surprising’, because of the provable syntactic irreducibility of the one class of vocabularies to the other. But if we step back from the context provided by the Chomsky hierarchy, we can see why the possibility of such pragmatic expressive bootstrapping should not, in the end, be surprising. For all the result really means is that context-free vocabularies let one say what it is one must do in order to say things they cannot themselves say, because the ability to deploy those context-free vocabularies does not include the abilities those vocabularies let one specify. Thus, for instance, there is no reason that an FSA could not read and write a vocabulary that included commands such as “Push an ‘a’ onto the stack,”—and thus specify the program of a PDA—even though it itself has no stack, and could not do what the vocabulary it is deploying specifies. A coach might be able to tell an athlete exactly what to do, and even how to do it, even though the coach cannot himself do what he is telling the athlete to do, does not have the abilities he is specifying. We ought not to boggle at the possibility of an expressively weaker pragmatic metavocabulary having the capacity to say what one must do in order to deploy an expressively stronger one. We should just look to see where this seems in fact to be possible for vocabularies we care about, and what we can learn from such relations when they do obtain.

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VI. SEMANTIC EXAMPLES OF PRAGMATIC EXPRESSIVE BOOTSTRAPPING AND FURTHER BASIC AND RESULTANT MURS Let us recall what motivated this rehearsal of some elements of automaton theory and introductory computational linguistics. I suggested that a way to extend the classical project of semantic analysis so as to take account of the insights of its pragmatist critics is to look analytically at relations between meaning and use. More specifically, I suggested focusing to begin with on two in some sense complementary relations: the one that holds when some set of practices-or-abilities is PV-sufficient to deploy a given vocabulary, and the one that holds when some vocabulary is VP-sufficient to specify a given set of practices-or-abilities. The composition of these is the simplest pragmatically mediated semantic relation between vocabularies: the relation that holds when one vocabulary is a sufficient pragmatic metavocabulary for another. It is a paradigm of the infinite, recursively generable class of complex, pragmatically mediated semantic relations that I propose to lay alongside the other semantic relations between vocabularies that have been investigated by analytic philosophers (for instance those who address the core programs of empiricism and naturalism): relations such as analyzability, definition, translation, reduction, truth-making, and supervenience. I suggested further that pragmatic metavocabularies might be of particular interest in case they exhibited what I called “expressive bootstrapping”—cases, that is, in which the expressive power of the pragmatic metavocabulary differs markedly from that of the target vocabulary, most strikingly, when the metavocabulary is substantially expressively weaker—a phenomenon Tarski has led us not to expect for semantic metavocabularies, which in general must be expressively stronger than the vocabularies they address. We have now seen that all of these notions can be illustrated with particular clarity for the special case of purely syntactically characterized vocabularies. The abilities that are PV-sufficient to deploy those vocabularies, in the sense of the capacity to recognize and produce them, can be thought of as various sorts of automata. There are several well-established, different-but-equivalent vocabularies that are known to be VP-sufficient to specify those automata. In this special syntactic case we can accordingly investigate the properties of pragmatic metavocabularies, and when we do, we find a striking instance of strict expressive bootstrapping in a pragmatically mediated syntactic relation between vocabularies. Of course, the cases we really care about involve semantically significant vocabularies. Are there any interesting instances of these phenomena in such cases? I have indicated briefly how some of Sellars’s pragmatist criticisms of various ways of pursuing the empiricist program can be understood to turn on pragmatically mediated semantic relations. And I mentioned Huw Price’s idea that although normative vocabulary is not semantically reducible to naturalistic vocabulary, naturalistic vocabulary might suffice to specify what one must do—the practices-or-abilities one must engage in or exercise—in order to deploy normative vocabulary. Here is another example that I want to point to, though I cannot develop the claim here.

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For roughly the first three-quarters of the twentieth century, philosophers who thought about indexical vocabulary took for granted some version of the doctrine that a tokening n of an expression of the type ‘now’ was synonymous with, definable or semantically analyzable as, ‘the time of utterance of n’, and similarly for ‘here’ and ‘the place of utterance of h,’ and so on. During the 1970s philosophers such as John Perry, David Lewis, and G. E. M. Anscombe, by focusing on the use of indexicals in modal and epistemic contexts, showed decisively that this cannot be right: what is expressed by indexical vocabulary cannot be expressed equivalently by nonindexical vocabulary. This fact seems so obvious to us now that we might be led to wonder what philosophers such as Russell, Carnap, and Reichenbach could have been thinking for all those years. I want to suggest that the genuine phenomenon in the vicinity is a pragmatically mediated semantic relation between these vocabularies. Specifically, in spite of the semantic irreducibility of indexical to nonindexical vocabulary, it is possible to say, entirely in nonindexical terms, what one must do in order to be deploying indexical vocabulary correctly: to be saying essentially and irreducibly indexical things. For we can formulate practical rules such as: If, at time t and place <x,y,z>, speaker s wants to assert that some property P holds of <x,y,z,t,s>, it is correct to say “P holds of me, here and now.” And If a speaker s at time t and place <x,y,z> asserts “P holds of me, here and now,” the speaker is committed to the property P holding of <x,y,z,t,s>. Nonindexical vocabulary can serve as an adequate pragmatic metavocabulary for indexical vocabulary. The fact that one nonetheless cannot say in nonindexical terms everything that one can say with indexical vocabulary just shows that these vocabularies have different expressive powers, so that the pragmatically mediated semantic relation between them is a case of strict pragmatic expressive bootstrapping. Here is another example. Besides pragmatically mediated semantic relations between vocabularies, there is another sort of pragmatic analysis, which relates one constellation of practices-or-abilities to another. It corresponds to another basic meaning-use relation: the kind of PP-sufficiency that holds when having acquired one set of abilities means one can already do everything one needs to do, in principle, to be able to do something else. One concrete way of filling in a definite sense of “in principle” is by algorithmic elaboration, where exercising the target ability just is exercising the right basic abilities in the right order and under the right circumstances. (Of course, this is just one species of the genus of practical projection that Wittgenstein brings to our attention.) As an example, the ability to do long division just consists in exercising the abilities to do multiplication and subtraction according to a particular conditional branched-schedule algorithm. The practical abilities that implement such an algorithmic PP-sufficiency relation are just those exercised by finite-state automata (in general, Turing machines). Indeed, automata should be

20

thought of as consisting in a definite set of meta-abilities: abilities to elaborate a set of primitive abilities into a set of more complex ones, which can accordingly be pragmatically analyzed in terms of or decomposed into the other.21 To get a usefully general concept of the PP-sufficiency of a set of basic abilities for a set of more complex ones, we need to move beyond the purely syntactic automata I have described so far. One way to do that is to replace their specialized capacities to read and write symbols—in the minimal sense of classifying tokens as to types and producing tokens of specified types—by more general recognitional and productive capacities. These are abilities to respond differentially to various in general nonsymbolic stimuli (for instance, the visible presence of red things), corresponding to reading, and to respond by producing performances of various in general nonsymbolic kinds (for instance, walking north for a mile), corresponding to writing. What practically implements the algorithmic elaboration of such a set of basic differential responsive abilities is a finite state transducing automaton (and its more sophisticated push-down brethren). A Finite-State Transducing Automaton

S1:R7

1

S4:R6

2

5

_:R7

4

3

S1:R3

S7:_

6

S3:_

This is a diagram of an FSTA that has an initial set of stimuli to which it can respond differentially, and an initial set of responses it can differentially produce. And the diagram indicates that in its initial state, if presented with a stimulus of kind 1, it will produce a response of kind 7 and shift to state 2, and if presented instead with a stimulus of kind 7 it will produce no response, but will shift to state 3. It is important to note that although the recognitive and performative abilities that such an automaton algorithmically elaborates are to be considered as ‘primitive’ or ‘basic’ with respect to such elaboration, this does not mean that they are so in any absolute sense. The stimulus-response formulation by itself does not keep us from considering as ‘primitive’ capacities the abilities to keep ourselves at a suitable

21

distance from a conversational partner, distinguish cubist paintings done by Braque from those done by Picasso, drive from New York to San Francisco, or build a house. The notion of the algorithmic decomposability of some practices-or-abilities into others suggests in turn a pragmatic generalization of the classical program of artificial intelligence functionalism—which, though a latecomer in the twentieth century, deserves, I think, to count as a third core program of classical semantic analysis, alongside empiricism and naturalism. AI functionalism traditionally held itself hostage to a commitment to the purely symbolic character of intelligence in the sense of sapience. But broadening our concern from automata as purely syntactic engines to the realm of transducing automata, we are now in a position to see automaton functionalism as properly concerned with the algorithmic decomposability of discursive (that is, vocabulary-deploying) practices-and-abilities. What I will call the ‘pragmatic’ thesis of artificial intelligence is the claim that the ability to engage in some autonomous discursive practice (a language game one could play though one played no other) can be algorithmically decomposed into nondiscursive abilities—where by “nondiscursive” abilities, I mean abilities each of which can in principle be exhibited by something that does not engage in any autonomous discursive practice. (Without that restriction on the primitive abilities out of which discursive ones are to be algorithmically elaborated, the claim would be trivial, since the null algorithmic decomposition is also a decomposition.) The capacity to talkand-think as I am addressing it is the capacity to deploy an autonomous vocabulary. But unlike classical symbolic AI, the pragmatic thesis of artificial intelligence does not presume that the practical capacities from which some transducing automaton can algorithmically elaborate the ability to engage in an autonomous discursive practice must themselves consist exclusively of symbol-manipulating abilities, never mind ultimately syntactic ones.22 The algorithmic practical elaboration model of AI gives a relatively precise shape to the pragmatist program of explaining knowing-that in terms of knowinghow: specifying in a nonintentional, nonsemantic vocabulary what it is one must do in order to count as deploying some vocabulary to say something, hence as making intentional and semantic vocabulary applicable to the performances one produces. In particular, it offers a construal of the basic claim of AI-functionalism as a pragmatic expressive bootstrapping claim about computer languages as pragmatic metavocabularies for much more expressively powerful autonomous vocabularies, namely natural languages. The arguments for and against this pragmatic version of AI-functionalism accordingly look quite different from those arrayed on the opposing sides of the debate about the prospects of symbolic AI. Combining the notion of PP-sufficiency that holds between two constellations of practices-or-abilities when one can be algorithmically elaborated from the other with the two sorts of basic meaning-use relations out of which I previously constructed the notion of expressively bootstrapping pragmatic metavocabularies— namely, a set of practices-or-abilities being PV-sufficient to deploy a vocabulary and a vocabulary being VP-sufficient to specify a set of practices-or-abilities—makes it

22

possible to define further kinds of pragmatically mediated semantic relations. As my final example, consider the relation between logical vocabulary—paradigmatically, conditionals—and ordinary, nonlogical, empirical descriptive vocabulary. I take it that every autonomous discursive practice must include performances that have the pragmatic significance of assertions and inferences (which I would argue come as an indissoluble package). I actually think this PP-necessary condition on any practices PV-sufficient for autonomously deploying a vocabulary can usefully be treated as sufficient as well—that is, as what distinguishes discursive practices as such. But nothing in what follows turns on that further commitment. To count as engaging in such practices, practitioners must exercise an ability, however fallible, to assess the goodness of material inferences: to sort them into those they accept and those they reject. This is part of what one must do in order to say anything. But it is easy to say how those recognitional and performative abilities, for these purposes counted as primitive, can be algorithmically elaborated into the capacity to use conditionals. An algorithm VP-sufficient to specify an automaton that practically implements such a pragmatic elaboration or PP-sufficiency relation is the following: • Assert the conditional ‘if p then q’ if one endorses the inference from p to q; • Endorse the inference from p to q if one asserts the conditional ‘if p then q’. These rules of usage codify introduction and elimination rules for the conditional. So the capacity to use conditionals can be algorithmically elaborated from the capacities to make assertions and assess inferences. This is the composition of a PPsufficiency relation with a PV-sufficiency relation, and is expressed in the following meaning-use diagram: Elaborating Conditionals

Vconditionals

Res1:VV 1–4

V1 1:PV-suff

4:PV-suff

2:PV-nec

Pconditionals

PAlgEl3:PP-suff

Pinferring/ asserting

5:PV-suff

PADP

VAlgorithm

23

The complex resultant meaning-use relation indicated by the dotted arrow at the top of the diagram is a further pragmatically mediated semantic relation. The diagram indicates exactly what constellation of sub-claims about basic meaning-use relations must be justified in order to justify the claim that this relation obtains between two vocabularies, and hence the diagram graphically presents a distinctive kind of meaning-use analysis of that semantic relation. In fact, if we think further about this example, by filling in another basic meaning-use relation that obtains in this case, we can define an even more articulated pragmatically mediated semantic relation between vocabularies. For when conditionals are deployed with the practical circumstances and consequences of application specified in the algorithm stated above, they let practitioners say what otherwise they could only do; that is, they express explicitly, in the form of a claimable, hence propositional, content, what practitioners are implicitly doing in endorsing some material inferences and rejecting others. This is a VP-sufficiency relation: conditionals let one specify the practices of taking-or-treating inferences as materially good or bad. Adding in this explicating relation between conditionals and the practices-or-abilities they make explicit yields a new pragmatically mediated semantic relation that conditionals stand in to every autonomously deployable vocabulary. Its meaning-use diagram is this: Elaborated-Explicating (LX) Conditionals

Vconditionals 4:PV-suff

Res1:VV 1–5

5:VP-suff

V1 1:PV-suff 2:PV-nec

Pconditionals

PAlgEl3:PP-suff

Pinferring

6:PV-suff

PADP

VAlgorithm The practical capacity to deploy conditionals (that is, something PV-sufficient for their use) both can be elaborated from practices PP-necessary for every ADP, and explicates those practices (in the sense of being VP-sufficient for them). It is elaborated-explicative relative to every autonomous vocabulary. We say, it is LX for every

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AV, hence for every vocabulary (since the use of any vocabulary presupposes, and in that sense is parasitic on, the capacity to use some autonomous vocabulary). I believe that this complex resultant pragmatically mediated semantic relation is important for understanding the distinctive semantic role played by logical vocabulary generally: not just conditionals, but also negation (which makes explicit a central feature of our practice of treating claims as materially incompatible), and even modal vocabulary (which makes explicit a central feature of our practice of associating ranges of counterfactual robustness with material inferences). In my initial characterization of the classical semantic project of philosophical analysis, I pointed to the special status that is accorded to logical vocabulary in that project. What I called “semantic logicism” is its commitment to the legitimacy of the strategy of using logical vocabulary to articulate the semantic relations between vocabularies that is its goal—paradigmatically in connection with the core projects of empiricism, naturalism, and functionalism. One interesting way to vindicate that commitment (that is, at once to explain and to justify it) would be to appeal to the fact that logical vocabulary is elaborated from and explicating of every autonomously deployable vocabulary whatsoever. For that means that the capacity to use logical vocabulary is both in this very clear and specific sense implicit in the capacity to use any vocabulary, and has the expressive function of making explicit something already present in the use of any vocabulary. I won’t say anything more here about how such a vindication might proceed, contenting myself with the observation that insofar as there is anything to an account along these lines, supplementing the traditional philosophical analytical concern with semantic relations between the meanings expressed by different kinds of vocabulary by worrying also about the pragmatic relations between those meanings and the use of those vocabularies in virtue of which they express those meanings is not so much extending the classical project of analysis as unpacking it, to reveal explicitly a pragmatic structure that turns out to have been implicit in the analytic semantic project all along. For the conclusion will be that it is because some vocabularies are universal pragmatically elaborated and explicitating vocabularies that semantic analysis of the logicist sort is both possible and legitimate at all. I don’t claim to have entitled myself to that conclusion here, only to have introduced some conceptual machinery that might make it possible to do so—and so at least to have sketched a way in which the insights of the pragmatist tradition can be assembled and developed so as to be constructively helpful to, rather than destructively critical of, the classical project of philosophical semantic analysis, and so to open the way to extending that project in promising new directions.

NOTES 1. In this usage, the logicism about mathematics characteristic of Frege’s Grundgesetze and Russell and Whitehead’s Principia is semantic logicism about the relations between mathematical and logical vocabularies.

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2. This argument occupies roughly the first half of his classic “Empiricism and the Philosophy of Mind” (reprinted by Harvard University Press, 1997). His critique of the phenomenalist version of empiricism can be found in “Phenomenalism,” in his collection Science, Perception, and Reality (Routledge Kegan Paul, 1963). 3. “Pragmatics and Pragmatisms,” in James Conant and Urszula M. Zeglen (eds.), Hilary Putnam: Pragmatism and Realism (Routledge, 2002), translated as “Pragmatik und Pragmatismus,” 29–58, in M. Sandbothe (ed.), Die Renaissance des Pragmatismus (Velbrück Wissenschaft, 2000). 4. Ibid. 5. Cf. Quine’s remark (in “Two Dogmas of Empiricism”): “Meaning is what essence becomes when it is detached from the thing and attached to the word.” 6. I am indebted for this way of thinking of Wittgenstein’s point to Hans Julius Schneider’s penetrating discussion in his Phantasie und Kalkul (Suhrkamp, 1992). 7. A patient and detailed investigation of the mechanisms of this phenomenon in basic descriptive and scientific concepts, and an extended argument for its ubiquity can be found in Mark Wilson’s exciting and original Wandering Significance (Oxford University Press, 2006). 8. I would be happy if those who dance with his texts find affinities here with Hegel’s insistence that the metaconceptual categories of Verstand must be replaced by those of Vernunft. It is characteristic of his philosophical ambition that draws the opposite of Wittgenstein’s conclusions from an appreciation of the dynamics of conceptual development and its sensitivity to arbitrary contingent features of the practitioners, devoting himself to elaborating what he insists is the logic of such processes and the conceptual contents they shape. 9. For the purposes of the present project, I will maintain a studied neutrality between these options. The apparatus I am introducing can be noncommittal as to whether we understand content-conferring uses of expressions in terms of social practices or individual abilities. 10. Somewhat more precisely: some theory (a set of sentences) formulable in the vocabulary in question, is such that if all those sentences are true of some interlocutor, then it thereby counts as exercising the relevant ability, or engaging in the relevant practices. 11. See his “Naturalism without Representationalism,” in Mario de Caro and David Macarthur (eds.), Naturalism in Question (Harvard University Press, 2004), 71–90. Price calls his view “subject naturalism,” as opposed to the more traditional (and more metaphysical) “object naturalism.” 12. I discuss this argument in greater detail in the final chapter of Tales of the Mighty Dead (Harvard University Press, 2004.) 13. Computational linguists, who worry about vocabularies in this sense, have developed metalanguages for specifying important classes of such vocabularies: the syntactic analogues of semantic metalanguages in the cases we will eventually address. So, for instance, for the alphabet {a,b}, ‘anbn’ characterizes the vocabulary that comprises all strings of some finite number of ‘a’s followed by the same number of ‘b’s. ‘a(ba)*b’ characterizes the vocabulary that comprises all strings beginning with an ‘a’, ending with a ‘b’, and having any number of repetitions of the sub-string ‘ba’ in between. 14. Here we can safely just talk about abilities, without danger of restricting the generality of the analysis. 15. In the syntactic metalanguage for specifying vocabularies that I mentioned in the note above, this is the vocabulary (ha/ho)*! 16. As a matter of fact, it can be shown that every vocabulary readable/writeable by a nondeterministic finite-state automaton—such as the laughing Santa automaton—is also readable/writeable by a deterministic one. (ref.) 17. For practice, or to test one’s grip on the digraph specification of FSAs, consider what vocabulary over the same alphabet that produces the laughing Santa is recognized/produced by this automaton:

26

The “I’ll Have What She’s Having”Automaton

o o

1

h

2

4

a a

3

!

5

h

o

18. By contrast to FSA’s, there need not in general be for every vocabulary computable by a nondeterministic PDA, some deterministic PDA that reads and writes the same vocabulary. 19. Thomas A. Sudkamp, Languages and Machines, 2nd ed. (Addison Wesley Longman, 1998), ch. 10. 20. In principle. There are subtleties that arise when we look at the details of actual implementations of particular computer languages, which can remove them from qualifying as strictly context-free. 21. There are various vocabularies that are VP-sufficient for specifying those meta-abilities. Specifying them in terms of the differentially elicitable capacities to change state and to store and retrieve symbols is just one of them. 22. For this reason, the frame problem, as it is often formulated, does not immediately arise for the pragmatic version of AI-functionalism. But as is explored in the third chapter of Between Saying and Doing, it does get a grip, at a different point.

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PHILOSOPHICAL TOPICS VOL. 36, NO. 2, FALL 2008

Varieties of Deflationism

Paul Horwich New York University

I The traditional view of truth—still widely endorsed—involves three assumptions. (i) Truth is a property; some beliefs and statements exemplify it and some don’t. (ii) It’s a substantive property, in that we can reasonably expect an account of what truth is, of its underlying nature. And (iii) this account should provide explanations of various important things about truth: including why the methods appropriate for its detection are what they are and why we are well advised to pursue it—that is, to strive for true belief. Deflationism is a reaction against this traditional picture. It was provoked, to begin with, by the inability of philosophers to come up with a good account meeting the above constraints. Amongst other ideas, we tried truth as correspondence with fact, as coherence, as provability, as utility, and as consensus; but they all turned out to be defective in one way or another.1 In light of this series of failures some of us began to question whether we’d had any reason in the first place to assume that there must be some such account—that truth must be a substantive property whose nature will rationalize our epistemic methods and explain the desirability of their goal. The outcome of these reflections—the deflationary perspective on truth—has been articulated in various different specific forms: there are various competing deflationary theories of truth. So we must confront the question of which of them

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is best. And my main objective in this review is to settle that question—to examine the pros and cons of these alternatives, and to recommend a particular one of them. But before we become immersed in these details I want to do two things: first, to be more explicit about what the competing proposals have in common—to say more about what makes a theory of truth deflationary; and second, to indicate something of the broad philosophical significance of deflationism by demonstrating its vital bearing on what can and should be said about the nature of meaning.

II On the first point: deflationary theories are characterized by a cluster of four interlocking ideas about the truth predicate:—one at the level of pragmatics, concerning its function; another at the level of semantics, concerning the way in which its meaning is fixed; a third at the level of metaphysics, concerning what sort of property, if any, the truth predicate stands for, and what the fundamental facts are concerning that property; and a fourth at the level of philosophical import, concerning the alleged theoretical profundity of the notion it expresses. More specifically, the four-pronged deflationary position is as follows: First: the word “true” has an idiosyncratic conceptual function, a special kind of utility. What exactly that function is said to be varies from one deflationary account to another: the truth predicate is taken to be primarily a device of emphasis (“It’s true!”), or concession (“True, I was a bit drunk; but I did see a flying saucer”), or generalization (“Every statement of the form, “p Æ p”, is true”), or anaphora (“Deflationism is an elegant theory”—“True”). But, despite this divergence of opinion, there is agreement that we must distinguish “true”’s raison d’être from that of other terms, and that we must especially beware against assimilating it to empirical predicates—such as “red”, “tree”, and “magnetic”—whose utility resides in their role in prediction and causal explanation. Second: the non-predictive non-explanatory role of the truth-predicate implies that its meaning is not empirical—i.e. its deployment is not based on a rule that instructs us to accept (x)(x is true ´ x is F)

where “F” articulates some observable content. Nor does it abbreviate a complex non-empirical expression—so that a definition of the standard explicit type would still explain its usage. Rather, the central principle governing our overall deployment of the truth predicate is, very roughly speaking, that each statement articulates the conditions that are necessary and sufficient for its own truth. In other words, we are required to accept that the statement made by “Dogs bark” is true just in case dogs bark, and so on. It is some such basic principle of use that provides the

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truth predicate with its distinctive meaning and which (as we shall see) equips it to perform its distinctive function. Third: insofar as “true” does not have the role and meaning-constituting use of an empirical predicate, we can appreciate a priori that there will be no reductive analysis of truth to empirical (i.e. naturalistic) properties. Similarly, we can see that the fundamental facts about truth will not be natural laws relating it to empirical phenomena. The most that can be expected, by way of theory, is a systematization—perhaps a mere list—of the superficial facts to which we are committed by the meaning of the truth predicate: for example, the fact that if dogs bark then it is true that they do, and so on.2 This is what is meant by saying that the property of truth is not ‘substantive’. And fourth: in light of the foregoing, truth is not, as often assumed, a deep concept and should not be given a pivotal role in philosophical theorizing. It cannot be the basis of our conceptions of meaning, or of justification, or of logic. Its actual philosophical significance is somewhat back-handed—lying in the fact that so many problems are exacerbated by our failure to appreciate its rather mundane function and the peculiar definition—i.e. principle of use—which enable this function to be fulfilled.3

III Let me illustrate the import of the deflationary perspective by sketching its relevance to the theory of meaning: (i) According to deflationism, the basic rule we follow in our use of “true” is to apply it to a statement, s, when we take s to have the same content (i.e. meaning) as something we are already disposed to assert. For example, we agree that “Schnee ist weiss” expresses a truth, because we know that it means the same as a sentence of our own that we accept. And we apply it to that ‘home’ sentence (i.e. “Snow is white”) because it (trivially) has the same content as “Snow is white”, which we accept. This practice with the word, “true”, insofar as it is explanatorily basic with respect to our overall use of it, is what engenders our possession of the concept of TRUTH. But it presupposes that we be able to recognize ‘sameness of meaning’. Thus the concept, MEANING, is more fundamental than the concept, TRUTH. We must therefore renounce the orthodox assumption that sentence meanings are to be analyzed in terms of truth conditions.4 (ii) Insofar as the truth-theoretic notions (TRUTH, BEING TRUE OF, and REFERENCE) are not naturalistic—insofar as they stand for properties and relations that are neither reducible to non-semantic (causal) phenomena, nor even nomologically correlated

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with them—these notions cannot be amongst the central concepts of an empirical causal/explanatory theory. In particular, no adequate scientific semantics can be truth-theoretic. Thus the current methodology of linguistics becomes questionable.5 (iii) If—as in the traditional inflationary conception—BEING TRUE OF were a natural (potentially reducible) concept, graspable independently of the concept of MEANING, then, since ‘w means F Æ w is true of the fs’ (e.g., ‘w means DOG Æ w is true of the dogs’), any decent account of w’s meaning would have to explain its truth-theoretic import. More specifically, we would be entitled to suppose that a given underlying non-semantic property of word w—say, U(w)—constitutes w’s meaning F only if the possession of U by w would explain why that word is true of exactly the fs. However, satisfaction of this requirement would be no trivial matter: U(w) would have to take the relational form, ‘w bears relation R to the fs’.6 Deflationism, in contrast, implies no such constraint. It leaves open the possibility of a much broader range of meaning-constituting properties—including internalistic inferential roles.7 (iv) The just-mentioned inflationary constraint on meaning-constituting properties may well prove so severe that nothing can satisfy it. Perhaps (as argued by Kripke) no relation R can be found that relates “dog” to the dogs, “electron” to the electrons, “number” to the numbers, etc. In which case one might be forced to concede that there can be no such thing as meaning. So a further virtue of deflationism is that it immunizes us against this skeptical threat.8

IV Thus it matters a great deal whether the general deflationary perspective is correct or not. So let’s consider various specific deflationary proposals in order to determine whether any of them is defensible. I take the most prominent and promising to be: 1. The redundancy theory, whereby “The proposition that p is true” merely rearticulates the meaning of “p”.9 2. The minimalist theory, whereby we mean what we do by the truth predicate in virtue of the fact that our overall use of it is explained by our propensity to accept instances of the material equivalence schema, “The proposition that p is true ´ p”.10 3. Tarski’s theory, whereby truth, for the sentences of a given language, is defined in terms of reference within that language, which is in turn defined by a mere list of what its words refer to. (Note that Tarski is quite clear that the meaning of the expression, “true in English”, is implicitly

32

fixed by a disquotation schema. The purpose of his further theorizing is to put this idea into the form of a ‘respectable’, explicit definition).11 4. The sentence-variable theory, whereby “x is true” is analyzed as “($p)(x=

& p)”.12 5. The prosentential theory, whereby “it is true” is a kind of dummy sentence, or sentence variable, whose relation to other sentences is similar to the relationship between pronouns and other singular terms.13 6. The disquotation theory, whereby our concept of truth for sentences (at least for the context-insensitive part of our own language) is captured by the strong equivalence of ““p” is true” and “p”.14 These accounts meet my four conditions for being deflationary. First, their advocates typically stress some distinctive, mundane function of our truth predicate. Second, any theoretical work that might be given to it is severely confined by this view of its function. Third, they each take the fundamental (meaning-constituting) use of the word to be (very roughly speaking, and each in its own way) the assumption that every statement articulates its own truth condition. And fourth, these theories concur in denying that the property of truth has any naturalistic reductive analysis, and in denying that its character may be captured by principles relating it to empirical phenomena. So much for the intension, extension, and philosophical interest of the concept, ‘deflationary view of truth’. Let me now compare and contrast the accounts that fall under it, and explain why I think that minimalism is the most attractive of them. My plan will be to consider the competitors one at a time, briefly stating what I take their relative advantages and disadvantages to be.

V According to the redundancy theory, “p” and “It is true that p” and “The proposition that p is true” say exactly the same thing. No meaning is added by “It is true that . . . ” or by “The proposition that . . . is true”; so they are redundant. This implies that the logical form of, for example The proposition that Fido is a dog is true

is simply Dog[Fido]

which in turn implies that the English truth predicate (like the English existence predicate) is not a ‘logical predicate’—i.e. the underlying logical formalization of a truth attribution will involve no predicate expressing the concept of TRUTH. But in that case we are unable to explain the validity of the following inference schema, whose deployment is vital to the term’s utility:

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X is true

Ed’s claim is true

X =

—————— \

is true —————— \p

Ed’s claim is that Fido is a dog ——————————————\ That Fido is a dog is true ——————————————\ Fido is a dog

For in order that the first part hold—as an instance of Leibniz’ Law, “a=b Æ (Fa ´ Fb)”—it is necessary that the truth predicate be a logical predicate.

VI Suppose, in order to rectify this crippling defect, we make a small adjustment to the redundancy theory—continuing to claim that the concept of truth is captured by the equivalence of “

is true” and “p”, but deploying a weaker notion of equivalence—no longer synonymy, but merely an a priori known and metaphysically necessary material equivalence. We thereby arrive at minimalism. More precisely, the minimalist contention is that our meaning what we do by “true” is engendered by our underived acceptance of the schema, “

is true ´ p” (from which we may then infer its necessity and apriority). Given this revision of the redundancy theory, the word “true” can be treated as a logical predicate; and so the sorts of inference that are essential (if there is going to be any point in having a truth predicate) will be evidently valid.15

VII Now suppose that someone, while fully sympathizing with this line of thought, nonetheless aspires to provide an explicit definition of truth. Is there some way of reformulating the content of minimalism so that it will take that desired shape? This was Tarski’s problematic, and his answer was yes. He recognized that it will certainly not do simply to say x is true º [x = <dogs bark> and dogs bark; or x = and pigs fly; or . . . and so on]

since this would be an ill-formed gesturing towards an infinitely long statement. But he was then forced, for the sake of finiteness, to focus on the truth of the sentences of specific languages. Because only for such a notion—i.e. “true in language L”—might it be feasible to derive each of the infinitely many conditions for its application from a finite base:—namely, of principles concerning the referents of the finitely many words in L. Note that it was not an option for Tarski to give an account of

34

how the truth-values of propositions depend on the referents of their components, because there are infinitely many such components (i.e. possible basic concepts) whose referents would each require specification. Rather, his only reasonable strategy was to offer a separate account for each language—an account that lists the referents of each of the words in the language and the principles determining how the referents (and truth-values) of complex expressions depend on them. Such axioms could then, with a considerable logical ingenuity, be re-jigged into the form of an explicit definition. This is an elegant result; but the costs are heavy: • In the first place, we don’t get an account of the notion that initially puzzled us:—namely, truth as applied to what we believe, to the things our utterances express. • In the second place, even if we decided to aim instead at an account of sentential truth—i.e. to aim at capturing what we mean by “expresses a truth of L”—the Tarskian definitions are clearly deficient. For amongst the features of one’s actual understanding of this expression that will not be captured by a Tarskian definition are (a) that it is based, compositionally, on what is meant by “expresses”, “true”, “in L”, etc., and on the way these terms are combined; (b) that it does not presuppose a prior understanding of every one of L’s words; and (c) that insofar as a notion of reference is presupposed by it, that notion will not be definable by a mere list of what each word of L happens to refer to. • And in the third place, it’s only for a limited range of formal languages that Tarski-style explanations of truth in terms of word-reference can unquestionably be supplied. There are notorious difficulties in giving such a treatment of attributive adjectives, belief attributions, conditionals, and many other natural language constructions.16 Supposing, for these reasons, that we judge Tarski’s account not to be good enough. Is there any alternative explicit definition that will articulate his insight that what must be conveyed is no more or less than the equivalence of “

is true” and “p”?

VIII Well there is the view that I called the sentence-variable analysis—first articulated by Frank Ramsey and urged these days by Christopher Hill and Wolfgang Künne: x is true ≡ ($p)(x=

& p)

35

Evidently, the variable, ‘p’, and quantifier, ‘$p’, that are deployed on the right-hand side are non-standard. Unlike the normal existential quantifier, which binds variables that occur in nominal positions and which formalizes the word “something”, this one binds variables that occur in sentence positions and does not appear to correspond to any of the expressions of a natural language. So one cause for concern is whether these notions are coherent. We might well be troubled by an inability to say what the variables range over, and by their use to quantify into opaque ‘that’-clauses.—And there is no easy escape from these difficulties in simply supposing that the new variables and quantifiers are substitutional. For substitutional quantifiers are defined in terms of truth:—“{$p}( . . . p . . . )” means “The result of substituting a sentence for ‘p’ in ‘. . . p . . .’ is true”—and therefore cannot be used to explain what truth is. But even if we set aside questions of coherence, there is the further objection that our actual understanding of the truth predicate cannot be built on notions that we don’t yet have—and it’s plausible, for a couple of reasons, that sentential quantifiers and variables don’t already exist either in natural languages or in languages of thought. In the first place, we can’t find any clear cases of them. For example, it would be implausible to suppose that when we say For any way things might be, either they are that way or they are not

what we are actually thinking is (p)(p v -p)

since this would miss a great deal of the original’s structure. Surely a better account of what we have in mind is given by the straightforwardly faithful (x)(y)[(x is an n-tuple of things & y is an n-adic property) Æ (x has y or x does not have y)]

And in the second place, if we did have the non-standard variables and quantifiers in question, then our actual deployment of the truth predicate would be very surprising. For the generalizations that it enables us to formulate (e.g. “Everything of the form, ‘pv-p’, is true”) could be articulated more directly in terms of our sentential variables. Why would there not be a natural language way of saying “(p)(pv-p)”? This is not to deny that one might now decide to introduce the new apparatus, and then proceed to formulate a definition of “true” in terms of it. But it can hardly be supposed that such a definition would constitute our present understanding of the truth predicate, since we don’t yet have the terms and notions that are needed for it. Against this point it might be protested that it is not really a requirement on a definition that it be psychologically accurate—that it fully capture our pre-existing basis for using the word. Consider, for example Frege’s innovative definitions of the numerals in terms of sets, or his definition of the ancestral relation in terms of second-order predicate logic.17

36

However, the moral here is that we must distinguish two conceptions of ‘definition’, corresponding to two things that we might be trying to do with such a thing. One kind is descriptive, the other revisionary; one attempts to articulate what is already meant, the other specifies and recommends a new meaning. In these terms, my objection to the sentence-variable analysis of truth was that it does not do the first job—it is not descriptively accurate. But nor does it have any evident value as a suggestion about what we ought to mean by “true”. In order to justify such a revision, we would need to identify some defect in our present notion—a defect that would be remedied by replacing it with the proposed new one; or else we would have to have some independent rationale for introducing the new forms of variable and quantifier in terms of which an equally useful, new notion of truth could easily be defined. But no such case has been made. And, even if it were to be made, we should not forget that the suggested revision would inevitably bypass our main original problem, which was to demystify truth as we actually conceive of it. Suppose then, in light of the failure of either Tarski’s account or the sentencevariable analysis to provide a plausible definition that is both explicit and deflationary, we face up to the fact that there was never any reason in the first place to expect the truth predicate’s meaning to be fixed by an explicit definition.18 Where does that leave us? Well, as we have seen, one possibility is to embrace minimalism, whereby the truth predicate applies to propositions, and its meaning is constituted, not by any explicit definition, but by our underived acceptance of the equivalence schema. However, perhaps something better than minimalism can be found?

IX For example, there is the prosentential point of view (initially proposed by Grover, Camp, and Belnap19), whereby the word “true” is a meaningless part of the dummy sentence, “it-is-true”, which, like a pronoun, gets its content from something in the context of utterance. Thus the “He” in “He was Austrian” can be used to refer to Wittgenstein; and the “it” in “If a triangle has equal sides then it has equal angles” is a bound variable—formally, “(x)(Sx Æ Ax)”. And, allegedly, the function of “itis-true” is analogous:—it can be intended to have the same truth-value as someone’s preceding remark that dogs bark. Moreover the “it-is-true” in “Everything is such that if Mary stated that it-is-true, then it-is-true” may be treated as a bound variable—formally, “(p)((Mary stated that p) Æ p)”. This approach clearly has a close affinity with the just-mentioned sentencevariable analysis. But instead of supposing that the word “true” is a genuine logical predicate, explicitly definable in terms of sentential variables and quantifiers, the prosententialist says that the English word “true” is not a genuine logical predicate, since it is an undetachable part of a sentence variable. As we have seen, the underlying logical form of “Everything Mary said is true” is supposed to be “(p)((Mary

37

said that p) Æ p)”, which contains no predicate corresponding to the word “true”. —Its role was merely to help us to construct the prosentence “it-is-true”, represented formally by the letter “p”. Thus the prosententialist denies the claim I made, in objecting to the sentencevariable analysis, that we don’t actually deploy the needed variables and quantifiers. Her view is that we are in fact deploying them in our use of the truth predicate. But of course, this response cannot help to salvage that analysis. For the sentence-variables that it invokes are composed from the word “true”, and therefore cannot qualify as a suitable basis in terms of which to define it. Thus prosententialism is a quite distinct point of view. However, it is no less problematic. After all, at least the sentence-variable analysis —to its credit—respects the strong indications that our truth predicate possesses its own definite meaning, and that it has the inferential role of an ordinary predicate. But prosententialism goes against this evidence and to that extent is unappealingly unnatural. Focusing for now on the orthodox version of the idea (as developed mainly by Dorothy Grover20), another difficulty is that most of our uses of the truth predicate do not occur in the context of the supposedly canonical phrase, “it-is-true”. Consider, for example: (a) Goldbach’s Conjecture is true

and (b) All Mary’s statements are true

In order for orthodox prosententialism to handle such cases they must be regarded as transformations of underlying sentences in which all the occurrences of the truth predicate do occur in the context of “it-is-true”—for example: (a*) Something is such that Goldbach’s Conjecture is the proposition that it-is-true, and it-is-true (b*) Everything is such that if Mary stated that it-is-true, then it-is-true

But notice that the quantifiers deployed here—namely, “Something” and “Everything”—could not be construed, as they must be in ordinary English, as binding the subsequent occurrences of “it”, but would have to be construed, rather, as binding the entire prosentence, “it-is-true”. Therefore the theory is open to one of the same objections that were made to the sentence-variable analysis—namely, that since we don’t actually deploy these non-standard variables and quantifiers, no account of truth tied to those notions can possibly be an account of our present concept.

38

X A further criticism of the orthodox approach, leveled by Robert Brandom, is that the quantificational regimentations suggested for cases like “Goldbach’s Conjecture is true” diverge to an implausible degree from their natural language formulations. And this concern leads him to propose a somewhat different version of prosententialism.21 According to his view (which he calls “the anaphoric theory”) “it-is-true” is far from the only prosentence. Rather, whenever “X” picks out a content (i.e. proposition), “X-is-true” is a prosentence. Within that context “X” does not have its normal (referential) function—namely, to identify X as the object of predication—but serves instead to specify the truth-value of the entire prosentence: namely, that its truth-value is the same as X’s. Supposedly, the sentence “Goldbach’s Conjecture is true” does not (as one might naively think) pick out a certain arithmetical proposition and predicate truth of it. Rather, it is a prosentence that is stipulated to have the same truth-value as Goldbach’s Conjecture—i.e. whatever truth-value is possessed by the proposition that every even number is the sum of two primes. However, both of our initial pair of objections to orthodox prosententialism count equally against Brandom’s new (‘anaphoric’) version:— 1. The alleged underlying form of (for example) “All Mary’s claims were true” as “Everything is such that if Mary claimed it-is-true, then it-istrue”) is implausible, given that “Everything”, as presently understood, does not govern sentence positions.22 2. “True” looks and acts and smells like a predicate! Therefore, insofar as the stated rationale for Brandom’s innovation is taken seriously (as it certainly should be)—insofar as a high premium is placed on minimizing, as far as reasonably possible, differences between grammatical and logical forms—then one should be unhappy, from the very outset, at the theory’s unwillingness to treat “true” as an ordinary meaningful predicate.23 Moreover, it seems to me that Brandom’s modification of prosententialism ought to be regarded as a significant retreat from the initial idea. In the first place, the motivating analogy with pronouns has been weakened.— For there is no such thing as a complex pronoun in which one component specifies the referent of the whole. And, in the second place, the substance of his central proposal is that <X is true> is stipulated to be equivalent to X

But this is tantamount to the minimalist claim:—namely, that we accept, underived, instances of the schema

39

is true ´ p

Thus Brandom’s attempt to improve prosententialism pushes it in the direction of minimalism.

XI Finally, we must take a hard look at the disquotational approach, suggested by Quine and championed these days by Hartry Field. The advantage of this approach, according to its proponents, is that it has no need for certain ‘creatures of darkness’—namely, propositions. For the truth predicate is applied, they say, to sentencetokens and its core meaning is given (for sentences of one’s home language, and uttered in one’s local context) by the equivalence of ““p” is true” and “p”. But precisely this alleged advantage may well be regarded as a disadvantage. For the ordinary truth predicate is primarily applied to such things as ‘what John believes’, ‘what we are supposing for the sake of argument’, ‘what Mary was attempting to express’, and so on:—that is, not to sentences, but to propositions. Therefore, insofar as we want to demystify our concept of truth—to clarify the meaning of our truth predicate—the disquotational approach is simply a non-starter.24 Not only that; but once we take into account how the approach will have to be developed if it is to be adequate even as a treatment of sentential truth, then its initial promise of dispensing with ‘creatures of darkness’ pretty much disappears. For the pure disquotation schema holds only insofar as the two “p”’s are replaced by sentences with the same meaning. Moreover, in order to account for applications of the truth predicate to utterances made in contexts that differ from one’s own, or that are couched in foreign languages, then disquotationalism needs a ‘projection’ principle, along the lines of u has the same meaning as my “p” Æ (u is true ´ my “p” is true)

which, when combined with the pure disquotation schema, yields u has the same meaning as my “p” Æ (u is true ´ p)

So it turns out that disquotationalism cannot, in the end, avoid entanglement with the notion of meaning. Granted, we haven’t yet shown that it needs to go all the way to the positing of propositions. But given the possibility of introducing these things by means of the schema u has the same meaning as my “p” Æ (u expresses the proposition that p)

that further step is small and innocuous. For assuming that our disquotationalist is already prepared to countenance some abstract objects (e.g. numbers, or sets, or

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word-types), then the abstractness of propositions cannot be what bothers him. The only reasonable worry could be over the prospect of supplying coherent identity conditions for such entities. But, as we have just seen, his disquotational theory can be adequate only insofar as sense can be made of the locution, “u has the same meaning as “p””—which implies that there is a coherent statement of such conditions.25 Thus the alleged benefit—the conceptual economy—that was supposed to compensate for the abandonment of our current concept of truth turns out to be non-existent.

XII Let me summarize what I hope to have accomplished in this review. First, I’ve tried to articulate the general deflationary perspective on truth—to say what features qualify an account of truth as ‘deflationary’. Second, I’ve tried to illustrate the broad philosophical significance of deflationism by indicating its impact on our theorization of meaning. It creates space for non-truth-conditional, non-relational accounts (such as Brandom’s normative inferentialism, and my own propensities-of-use theory), and thereby protects meaning from the threat of Kripke-style skepticism. And third, I’ve tried to show that minimalism is the best of the competing specific theories of truth that fall under the deflationary umbrella. I recognize that the situation here somewhat resembles the competition between subtly different religious sects or between political factions that strike outsiders as barely worth distinguishing. But, as someone with a dog in this race, I can’t deny that I think it matters which particular deflationary account of truth is the right one. Still, I admit that the main virtue of identifying a defensible specific theory is that we thereby show that the general deflationary perspective is defensible. For that is what has the important philosophical ramifications.26

NOTES 1. For discussion of these defects see R. L. Kirkham, Theories of Truth (Cambridge, Mass.: MIT Press, 1992); P. Engel, Truth (Chesham, Bucks: Acumen Publishing Limited, 2002); and W. Künne, Conceptions of Truth (Oxford: Oxford University Press, 2003). 2. For arguments in support of this claim, see my Truth, 2nd edition (Oxford: Oxford University Press, 1998), 50–51. 3. Recent philosophical literature is replete with conflicting proposals about the right way to distinguish between ‘deflationary’ and ‘non-deflationary’ theories. Now one might suspect that, since the term at issue here is a piece of jargon whose meaning is to be stipulated, there would be no possibility of any rational way of deciding between these alternative proposals. But that is not so. The merits of each candidate may be determined by reference to two considerations: first, whether the suggested basis of classification is deep and interesting; and second, whether “deflationism”

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4.

5. 6.

7.

8. 9. 10. 11.

12.

13.

14.

15.

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would be an apt label for that basis. On the first point, I believe it is indicative of the theoretical depth of the proposal just advanced (a) that its four criteria correlate so well with one another, and (b) that the issue of whether or not they are satisfied has considerable philosophical import (e.g. for theories of meaning). And on the second point, the word “deflationism” nicely captures the idea that truth is less profound and potent than has traditionally been assumed, and (as a consequence) that it does not require the sort of theoretical characterization that has traditionally been sought. I am not claiming that these considerations amount to a demonstration that my definition of “deflationism” is best. Indeed, given the vagueness of the terms (such as “interesting” and “appropriate”) in which this matter is to be judged, there are likely to be other reasonable definitions. Note, however, that even if some other characterization of ‘deflationism’ turns out to be preferable to mine, that could not bear on the plausibility and significance of the specific (‘minimalist’) account of truth that I advocate below. For further discussion, see “A Defense of Minimalism” (response to Objection 9)—chapter 3 of Truth-Meaning-Reality (Oxford: Oxford University Press, 2010). The conflict between deflationism and truth conditional semantics is emphasized by Michael Dummett. See, for example, his “Truth,” Proceeding of the Aristotelean Society, 59 (1959): 141–62. See my “Semantics: what’s truth got to do with it?”—Chapter 8 of Truth-Meaning-Reality, op. cit. For example: ‘We are, in ideal conditions, disposed to apply w to a thing just in case that thing is an f ’. For further discussion see “Kripke’s Paradox of Meaning”—chapter 6 of Truth-MeaningReality, op. cit. See “Regularities, Rules, Meanings, Truth Conditions, and Epistemic Norms”—chapter 7 of TruthMeaning-Reality, op. cit.; and see chapter 3 of my Reflections on Meaning (Oxford: Oxford University Press, 2005). See Saul Kripke’s Wittgenstein on Rules and Private Langauge (London: Blackwell, 1982), esp. 22–23. And see “Kripke’s Paradox of Meaning,” op. cit. P. Strawson, “Truth,” Proceedings of the Aristotelian Society, Supp. Vol. 24 (1950): 129–56. See my Truth, op cit. A. Tarski, “The Concept of Truth in Formalized Languages,” Logic, Semantics, Metamathematics: Papers from 1923 to 1938 (Oxford: Oxford University Press, 1958), 152–278; A. Tarski, “The Semantic Conception of Truth,” Philosophy and Phenomenological Research 14 (1943/44): 341–75. F. Ramsey, “Facts and Propositions,” Proceedings of the Aristotelian Society, Supp. Vol. VII (1927): 153–70; F. Ramsey, “The Nature of Truth,” Episteme 16 (1991): 6–16 [On Truth: Original Manuscript Materials (1927–1929) from the Ramsey Collection at the University of Pittsburgh, ed. N. Rescher and U. Majer]; A. N. Prior, Objects of Thought (Oxford: Clarendon Press, 1971), esp. 24–38; C. S. Hill, Thought and World (Cambridge: Cambridge University Press, 2002); W. Künne, Conceptions of Truth (Oxford: Oxford University Press, 2003). Note that “

“ is an abbreviation of “the proposition that p”. D. Grover, J. Camp, and N. Belnap, “A Prosentential Theory of Truth,” Philosophical Studies 27 (1975): 73–125. R. Brandom, Making It Explicit (Cambridge, Mass.: Harvard University Press, 1994), esp. ch. 5. W. O. Quine, Pursuit of Truth (Cambridge, Mass.: Harvard University Press, 1990); S. Leeds, “Theories of Reference and Truth,” Erkenntnis 13 (1978): 111–29; H. Field, “Deflationist Views of Meaning and Content,” Mind 94, no. 3 (1994): 249–85. Another way of modifying the Redundancy Theory that will address the above objection is to formulate it as the schema, ‘<X is true> = X’ (where “X” can be replaced with any proposition-designating term). For, in that case, one could reason that <Ed’s claim is true> = Ed’s claim = . And then, given the first premise (‘Ed’s claim is true’), and given the rule ‘(

= & p) \ q’, one could infer ‘Fido is a dog’. But a person might believe that the proposition designated by “X” is true (e.g. on the basis of testimony) without knowing which proposition that is—i.e. without being able to articulate it. So the modified Redundancy Theory can be plausible only relative to a coarse-grained, nonFregean conception of proposition. With respect to a Fregean proposition, XF, the import of the modified Redundancy Theory is merely that XF and <XF is true> are strongly equivalent (but not identical). So again we arrive at the minimalist theory.

16. For further discussion, see “A Minimalist Critique of Tarski”—chapter 5 of Truth-MeaningReality, op. cit. That discussion considers, in addition, the semantic (‘liar’) paradoxes, and shows how solution-strategies, based on the notion of grounding, which have usually been associated with Tarski-style compositional truth-theories, can also be taken over by non-compositional theories such as minimalism. 17. Thanks to John MacFarlane for pressing me on this point. 18. It is argued by some philosophers (following A. Gupta, “A Critique of Deflationism,” Philosophical Topics 21 [1993]: 57–81) that an explicit definition is needed in order to explain our acceptance of generalizations about truth (such as “Every instance of ‘If p, then p’ is true”). I attempt to rebut this argument on pp. 137–38 of Truth (2nd edition), and in “A Minimalist Critique of Tarski,” op. cit. 19. See their paper, “A Prosentential Theory of Truth,” op. cit. 20. See the papers collected in her book, A Prosentential Theory of Truth (Princeton: Princeton University Press, 1992). 21. See chapter 5 of his Making It Explicit (Cambridge, Mass.: Harvard University Press, 1994); his “From Truth to Semantics: A Path Through Making It Explicit,” Philosophical Issues 8 Truth (1997): 141–54; and his “Explanatory vs. Expressive Deflationism about Truth,” in Richard Schantz (ed.), What Is Truth? (Berlin: de Gruyter, 2002), 103–19. 22. Brandom acknowledges that minimalistic/disquotational theories can handle quantified uses of “true” (such as “Everything Mary said is true”), but thinks that “. . . these uses are incorporated in a more natural way in the prosentential account, by means of the analogy between lazy and quantificational uses of pronouns” (“From Truth to Semantics,” fn. 2). But I can’t agree. The fact that pronouns have two non-unifiable uses makes the best theory of them regrettably disjointed. And so it is to be hoped, for the sake of theoretical economy, that such terms are few and far between. By contrast the minimalist account of truth extends seamlessly to quantified cases in virtue of the general inferential roles of “some” and “all”. Only one principle is needed:

is true ´ p. 23. Another pro-prosententialist consideration that Brandom cites (—see “From Truth to Semantics”) is that he has a simple response to Paul Boghossian’s argument (in “The Status of Content,” The Philosophical Review [April 1990]) that deflationism is incoherent (—since some stronger notion of truth is needed in order to mark the distinction between robust properties and merely deflationary ones). For the prosententialist thesis is that there is no property of truth—a thesis whose formulation evidently does not call on the above distinction between kinds of property. But minimalism has an equally simple response. For it says merely that truth is fully captured by the equivalence schema. Again, there’s no call for any further notion of truth. Granted, the minimalist may go on to observe that truth is not a ‘substantive’ property, i.e. that it has no underlying nature (—NB the third prong of my initial characterization of deflationism). But no inflationary notions are needed to make this point. 24. Unlike other disquotationalists, neither Quine nor Field would be greatly perturbed by the present point. For they advance the doctrine in a revisionary spirit, aiming to improve upon our ordinary concept of truth and not to capture it. 25. This is not to deny that it will sometimes (perhaps often) be indeterminate whether or not a given foreign utterance, u, has the same meaning as a given local sentence, “p”. But that would not count at all against the idea that some proposition is expressed by u. The implication would merely be that there is an indeterminacy in which one it is—an indeterminacy in whether it is the proposition expressed by our “p”, or the one expressed by our “q”, etc. 26. This essay is based on material drawn from my entry, “Truth,” in The Oxford Handbook of Contemporary Philosophy, ed. Frank Jackson and Michael Smith (Oxford: Oxford University Press, 2005), 454–68. However, the critique of prosententialism to be found there has been substantially revised and expanded for the present version. And the discussion here of deflationism’s bearing on theories of meaning is entirely new. I am indebted to Frank Jackson, John MacFarlane, Ed Minar, and Stephen Neale for their helpful suggestions about how to improve on a draft of the earlier piece. And I would also like to thank those who attended and discussed my presentation of this material at the 2007 Brandom Meetings in Prague.

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PHILOSOPHICAL TOPICS VOL. 36, NO. 2, FALL 2008

Comment on Lecture One

John McDowell University of Pittsburgh

I In this first lecture, Robert Brandom gets his project under way partly by putting it in a context in the history of analytic philosophy. His avowed aim is to breathe new life into a kind of philosophical activity that took shape, in analytic philosophy, as the classical project of analysis. In its classical form, as Brandom sees things, analytic philosophy aimed to cast light on semantic relations between vocabularies. The exemplary activity of analytic philosophers, in his account, was directed toward showing how we can make sense of vocabularies thought to be in some way problematic in terms of vocabularies thought not to be problematic in that way. In putting things like that, Brandom is aiming at a formulation that fits a number of different ways of doing philosophy. The idea of making sense of one vocabulary in terms of another is meant to cover a great range of semantic relations (or supposed semantic relations) between vocabularies, all the way from synonymy to just having the same subject matter. The one constant, in the philosophical programs Brandom means his description to cover, is that they give logic a privileged position in specifying the semantic relations between vocabularies that they appeal to. This is what Brandom calls “semantic logicism.” In the kind of analytic philosophical activity he has in mind, we are supposed to reassure ourselves about some vocabulary we were finding problematic by engaging in “logical elaboration” of some vocabulary we were already comfortable with.

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In Brandom’s historical narrative, now, this classical analytic tradition comes under challenge from a methodological pragmatism, which aims to displace the notion of meaning from the center of philosophical attention in favor of the notion of use, the notion of what people do with language. At its most extreme, the thrust of the pragmatist challenge as Brandom reads it is that the whole project of theorizing about semantic relations between vocabularies should be scrapped. But he aims to disarm the challenge. A fundamental pragmatist insight is that expressions have their significance only within a practice of using them in certain ways. And Brandom proposes to co-opt that insight in the service of a transformed version of the project of analysis. If we have a systematic interest in the semantics of a vocabulary, the pragmatist insight requires us to pursue that interest in the context of the question what practice one must engage in to count as using the vocabulary with the significance it has. Answering that question in a particular case would be affirming a practicevocabulary relation. Brandom calls this kind of relation “PV-sufficiency.” This label might raise some eyebrows, given that he speaks of “what one must do in order to count as saying what the vocabulary lets practitioners express,” which seems to fit a practice that is necessary, rather than sufficient, for a vocabulary to have its semantic character. But in this context a condition identified as necessary is a sufficient condition. If one uses a vocabulary as one must for it to have a certain significance, then the vocabulary has that significance. And Brandom needs sufficient conditions for what he goes on to do with the idea. Besides PV-sufficiency, which relates a practice to a vocabulary, we can also consider what vocabulary suffices for specifying a practice, perhaps one that is PVsufficient for another vocabulary. Answering this second question in a particular case gives a vocabulary-practice relation, a case of VP-sufficiency. And now we can combine relations of these two kinds, PV-sufficiency and VPsufficiency, into a vocabulary-vocabulary relation: the relation that holds between two vocabularies when the first enables one to specify a practice that suffices for the second to have the significance it has. When this resultant vocabulary-vocabulary relation holds, the first vocabulary is, in Brandom’s terms, a pragmatic metavocabulary for the second. This relation between vocabularies, a VV-sufficiency relation, is the first and simplest example of the kind of relation Brandom wants to draw attention to: pragmatically mediated semantic relations between vocabularies. It, and its kin, are resources for his new version of the project of analysis. We can still say the project of analysis aims to display semantic relations between vocabularies. But in doing that, we can now exploit a new kind of semantic relation. The very idea of semantic relations of this new kind incorporates the thought that drives the pragmatist challenge, the thought that vocabularies have their semantic character only as used. Surely, Brandom suggests, that disarms the challenge. These semantic relations can figure in a version of the project of analysis that does not conflict with the fundamental pragmatist insight.

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II I yield to no one in my admiration for the creativity and resourcefulness with which Brandom elaborates this vision of a pragmatically inflected descendant of the classical project of analysis. But I want to express skepticism about whether breathing new life into the classical project should seem a good idea. (I am not sure to what extent it is necessary for what he goes on to do in these lectures.) By framing his proposal in what are in effect such terms, Brandom risks making his new creature look like a sort of Frankenstein monster, enabled to stumble about in a semblance of life by dint of the grafting of new organs, donated by pragmatism, into something that would otherwise have been a corpse, and should have been allowed to stay that way. Brandom’s exemplary instances of the classical project of analysis are what he identifies as two core programs in it, empiricism and naturalism. These programs reflect two different selections, or—since each comes in multiple versions—two different styles of selection, of supposedly unproblematic vocabulary, in the interest of a thought with this shape: philosophy needs to vindicate the semantic innocence of all other vocabulary by displaying it as standing in suitable semantic relations to some selected base vocabulary, or, failing that, to consign all documents containing such non-base vocabulary to the flames. Versions of empiricism, in the relevant sense, work with base vocabularies that are supposed to be unproblematic by virtue of their capacity to capture the immediate deliverances of experience, on some conception of what it might be to do that. Versions of naturalism work with base vocabularies that are supposed to be unproblematic by virtue of their capacity to figure in giving expression to thoughts that are candidates for being validated by the natural sciences. Now empiricism is dead, at least in the guise of a program for reassuring us about vocabularies we were finding problematic by displaying their semantic relations to a vocabulary that is supposedly unproblematic because it captures the immediate deliverances of experience. Sellars has put paid to any empiricism of that kind (not necessarily single-handedly). Such a program could seem to be a starter only if one thought the base vocabulary could be viable on its own, not needing to be part of a wider vocabulary that includes the vocabulary one is supposed to explain by way of logical elaboration from the base vocabulary. If we can make sense of the base vocabulary only by seeing it as part of a vocabulary that already includes the target vocabulary, there is no go in the idea that the intelligibility of the supposed base vocabulary fits it to cast light, by logical elaboration, on the target vocabulary. And that is just how things are, according to Sellars, with any candidate for the role of base vocabulary for the empiricist program. Sellars argues that there could not be a linguistic practice whose only moves are reports of immediate observation. The capacity to make reports of observation, Sellars argues, presupposes a capacity to give expression to knowledge that cannot be seen as an immediate deliverance of experience. If that is right, it must be wrong to think we can be entitled

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to take in our stride a base vocabulary for the empiricist program while still needing to be reassured about other vocabularies. The empiricist core program responds to a supposed philosophical predicament in which we understand an empiricist base vocabulary but do not yet understand any other vocabulary. But there is no way to make sense of this supposed predicament. Brandom cites Sellars as one of his heroes, and of course he acknowledges the Sellarsian thesis that there could not be a practice restricted to reports of observation. In passing, let me say that I think he misrepresents the argument Sellars gives for the thesis in “Empiricism and the Philosophy of Mind.” As Brandom reads him, Sellars argues that the forms of words used in observation reports count as having conceptual content only insofar as, besides being usable in noninferential claims, which is what reports of observation are, they can also figure as premises for inferences, so that besides the noninferential claims made in observation reports there must also be inferential claims. But that is not how Sellars argues. Sellars argues that the knowledge expressed in an observation report cannot be conceived as acquired all by itself, atomistically, by undergoing the observation that the report expresses. Sellars urges that acquiring knowledge by observation presupposes other knowledge, including knowledge of a sort that could not be expressed in observation reports. In his account of what happens in “Empiricism and the Philosophy of Mind,” Brandom reads into Sellars his own overestimation of the power of an inferentialist conception of meaning to do philosophical work, and the result is that he obscures an epistemological dimension of Sellars’s thought. But for my present purposes I can leave this complaint on one side. Brandom is right that Sellars undermines the idea of a stand-alone practice of making observation reports. The question how Sellars does that is not important here. Brandom mentions this strand in Sellars in a context in which he is considering locally corrosive pragmatist challenges to the project of analysis. And it is true that Sellars’s thesis demolishes only the empiricist core program. Sellars’s thesis does not address the naturalist core program, or any other analytic activity. In that sense Sellars’s challenge is indeed local. But it is still true that the empiricist core program is, along with the naturalist core program, central to the way Brandom introduces the very idea of the project of analysis. And by Brandom’s own lights, a project partly defined in terms of the empiricist core program does not look like a promising candidate to have new life breathed into it. What about the naturalist core program? Versions of the naturalist program are actively pursued in contemporary philosophy. But that much is true of the empiricist program. However, the sheer fact that there are philosophers who engage in a certain activity does not by itself establish the credentials of the activity. And of course Brandom would not suggest it does. If we are invited to join in pursuing an analytic program, we need to look critically at the supposed grounds for the privileging of a vocabulary that defines the program, the supposed grounds for regarding the selected vocabulary as unproblematic in some way in which other

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vocabularies are supposedly problematic. If the grounds do not pass muster, we should decline the invitation. And Brandom does not think we should accept the privileging that characterizes the naturalist program. In this lecture, he mentions Huw Price’s proposal for a naturalistic treatment of normative vocabulary, but only as an illustration for the idea of bootstrapping, and he carefully refrains from endorsing it himself. So by Brandom’s own lights neither of the two core programs in terms of which he introduces the idea of the project of analysis is a promising candidate to be something that might, in a new shape, figure in a reinvigorated form of the project, exploiting not just the old inventory of semantic relations between vocabularies but also Brandom’s new kind, pragmatically mediated semantic relations. It may seem beside the point to harp on this. After all, the two core programs Brandom exploits in his introduction of the project of analysis are only examples, and it is reasonable to say they belong specifically to the classical version of the project. It would of course be a gross misunderstanding to think Brandom is urging us to engage in pragmatically inflected descendants of those core programs. But the project of analysis he is recommending is like the core programs of the classical project in this respect: it privileges one vocabulary over others. When one opposes those core programs, one is opposing the relevant claims of privileged status for one vocabulary as against others. And there is room for a general suspicion of all such claims. A thought that is central to pragmatism in the guise in which Richard Rorty has embraced it can be put like this: given that there are several vocabularies, all with some currency, it is a mistake for philosophers to think they should be in the business of discriminating among them, selecting one to be the basis on which all the rest are to be made intelligible. If that is a mistake in general, why should we suppose it is any less a mistake if the selected vocabulary is language for describing linguistic practices than if the selected vocabulary is language for stating the deliverances of experience or language for giving expression to bits of a naturalistic worldview? Besides the two core programs, Brandom also mentions, as high points in the classical project of analysis, the attempt to reduce arithmetic to logic, and the theory of descriptions. Frege had to acknowledge that his logicism about arithmetic failed. But his project yielded achievements that stand firm in spite of that failure. He devised new ways, beyond those available to the logicians whose work he superseded, to use logical vocabulary in order to make explicit what certain claims commit one to, so that inferences to those consequential commitments could be codified in a form that required no leaps of intuition. And that is quite analogous to what the theory of descriptions aims to do. In these two cases it would be a stretch to talk of logical elaboration from a privileged vocabulary. There is indeed logical elaboration, from a vocabulary usable to express significances that, for these purposes, need not be conceived as internally structured to a vocabulary usable to express significances that we can see as built out of those simple contents. But that does not amount to privileging the simple

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vocabulary. There is, if you like, privileging of the logical vocabulary that combines with the simple vocabulary to make fully explicit the significance of the vocabulary analyzed in terms of the simple vocabulary. But this privileging of logical vocabulary amounts to no more than accepting that logical vocabulary is uniquely well suited for making logical structure explicit. How could that be open to dispute? This is not a case of the kind of essentially contestable privileging of one vocabulary over others that figures in the core programs of empiricism and naturalism, and still figures in Brandom’s new version of the project of analysis.

III I asked why we should suppose that privileging a vocabulary for saying what speakers do with words is any better than the kind of privileging that is characteristic of the empiricistic program or the naturalistic program. I suggested that Rortyan pragmatism recommends a general suspicion of all such claims of privilege. Now I had better acknowledge that there may be a ready response to that suggestion. Those Rortyan suspicions attach to singling out vocabularies on such grounds as that they capture how things really are, or that they capture foundations for our knowledge of how things really are. And that is not the kind of privilege that is supposed to attach, in Brandom’s analytic pragmatism, to vocabularies for specifying linguistic practices. Brandom’s favored vocabularies do not owe their claim on us to their being supposedly closer to the language in which the world describes itself or the language in which the world immediately makes itself known to us. So perhaps Brandom’s privileging is not vulnerable to Rortyan strictures. But what that indicates is at most that the privileging Brandom envisages need not be suspect in the way I was suggesting. It does not positively recommend his privileging. What does? In this lecture, he wants to generate a positive presumption in favor of privileging vocabularies for describing the use of language, on the ground that it reflects an insight of what he calls “methodological pragmatism”: in particular, an insight that can be credited to the later Wittgenstein. He acknowledges that his way of reading Wittgenstein is risky, in that he finds support in Wittgenstein for a kind of undertaking Wittgenstein does not engage in himself or encourage in others. I have to say that I think Brandom’s treatment of Wittgenstein’s later philosophy largely misses its point. Brandom finds in Wittgenstein a general picture of linguistic practice according to which language is polymorphous (a “motley”), and indefinitely open to new ways of using words. So far, I think, so good. But Brandom represents the anti-systematic slant of Wittgenstein’s philosophy as a conclusion Wittgenstein draws, idiosyncratically, from that picture of language. (He says: “Those who are moved by the pragmatist picture generally accept the par-

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ticularist, quietist, anti-theoretical conclusions Wittgenstein seems to have drawn from it.”) Thus he purports to respect the fundamentals of Wittgenstein’s approach to language while refusing to take the supposed inferential step from the basic picture to the thought that we ought not to be aiming at anything systematic. He must be inviting us to regard that thought as an inessential excrescence in Wittgenstein’s thinking. On these lines he aims to represent his own systematic approach to language as accommodating, indeed inspired by, the main insight of Wittgenstein’s approach. But this gets things backwards. Wittgenstein’s so-called quietism is not a conclusion disputably inferred from a general pragmatist picture that encapsulates the substance of Wittgenstein’s philosophy of language. On the contrary, the “quietism” is the whole point. I doubt that Wittgenstein would find much interest in the style of philosophy exemplified by the core programs of the classical analytic project. His characteristic concern is not a frame of mind in which the meanings expressed in some singledout region of language are taken to be unproblematic while the meanings expressed in other regions are taken to be problematic, and thus thought to need illumination in terms of the supposedly unmysterious base. His characteristic concern, rather, is a frame of mind in which meaningfulness überhaupt is experienced as a mystery, whether in the guise of a word being a word for a thing, of a signpost pointing in a certain direction, or of a specification of a number series determining what it is correct to write down when one reaches a certain point in extending the series. The target frame of mind can express itself in a superstitious—specifically, fetishistic—conception of the bearers of meaning, according to which minds, conceived as seats of remarkable powers, can somehow, perhaps magically, invest mere inanimate things with properties that seem to make sense only as attributed to animate beings, so that an arrow’s pointing, say, takes on the appearance of “a hocuspocus which can be performed only by the soul” (Philosophical Investigations §454). And Wittgenstein’s response, which I have to reduce to its bare essentials for the purposes of a quick sketch, is to suggest that when we fall into this kind of puzzlement about how a mere inanimate thing can have such properties, we are forgetting that the meaningful thing we are thinking about—a word, a signpost, a specification of a number series—is what it is by virtue of its involvement in a human practice. If we do not forget that context, we shall not be tempted to think we are dealing with mere inanimate things mysteriously infused with powers that properly belong to souls. Ideally, that enables us to take in stride the idea of words for things, or signposts that indicate directions, or specifications of number series. That is, the felt mystery, in principle, evaporates, though of course that cannot happen in as short a time as it takes to describe it. Now it needs to be stressed that this kind of move, in which we remind ourselves of the human context in which, say, signposts are what they are, does not require us to describe what people do in the relevant practice without using the concept of, to stay with the same example, a signpost: something that points in a

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certain direction. There is nothing in Wittgenstein to suggest that alleviating puzzlement about the concept of an inanimate thing that points the way requires us to describe a practice within which that concept has application, but without using the concept itself in our description of the practice. The mystery about how a mere inanimate thing can indicate a direction evaporates when we remind ourselves of the familiar human practice in which signposts are used. Signposts are not mere inanimate things, in the sense that figures in the puzzlement; on the contrary, they are signposts. And there is no reason to avoid using the idea of something that points in a certain direction when we state the content of this reminder. Nothing here recommends aiming to give an analysis of the concepts that figure in the style of philosophical puzzlement Wittgenstein is concerned with—not even an analysis that is pragmatically mediated. Brandom notes that the interest of his analytic project is sensitive to the vocabulary in which we specify a practice PV-sufficient for some vocabulary we are aiming to cast light on. But he does not dwell on the question whether we can expect to be able to do that in a way that permits something we can conceive as analysis of the target vocabulary. And the question is surely crucial for the prospects of his new project of analysis. In specifying a practice PV-sufficient for a vocabulary, we might simply use, in second intention, expressions that belong to the vocabulary whose use we are describing. (“You have to use the word ‘person’ in such a way as to be able to be understood to be saying things in which the concept of a person figures.”) If we use such terms in describing how a vocabulary needs to be used to have its significance, we do not produce something with a counterpart, now in a pragmatically inflected version, of the kind of interest that was supposed to be possessed by achievements in the classical project of analysis. We do not contribute to anything that would deserve to be called “a project of analysis.” And I have been urging that Wittgenstein’s response to philosophical anxiety about meaningfulness überhaupt contains nothing to encourage analytic aspirations for pragmatic metavocabularies. In some areas it may be possible to do better than that by analytic standards. But it is not really clear why we should think “better by analytic standards” implies “better, period.” Surely whether a pragmatic analysis of a target vocabulary would be a good thing to have would depend on what, if any, legitimate puzzlements there are about the target vocabulary. Brandom does not here consider such questions. Note that Sellars’s argument that there could not be a stand-alone practice of making observation reports does not depend on describing the practice otherwise than as the practice of making observation reports. Sellars’s argument does not need to exploit something that could be turned into a pragmatist analysis of the contents, or kinds of content, expressible in the practice.

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IV In this lecture Brandom mentions a putative example of pragmatist analysis that I think is open to question, and I shall end by questioning it. It used to be common to explain indexical vocabulary in terms of nonindexical vocabulary, on a pattern exemplified by saying that a tokening of “I” refers to the speaker of the utterance that includes itself. More recent work has made it obvious that nothing like synonymy is in question here; so obvious that, as Brandom says, the question arises what the philosophers who offered such explanations can have been thinking. Brandom suggests they were ineptly registering a pragmatically mediated semantic relation between indexical and nonindexical vocabulary. Their real point was that we can say, entirely in nonindexical terms, what one must do to be deploying indexical vocabulary correctly. Brandom offers to do that for indexicals in general. But I shall restrict attention, for simplicity, to the case of the first person. Brandom’s proposal about this is that there is a practical rule on these lines: if a speaker s wants to assert that some property P holds of s, it is correct for s to say “P holds of me.” But that seems wrong. It is correct, in the only sense that seems relevant, for s to say “P holds of me” only if what he wants to assert is that P holds of himself, where “himself ” is the kind of reflexive that, as Anscombe explains, can be understood only as an oratio obliqua counterpart of the first person. If that is right, an accurate formulation of the correctness condition is after all not intelligible independently of understanding the first-person form. That is, it is not intelligible independently of understanding the relevant region of indexical vocabulary. Suppose s wants to say that P holds of s without wanting to say the property holds of himself, as he may if he does not know that s is himself. His wanting to say that P holds of s does not make it relevantly correct for him to say “P holds of me.” Admitttedly, if he were to say “P holds of me,” he would be saying something that would be true just in case the property does hold of what, on our hypothesis, he wants to say the property holds of. But saying “P holds of me” would not be a correct way for him to say what, on the hypothesis, he wants to say, namely that P holds of s. This is just the point on which the classical analysis goes wrong; it seems to undermine Brandom’s sketch of a pragmatist analysis too. There is an obvious answer to the question Brandom raises, the question what Russell, Carnap, and Reichenbach can have been thinking. Their nonindexical formulations give, correctly enough so far as this goes, conditions under which the indexical utterances they are concerned with are true. Their mistake was to take that relation between the nonindexical formulations and the indexical utterances to be something on the lines of synonymy. It is not clear that Brandom’s recasting of their claims in terms of a pragmatically mediated relation between vocabularies is any improvement.

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PHILOSOPHICAL TOPICS VOL. 36, NO. 2, FALL 2008

Brandom’s Demarcation of Logic

John MacFarlane University of California, Berkeley

I find Robert Brandom’s proposal for the demarcation of logic very exciting.1 I’ll try to explain why. Then I’ll mention a few things I still find puzzling about the proposal, in the hopes that Brandom can clarify them.

I In my dissertation (which I wrote under Brandom’s supervision), I argued that in order to understand the confused state of contemporary debates about the demarcation of logic, one has to go back to Kant.2 Following tradition, Kant thought of logic as a normative discipline, with the job of identifying norms for thought. On this broad construal, it makes sense to talk of (say) the logic of jurisprudence, or of geometrical thinking, or of biological thinking. Kant called these “special logics.” But in addition to all the special logics, which provide “rules of correct thinking as regards a certain kind of object,” Kant recognized a “general” logic, which provides rules for thought as such, regardless of its objects (and even regardless of whether it has an object). When Kant made his critical turn, the notion of general logic posed a serious problem for him. He held that concepts could have representational content (objective validity) only insofar as they applied to some object that could be given to us

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in intuition (that is, in a singular representation). And he now held that (for us mortals) all singular representation is sensible. It follows that concepts can have content only insofar as they apply to potential objects of the senses. So, if we are after norms for thought as such, and accordingly abstract entirely from sensibility, we thereby abstract entirely from representational content, and hence, from truth. The norms of general logic, then, could not be rooted in very general facts about reality, as Kant’s Leibnizian predecessors seem to have thought. (Wolff: “It is plain . . . that principles should be sought from ontology for the demonstration of the rules of logic.”3) The problem, then, was to explain how there could be norms for thought as such, if thought is intelligible independently of its relation to objects. These norms could not be grounded in metaphysics, for the reasons given above; nor could they be grounded in empirical psychology, which tells us how we do think, not how we ought to. So by virtue of what are thinkers qua thinkers bound by these norms? Kant’s solution is well known, because it had a profound impact on thinking about logic well into the twentieth century. The norms of general logic, he says, concern only the form of thought, “the formal conditions of agreement with the understanding.”4 That is why they are binding on thought as such, whether or not it relates to potential objects of the senses. But “since these conditions can tell us nothing at all as to the objects concerned, any attempt to use logic as an instrument (organon) that professes to extend and enlarge our knowledge can end in nothing but mere talk.”5 So we explain the universal bindingness of general logic on thought by taking it to be formal and denying that it has any content or distinctive concepts of its own. This is a nice, satisfying story, but in later thinking about logic, it begins to unravel. What happens in Frege is particularly interesting, because given Frege’s ambition to show that arithmetic is implicit in pure logic, it really matters how logic is demarcated. Frege retains the Kantian idea that logic is distinguished from other disciplines by providing norms for thought as such, but he rejects the Kantian conception of logic as “formal.” His rejection is, I think, overdetermined: it is due in part to his important technical advances and in part to his philosophical differences from Kant.6 Frege’s replacement of the old subject-predicate conception of logical structure with a function-argument conception makes Kant’s story about the form of thought, as represented in the Table of Judgements, unavailable to him. Universality and negation are no longer regarded as ways in which subject and predicate can be related in judgment, but as concepts in their own right, in the same semantic categories as many nonlogical concepts. “∀x” refers to a second-level concept, just like “applies to Socrates”; “¬” refers to a first-level concept, just like “is a horse.” If there is any notion of the “form of a thought” available to Frege, it is the pattern of functional application, but this is too meager to form the basis of anything recognizable as logic.

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In addition, Frege rejects some of the Kantian assumptions that required Kant to claim that logic was “formal.” He rejects Kant’s idea that concepts have content or significance only insofar as they can be applied to objects given in intuition (in part because of his new function/argument conception of logical structure, which allows him to see purely quantified judgments as relating concepts, with no “relation to an object”). He also rejects the Kantian view that all singular representation is sensible, claiming that we can have singular thoughts about nonsensible objects, like numbers. So unlike Kant, he is not forced to the view that norms for thought as such must be grounded in the formal conditions of thought. In the end, Frege clearheadedly rejects the Kantian doctrine that general logic must be formal. He takes logical norms to be grounded in very general truths about the world, and he takes logic to have its own concepts, from whose content it cannot abstract. “Just as the concept point belongs to geometry,” he says, “so logic, too, has its own concepts and relations; and it is only in virtue of this that it can have a content.”7 The trouble is, having jettisoned Kant’s explanation of the absolutely general bindingness of logical norms on thought as such, Frege has no very good explanation of his own. What is it about thought that makes it the case that these very general truths about the world—the truths described in Frege’s logical axioms—give rise to norms for thought as such? On this point, he says nothing very useful, and even hints that nothing useful can be said. Frege’s student Carnap takes a different approach. He embraces the Kantian “formality” idea that Frege rejected, while rejecting the conception of logic as normative for thought as such. “The formal sciences do not have any objects at all,” he says; “they are systems of auxiliary statements without objects and without content.”8 They are, as such, completely unconstrained by facts about the world; they constrain thought by defining a “linguistic framework” within which thought can proceed. But because we can pick different frameworks for different purposes, no one framework can lay claim to being “general” in Kant’s sense; that is, normative for thought as such. We may use different, incompatible systems of rules in different inquiries, for different purposes. Other thinkers rejected both elements of the Kantian view of logic, finding them insufficiently clear for scientific purposes. Since this is Prague, I must mention Bolzano, who combined criticism of Kantian talk of formality with skepticism that any principled line can be drawn between logical and nonlogical notions.9 In the twentieth century, we find Tarski first echoing Bolzano’s skepticism that any principled line can be drawn between logical and nonlogical notions,10 and then, later in life, proposing a demarcation of logical concepts as those that are invariant under permutations of the underlying domain.11 Here he appeals to considerations independent of either generality (in Kant’s and Frege’s sense) or formality, and certainly incapable of justifying a privileged role for logical vocabulary in conceptual analysis.

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By the late twentieth century, things had gotten very confused. There was no shortage of principled proposals for how to demarcate logic. All of these proposals made some contact with how the discipline was historically conceived. But it had become quite unclear what the debate is really about. Reflecting on the situation, some thinkers quite reasonably concluded that the demarcation problem is a pseudoproblem—either because logic is a family resemblance concept with no principled definition, or because all analytic consequences are to be counted as logical, or because the historical “trunk” of logic had branched into many different things with nothing particular in common.12 What I like about Brandom’s proposal is that it connects quite directly with what I regard as the historically central tradition of thinking about logic, the one that runs through Leibniz, Kant, and Frege. It can even be regarded, I think, as a “pragmaticized,” modernized version of the Kantian view. On Brandom’s view, thought—or as he would prefer to say, discursive activity—has a form, insofar as it is made possible by the existence of certain basic “practices or abilities.” For example, in order to count as engaging in discursive activity at all, one must be able to do something that counts as classifying propositions into those one would assert and those one would reject, and one must be able to do something that counts as classifying inferences as good and bad. Logical vocabulary is vocabulary that is both elaborated from and explicative of these basic practices, which we might regard as the pragmatic “form” of discursive activity. It can be legitimately applied in explicating any other vocabulary, because the ability to deploy that vocabulary already suffices, when appropriately “algorithmically elaborated,” to deploy the logical vocabulary as well. So we have a kind of explanation of the universal applicability and universal bindingness of logic on discourse that appeals to logic’s essential connection to the underlying form or basis of discursive activity. In short, a view with the same basic shape as Kant’s. (There are also many differences, to be sure—for example, Brandom has no need to deny that logic has its own contentful concepts—but I want to emphasize the similarities.) Once Brandom’s proposal is in view, I think, we can see how other demarcation proposals—specifically the Gentzen-inspired proposals of Popper, Kneale, Hacking, and others13—might be seen in a similar light. For they all take the logical vocabulary to be vocabulary whose use can be explained by algorithmic elaboration from certain basic abilities, like the ability to distinguish good inferences from bad or to recognize certain kinds of patterns. The missing piece in all these projects is an argument that these basic abilities are essential to anything that can count as discursive activity at all. (Here there’s plenty of room for interesting argumentation. For example: if quantifiers are to count as logical, on Brandom’s view, it must be the case that any autonomous discursive practice must include subsentential structure. But why should that be the case?)

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II Having said why I like Brandom’s proposal, I now want to raise some questions about it. At the heart of Brandom’s account of logicality is the notion of a “universal LX-vocabulary.” A vocabulary V is universal LX just in case there are sets PA and PB of practices-or-abilities such that: 1. V is VP-sufficient for PA (that is, V suffices to explicate PA). 2. PA⊆PADP (that is, PA is PV-necessary for every autonomous vocabulary), 3. PA is PP-sufficient for PB (that is, PB can be algorithmically elaborated from PA), and 4. PB is PV-sufficient for V (that is, PB suffices for the deployment of V). The paradigm of a universal LX-vocabulary is the vocabulary of conditionals, Vcond. Vcond, Brandom says, is VP-sufficient for Pinf, the practice-or-ability of distinguishing good material inferences from bad ones. That is, Vcond is sufficient to make this practice explicit. Pinf is, in turn, PP-sufficient for Pcond, the practices-or-abilities that underlie our use of Vcond. That is, the practices underlying use of conditionals can be algorithmically elaborated from the practices involved in distinguishing good material inferences from bad ones. So we have a neat triangle. The vocabulary of conditionals is elaborated from the very same inferential practice that it explicates. My questions concern the key relations of PP-sufficiency and VP-sufficiency— the L and the X in “universal LX.” Let’s start with PP-sufficiency. Brandom says that the notion of algorithmic elaboration gives a definite sense to the claim that the one set of abilities is in principle sufficient for the other. This is the sense in which deploying logical vocabulary requires nothing new on the part of discursive practitioners: anyone who can use any base vocabulary already knows how to do everything needed to deploy any universal LX-vocabulary. (33)

But of course this is true only for practitioners who already possess whatever abilities are needed for the algorithmic elaboration of one practice-or-ability from others: for example, the ability to select which practice-or-ability to exercise based on the state it is in, or the ability to chain together two practices-or-abilities so that the output of one serves as the input to the other, or to substitute one response for another in a repertoire it already possesses. A creature that did not possess these basic algorithmic meta-abilities would not have everything needed in order to deploy any universal LX-vocabulary. So a more careful statement of Brandom’s claim would be this: Anyone who can use any base vocabulary and who also has capacities for algorithmic elaboration already knows how to do everything needed to deploy any universal LX-vocabulary.14

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This restatement makes it obvious that underlying Brandom’s demarcation of logical vocabulary is a pragmatic demarcation of capacities into “algorithmically elaborative” capacities and all others.15 What vocabularies count as universal LX will depend, for example, on whether the capacities that count as algorithmically elaborating are limited to those that can be implemented in a finite state automaton. I wonder, then: how much of the work of demarcating universal LX-vocabulary is being carried by the underlying demarcation of algorithmically elaborative capacities? How sensitive is Brandom’s demarcation of logic to this underlying demarcation? And what demarcation is he presupposing? As Brandom notes, there are serious differences in strength between different idealizations of algorithmic elaborability (single-state automata, finite-state automata, two-stack push-down automata, etc.). But he does not say which he is presupposing in his analysis, and he does not make clear how much of the load of demarcating logical vocabulary is borne by this choice.

III Let’s now turn to VP-sufficiency. Consider the paradigm example of conditionals. The vocabulary of conditionals is supposed to “suffice to explicitly specify” the practice-or-ability of distinguishing good material inferences from bad ones. On a weak reading, the claim might be just that by using conditionals, we can partially describe the inferential practice. On a stronger reading, the claim is that using the language of conditionals, we can fully describe the inferential practice. I suspect that Brandom intends the stronger reading here. He says in Lecture 1 that VP-sufficiency is the relation that holds between a vocabulary and a set of practices-or-abilities when that vocabulary is sufficient to specify those practices-or-abilities. . . . VP-sufficient vocabularies let one say what it is one must do to be engaging in those practices or exercising those abilities. (16)

To specify a practice, one assumes, is not just to say some true things about it, but to characterize it completely. The stronger reading is also suggested by Lecture 1’s syntactic examples: when Brandom notes that context-free vocabularies suffice to specify any Turing machine, he means that they suffice to specify the Turing machines completely, not just partially. (The latter claim wouldn’t be very interesting.) And it seems required for the idea that “pragmatic expressive bootstrapping” can occur when one vocabulary is VP-sufficient for practices-or-abilities that are PV-sufficient for another vocabulary. However, it seems to me that in the paradigm case of conditionals, Brandom is only entitled to the weaker claim. It is plausible that by using conditionals, we can partially describe the inferential practice that gives our concepts their contents. But to completely characterize this practice, we will need more expressive power.

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One reason for this is that, in order to use conditionals to explicitate an inferential practice involving sentences A, B, and C, one would need to use these sentences. “If A and C, then B” expresses an inferential propriety; “If ‘A’ and ‘C’, then ‘B’,” which mentions the sentences without using them, is ungrammatical; and “if . . . then” by itself says nothing. So a vocabulary V cannot completely describe an inferential practice involving, say, snail talk, unless it contains lots of sentences about snails, in addition to conditionals. It is difficult to see how this simple point can be squared with Brandom’s view that the vocabulary of conditionals, Vcond, is universal-LX. If Vcond includes sentences about snails, then it is implausible that a set of practices-or-abilities that is PV-sufficient for deploying Vcond could be elaborated out of a set of practices-or-abilities that is PV-necessary for every autonomous vocabulary. However, if Vcond doesn’t include sentences about snails, it is implausible that it is VP-sufficient for any set of practices or abilities at all. Even if we ignore this problem and allow the explicitating vocabulary to include not just conditionals, but sentences for them to connect, we will still not have enough to make a material inferential practice fully explicit. For whether one takes the inference from A to B to be a good one will depend not just on A and B but on one’s other commitments. For example, I might endorse the inference from “The match is struck” to “it will light” in most circumstances, but not when I also endorse “the match is wet.” The language of conditionals allows one to make explicit the inferential proprieties one recognizes relative to one’s current background commitments. But doing this only partially characterizes one’s inferential practices. Two inferential practices that agree on which inferences are good relative to a set K of background commitments might diverge wildly on which inferences are good relative to a different set K' To describe the difference between these practices, it seems to me, we will need more than the language of conditionals. (It won’t help to add the background commitments explicitly to the antecedents of the conditionals, because in general the required “ceteris paribus” clause will not be finitely specifiable. As Brandom says in Lecture 4: “There need be no definite totality of possible defeasors, specifiable in advance.”) If conditionals aren’t VP-sufficient to specify an inferential practice, is there some other vocabulary that is? I don’t think bringing in modal vocabulary and counterfactual conditionals will help. Counterfactuals can give us partial information about how the inferences a speaker endorses depend on background assumptions. But I don’t see how they can give us the full information about this we would need for a complete specification of an inferential practice. The reason, again, is that endorsement of the counterfactuals themselves will depend on background assumptions. If I think there’s a trampoline below me, I’ll endorse the counterfactual “If I jumped out of this building, I’d live,” but not if I think there is a moat containing crocodiles. A vocabulary V such that a set of sentences in the language L∪V can completely specify the material inferential practices underlying the language L will presumably need to contain a sign for entailment and a way of talking about (countably

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infinite) sets of sentences. We’ll then be able to say things like, “the set X of sentences entails the sentence A relative to the set Y of background commitments.” The totality of true statements of this form will completely specify the background inferential practices. But now we are outside of paradigm “logical” territory. Certainly this is a far cry from the comfortable conditional, and it seems highly unlikely that this vocabulary could be supported by practices algorithmically elaborable from practices necessary for any autonomous vocabulary.

NOTES 1. This is a lightly revised version of my comments on Robert Brandom’s second Locke Lecture, “Elaborating Abilities: The Expressive Role of Logic,” as delivered in Prague at the “Prague Locke Lectures” in April 2007. 2. John MacFarlane, What Does It Mean to Say That Logic Is Formal? (Ph.D. dissertation, University of Pittsburgh, 2000). Available at http://johnmacfarlane.net/dissertation.pdf. 3. Christian Wolff, Philosophia Rationalis Sive Logica, sec. 89. In Gesammelte Werke 2.1, ed. J. École et al. (Hildesheim and New York: Georg Olms, 1983). 4. Critique of Pure Reason, A61/B86, trans. Norman Kemp Smith (New York: St. Martin’s, 1929). 5. Ibid. 6. For a much more detailed discussion, see my “Frege, Kant, and the Logic in Logicism,” Philosophical Review 111 (2002): 25–65. 7. “On the Foundations of Geometry: Second Series,” trans. E.-H. W. Kluge, in Gottlob Frege, Collected Papers on Mathematics, Logic, and Philosophy, ed. Brian McGuiness (Oxford: Blackwell, 1984). 8. “Formalwissenschaft und Realwissenschaft,” Erkenntnis 5 (1934); translated as “Formal and Factual Science,” in Readings in the Philosophy of Science, ed. H. Feigl and M. Brodbeck (New York: Appleton-Century-Crofts, 1953), 128. 9. Wissenschaftslehre, second edition, ed. Wolfgang Schultz (Leipzig: Felix Meiner, 1929). Partial translation as Theory of Science, ed. and trans. Rolf George, (Berkeley and Los Angeles: University of California Press, 1972). 10. “On the Concept of Logical Consequence” (1936), in Logic, Semantics, Metamathematics, second edition, trans. J. H. Woodger, ed. John Corcoran (Indianapolis: Hackett, 1983), 409–20. Morton White, “A Philosophical Letter of Alfred Tarski” (1944), Journal of Philosophy 84 (1987): 28–32. 11. “What are Logical Notions?” (1966 lecture), ed. John Corcoran, History and Philosophy of Logic 7 (1986): 143–54. 12. For a survey and critical discussion, see Mario Gómez-Torrente, “The Problem of Logical Constants,” Bulletin of Symbolic Logic 8 (2002): 1–37, and my article “Logical Constants” in the Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/logical-constants. 13. Karl Popper, “Logic Without Assumptions,” Proceedings of the Aristotelian Society n.s. 47 (1946–7): 251–92; William Kneale, “The Province of Logic,” in Contemporary British Philosophy, ed. H. D. Lewis (London: George Allen and Unwin, 1956), 237–61. Ian Hacking, “What is Logic?”, Journal of Philosophy 76 (1979): 285–319; Kosta Došen, “Logical Constants as Punctuation Marks,” in What Is a Logical System?, ed D. M. Gabbay (Oxford: Clarendon Press, 1994), 273–96. 14. Cf. Lecture 2, p. 10: “Algorithmic PP-sufficiency is what holds in case if a system does have those algorithmic abilities, then that is all it needs to elaborate its basic abilities into the complex one in question.” 15. This is explicit in Lecture 2, p. 5: “algorithmic elaboration of primitive abilities into complex ones plays the same role in pragmatic analysis that logic does in semantic analysis.”

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PHILOSOPHICAL TOPICS VOL. 36, NO. 2, FALL 2008

The Computational Theory of Mind and the Decomposition of Actions

Pirmin Stekeler-Weithofer University of Leipzig

I. INTRODUCTION At the latest since the time of Thomas Hobbes and René Descartes, a ‘new’ image of man begins to replace an ‘old’, religion-based, self-image.1 According to the old image, human beings consist of a mortal body and an immortal soul. According to the new picture, man appears as a kind of cross between an animal and a computing being. But what seems to be ‘new’ from a Christian or theological perspective, in effect, has its roots in Ancient philosophy, where we already find a comparison of thinking, or language-use, with calculation. The word “logos” stands for “word,” “expression,” “language,” “mathematical ratio,” “number,” as well as for “reason.” Reasoning as the (silent or audible) use of words is often called “logizesthai,” “ratiocinari,” i.e. computing. Hence, Aristotle’s formula “zoon logon echon” for man as a rational animal supports already, at least implicitly, an understanding of man’s thinking as calculating with expressions. Modern functionalism and the artificialintelligence approach to human ‘sapience’, as Robert Brandom calls it, is thus deeply rooted in age-old linguistic analogies, partly developed by philosophers. It is this highly attractive self-image of us humans as rational animals,2 which Martin Heidegger opposes in his famous (or perhaps infamous) criticism of what he calls ‘humanism’.3 In fact, Heidegger’s deconstruction of the basic contentions in the contemporary philosophy of mind and the theory of cognition tries to show

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(hopelessly, for most readers) that we go astray when we identify language-use with calculating. Thinking is much more than (and something different from) computing. Language is much more than (and something different from) a mathematical calculus. Ludwig Wittgenstein in his later philosophy also rejects the idea of language-use as schematic calculation and opposes what he calls the mainstream of the twentieth century’s civilization and philosophy. Wittgenstein sees, moreover, that computing is a very special language game. Exact, i.e. schematic, mathematical thinking presupposes very special linguistic techniques of regimentation. In other words, making sense of the use of mathematical language and rules, especially in applied mathematics or in the ‘exact’ sciences, e.g. in physics, presupposes a much more rigorous understanding of language as a whole and of our common generic experience than twentieth-century ‘empiricist’ and ‘logicist’ accounts of scientific methodology usually convey. According to these accounts, scientific knowledge as a whole appears as a kind of unclear, ‘holistic’, mixture between empirical perception (in the extreme case, of merely subjective sense-data) and theoretical inference. According to Brandom’s pragmaticist approach, we use formal theories and formal logic in order to make implicit norms of material inferences explicit. This is an important idea, which goes back to Wilfrid Sellars. Unfortunately, however, the idea that the rules of deduction and the axioms of formal theories make implicit forms of material, i.e. empirical, inferences explicit may eventually mislead us. For example, it can be abused as an excuse for not reflecting rigorously upon the complicated practices of theory formation, theory evaluation, and theory application. It is not enough to appeal to some general ‘usefulness’ of a formal explication, as some versions of holistic pragmatism or pragmatic holism suggest. The pragmatist and inferentialist understanding of formal theories (and their internal logics) may be not much better off than psychology, which (still) is an ill-understood amalgam of empirical observation and theoretical formalization or computational explanation, as Wittgenstein famously put it. These preliminary remarks are meant to set the stage for my reflections on Brandom’s approach to artificial intelligence and analytic pragmatism.4 My leading question is this: What does it mean to be satisfied with a (partly ‘theoretical’ or ‘scientific’, partly empirical) ‘account’ of the rational faculties that make us human? What does it mean to say that we (want to) ‘understand’ the difference between man and animal? In our everyday life, we know this difference all too well. So, what kind of game do we play when we ‘forget’ what we already know—just in order to be ‘reminded’ by a theoretical account of what being human allegedly consists in?5 Since the usual notion of ‘implicit knowledge’ presupposes that we can make it fully explicit, it is often helpful to use Karl Bühler’s neologism ‘empractical knowledge’6 for something we already know how to do. Such a competence is usually manifested by a ‘habitus’ of correctly taking part in a joint and generic ‘practice’—at will, as we say, when it comes to concrete actualizations of the generic competence. When we talk about the form(s) of human life, we talk about systems of such prac-

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tices and the corresponding actions.7 The question is what to expect from an ‘analysis’ of such practices, actions, and faculties. Why are we not satisfied with an appeal to empractical knowledge? I.e., what do we ask for when we ask for an explicit account for how we know how to do things? And how does such an account relate to appellative knowledge, as I would like to call the knowledge of what vague and comprehensive titles like “thinking” and “speaking” or “acting” and “intending” appeal to?

II. ON SECTION 1: AI-FUNCTIONALISM This leads me to my first question: What could be “an account of what one must do in order to count as saying something”? I.e., for what purpose do we need such an account? And what are possible satisfaction conditions? Brandom sees, of course, that such an account makes implicit (empractical) forms of actions and practices explicit. Hence we need “a characterization of another vocabulary that one can use to say what it is one must do in order to be saying something else.”8 The dream of all philosophical constructivists is to develop a pragmatic metavocabulary which is, in one sense or another, “demonstrably expressively weaker than the vocabulary for which it is a pragmatic metavocabulary.” The idea is to develop a language that is somehow less complicated than the language we want to give an account of. As a result, we can use this metalanguage on the meta-level in order to explicate our empractical knowing-how that is involved in using the object-language for which we wish to develop a reflective reconstruction, i.e. the ‘account’ in question. A paradigm for such a project can be found in Paul Lorenzen’s construction of an ortho-language and his distinction between a merely commenting ‘para-language’ and a preliminary ‘protreptic’ language, in which the goals of the (re)constructions are (vaguely) specified. Brandom calls an enterprise like this “pragmatic expressive bootstrapping.” Another example for a similar program is W. V. Quine’s story about an alleged behavioral foundation of language-use and the formal or logical roots of reference in his masterpiece Word and Object (1960). But I already have an initial problem with Brandom’s own most cherished example. The example appears in chapters 1 and 2 under the title “Syntactic Pragmatic Bootstrapping within the Chomsky Hierarchy of Grammars and Automata.” My question is this: In which sense is it true that “context-free vocabularies are VPsufficient to specify Turing machines (two-stack push-down automata)”? Things get more perspicuous if we replace Turing machines by recursive functions. Then it appears as a trivial fact that the recursive definitions of syntactically complex standard names for such functions are much more ‘basic’ and ‘primitive’ than the functions named by these terms. But the use of these terms is not completely defined by the syntactic definition of the terms, as I will show. Hence, the ‘bootstrapping’ of making explicit what recursive functions are has to appeal to our empractical knowledge of how to use the terms. We tend to forget this. The fact

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that we can realize some Turing machines by real automata is the ground for this forgetfulness. This much is true, however: The primitive steps used in recursive calculations and in Turing machines follow extremely easy schemes of calculating behavior. But meta-level judgments by which we determine whether an automaton is operating (functioning) properly or whether it is defective (‘dead’, as we say metaphorically) transcend these schemes by far, as we shall soon see. As it is well known, recursive functions are defined by descriptive finite terms T(x,y, . . . for only partially defined recursive functions in the natural numbers or, what is essentially the same, for recursive search procedures or proto-Turing machines). I do not specify here the internal structure of T; but T ‘describes’ a systematic search for a numerical value for any given numerical arguments m,n, . . . . The ‘machine’ stops, if it finds a value. The important halting problem focuses on the crucial word “if”: In order to know if a proto-Turing machine halts for any m,n, . . . or if a partial recursive function is a total recursive function, we need a proof that T(m,n, . . .) gives a value for any number m, n, . . . . Such a proof must show that, for any single ‘argument’ m, n, . . . , the proto-machine generates a value. As a consequence, we (must) use half-formal truth-valued arithmetic, not just axiomatic Peano-arithmetic with its merely schematic deductions of mathematical formulas, when we want to talk about the total functions represented by semantically well-formed names for or by some explication of a particular (abstract) ‘Turing machine’. A definition or a proof is called ‘half-formal’ if a rule of the following sort with infinitely many premises is involved: The value for “∀x.A(x).” (or for “all x.A(x).” is defined as T (for Truth or the True) if and only if the value of A(t) is the True for any semantically well-formed number term t, or F (for Falsehood or the False) in any other case. We can use induction on the logical depth of a sentence p (the number of logical signs occurring in p) in order to see that any complex sentence p of elementary arithmetic is, in the sense just explained, true or false. I.e., by the above explanation, we have fixed exactly one truth-value for any such p, even though we do not know of general procedures for how to decide which truth-value applies for any arbitrary p. But we know perfectly well what it means to prove for any arithmetically well formed p that it is true. It means to show that the value that we have attached to p in the ‘half-formal’ definition above is T, not F. Half-formal arithmetic is, in a sense, the metalanguage for any kind of axiomatic system of formal inferences or deductions. As Kurt Gödel’s proof of his first incompleteness theorem (and also Gerhard Gentzen’s proof theory) shows, the very concept of a formal deduction is structurally identical with a finitely branched tree in which each branch is finite. A half-formal proof shows that in an appropriately defined infinitely branched tree (fitting to a corresponding half-formal definition of truth and to possible proofs), each branch is (or ‘must be’) finite. Natural language is ‘the’ metalanguage for explaining the notions of truth and proof in half-formal systems. Unfortunately, the relation between a fully formal axiomatic system and a halfformal interpretation is often confused with the relation between a fully formal

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object-language and a fully formal metalanguage. The latter is a relation between an axiomatic object theory T and a meta-theory T* that contains a truth-predicate for the object theory T. Such theories are investigated in the framework of Tarskian ‘semantics’ or axiomatic model theory. In fact, Alfred Tarski asks for a possible construction or the existence of a meta-level axiomatic system T* that contains some truth-predicate of the form “x is true” for a given deductive system T, such that (hopefully) all closed formulas of the form “Np is true if and only if p” can be derived in T* for any sentence (‘closed formula’) p of T and an operator N that turns (all) T-sentences p into (unique) names Np in the meta-theory T*. Np is a name of the sentence p. The process of abstraction involved in the naming-operation is often overlooked or undervalued when the naming-operation Np is articulated in the usual form “p.” Tarskian semantics proper does not know of (half-formal) definitions of truthvalues. Rather, there is a widespread confusion between half-formal models for axiomatic systems explained in normal language and merely axiomatic ‘semantics’. This confusion lies at the ground of Davidson’s and post-Davidsonian theories of language, meaning, interpretation, and truth. The crucial point is this: Tarskian semantics does not have the expressive power of defining standard models at all but allows only for considerations of the relative consistency or coherence of fully formal axiomatic theories or deductive systems. Davidson’s theory of radical interpretation suffers heavily from this defect. Another basic point relates to the difference between formal ‘languages’ and ‘theories’ on one side, and ordinary languages on the other. We always have to presuppose the empractical mastery of ordinary language when we employ it to explain the formal rules of syntax and the half-formal rules of semantics for mathematical systems. The crux of finitism, e.g. in intuitionism and axiomaticism in twentieth century philosophy of mathematics, from L. E. J. Brouwer and David Hilbert down to Dummett, is that these main movements against so-called mathematical Platonism, make us believe that we, like machines, are only capable of handling finite schemes of calculation and that we allegedly do not ‘understand’ truth-value arithmetics and infinite proofs. We allegedly can ‘understand’ only ‘finite proofs’, that is deductions of finite formulas or sentences according to schematic rules or procedures of computation. But this claim of ‘finitism’ is blatantly wrong. We widely, and competently, use half-formal arguments in mathematics. And it is a very good idea that we do so. Standard arithmetic is even the semantic metalanguage for any system of recursive functions9 or computing machines. There is no merely syntactic bootstrapping for this semantic system at all. The reason is this: Axiomatic systems in the formal sense, by which we want to produce true arithmetical sentences recursively, can be evaluated as correct (or consistent) only by presupposing the very concept of arithmetical truth in one way or another.10 Hence, the significance of the fact that “context-free vocabularies are VP-sufficient to specify Turing machines (twostack push-down automata)” is fairly unclear. For the word “specify” refers only to

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the description of the operations or search procedures. It does not refer to our possible knowledge about the functions represented by these operations. The second part of Brandom’s claim is, in a sense, harmless. It says that Turing machines “are in turn PV-sufficient to deploy (produce and recognize) recursively enumerable vocabularies.” But the hidden problem is here, again, the halting problem. The difference between merely partial recursive functions and totally defined recursive functions or merely proto-Turing machines and Turing machines is, so to speak, crucial for distinguishing between a ‘machine’ without bugs and a machine with bugs. Any real computing machine is built in a way that it either presents us with a value (of the input argument) or stops running at some place. But if we do not know if the machine has ‘bugs’ (which presupposes a comparison of the program with an intended total function), we do not know if the machine stops (without giving us a value) because the calculation takes too long, or because its correct value is not defined at all. In order to know things like these, and in order to make this knowledge explicit, we need the full-fledged concept of arithmetical truth, as it is half-formally defined for quantificationally complex arithmetical sentences. Brandom’s claim that the isomorphism in Descartes’ algebraization of geometry “amounts to an encoding of semantic properties in syntactic ones” shows that reflections like these are relevant. For Brandom’s claim is just not true. Algebraic geometry is, like arithmetic, no purely syntactic system. It presupposes a half-formal semantics of truth-values, as I have recently shown in much more detail.11 Brandom asks if “computer languages” are “sufficient pragmatic metavocabularies for any autonomous vocabulary?” The correct question would rather be, however, why they are not. My answer runs like this: Any competence to use an autonomous vocabulary must include the faculty to reflect upon, and change, schematic rules. Precisely for this purpose, we need the faculty of making implicit norms explicit. This is done by employing terms that can be used as names for rules, and by employing sentences and forms of judgments in which we talk about the rules. This includes not only the faculty of following the rules, but also the faculty of not following them—if only in order to demonstrate the autonomy of speech acts, or in order to show publicly that following rules is always a free (spontaneous) action which must be distinguished from (physically caused) behavior on one side, and from mere possibilities on the other. In other words, machines do not follow rules in the sense of a free, autonomous action. And they cannot talk about rules and functions in the proper sense of ‘talking about’. We cannot figure out if a being is a person by just comparing her behavior with what we expect as proper conduct. What we need is a test if the being or ‘something’ can act, i.e. do things or refrain from doing things ‘at will’ or ‘spontaneously’,12 just as I can ride my bike or dance or utter a certain word at will—or refrain from doing so, and this repeatedly. In fact, I must be able to show it, virtually, to anybody at any time—according to the conceptual rule ‘hic Rhodos, hic salta’: if you can dance, dance here! A machine cannot show things like this. And merely fictional ‘persons’ in utopian stories like Pygmalion or Frankenstein obviously also do not fulfill the Rhodos condition.

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The basic problem is to give a correct account of how we test abilities or faculties and their limits: Testing the faculty of deploying an autonomous vocabulary consists not only in controlling whether the performance meets certain standards, or agrees with our normative expectations, of correctness. Free and spontaneous action sometimes fulfills the conditions of following explicit rules or principles and sometimes not. A child shows her spontaneous ability of, say, singing a song not only by singing it when asked, but sometimes, or even often, also by refusing to sing it. This fact makes it impossible to decide whether a certain person has certain autonomous abilities, faculties or a certain empractical knowledge or knowing-how like the ability to say something or to use an autonomous vocabulary (autonomously), just by looking at singular instances of a certain behavior. When we now turn to the “program of artificial intelligence,” Brandom says that “artificial intelligence is to be real intelligence, created by artifice. But artificial diamonds are not real diamonds created by artifice. They are fake diamonds.” Brandom speaks of a “terrible way to pick out the topic.” And he is right, “real diamonds created in a laboratory are synthetic diamonds.” But synthetic ‘intelligence’ is, indeed, only so-called intelligence. This disagreement does not only hang on words. Its deeper point is this: We should use the expression “artificial intelligence” as a label for what researchers in the important field of ‘intelligent systems’ really do and really achieve. This (theoretical and practical) branch of computer science creates only fake diamonds, i.e. intelligent systems so-called. Brandom, however, seems to presuppose that real sapience can be reconstructed as if it were synthetic sapience. Brandom certainly disagrees with this assessment. For he does not want to do what he in fact does. He says, “what is at issue is not intelligence—a phenomenon that admits of degrees and has its primary application to comparative assessments within the discursive community. It is really sapience that is at issue—something we language-users have and cats do not.” But this does not help much. For it is just utopian to claim “that a computer could in principle do what is needed to deploy an autonomous vocabulary, that is, in this strong sense, to say something.” I agree that it is not easy to show why this is utopian. But I stick to my claim that it is. Let me note, first, that computer languages are not even sufficient to specify “abilities that are PV-sufficient to deploy an autonomous vocabulary” if we think of the autonomous language of full-fledged arithmetics, taken to consist not just of a system of configurations of basic words (vocabulary and syntax), but also of a semantically guided language use, at least with respect to the (half-formal) truth conditions for arithmetical sentences.

III. ON SECTION 2: CLASSIC SYMBOLIC ARTIFICIAL INTELLIGENCE I do not want to question that thought-experiments can produce feelings of satisfaction with respect to certain claims. But I do question the whole method. Arguments

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appealing to intuitions and feelings do not help at all. This criticism of method applies especially to all feelings of satisfaction with functionalism, i.e. with mainstream philosophy of mind in the second half of the twentieth century. For any serious assessment of the real achievements in philosophy, computer science, psychology, linguistics, or other cognitive and neuro-sciences, such feelings, produced by thought-experiments, should not count at all. What we rather need is a critical and realistic assessment of the whole program of twentieth-century empiricism and naturalism, especially for what I would like to call Utopian Artificial Intelligence. To what extent are the accounts of human (sentience and) sapience provided by the framework of artificial intelligence just fake accounts, i.e. merely analogical models which still have to be interpreted in an appropriate way, as metaphors always have to? I.e., under which aspects are the analogies enlightening, under which readings misleading? They can, of course, provide some ‘true improvements’ of our self-image in comparison to some outdated weltanschauung or ideological image of man. But it may happen as well that we fight an anachronistic battle, if the theories of the opponents are already completely outdated. For example, believing in an immortal individual soul is no life option for any serious philosophy anymore, for at least two centuries.13 Now, the real challenge for functionalism is, as Brandom says, understanding beliefs and intentions, rather than pains or sensations (e.g. of red). But for 2,600 years, since Heraclitus and Parmenides, philosophy knows (and therefore anybody is in principle able to know) that a belief that p must be distinguished from, and at the same time related to, saying aloud or silently thinking p*, where p* is one of the many possible linguistic or semiotic representations of p. Moreover, the relation between p* and p is just the relation between logos and eidos, expression and its content. Even though I would be the last not to agree that meanings and contents cannot be grasped independently from context, still we should not get drawn into a sweeping contextualism. Nevertheless, it is true that the meaning of a term is the role it plays in a more complex system. In the case of words, the important contexts are sentences. In the case of sentences and utterances, the important contexts are not only the situations in the world referred to, but the situation of performing speech acts, which involve (a) the role of the speaker, (b) the role of actual and possible hearers, (c) the individual act, (d) the generic action performed, (e) joint generic practices defining the generic action and, in the end, (f) our whole human life. We certainly need a via media between traditional dualism (of mind and body) and modern naturalism. But I doubt that the word “function” is of much help in finding one.14 It only says that something plays some part or role in a larger process. Functionalism presupposes, in the end, that words and sentences have functions (meaning or reference) in speech acts just as things in physical processes. The crucial differences are, however, those between merely physical and biological processes on one side, individual and joint action on the other. Talking and listening, writing and reading are such cooperative practices.15 I.e., written words and sentences rep-

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resent possible parts of speech acts, which, in turn, are already parts of a communicative practice. Words and sentences get their ‘meanings’ only mediated by this practice. This is, in a sense, Brandom’s own insight. We could name it ‘pragmatic contextualism’. But now we should handle with uttermost care a claim like the following: “Functional vocabulary applies exclusively to physical objects.” For this claim is already not really true for life processes. If we read the expression “physical object” as referring to an object of physics (taken as a particular science in the concert of sciences and human knowledge) it is just wrong that a living body (in German Leib) is a ‘physical’ object with some emerging biological property, called “life.” Only dead corpses, stones, or machines are physical objects proper. The real problem is a non-obvious ambiguity in our usage of words like “physical” and “physics.” There are parallel ambiguities in our talk about ‘physical objects’. One sense is ‘being an object of the science of physics’. My body can, of course, be treated as an object of science, and of techniques, of physics, chemistry, biology, or of medicine, for that matter. But it is still questionable if my body, as I am still living, can really be described and explained as a whole by the methods of contemporary physics. The deep problem is that we do not know what we say (today) when say that we eventually might be able to explain human life completely by physics or that it is an empirical question if the search for such an explanation might succeed or not. Nobody should deny the truism that if we enlarge the institution of physics in a way that it incorporates all sciences, including biology, psychology, perhaps even all humanities, then we can ‘explain’ human life in such an extended ‘physical’ science. But then we just return to an ancient reading of ‘phusis’, which just means ‘all there is’, as the etymological connection of “phuein” with “to be” (cf. Latin “fui” or German “Wesen”) nicely shows.16 If we talk that way, we just annihilate our disciplinary division of labor and neglect the Rhodos principle. The principle bars our judgments from (usually sweeping) appeals to a possible utopian future of physics or natural sciences: We have to use our concepts today as they are. And this includes the particular forms in which they refer to our world of real (joint and generic) experience via our institutions of making differences and explaining different processes, behavior, and individual and joint actions in different vocabularies by using different categories and systems of generic inferences. We have, so to speak, to dance here and now conceptually. It is absolutely crucial for any critical science and philosophy to acknowledge that we do not really understand speculations about what we might be able to do empirically in a distant future, just as we do not understand stories about a possible paradise inhabited by angels. What we understand about these stories is only what we know from today’s world around us. If we stick to our actual concept of physics and physical objects, it is just wrong to claim that we can explain life processes physically. In precisely this sense we know why analogies of valves and thermostats are misleading metaphors. They mislead us into the category mistake of assuming that the function of a (merely physical)

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tool, defined by our goals, plays a similar role as the functions of organs or other animal parts for a good animal life, or that this role was similar to the roles of symbols in joint human actions or practices.17 John Searle characterizes the “strong thesis of AI” or “classical symbolic AI” by the slogan: “Mind is to brain as software is to hardware.” Already this analogy overestimates what computers or “multistate transducing automata” can do. For even sentience used in the self-orientation of animal movement and animal behavior (as it may be directed by nonpropositional desires18) transcends the possibilities of computers and robots by far, as Searle rightly reminds us in this context under the label of ‘intentionality’. But there is still the quite important terminological distinction between animal and human intentionality. The distinction goes back to Franz Brentano and belongs to the central insights of Husserl’s and Heidegger’s philosophical phenomenology: Only human intentionality, not animal desire, refers to nonpresent possibilities. Such possibilities can (and often must) be made present by symbolic representations, for example by linguistic propositions. These propositions describe or define conceptually the fulfillment conditions of the intentional relation to the possible state. In a sense, Brandom focuses on this difference between human intentionality and animal desires.19 And he agrees that thinking (taken as the faculty of sapience) does not just reduce to “manipulating symbols according to definite rules (the algorithms implicit in automaton state-tables).” Moreover, “physics does not find meanings or semantic properties in its catalogue of the furniture of the world.”20 Only human symbolic actions, or traces of them, can have meaning. Hence, the operations of transducing automata are ‘meaningful’ only insofar as we can view them as the traces of the human action of building, running, and controlling the automata with respect to the purposes for which we have created them.21 But then, Brandom returns nevertheless to the crucial claim of Artificial Intelligence that manipulating symbols according to some internal computational pattern “is not just a simulation of thinking, but is thinking itself.” This is “a very substantive, potentially controversial theory, with a correspondingly large burden of proof,” as Brandom says. In contradistinction to Brandom, who believes that it is an empirical question if the theory is true, my contention is that the theory is conceptually wrong, or rather, that we can show that (and why) we should never believe it.

IV. ON SECTION 3: A PRAGMATIC CONCEPTION OF ARTIFICIAL INTELLIGENCE The crucial point is that I do not believe “that classy AI’s focus on the Turing test is appropriate.” I rather would like to distinguish Utopian Artificial Intelligence, or UAI, from real artificial intelligence. Real artificial intelligence develops and investigates intelligent systems. Real artificial intelligence does not make use of the Turing test at all. It only asks what we really can do with our computers and robots.

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In contrast to real artificial intelligence, Utopian Artificial Intelligence with capital letters asks us, under the heading of the so-called Turing test, to judge from mere observations and evaluations of the verbal behavior of a certain opponent in a game of questions and answers if the opponent is a machine or a human being. Of course, we should assume that the machine has some perception devices as inputs and even ‘can do’ some things as outputs. I.e., we rather should think more along the lines of a robot as opposed to a mere computer. But we can notice the deep problem of the task nevertheless if we translate the Turing test into arithmetic language. Then it is totally analogous to the following task: The tested ‘person’ is presented with a finite sequence of numbers produced by the other party, the tested ‘machine’. The person is asked to guess which machine or recursive function has produced the sequence. It is trivially clear that this task will result in a predictable loss of the tested person. For in order to know if a recursive function produces the sequence and which function it is, the finite sequence does not suffice. What I have to know is the function itself, i.e. a representation of it as a whole by a term for a recursive function or by a description of the program of the machine. In other words, it is trivially true that we cannot reconstruct the program of a (Turing) machine by the mere observation of some of its outputs, or rather, of some observed pairs of input and output. Notice that to know that we deal with a machine and to know its program is almost one and the same thing. For if I know the program, I know that it is a machine. If I do not know the program, I do not know if there is, by chance, a human being behind the screen that answers my question just like the dwarf in the famous chess machine of the eighteenth century. In order to know for sure that I deal with an automaton, I obviously have to know not only something about the observed behavior of my opponent. I have to know something totally different. In the end I have to know, again, the function or program. Hence, the whole setting of the usual Turing test is already flawed. It is flawed because the tested person does not have a chance to succeed at all, on a priori grounds, if the program of the tested ‘machine’ is ‘clever enough’. Or rather, there are no appropriate nonsubjective winning conditions defined. The questions I am allowed to ask the supposed ‘machine’ are not described precisely enough, not to mention how I am to evaluate the answers. May I ask, for example, how my opponent chooses to calculate the results, for example, if the input is converted into a coding number, and how? And if I may ask such a question, it is not clear if the machine is allowed to lie.22 It is obviously difficult to find out if the machine lies in such cases. In other words, the illusions created by the Turing test are just consequences of the fact that I am, by definition, barred from some knowledge other people really have. Hence, the case is fairly similar to the following famous example: When I, standing in front of a barn-façade, am not allowed to enter or walk around it, I cannot ‘know’ (for sure) that it is a barn.23 If we consider this, it becomes clear why it is unclear to say, with Brandom, that “something passes” the Turing test as a talking test “if one cannot tell it from a

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human speaker.”24 The basic problem of the Turing test is that the person tested is not allowed to use structural knowledge about the form of operation of a computer and a recursive function. If I were allowed to use such knowledge, I would be able to represent the inner operations of my opponent by something like a two-place recursive function f(x,y) of the natural numbers into the natural numbers, where y is a kind of parameter defining a set of one-place recursive functions fy(x). If I can do this, I already know the limits of the operations the opponent is capable of performing. I.e., I know that the opponent is an automaton.25 Now let us assume that there is some ‘thing’ that ‘behaves’ in a certain way and I want to know if it is a (hidden) (Turing) machine. The right thing to do is this: I go and ask the people who have constructed the machine and know about the program. But precisely this is not allowed by the whole setting of the Turing test.26 It is rather amazing that no one seems to see that this procedure is a way of begging the question. For if there is a person or only a random process behind the screen of the Turing test, the situation can be presented in the following way: Assume that there are two observers, who both do not know if a person has produced the behavioral results they observe. And assume that the one says it was a person, the other says no. Then the two behave just like a believer in God and a nonbeliever. Of course, we can implement random devices and we can build perception machines reacting to their surroundings in a way that it is actually impossible to predict what they will do. But this does not turn the machine into a non-machine. It is not prediction as such that makes a crucial distinction here, but the possibility to freely or spontaneously react to knowledge about the program of such a machine. Nobody can be barred from treating a machine like a person, just as nobody can be hindered in treating animals, rivers, or trees as gods. The point is that our distinction between what is and what is not reasonable to do rests, in the end, on all real knowledge available to us. The same holds for conceptual inferences. They always have a certain material background. Their real ‘place’ in our joint practice and experience distinguishes them from any merely ‘formalist’ use of words and sentences. Such formalist rules can make the content of the words empty, ‘utopian’, i.e. place-less, without a topos or topic. In fact, the real problem of empiricism is its abstract nominalism. It presupposes a formalist split between the ‘empirical’ and the ‘conceptual’, where the former is interpreted as mere sensory input, the latter as a merely formal verbal processing. Moreover, real knowledge and conceptual inference surpasses by far ‘my’ parochial knowledge, which, as such, depends on too many contingent facts of my subjective history and perspective(s). It is to be admitted, though, that the distinction between singular knowledge claims in an I-mode, limited by the subjective perspective of the individual speaker, on the one hand, and joint and general knowledge in a we-mode, on the other hand, is difficult to grasp. The problem lies in the difficult differentiation between ‘us’ as a singular group of individual people and ‘us’ in a generic sense. This difficulty makes it appear as if our knowledge about how to distinguish between men

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and machines could be of the same form as my knowledge. But this is not so. In our example, at least someone must know that there is a machine and not a person behind the screen. And if he knows this, it is because he knows something about the construction of the machine, its program. This means that he knows something about the recursive function defined for the coding numbers represented by the machine: If the machine does not calculate this function, the machine is defective: Our knowledge about the function represented by the machine counts as a norm for evaluating the machine as still functioning, as not having a defect, as giving the correct results in a calculation. Brandom says about the Turing test that there “is just no point in insisting that something that is genuinely indistinguishable from other discursive practitioners in conversation—no matter how extended and wide-ranging in topic—should nonetheless not be counted as really talking, so thinking (out loud), and deploying a meaningful vocabulary.” But notice, first, the misuse of the word “indistinguishable” in the whole setting is of a kind that it excludes the relevant distinctions a priori. Second, the very phrase “no matter how extended and wide-ranging in topic” does not apply for the set-up of the Turing test at all. Since all (at least most) claims of “AI-functionalism” or “automaton functionalism about sapience” rest on sweepingly intuitive answers to the Turing test, it is just an empty promise to say that ‘we’ can give an AI-account of “what it is in virtue of which intentional-state vocabulary such as ‘believes that’ is applicable to something,” and “the capacity to engage in any autonomous discursive practice, to deploy any autonomous vocabulary, to engage in any discursive practice.” But even though I do not acknowledge “the criterial character of the Turing test” at all, I certainly agree with Brandom that it would be still “a long way to endorsing the computational theory of the mind” provided by ‘classy’ (or ‘utopian’) artificial intelligence (UAI). And I agree that “the most important issue is the claimed algorithmic character (or even characterizability) of thought or discursive practice. The issue is whether whatever capacities constitute sapience, whatever practices-or-abilities it involves, admit of such a substantive practical algorithmic decomposition.” But even classical arithmetic and mathematics only seemingly admit of a ‘substantive’ algorithmic decomposition. With Frege, we understand the importance of syntax for semantics. But this does not mean at all that we can reduce (with Rudolf Carnap, Tarski, Quine, or Haugeland) the semantics of arithmetic or set theory to the syntax of formal deductions from Peano-axioms and from the axioms of Zermelo and Fraenkel. Axiomatic-deductive systems are only technical means to facilitate our linguistic representations of some proofs. They do not define the inferential content of sentences. They only help to make proofs more general. In other words, formal axiomatic systems definitely do not make the concept of proof and truth, semantic content and content-dependent inference explicit.27 But this is precisely what Brandom purports. Brandom believes that the “principal significance of automata” lies “in their implementing a distinctive kind of PP-sufficiency relation.” The idea is to reconstruct

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discursive abilities as complex abilities. I.e., they are supposed to appear as a kind of ‘combination’ of more primitive abilities, which are, with respect to an algorithmic elaboration of these ‘combinations’, not discursive themselves. In a similar vein, the early Wittgenstein tried to explain sentences with empirical content as logically complex sentences. In his picture, the ‘primitive’ sentences do not express content. We must learn to use them by training. For this, he assumes some deep-structural coordination of observation (Anschauung) with (holistic) ‘names’. Or rather, he thinks that elementary sentences are somehow glued to elementary states of affairs or Sachverhalte. This gluing defines, in Wittgenstein’s model, the projection method of empirically contentful, true or false, sentences, by which we can refer to (possibly non-present) states of affairs (komplexe Sachlagen). Brandom’s version of “AI-functionalism” now claims, under the heading “algorithmic pragmatic elaboration” (APE), “that there is a set of (primitive) practicesor-abilities” which “can be algorithmically elaborated into (the ability to engage in) an autonomous discursive practice,” such that every primitive practice or ability can “be understood to be engaged in, possessed, exercised, or exhibited by something that does not engage in any ADP (autonomous discursive practice).” I agree that we should not overestimate the role of symbolic acts for thought and sapience and put actions more to the front. But we should not underestimate symbolic acts and practices either. Be that as it may, Brandom wants to focus on the “PP-sufficiency of the algorithmic elaboration” of complex faculties, including the faculties of using symbols in communication, and in the planning of one’s own actions. In a sense it may be true that “for any practice-or-ability P, we can ask whether that practice-or-ability can be (substantively) algorithmically decomposed (pragmatically analyzed) into a set of primitive practices-or-abilities.” And we are often interested in a methodical order of learning and training, such as in the case of multiplication or subtraction of decimal numbers or in the decomposition of division into a systematic search procedure using multiplications and subtraction. For Brandom, it is an empirical question of whether we really can decompose, say, piano playing, riding a bicycle, or playing the violin in such a ‘substantial’ way.28 “So the question of whether some practice-or-ability admits of a substantive practical algorithmic decomposition is a matter of what contingent, parochial, matterof-factual PP-sufficiencies and necessities actually are exhibited by the creatures producing the performances in question.” Let us notice, however, that it heavily depends on our notion of ‘empirical’ and ‘matter of fact’, ‘contingent’ and ‘conceptual’ whether we want to say that it is an empirical and contingent fact that, say, my brother was able to learn German, whereas my brother-in-law was able to learn French, or not. The point is that generic statements about what a species of creatures can do are in a fairly different sense empirical and contingent than statements about singular objects or facts—like the one that, say, a certain individual is mentally retarded by birth and cannot learn a language at all. The latter are in a much stronger sense empirical and contingent than the former. I agree, of course, that the question of ‘learnability’ “is very general and abstract, but also both empirical and important. It is a very general structural ques-

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tion” about certain abilities of members of a species . . . and that this “issue, as such . . . has nothing . . . to do with symbol-manipulation.” Brandom suggests “that we think of the core issue of AI-functionalism as being of this form. The issue is whether whatever capacities constitute sapience, whatever practices-or-abilities it involves, admit of such a substantive practical algorithmic decomposition.” Any differential analysis of the faculties of men, primates, and of cunningly invented robots will have to take certain matters of fact into account. But its result will be, nevertheless, conceptual accounts, as I would like to call any account which is able to explicate generic similarities and distinctions. In other words, we should identify the conceptual with the generic (Hegel’s category of Allgemeinheit), the empirical with the singular (Hegel’s category of Einzelheit). Then we can see in which sense empirical or singular facts are contingent, and in which sense generic facts are not just contingent, but define the modality of conceptual necessity. Even though Brandom does some important terminological work here, it is not enough. He distinguishes “classical symbolic AI-functionalism” as merely one species of “algorithmic practical elaboration of AI-functionalism.” However, we would mislocate the central issues if we only focused on the symbolic nature of thought. But we can show even for mathematical thinking that there is no sufficient “practical algorithmic analyzability” of mathematical proofs. If we widen the scope to “whatever practices-or-abilities,” as Brandom suggests, we should distinguish extremely carefully between the question whether a certain ability is a necessary condition for full-fledged sapience and the question whether it is already sufficient.

V. ON SECTION 4: ARGUMENTS AGAINST AI-FUNCTIONALISM: RANGES OF COUNTERFACTUAL ROBUSTNESS FOR COMPLEX RELATIONAL PREDICATES Mathematical (arithmetical) truths can be seen as results of our reflections on the very possibilities and limits of using schematic rules altogether. As such, the notion of mathematical content by far transcends merely syntactic isomorphy, which therefore is not sufficient for mathematical contentfulness. My arguments for this claim are completely independent from any preference for the first-person point of view or any assumed limitation of a “third-person point of view,” as Searle has epitomized it in his Chinese room thought experiment. Searle talks about an automatic translator who does not comprehend anything itself. I agree with Brandom that the appeal to a “first-person understanding” does not lead us anywhere. The real problem has to do with the “particular variety of pragmatism” in question, viz. of ‘classy’, i.e. Utopian, Artificial Intelligence. The problem is the corresponding concept of (complex) action. In a sense, I agree with Hubert Dreyfus’s contention that UAI sweepingly claims that it is possible to explain any such action computationally.

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Brandom, on the other side, hails “the relatively precise shape” that artificial intelligence “gives to the pragmatist program of explaining knowing-that in terms of knowing-how: specifying in a nonintentional, nonsemantic vocabulary what it is one must do in order to count as deploying some vocabulary, hence as making intentional and semantic vocabulary applicable to the performances one produces (a kind of expressive pragmatic bootstrapping).” But no content is produced by exact rules or schemes of verbal and practical inference, as an automaton can perform them. Content rather is a form of joint action, of communication and cooperation. The forms and norms that make this jointness possible are not at all ‘exact’. For the jointness must be a result of free actions on the side of the persons taking part in the cooperation. In other words, comprehending content presupposes the faculty of free action and free judgment. No automaton, no machine, can have such a faculty, or else it stops being a machine. Even proving in mathematics, the ‘mother of all exact sciences’, is in its core not at all merely exact rule-following and hence cannot be sufficiently elaborated in this way, pace Hilbert, Carnap, or Brandom. It is already wrong to assume a mere “stimulus-response vocabulary” as “VPsufficient to specify all the primitive abilities that can serve as inputs to the process of algorithmic elaboration.” The reason is that if we widen the scope of basic abilities or primitive capacities in a way that goes far beyond what a machine can do, we use the word “machine” only metaphorically. Then, of course, nobody can deny that there is some “algorithmic decomposability of sapience.” The question is how we should understand such a metaphor, and how to make its true content explicit in a more literal way. Already Frege’s philosophy of language and Wittgenstein’s Tractatus contain metaphors like this. They use analogies with formalized languages of mathematics when they ‘explain’ or ‘explicate’ semantic competence by logical decomposition. Brandom says, accordingly, that the decomposition should be substantive. I.e., the basic thing we start with “must be something that could be exhibited by a creature that does not deploy an autonomous vocabulary.” And he continues: “That is a substantial restriction—one that very well may, as a matter of empirical fact, rule out the abilities I just offered as examples of sophisticated discriminative and performative abilities that would otherwise qualify as ‘primitive’ for the purposes of practical algorithmic elaboration.” Brandom himself wants to “find some aspect exhibited by all autonomous discursive practices that is arguably not algorithmically decomposable into nondiscursive practices-or-abilities.”29 And he finds it in “the practice of doxastic updating— of adjusting one’s other beliefs in response to a change of belief.” This is the most interesting core of his argument. For now he himself comes back to the point that our particular way of dealing with (relevant) possibilities makes and marks the difference not only between us humans and animals, but also between men and machines. This brings Brandom back to considerations we can find in Husserl and Heidegger (if we look for them in an appropriate way).

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The practice of doxastic updating “is a PV-necessary aspect of the deployment of any vocabulary,” for it is necessary for making claims, and “of being a reason for or against” such claims. The crucial question is “what follows from it and what it follows from, what other commitments and entitlements the various commitments it can be used to undertake include and preclude. And that is to say that one understands what a bit of vocabulary means only insofar as one knows what difference undertaking a commitment by its use would make to what else the one using it is committed or entitled to—that is, insofar as one knows how to update a set of commitments and entitlements in the light of adding one that would be expressed using that vocabulary.” “The updating process is highly sensitive to collateral commitments or beliefs.” Brandom promises to show in the next (fourth) lecture how a “global updating ability” results from “a collection of sub-abilities: as the capacity, in one’s actual doxastic context, to associate with each commitment a range of counterfactual robustness.” Even though the dependence on context “can be algorithmically elaborated from . . . abilities to discriminate ranges of counterfactual robustness,” Brandom believes that such an algorithmic decomposition is not substantive, for it presupposes that we already are discursive creatures. In fact, explicit modal knowledge presupposes this. And: “Being able to entertain semantic contents with that character is being sapient.” I could not agree more. But I would like to add that this semantic updating is a fairly complex joint enterprise. In fact, science works on ‘the concept’ and is ‘conceptual work’ in the following sense: We propose, and test, default, or normal, inferences, and make them explicit in the form of verbal rules. These rules represent empractical norms of (correct) inferences. These empractical norms are materially (‘empirically’) grounded in joint generic experience (a word avoided by Brandom). But they already count as conceptual, just because they are generic. We also always develop these empractical norms, forms, or practices, because we always need improvements of our particular projections of such generic truths and inferences on situations, contexts, and cases. These particular empractical forms define Hegel’s special category of Besonderheit. Making these forms of particular projections of generic verbal rules onto the world of individual and joint experience explicit presupposes a correct empractical use of these explications. In the end, there is no relation of linguistic forms to the world without the empractical category of competent judgment. As a result, it is grossly exaggerated to say that “any new information about any object carries with it new information of a sort about every other object.” Our differential and relational predicates are usually limited to certain domains in an empractical way. In other words, there is no comprehensive universe of discourse as a joint domain for variables, names, and objects. Second, an automaton cannot deal autonomously with new generic knowledge of the category of particularity; it

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cannot, because we judge about the default-norms of correct (empractical) applications of conceptual rules of verbal inferences in view of our interest in a good development of cooperative experience and its generic articulation. Nevertheless, doxastic updating is a most interesting aspect of our joint conceptual (generic) knowledge. We must ask how we jointly develop and control this updating. And I agree that the most important feature here is relevance and that “no non-linguistic creature can be concerned with totally irrelevant properties ‘like fridgeons or old-Provo eye colors.’” But an automaton might be programmed in a way that it does not care for weird properties. Updating or developing (conceptual) knowledge requires judgments about relevance. And this requires “the capacity to ignore some factors one is capable of attending to.” But which ones? Any answer to this question has to leave the level of ‘rational understanding’ (Verstand) in the sense of following learned norms and rules behind. We rather have to turn to the practice of good judgment and ‘experienced reason’, as I would like to translate the German title(-word) “Vernunft.” My contention is that we develop in a joint institution of generic knowledge (or general science in the old comprehensive sense of Latin scientia) systems of default inferences not only in a theoretical, verbal, and explicit way, but also by developing empractical forms and norms of correct application. By this we define ranges of counterfactual robustness of individual claims and inferences and the ability to deal with them. Brandom’s own position seems to be much weaker, in the end. For he only says: “. . . it is not plausible . . . that this ability can be algorithmically decomposed into abilities exhibitable by nonlinguistic creatures.” This is certainly true. But if we view robots as linguistic creatures, the interesting question is why they do not have the required ability, at least not in the comprehensive form needed. The challenge of classy or utopian AI has been that human intelligence is taken to be a kind of crossing between animal sentience and artificial intelligence. But artificial intelligence as such is not ‘nonlinguistic’. Therefore, Brandom’s claim that “nonlinguistic creatures have no semantic, cognitive, or practical access at all to most of the complex relational properties” does not help us much. A good intelligent system should have to “assess the goodness of many material inferences” and work with some versions of counterfactual robustness. I agree with Brandom’s contention that this faculty could not “be algorithmically elaborated from the sort of abilities” those creatures (namely robots) do have. But I do not see the argument in Brandom’s account. Does he want to say that robots do not grow on trees? Surely, judgments of relevance cannot belong to a primitive, nondiscursive, level of faculties. For they presuppose complex linguistic abilities. But what does this show above the fact that we need a hierarchy of levels of reflection on symbols or language and language use? The task would be to show that there is no intelligent formal system that can do this trick, namely to talk about language and language use. I do not see that Brandom has shown us anything about this problem.30 “What is at issue here is the capacity to assess the goodness of nonmonotonic material inferences, by practically associating with each a range of counterfactual

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robustness.” But once again it is only a claim to say: “This function is not computable by substitution inferences, or even from the incompatibilities of sets of nonlogical sentences. And that lack cannot be repaired by introducing a nonmonotonic logic, because what is at issue is the propriety of nonmonotonic material inferences.” For Brandom, the “issue is an empirical one, and these arguments are accordingly probative rather than dispositive. They offer reasons supporting pessimism about the algorithmic practical elaboration of the AI thesis, but not reasons obliging us to offer a negative verdict.” I think, we can do better, if we improve our understanding of (a) the Rhodos principle, (b) the relation between technical AI and UAI, (c) the distinction between contingent (or empirical) arguments and conceptual (or generic) knowledge, (d) the fact that we always need good relevant judgment in applying concepts to particular cases, and (e) what it means to reflect on the scope and limits of rule-governed intelligent systems, especially with respect to their relation to the real world and to our way of using languages.

VI. ON SECTIONS 5 AND 6: PRACTICAL ELABORATION BY TRAINING, PEDAGOGICAL DECOMPOSITION, AND PEDAGOGICAL POLITICS In the last section, Brandom contrasts (a) verbal teaching and practical training resp. (b) learning by talking and learning by doing or by being trained to do something at will.31 Moreover, Brandom distinguishes pedagogical decompositions of teaching and training into a series of steps that, in the end, empirically lead to the desired results in normal cases from algorithmic decomposition. Considerations like these are interesting in their own right. For they ask if what one person can learn or be trained to do is of the form that any other person can learn it also. Guided by this question, we should organize our schools (Dewey). Here it certainly is ‘only an empirical’ fact that for some persons to learn something takes longer than for others, perhaps too long for not losing temper. For example, there seems to be no fool-proof method of teaching subtraction n-m of arbitrary (decimal) numbers n and m. Even though we have a computational decomposition of the task, the problem obviously is that we are too slow and lazy to count from m to n. Decimal subtraction, on the other hand, is a technique which presupposes some short-term memory and discipline of keeping track of the ‘position-numbers’. Therefore, it seems to be hard for some pupils to learn this method in adequate time. Brandom thinks that pedagogical decomposition, or for that matter, the methodical order of learnabilities is “one of the master ideas animating the thought of the later Wittgenstein.”32 I do not agree. But the real problem with this idea is that it cannot be a matter of contingent fact what we can learn. When Wittgenstein

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“emphasizes the extent to which our discursive practices are made possible by facts” like the one that we can acquire a set of abilities in a series of steps, he talks about generic forms, not about empirical facts in the narrow sense of frequent occurrences. Therefore, he also does not talk about ‘all’ human beings. On the other hand, the pedagogical problem of decomposition of subtraction may be empirical and contingent in the following sense: there may just be too many children, or too many teachers, who do not have the patience, and discipline, needed for learning, or teaching, the trick. But this would lead us into another debate, namely how to distinguish between what can be learned by training and/or verbal teaching ‘in principle’ by anyone and what should count as a contingent fact about ‘actual’ learnability, i.e. that many of us do not learn this and that, for whatever reasons, most of which have to do with speed, discipline, and patience. Things get even more complicated, of course, when the task is to learn to freely deal with analogies and metaphors, irony, and other figures of speech and with all kinds of regular and open ‘abuses’ or new uses of language. I will, however leave things at that, for these questions lead us into fairly new fields, far away from the claims, and prospects, of artificial intelligence.

NOTES 1. Comments on Robert Brandom’s John Locke Lectures “Between Saying and Doing,” Lecture No. 3: “Artificial Intelligence and Analytic Pragmatism.” 2. We find this image of ourselves as rational animals nicely exposed in Donald Davidson’s paper “Rational Animals,” reprinted in Davidson 1984. 3. Cf. M. Heidegger, Platons Lehre von der Wahrheit. Mit einem Brief über den Humanismus. (On Humanism. Letter to Jean Beaufret), Bern 1947. 4. Brandom himself says: “This computational theory of the mind ( . . . ) is (indeed) . . . a view that long antedates the advent of computers, having been epitomized already by Hobbes in his claim that ‘reasoning is but reckoning.’” 5. Heidegger asks a similar question in his reactions to Edmund Husserl’s philosophical method of ‘epoch ’. This method tries to make things more explicit by bracketing, in a first step, all ‘usual’ knowledge and familiar ways of talking about ourselves, and to start afresh with a kind of rigorous philosophy as a phenomenologically and logically controlled account of what we can do already. 6. Cf. Karl Bühler 1934 and Lorenzen 1986, p. 20, with Gilbert Ryle 1949 and his analysis of ‘knowing-how’. 7. I sometimes use the terms ‘title’ and ‘title-word’ for words that refer to aspects of our life and world in a highly general way, like “action,” “practice,” or “language.” In German philosophical terminology, name-like labels of this sort are also called “Reflexionstermini.” They appeal to our (joint) experience, which determines the generic content of these labels, in an empractical way (cf. Bühler, ibid., 28ff). Such terms refer to whole domains of knowing how to do things in a rather vague and comprehensive way. 8. “—that is, of a vocabulary that is VP-sufficient to specify the practices-or-abilities PV-sufficient to deploy the first vocabulary.” 9. An arithmetical function is defined via an equivalence relation between many different operations or other representations ‘of the function’, as we say in retrospect. The domain in which the equivalence relation is defined is the domain of all possible arithmetical descriptions of functions. Two such descriptions are equivalent if and only if they lead to the same ‘course of values’, i.e. the same

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10. 11. 12.

13.

14. 15.

16.

17.

18. 19.

20.

21.

22.

23.

24.

‘extension’, which we can identify with a ‘set’ of pairs consisting of arguments and values ‘of the function’. In a sense, this can be seen as a deep side-result of Kurt Gödel’s second theorem, if understood in a proper way. To show this in detail would need more space and time. Cf. my “Formen der Anschauung. Eine Philosophie der Mathematik” (Berlin: de Gruyter, 2008). I use the word “spontaneity” here in a ‘Kantian’ sense: There is another, quite contrary, sense in which I do something spontaneously if I do it ‘just like this’, ‘by chance’, ‘unwillingly’, if I behave ‘without control’, so to speak. Any academic discipline or science should refrain from fighting dead enemies. For this, we always need historically informed judgments of relevance. They tell us if a question has to be treated as still open and living, or if it has to count as settled. A different task is education, as it may be especially needed in the proverbial southern states of countries like the United States, Europe, or Germany, for that matter. Brandom’s analogy is not too helpful: “the relations between ‘belief ’, ‘desire’, ‘intention’, and ‘action’ might be modeled on the relations between ‘valve’, ‘fluid’, ‘pump’, and ‘filter’.” Symbols of written language only seem to be just physical things; they usually get their “meaning” or “content’ by representing possible oral interactions or by adding spoken comments, as Plato famously saw. No matter who invented the titles for Aristotle’s books on which grounds, metaphysics in its correct understanding is and always was (meta-level) ontology, i.e. logico-semantical reflection on what it means to claim that something is the case. To grasp these categorical distinctions requires a kind of sensitive taste for relevant and irrelevant aspects. In the later case, judgments of equivalence define generic identities. Not to get confused by vague analogies, metaphors, or vague ‘thought experiments’ depends on such scientific scrutiny and logico-linguistic ‘accuracy’ in the sense of Bernard Williams or jointly controlled and dialectically developed ‘rigor’ in the sense of Friedrich Kambartel. The ‘sincerity’ of merely subjective beliefs and intuitive feelings of satisfaction are not enough. A state of desire, which we share with animals (in German: mere Begierde) has to be understood here in contradistinction to an already conceptually informed wish. Neither the fact that computers as such do not have devices for perception and do not move (like robots do), nor Searle’s appeal to sentience and his concept of ‘intentionality’ (as he calls the structure of animal desire) can be reasonably used as an argument against the claims of AI. I agree with Brandom “that functional properties are not physical properties.” We are usually interested in particular representations of these ‘software-properties’ by some (efficiently working) ‘hardware’. Not everybody is able to figure this purpose out, just as not everybody can know what a special machine is good for. Therefore, not everybody can evaluate if something is a correct running machine or a defected one, or a random generator, or if there is a human being hidden behind a screen. I do not deny that a computer can manipulate symbols in ways that accord with the ‘meanings’ we have given to them. But I totally disagree with John Haugeland’s slogan “that if the automaton takes care of the syntax, the semantics will take care of itself.” We have to take care for the syntax and the corresponding semantics, which usually transcends the schemes of merely formal computations by far. In order to sharpen the winning conditions against a computer, we certainly should say: If I know that the answer given by the machine is false (because of her mode of operation), I certainly should be the final winner. Quite many debates in recent philosophy result from the trick to allow only partial knowledge to a certain party and compare it with ‘our’ knowledge. If I see the barn and use the barn as a barn it does not make any sense to doubt any longer that it is a ‘real barn’. Hence, Gettier’s (or Alvin Goldman’s) problems just remind us of something we never should have forgotten, namely that individual knowledge claims are always limited (finite) by the limited (finite) perspective of the speaker. What does it mean that ‘one cannot’ tell a robot from a human speaker? Only sufficiently intelligent methods of approaching the Turing test should be taken into account. As Joseph Weizenbaum

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25.

26. 27.

28.

29.

30.

31.

32.

shows in Computer Power and Human Reason: From Judgment to Calculation (W. H. Freeman & Co. 1976) about the computer program Eliza, there often is some lack of intelligence on the side of the persons who deal with so-called intelligent systems. The diagonal argument is an easy way to reflect on the limitations of such a set of functions defined by parameters. For if the function g(x) is defined to be f(x,x)+1, we know that for no y the function fy represents g. This shows that we can define g, but the machine cannot. Hence, we can ask the machine to calculate g. And we are sure that it takes only finite time until we come to a place where the answer of the machine must be wrong. If I know the function defining the machine and how the parameters are set, I can, in principle, predict the answers of the machine to my ‘questions’ (arguments). Insofar as deductions from axioms according to formal rules of inference turn into real proofs only via interpretations of the quantifiers in (usually half-formal) semantic models, we must distinguish formalist algebra and real algebra, formalist arithmetic and real arithmetic, formalist geometry and real geometry, formalist set theory and real set theory. Only then we see why a certain formalist branch of inferentialism is misleading already as an understanding of mathematics and proofs, not to speak of language and arguments. One way of investigating the sort of PP-necessity relations involved in the requirement that a practical algorithmic decomposition be substantive is to look at organisms that have been damaged in various ways, for instance, by localized strokes or bullets in their brains. Thus, we might find out that a whole suite of abilities comes together—that, as a matter of empirical fact, anyone who has lost the ability to do A will also have lost the ability to do B. What we can tell on a priori grounds is only that there must be some things that we can just do, without having to do them by doing something else, by algorithmically elaborating other abilities. This is compatible with there being clusters of abilities such that we can do some of the component things by doing some—possibly conditioned—sequence of others. “That would be something that is PV-necessary for deploying any autonomous vocabulary (or equivalently, PP-necessary for any ADP) that cannot be algorithmically decomposed into practices for which no ADP is PP-necessary.” Brandom says: “We have no idea at all how even primitive non-discursive abilities that could be substantively algorithmically elaborated into the capacity to form the complex predicates in question could be further elaborated so as to permit the sorting of them into those that do and those that do not belong in the range of counterfactual robustness of a particular inference.” Training is “a course of experience, in Hegel’s and Dewey’s sense (Erfahrung rather than Erlebnis) of a feedback loop of perception, responsive performance, and perception of the results of the performance.” I would like to add that responsive performance must be performed at will. I.e., we have not only to learn to respond properly (according to some norms defining normality), but also not to respond properly, for example when we want to show that it is up to us how we decide to respond. This is the reason why irony and all other free tropes of discourse are so important: They show that any speech act has the characteristic of a free action. “Wittgenstein sees this sort of non-algorithmic practical elaboration as ubiquitous and pervasive,” says Brandom.

REFERENCES Bar, Hillel Y. 1964. Language and Information: Selected Essays on Their Theory and Application. Reading, Mass.: Addison-Wesley. Brandom, R. B. 1994. Making It Explicit: Reasoning, Representing and Discursive Commitment. Cambridge, Mass.: Harvard University Press. Brandom, R. B. 2000. Articulating Reason: An Introduction to Inferentialism. Cambridge, Mass.: Harvard University Press. Bühler, Karl. 1982 [1934]. Sprachtheorie: Die Darstellungsfunktion der Sprache. Jena: Verlag Gustav Fischer.

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Cresswell, M. J. 1973. Logics and Languages. London: Methuen. Carnap, R. 1942. Introduction to Semantics. Studies in Semantics I. Cambridge, Mass.: Harvard University Press. Chomsky, N. 1957. Syntactic Structures. Den Haag: The Hague Mouton. Chomsky, N. 1980. Rules and Representations. New York: Columbia University Press. Davidson, D. 1970. “Semantics for Natural Languages.” In Linguaggi nella Società e nella Tecnica, ed. B. Visentini et al. Milano: Edizioni di Communita. Davidson, D. 1980. Essays on Actions and Events. Oxford: Oxford University Press. Davidson, D. 1984. Inquiries into Truth and Interpretation. Oxford: Oxford University Press. Davidson, D., and G. Harman, eds. 1972. Semantics of Natural Language. Dordrecht: Reidel. Dennett, D. 1988. The Intentional Stance. Cambridge, Mass.: MIT Press. Dummett, M. A. E. 1975. “What Is a Theory of Meaning.” In Mind and Language, ed. Guttenplan, 97–138. Oxford: Clarendon Press. Dummett, M. A. E. 1976. “What Is a Theory of Meaning II.” In Truth and Meaning: Essays in Semantics, ed. Evans and McDowell. Oxford: Clarendon Press. Etchemendy, J. 1990. The Concept of Logical Consequence. Cambridge, Mass.: Harvard University Press. Evans, G. 1982. The Varieties of Reference. Oxford: Clarendon Press. Evans, G., and J. McDowell, eds. 1976. Truth and Meaning: Essays in Semantics. Oxford: Clarendon Press. Feigl, H., and W. Sellars, eds. 1949. Readings in Philosophical Analysis. New York: Appleton-CenturyCroft. French, P., T. Uehling, and H. Wettstein, eds. 1979. Contemporary Perspectives in the Philosophy of Language. Minneapolis: University of Minnesota Press. Gödel, K. 1930. “Die Vollständigkeit der Axiome des logischen Funktionen-Kalküls”; Monatshefte für Mathematik und Physik 38: 213–42. Gödel, K. 1931. Über Formal Unentscheidbare Sätze der Principia Mathematica und Verwandter Systeme”; Monatshefte für Mathematik und Physik 38: 173–98. Goldman, A. 1978. “Discrimination and Perceptual Knowledge.” Journal of Philosophy 73, 20: 771–91. Grover, D., J. Camp, and N. Belnap. 1975. “A Prosentential Theory of Truth.” Philosophical Studies 27: 73–125. Guttenplan, S., ed. 1975. Mind and Language. Wolfson College Lectures 1974. Oxford: Clarendon Press. Hahn, L. W., and P. A. Schilpp, eds. 1986. The Philosophy of W. V. Quine. La Salle, Ill.: Open Court. Halmos, P. R. 1960. Naive Set Theory. Princeton: Princeton University Press. Horwich, P. 1990. Truth. Oxford: Blackwell. Kambartel, F. 1977/78. “Symbolic Acts.” In Contemporary Aspects of Philosophy, ed. G. Ryle, 70–85. Stocksfield: Oriel Press. Kambartel, F. 2000. “Strenge und Exaktheit. Über die Methode von Wissenschaftund Philosophie.” In Formen der Argumentation, ed. G.-L. Lueken, 75–85. Leipzig: University of Leipzig Press. Lewis, D. 1983. Philosophical Papers I. Oxford: Oxford University Press. Lewis, D. 1984. On the Plurality of Worlds. Oxford: Oxford University Press. Lorenz, K., and P. Lorenzen. 1978. Dialogische Logik. Darmstadt: Wiss. Buchg. Lorenzen, P. 1987. Lehrbuch der Konstruktiven Wissenschaftstheorie. Mannheim: Bibl. Inst. Lueken, G.-L. 2000. Formen der Argumentation. Leipzig: University of Leipzig Press. McDowell, J. 1994. Mind and World. Cambridge, Mass.: Harvard University Press. McDowell, J. 1998. Meaning, Knowledge and Reality. Cambridge, Mass.: Harvard University Press. Millikan, R. 1984. Language, Thought, and Other Biological Categories. Cambridge, Mass.: MIT Press. Montague, R. 1974. Formal Philosophy, ed. R. Thomason. New Haven, Conn.: Yale University Press. Peregrin, J. 1995. Doing Worlds with Words: Formal Semantics Without Formal Metaphysics. Dordrecht: Kluwer. Peregrin, J. 2001. Meaning and Structure: Structuralism of Postanalytic Philosophers. Aldershot: Ashgate. Putnam, H. 1975b. Mathematics, Matter and Method. Cambridge: Cambridge University Press. Putnam, H. 1975b. Mind, Language and Reality: Philosophical Papers, vol. 2. Cambridge: Cambridge University Press. Quine, W .V. O. 1960. Word and Object. Cambridge, Mass: MIT Press.

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Rorty, R., ed. 1967/1992. The Linguistic Turn: Recent Essays in Philosophical Method. Chicago: University of Chicago Press. 1–39. Rosenberg, J. F. 1994. Beyond Formalism. Philadelphia: Temple University Press. Ryle, G. 1949. The Concept of Mind. London: Hutchinson & Co. Searle, J. R. 1983. Intentionality: An Essay in the Philosophy of Mind. Cambridge: Cambridge University Press. Sellars, W. 1963. Science, Perception, and Reality. London: Routledge & Kegan Paul. Sellars, W. 1974. “Meaning as Functional Classification: A Perspective on the Relation of Syntax to Semantics.” Synthese 27: 417–37. Sellars, W. 1980. Pure Pragmatics and Possible Worlds: The Early Essays of W. Sellars, ed. J. Sicha. Atascadero: Ridgeview. Sellars, W. 1997. “Empiricism and the Philosophy of Mind.” Study Guide by R. B. Brandom. Cambridge, Mass.: Harvard University Press (cf. also Sellars 1963). Stekeler-Weithofer, P. 1986. Grundprobleme der Logik: Elemente einer Kritik der formalen Vernunft. Berlin: de Gruyter. Strawson, P. F. 1968. Studies in the Philosophy of Thought and Action. Oxford: Oxford University Press. Williams, B. 2002. Truth and Truthfulness: An Essay in Genealogy. Princeton: Princeton University Press Wittgenstein, L. 1921. Tractatus logico-philosophicus: Annalen der Naturphilosophie; Werke, Bd. 1. Frankfurt a. M. 1984: 1989. Wittgenstein, L. 1953. Philosophical Investigations / Philosophische Untersuchungen. Oxford: Blackwell and Frankfurt / M. 1984: Suhrkamp. Wright, C., ed. 1984. Frege: Tradition and Influence. Oxford: Blackwell. Ziff, P. 1960 Semantic Analysis. Ithaca, N.Y.: Cornell University Press.

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PHILOSOPHICAL TOPICS VOL. 36, NO. 2, FALL 2008

Will There Be Blood? Brandom, Hume, and the Genealogy of Modals

Huw Price University of Sydney

I. THE GENEALOGY OF MODALS Robert Brandom begins Lecture 4 with the suggestion that modality is problematic for empiricism but not for naturalism. The status and respectability of alethic modality was always a point of contention and divergence between naturalism and empiricism. It poses no problems in principle for naturalism, since modal vocabulary is an integral part of all the candidate naturalistic base vocabularies. Fundamental physics is, above all, a language of laws; the special sciences distinguish between true and false counterfactual claims; and ordinary empirical talk is richly dispositional. By contrast, modality has been a stumbling block for the empiricist tradition ever since Hume forcefully formulated his epistemological, and ultimately semantic, objections to the concepts of law and necessary connection. (2008, 93)

Associating Hume’s challenge to the status of modality with his empiricism rather than his naturalism, Brandom goes on to suggest the late twentieth century’s rejection of empiricism’s semantic atomism then clears the way for the modal revolution. It seems to me that this way of reading the history misses an important ingredient in Hume’s treatment of modality, namely, Hume’s interest in what might be called the genealogy of modality. This project has the following key features, in my view:

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1. While it may be motivated for Hume by empiricism, it doesn’t depend on that motivation, and stands alone as a project for the philosophical understanding of modality—a project in one sense entirely within the scope of a well-motivated philosophical naturalism. 2. Despite its naturalistic credentials, it represents a profound challenge to the view of modality reflected in Brandom’s (accurate) characterization of the attitude of many contemporary naturalists. 3. It is a precursor of Brandom’s own project, as described in this lecture; with the result that his project, too, represents a powerful challenge to this same form of contemporary naturalism (the kind that “takes modality for granted,” as it were). The genealogy of modality is the project of understanding how creatures in our situation come to go in for modal talk—how we get in the business of using modal vocabulary and thinking modal thoughts. In Hume, as in Brandom, this is supposed to be a thoroughly naturalistic inquiry, in the sense that it takes for granted that we ourselves are natural creatures, without supernatural powers. The interesting thing is that this naturalistic attitude to modal talk—to the use of modal vocabulary—can easily challenge a naturalistic view of the subject matter, if by this we mean the view that modality itself is part of the furniture of the natural world.1 If this seems puzzling, think of the normative analogy. The project of a genealogy of normative and evaluative notions is to explain why natural creatures like us go in for using normative concepts and vocabulary. It is naturalistic in the sense that it regards us and our vocabularies as part of the natural order, but not (or at least not necessarily) in the sense that it regards norms and values as part of our natural environment. Many contemporary philosophers seem to find the point much easier to grasp in the normative than the modal case, a fact which no doubt reflects, in part, the role that modal notions have come to play in the foundations of contemporary philosophy. Hume’s expressivist genealogy is a threat to the status of those foundations, in a way which may seem to have no parallel in the normative case. Another factor is the one noted in Brandom’s remarks above: physics seems modal through and through. In my view, however, any naturalist worth her salt ought to be cautious of this kind of appeal to physics. We can grant that physics as it stands is irreducibly modal, without simply throwing in the towel on the question as to whether this should be taken as reflecting the way the physical world is independently of us, or a deeply entrenched aspect of the way in which creatures in our situation need to conceptualize the world. Of course, these are deep and difficult questions—it isn’t immediately clear that there’s a standpoint available to us from which to address them. But this difficulty is no excuse for giving up the game—for simply assuming, in effect, that physics views the world through perfectly transparent lenses. (Where better than physics to remember our Copernican lessons? )

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The point I want to stress is that a plausible naturalistic genealogy for modal discourse might count heavily on one side of these issues. In effect, it might tell us why creatures in our situation would be led to develop a modal physics, even if they inhabited a nonmodal world (perhaps a Hume world, as contemporary metaphysicians sometimes say). As I’ve said, such a genealogy would be naturalistic in the Humean sense, which puts the emphasis on the idea that we humans (and our thought and talk) are part of the natural order. But many mainstream contemporary philosophers, keen to think of themselves as naturalists, would be discomforted by it. Why? Because it would challenge the idea that the function of modal vocabulary is to keep track of distinctively modal features of the natural world, and challenge the project of resting realist metaphysics on modal foundations. Thus I think that Brandom’s presentation of his own genealogical project in this lecture obscures both some enemies and some allies. Its enemies, as I’ve already said, are the people in contemporary philosophy who assume a more robust, metaphysical approach to modality. There isn’t an easy accommodation between Brandom’s project, on the one side, and naturalism as widely commonly and metaphysically conceived, on the other. And the tension is one of the most important in contemporary philosophy, for the reasons Brandom himself puts his finger on: the role of modality in the revolution that swept through analytic philosophy in the last third of the twentieth century. Brandom thus has a bigger fight on his hands than he realizes, I think. But he’s on the side of (Humean) virtue, in my view, and should be leading the charge— leading the pragmatists’ campaign against modal metaphysics. The best reason for optimism about the outcome of the campaign is that we pragmatists hold the naturalistic high ground, and cannot be dislodged—at least, not without dislodging Darwin, too, for he’s the rock on which we stand. The second-order, naturalistic reflection on the origin of our vocabularies always trumps, in principle, the unreflective first-order intuitions which merely exercise those vocabularies. As for Brandom’s allies, they are Hume and his expressivist descendants, fellow travelers in the quest for a pragmatist genealogy of modal idioms. Here are some leading lights, concerning a mixed bag of modal notions: Ramsey (1926) and other subjectivists about probability; Ramsey (1929) again, about causation and laws; Ryle (1950), whom Brandom mentions, about laws and conditionals; Wittgenstein (1981), about claims of necessity; various advocates of the project of understanding causation in terms of manipulation (e.g., Collingwood [1940], von Wright [1971], Gasking [1955], and Menzies and Price [1993]); and Simon Blackburn (1993), of course, who has done more than anyone else in recent years to defend a kind of modest Humean expressivism (stressing in particular the parallel between the moral and the modal cases). Common to all these writers, as to Brandom, is a concern to explain one or other of the modal notions in terms of what we do with them, what practical role they play in our lives, rather than in metaphysical terms. This brings me to the more general issue I want to raise, viz., Brandom’s somewhat ambiguous attitude to ontology and metaphysics. In general, pragmatists have

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not been shy about expressing some antipathy to metaphysics. Here again, Hume— an exemplary genealogical pragmatist, in the present sense—is a shining example, known for his remarks about committing volumes of school metaphysics to the flames. More recently, one thinks of Wittgenstein’s dismissal of modal realism as ‘the slightly hysterical style of university talk’ (1981, §299); and of Ryle’s remark that being a professor of metaphysics was like being a professor of tropical diseases—in both cases, Ryle said, the aim was to eradicate the subject matter, not to promote it. We don’t find this kind of anti-metaphysical attitude in Brandom. Rather, we find what looks to me to be a degree of ambiguity, or uncertainty, about the goals of his project, with respect to what are traditionally treated as metaphysical questions. I think that Brandom hasn’t seen clearly the importance of a distinction which is marked relatively sharply in the Humean tradition, between two views of the philosopher’s project. In the remainder of the paper I want to say something about this distinction, and offer some textual evidence that Brandom hasn’t properly faced up to the need to take a stand on it, on one side or other.

II. THE LESSONS OF HUMEAN EXPRESSIVISM Expressivist views (in what I’m taking to be the Humean sense) are often responses to what are now called ‘location’ or ‘placement’ problems.2 Initially, these present as ontological or perhaps epistemological problems, within the context of some broad metaphysical or epistemological program: empiricism, say, or physicalism. By the lights of the program in question, some of the things we talk about seem hard to ‘place’, within the framework the program dictates for reality or our knowledge of reality. Where are moral facts to be located in the kind of world described by physics? Where is our knowledge of causal necessity to go, if a posteriori knowledge is to grounded on the senses? The expressivist solution is to move the problem cases outside the scope of the general program in question, by arguing that our tendency to place them within its scope reflects a mistaken understanding of the vocabulary associated with the matters in question. Thus the (apparent) location problem for moral or causal facts was said to rest on a mistaken understanding of the function of moral or causal language. Once we note that this language is not in the business of ‘describing reality’, says the expressivist, the location problem can be seen to rest on a category mistake. Note that traditional expressivism thus involves both a negative and a positive thesis about the vocabularies in question. The negative thesis was that these vocabularies are not genuinely representational, and traditional expressivists here took for granted that some parts of language are genuinely representational (and, implicitly, that this was a substantial theoretical matter of some sort). As many people have pointed out, this thesis is undermined by deflationism about the semantic notions

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on which it rests. Less commonly noted is the fact that deflationism leaves entirely intact the expressivists’ positive thesis, which proposes some alternative expressive account of the function of each vocabulary in question. As I’ve argued elsewhere (Macarthur and Price 2007), this kind of positive thesis not only survives deflation of the negative thesis by semantic minimalism; it actually wins by default, in the sense that semantic deflationism requires some nonrepresentational account of the functions of the language in question—in other words, it ensures that the positive work of theorizing about the role and functions of the vocabularies in question has to be conducted in nonsemantic or nonreferential terms. What’s happening at this point on the metaphysical side—i.e., to those ontological issues that expressivism originally sought to evade? Note, first, that traditional expressivism tended to be an explicitly antirealist position, at least in those versions embedded in some broader metaphysical program. In ethics, for example, noncognitivism was seen as a way of making sense of the language of morals, while denying that there are really any such things as moral values or moral facts. But this was always a little problematic: if moral language was nondescriptive, how could it be used to make even a negative ontological claim? Better, perhaps, to say that the traditional metaphysical issue of realism versus antirealism is simply ill-posed—an attitude to metaphysics that has long been in play, as Carnap makes clear: Influenced by ideas of Ludwig Wittgenstein, the [Vienna] Circle rejected both the thesis of the reality of the external world and the thesis of its irreality as pseudo-statements; the same was the case for both the thesis of the reality of universals . . . and the nominalistic thesis that they are not real and that their alleged names are not names of anything but merely flatus vocis. (1950, 252)

Famously, Carnap recommends this kind of metaphysical quietism quite generally, and this is surely a desirable stance for an expressivist, especially when semantic minimalism deflates what I called the expressivist’s negative thesis. An expressivist wants to allow that as users of moral language, we may talk of the existence of values and moral facts, in what Carnap would call an internal sense. What’s important is to deny that there is any other sense in which these issues make sense. Here Carnap is a valuable ally. So construed, expressivism simply deflates the traditional ontological questions—it sets them aside, aiming to cure us of the urge to ask them, as Wittgenstein or Ryle might put it. In their place, it offers us questions about the role and genealogy of vocabularies. These are questions about human behavior, broadly construed, rather than questions about some seemingly puzzling part of the metaphysical realm. So expressivism isn’t a way of doing metaphysics in a pragmatist key. It is a way of doing something like anthropology (by which for present purposes I mean a small but interesting sub-speciality of biology). Hence my Humean slogan: biology not ontology.

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III. BRANDOM AND METAPHYSICS Where does Brandom stand with respect to this distinction between ontology and biology, metaphysics and anthropology? My impression is that he sometimes tries to straddle the divide, or at least doesn’t sufficiently distinguish the two projects. This is a large topic, deserving a more detailed treatment elsewhere, but I want to sketch some reasons in support of this assessment.3 On the one hand, as I have already noted, Brandom often writes as if his project is metaphysical, in the present sense—as if he is concerned to give us an account of the nature and constitution of particular items of philosophical interest, such as conceptual content and the “representational properties” of language: The primary treatment of the representational dimension of conceptual content is reserved for Chapter 8 . . . [where] the representational properties of semantic contents are explained as consequences of the essentially social character of inferential practice. (1994, xvii)

On the face of it, this is a metaphysical stance: it is concerned with representational properties, after all. And at a more general level, consider this: [T]he investigation of the nature and limits of the explicit expression in principles of what is implicit in discursive practices yields a powerful transcendental argument—a . . . transcendental expressive argument for the existence of objects. (1994, xxii–xxiii)

On the other hand, Brandom often makes it clear that what is really going on is about the forms of language and thought, not about extra-linguistic reality as such. The passage I have just quoted continues with the following gloss on the transcendental argument in question: it is an “argument that (and why) the only form the world we can talk and think of can take is that of a world of facts about particular objects and their properties and relations” (1994, xxii–xxiii, latter emphasis mine). Similarly, at a less general level, Brandom often stresses that what he is offering is primarily an account of the attribution of terms—‘truth’, ‘reference’, ‘represents’, etc.—not of the properties or relations that other approaches take those terms to denote. Concerning his account of knowledge claims, for example, he says: Its primary focus is not on knowledge itself but on attributions of knowledge, attitudes towards that status. The pragmatist must ask, What are we doing when we say that someone knows something? (1994, 297, latter emphasis mine)

But a few sentences later, continuing the same exposition, we have this: “A pragmatist phenomenalist account of knowledge will accordingly investigate the social and normative significance of acts of attributing knowledge” (1994, 297, my emphasis). Here, the two stances are once again run together: to make things clear, a pragmatist should deny that he is offering an account of knowledge at all. (That’s what it means to say that the project is biology, not ontology.)4

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Another point in Brandom’s favor (from my Humean perspective) is that he often makes it clear that he rejects a realist construal of reference relations. Thus, concerning the consequences of his preferred anaphoric version of semantic deflationism, he writes: One who endorses the anaphoric account of what is expressed by ‘true’ and ‘refers’ must accordingly eschew the reifying move to a truth property and a reference relation. A line is implicitly drawn by this approach between ordinary truth and reference talk and variously specifically philosophical extensions of it based on theoretical conclusions that have been drawn from a mistaken understanding of what such talk expresses. Ordinary remarks about what is true and what is false and about what some expression refers to are perfectly in order as they stand; and the anaphoric account explains how they should be understood. But truth and reference are philosophers’ fictions, generated by grammatical misunderstandings. (1994, 323–24) Various word-world relations play important explanatory roles in theoretical semantic projects, but to think of any one of these as what is referred to as “the reference relation” is to be bewitched by surface syntactic form. (1994, 325)

On the other hand, Brandom’s strategy at this point suggests that in some ways he is still wedded to a traditional representational picture. Consider, in particular, his reliance on syntactic criteria in order to be able to deny, as he puts it, that claims expressed using traditional semantic vocabulary make it possible for us to state specifically semantic facts, in the way that claims expressed using the vocabulary of physics, say, make it possible for us to state specifically physical facts. (1994, 326)

Here Brandom sounds like a traditional expressivist, who is still in the grip of the picture that some parts of language are genuinely descriptive, in some robust sense. He hasn’t seen the option and attractions of allowing one’s semantic deflationism to deflate this picture, too; and remains vulnerable to the slide to metaphysics, wherever the syntactical loophole isn’t available. This reading is born out by the fact that at certain points he makes to confront these traditional metaphysical issues head-on. “None of these is a naturalistic account,” he says (2000, 27), referring to various aspects of his account of the referential, objective, and normative aspects of discourse. And again: Norms . . . are not objects in the causal order. . . . Nonetheless, according to the account presented here, there are norms, and their existence is neither supernatural nor mysterious. (1994, 626)

Once again, this passage continues with what is by my lights exactly the right explanation of what keeps Brandom’s feet on the ground: “Normative statuses are domesticated by being understood in terms of normative attitudes, which are in the causal order” (1994, 626). But my point is that he shouldn’t have to retreat in this

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way in the first place. His account only looks non-naturalistic because he tries to conceive of it as metaphysics. If he had stayed on the virtuous (anthropological) side of the fence, there would have been no appearance of anything non-naturalistic, and no need to retreat. (Rejecting the traditional naturalist/non-naturalist debate is of a piece with rejecting the realist/antirealist debate.) I have one final example, which seems to me to illustrate Brandom’s continuing attraction to what I am thinking of as the more representationalist side of the fence—the side where we find the project of reconstructing representational relations using pragmatic raw materials. It is from Brandom’s closing lecture in the present series, and is a characterization he offers of his own project, in response to the following self-posed challenge: “Doesn’t the story I have been telling remain too resolutely on the ‘word’ side of the word/world divide?” He replies: Engaging in discursive practices and exercising discursive abilities is using words to say and mean something, hence to talk about items in the world. Those practices, the exercise of those abilities, those uses, establish semantic relations between words and the world. This is one of the big ideas that traditional pragmatism brings to philosophical thought about semantics: don’t look, to begin with, to the relation between representings and representeds, but look to the nature of the doing, of the process, that institutes that relation. (2008, 177–78)

I have been arguing that the right course—and the course that Brandom actually often follows, in practice—is precisely to remain “resolutely on the ‘word’ side of the word/world divide.” This resolution doesn’t prevent us from seeking to explain referential vocabulary—the ordinary ascriptions of semantic relations, whose pervasiveness in language no doubt does much to explain the attractiveness of the representational picture. Nor does it require, absurdly, that we say nothing about word–world relations. On the contrary, as Brandom himself points out in a remark I quoted above: Various word-world relations play important explanatory roles in theoretical semantic projects, but to think of any one of these as what is referred to as “the reference relation” is to be bewitched by surface syntactic form. (1994, 325)

Biological anthropologists will have plenty to say about the role of the natural environment in the genealogy and functions of vocabularies. But the trap they need to avoid is that of speaking of “semantic relations between words and the world,” in anything other than a deflationary tone. For once semantic relations become part of the biologists’ substantial theoretical ontology, so too do their relata, at both ends of the relation. The inquiry becomes committed not merely to words, but to all the things to which it takes those words to stand in semantic relations—to norms, values, numbers, causes, conditional facts, and so on: in fact, to all the entities which gave rise to placement problems in the first place. At this point, expressivism’s hardwon gains have been thrown away, and the subject has become infected once more with metaphysics. That’s why it is crucial that my (biological) anthropologists

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should remain semantic deflationists, in my view, and not try to recover substantial semantic relations, even on pragmatic foundations. In calling the possibility of this kind of liberation from metaphysics an insight of Humean expressivism, I don’t mean, of course, to belittle the respects in which pragmatism has moved on from Hume. Brandom notes that Wilfred Sellars characterized his own philosophical project as that of moving analytic philosophy from its Humean phase to a Kantian phase, and glosses the heart of this idea as the view that traditional empiricism missed the importance of the conceptual articulation of thought. Rorty, in turn, has described Brandom’s project as a contribution to the next step: a transition from a Kantian to an Hegelian phase, based on recognition of the social constitution of concepts, and of the linguistic norms on which they depend. For my part, I’ve urged merely that Brandom’s version of this project is in need of clarity on what I think it is fair to describe as a Humean insight. Hume’s expressivism may well be a large step behind Kant, in failing to appreciate the importance of the conceptual; and a further large step behind Hegel, in failing to see that the conceptual depends on the social. But it is still at the head of the field for its understanding of the way in which what we would now call pragmatism simply turns its back on metaphysics.

IV. THERE WILL BE BLOOD By my lights, then, Brandom’s attitude to metaphysics seems excessively irenic. I want to follow Hume, Ramsey, Ryle, Wittgenstein, and Blackburn, in dismissing, or at best deflating, large parts of that discipline. Whereas Brandom—though engaged in fundamentally the same positive inquiry, the same pragmatic explanatory project—seems strangely reluctant to engage with the old enemy. Nowhere is this difference more striking than in the case of modality. In my view, modality is the soft under-belly of contemporary metaphysics: the belly, because as Brandom himself notes in Lecture 4, so much of what now passes for metaphysics rests on it, or is nourished by it; and soft, because it is vulnerable to attack from precisely the direction to which the subject itself is most keen to be most receptive, that of naturalism. It seems to me that Brandom’s treatment of modality provides precisely the tools required to press this advantage—precisely the sharp implements we need to make mincemeat of modern metaphysics. Hence my puzzlement, at his reluctance to put them to work.5 I had planned to end there, but the story is a little more complicated. Modern metaphysics turns out to have two under-bellies, both of them soft—a fact which underlines what a strange and vulnerable beast it is, in my view. The second belly is ‘representationalism’—the fact that much of the subject is built on appeals to reference, and other robust semantic notions. Here, too, as I’ve said, I read Brandom as a somewhat ambiguous ally of the traditional pragmatist attack. On the one

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hand, he offers us profound new insights into how to do philosophy in another key; on the other hand, as the remark I quoted from Lecture 6 indicates, he sometimes seems to want to get out of it some pragmatist substitute for platonic representation—some surgery which would reconstruct the referential belly of the beast, as it were, in a new and healthy form.6 Once again, I think that that’s the wrong move. The two-bellied beast should simply be put out of its misery, and no one is better placed than Brandom to administer the coup de grâce.

ACKNOWLEDGMENTS This is a lightly edited version of my comments on Lecture 4 of Brandom’s Locke Lectures, as delivered in Prague in April 2007. I am grateful to Bob Brandom and Jarda Peregrin for inviting me to take part in the Prague meeting, and to the Australian Research Council and the University of Sydney, for research support.

NOTES 1. This is an example of how subject naturalism can challenge object naturalism, as I put it elsewhere (Price 2004). 2. See Jackson (1998), for example, for this usage. 3. This section draws extensively on Price (2010a). I am grateful to the editor and publisher of that volume for permission to re-use this material here. 4. It might seem that I am being uncharitable to Brandom here, taking too literally his claim to be giving an account of knowledge (and similar claims about other topics). By way of comparison, isn’t it harmless to say, at least loosely, that disquotationalism is an account of truth, even though it isn’t literally an account of truth, but rather of the functions of the truth predicate? But I think there are other reasons for taking Brandom to task on this point—more on this in a moment. 5. Like Prague itself, this is no country for vegetarians. 6. See Price (2010a) and (2010b, Ch. 1) for more on this theme.

REFERENCES Blackburn, S. 1993. Essays in Quasi-Realism. New York: Oxford University Press. Brandom, R. 1994. Making It Explicit. Cambridge, Mass.: Harvard University Press. Brandom, R. 2000. Articulating Reasons: An Introduction to Inferentialism. Cambridge, Mass.: Harvard University Press. Brandom, R. 2008.Between Saying and Doing: Towards an Analytic Pragmatism. Cambridge, Mass.: Harvard University Press. Carnap, R. 1950. “Empiricism, Semantics and Ontology.” Revue Internationale de Philosophie 4: 20–40; reprinted in Philosophy of Mathematics, ed. Paul Benacerraf and Hilary Putnam, 241–57. Cambridge, Mass.: Cambridge University Press, 1983. (Page references are to the latter version.) Collingwood, R. 1940. An Essay on Metaphysics. Oxford: Clarendon Press.

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Gasking, D. 1955. “Causation and Recipes.” Mind 64: 479–87. Jackson, F. 1998. From Metaphysics to Ethics. Oxford: Clarendon Press. Macarthur, D., and H. Price. 2007. “Pragmatism, Quasi-realism and the Global Challenge.” In The New Pragmatists, ed. Cheryl Misak, 91–120. Oxford: Oxford University Press. Menzies, P., and H. Price. 1993. “Causation as a Secondary Quality.” British Journal for the Philosophy of Science 44: 187–203. Price, H. 2004. “Naturalism Without Representationalism.” In Naturalism in Question, ed. David Macarthur and Mario de Caro, 71–88. Cambridge, Mass.: Harvard University Press. Price, H. 2010a. “One Cheer for Representationalism?” In The Philosophy of Richard Rorty (Library of Living Philosophers 32), ed. R. Auxier. Chicago: Open Court. Price, H. 2010b. Naturalism Without Mirrors. New York: Oxford University Press. Ramsey, F. P. 1926. “Truth and Probability.” In Philosophical Papers, ed. D. H. Mellor, 52–94. Cambridge: Cambridge University Press. Ramsey, F. P. 1929. “General Propositions and Causality.” In Philosophical Papers, ed. D. H. Mellor, 145–63. Cambridge: Cambridge University Press. Ramsey, F. P. 1990. Philosophical Papers, ed. D. H. Mellor. Cambridge: Cambridge University Press. Ryle, G. 1950. ‘‘‘If ’, ‘So’, and ‘Because’,’’ in Philosophical Analysis, ed. M. Black. Ithaca, N.Y.: Cornell University Press. von Wright, G. 1971. Explanation and Understanding. Ithaca, N.Y.: Cornell University Press. Wittgenstein, L. 1981. Zettel, ed. G. E. M. Anscombe and G. H. von Wright and trans. G. E. M. Anscombe, 2nd edition. Oxford: Blackwell.

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PHILOSOPHICAL TOPICS VOL. 36, NO. 2, FALL 2008

Brandom’s Incompatibility Semantics

Jaroslav Peregrin Prague

I. WHY FORMAL SEMANTICS? Formal semantics is an enterprise which accounts for meaning in formal, mathematical terms, in the expectation of providing a helpful explication of the concept of the meaning of specific word kinds (such as logical ones), or of words and expressions generally. Its roots go back to Frege, who proposed exempting concepts, meanings of predicative expressions, from the legislation of psychology and relocating them under that of mathematics. This started a spectacular enterprise, fostered at first within formal logic and later moving into the realm of natural languages, and featuring a series of eminent scholars, from Tarski and Carnap to Montague and David Lewis. Partly independently of this, Frege set the agenda for a long-term discussion of the question of what a natural language is, his own contribution being that language should be seen not as a matter of subjective psychology, but rather as a reality objective in the sense in which mathematics is objective. His formal semantics, then, was just an expression of this conception of language. And many theoreticians now take it for granted that formal semantics is inseparably connected with a Platonist conception of language. Moreover, the more recent champions of formal semantics, Montague and David Lewis, took for granted that natural language is nothing else than a structure of the very kind envisaged by the theories of formal logicians. While Montague

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claims quite plainly that there is no substantial difference between formal and natural languages (“I reject the contention,” he says [1974, 188], “that an important theoretical difference exists between formal and natural languages”), Lewis states that it is fully correct to say that a linguistic community entertains a language in the form of a mathematical structure (“we can say,” states Lewis [1975, 166], “that a given language L [a function from a string of sounds or of marks to sets of possible worlds] is used by or is a (or the) language of a given population P”). However, in the last third of the twentieth century, many (direct and indirect) participants of the discussion of the question what is language? underwent a distinctively pragmatic turn. Philosophers of language started to revive American pragmatism, or the ideas of the later Wittgenstein, or Austinian speech act theory, and they began to picture language primarily as an activity—or as a toolbox for carrying out an activity—rather than as a mathematical structure. In response to the Montague-Lewisian conception of language, Donald Davidson (1986) wrote that “there is no such a thing as language, not if a language is anything like what many philosophers and linguists have supposed.” Robert Brandom’s philosophy of language undoubtedly fits with the latter stream. For Brandom, language is first and foremost an activity, albeit a rule-governed one. From this it might be expected that his attitude toward formal semantics would be very reserved. But surprisingly, this does not seem to be the case—what Brandom urges in the fifth of his Locke Lectures is strongly evocative of a formal semantics. Is this viable? Does not the approach to semantics entertained by Montague (1974) or Lewis (1972) presuppose a kind of ‘formal metaphysics’ which is utterly at odds with pragmatism? Can a Brandomian-style inferentialist really embrace formal semantics? To sort things out, I will concentrate, in this paper, on the following three questions: (1) Is a formal approach to semantics compatible with pragmatism and inferentialism? (2) If so, what kind of formal semantics is useful from the inferentialist perspective and of what good can it be from this perspective?; and (3) Is Brandom’s incompatibility semantics a suitable kind and does it bring us some new insights into the phenomena of meaning and language? My answer to question (1) is, as expected, positive. For some time now, I have been urging a reconciliation of pragmatism and formal semantics—see esp. Peregrin (2001; 2004). I am unsure about how far my reasons for giving this answer overlap with the reasons that made Brandom produce his incompatibility semantics; but I think that writing this paper might be a good way to find out. I personally think that it is vital to appreciate the distinction between claiming that language is a mapping of expressions on objects and saying that it is useful to

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model it as a mapping of expressions on objects. The former claim commits us to a radically limiting statement about what meaning is and how an expression can come to have it. Elsewhere (ibid., §8.4) I compared this to the relationship between the Bohr model of the internal workings of an atom (the tiny sun-nucleus orbited by even tinier planet-electrons) and its actual innards. It is clear that the atom’s innards are not identical to what the Bohr model shows; but neverthless it is useful to model it in this way. Why? Because, first, what the inside is precisely like anyway defies description by the usual means of our language; and, second, it renders the inside more comprehensible to us (at the cost of oversimplifications). In short, it provides for what Wittgenstein (1953, §122) called, in the case of language, perspicuous representation [übersichtliche Darstellung]; or what Haugeland (1978) called structural explanation. An important point is that whereas saying that a language is a set of labels stuck on objects (a claim that is often ascribed to anybody doing formal semantics) involves saying that the way an expression acquires meaning is by becoming a label, saying that language can be modeled as such a set of labels involves no such commitment. Especially, the latter is fully compatible with seeing meanings as roles: though an expression would acquire such a role by means of being engaged within a praxis, there is no reason not to envisage the roles by means of a model in which the expressions are put side by side with their roles, which are encapsulated into some kind of formal objects.

II. WHAT DOES IT TAKE TO BE A MODEL OF LANGUAGE? Given that there is a point in doing a logico-mathematical model of language, we should ask ourselves what kind of model we want, what such a model is to show us, and how are we to assess its adequacy (and hence ‘reasonableness’). This brings us to the above question (2). To answer it, let us consider the standard format of the definition of the formal languages of logic, which are to serve us as our models. Such a language usually has three parts (one of the latter two might be missing). First, there is syntax (proper), the delimitation of well-formed formulas (and more generally well-formed expressions). Second, there is an axiomatics (logical syntax, in Carnap’s phrase), the delimitation of the relation of inference among wffs and/or the set of theorems. Third, there is a (formal) semantics, the delimitations of acceptable assignments of denotations to expressions, which ground the relation of consequence and/or the set of tautologies.3 If we want to use such a language as a model of an actual language, then which of its features should be aligned with corresponding features of the natural language to be modeled? It is clear and uncontroversial that the first component, the delimitation of wffs, should somehow correspond to the grammar of the language to be modeled. Of course, the correspondence may be very indirect (we may want

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to have the grammar of the formal language significantly simpler than the grammar of the natural one)—the important thing is that we should be able to say which wff (if any) corresponds to a given sentence and which sentence corresponds to which wff. Many logicians would say that the point of contact between the real language and the model is the semantics—that the denotations of the expressions of the formal language assigned to expressions should correspond to, or model, or capture, or simply be the meanings of the corresponding expressions of natural language. Thus, classical logic maps ‘∧’ on the usual truth table, the story goes, because the corresponding truth function is the meaning of English ‘and’, which gets regimented as ‘∧’. This amounts to saying that the denotation-assignment function of a formal model should be seen as reflecting the real association of meanings with expressions. Continuing along these lines, then, it would appear that there is no direct relationship between the inferential component of the formal language and natural language—there being nothing in natural language that would directly correspond to inference. Inference, from this viewpoint, is merely the logicians’ tool of getting a better grip on consequence, which itself is a matter of semantics (and can be defined via denotation-assignments). Inference is thus the theoretician’s attempt to approximate consequence by finite and hence convenient means. Needless to say, were this to be the sole way of aligning the formal model with a real language, then the inferentialist should best refrain from taking formal models seriously—for he does not believe that there is a meaning, independent of inference, that can be thus compared with the semantic interpretants of the formal language. But fortunately it is not the only way; there exists an alternative: we can say that where the model connects with reality is not semantics, but inference. We may then say that the model is adequate if the stipulated inferential rules explicate the inferential rules constitutive of the real language. And we may say that semantics is simply our way of seeing the inferential roles as distributed among individual expressions—as the expressions being mapped on their contributions to the inferential patterns they support. This, of course, presupposes that inference, besides being a tool employed by the logician as an expedient within her pursuit of consequence, is also something already present within natural language. And this is precisely the basic inferentialist credo: that language is generally constituted by rules and that meaning, in particular, is constituted by inferential rules—so much so, that what makes an expression meaningful in the first place is the fact that it is governed by an inferential pattern. To illustrate this, let me consider the simple case of classical logical constants. The denotationalist would say that classical logic can be seen as a model of natural language insofar as the logical constants denote the very same things as their natural language counterparts (modulo a reasonable simplification and idealization); and that the soundness and completeness proof for the classical propositional calculus shows that the ensuing relation of consequence can be conveniently captured

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in terms of a couple of axioms and the rule MP. The inferentialist, by contrast, would say that classical logic models natural language insofar as the axiomatics (or the natural deduction rules) of classical logic capture the inferential patterns actually governing their counterparts in natural language (modulo a reasonable simplification and idealization); and that the soundness and completeness proof shows that the usual semantics can be seen as a way of presenting the inferential structure as distributed among individual expressions. This brings us to the problem of the primitives, the ‘unexplained explainers’ the theory of language is to rest upon. The central concept of this enterprise is, no doubt, meaning. But when we look at early semantic theories within modern logic (what Tarski called “scientific semantics”), we see this concept fading into the background: the crucial concept appears to be that of truth. This might be explained by the fact that these theories never targeted the intuitive concept of meaning (except, perhaps, its ‘extensional component’); however, an explicit defense of taking the concept of meaning as secondary to the concept of truth is also available: in its most elaborated version from Davidson. Thus, in these theories, the concept of truth is what generally stands as the ‘unexplained explainer’ of semantics—in the sense that this concept is either not explained at all, or is reduced to some nonsemantic concepts and serves as the basis for the explanation of other semantic notions. In this order of explanation, consequence is construed as truth-preservation and inference as the best possible approximation to truth-preservation in terms of rules (besides this, there is the purely formalistic concept of inference, where it is stripped down to transformability according to an arbitrarily chosen set of rules, but this has little to do with semantics). From the inferentialist perspective, however, the situation looks very different. From the perspective Brandom is advocating, the core of any linguistic practices is the game of giving and asking for reasons. And hence we should ask what conditions must be fulfilled by a language, understood as a collection of expressions, in order for it to be able to facilitate this game? It is clear that to ask for reasons, I need a way of challenging an utterance; i.e., I need some statements to count as a challenge to other statements. Thus, language must provide for statements that are incompatible with other statements. Contrastingly, to give reasons, I need a statement from which the statement constituting the utterance I strive to substantiate follows; and thus language must also provide for statements that are correctly inferable from other statements. Hence it seems that the key concepts upon which a Brandomian style theory of semantics must rest, and which it must take for granted, are those of incompatibility and inference.

III. INFERENTIAL SEMANTICS A model based on the concept of inference consists primarily of a formal language L and a relation Í– between finite sequences of its statements and its statements. The

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structure of the model language approximates the grammatical structure of the natural language in question (the potentially infinite number of sentences of L must be certainly ‘finitely generated’, by means of a finite lexicon and a finite set of rules for producing expressions from expressions), and the relation approximates the inferential structure of the language (which the inferentialist sees as existing and as identifiable): hence A1, . . . , An Í– A if the counterpart of A is correctly inferable from the counterparts of A1, . . . , An. In a sense, the job of the inferentialist modeler is done once he produces this structure to his satisfaction. Of course, Í– must also be ‘finitely generated’, in this case resting on the grammatical structure of L, for there is no way of presenting an infinite relation other than to present some basic instances together with some recursive ways of extending them; and there is no nontrivial way of specifying such recursive ways save as resting on the recursive structure constitutive of its linguistic carrier, i.e. on the rules of grammar. Note, however, that there is no reason to assume that each expression will have an inferential pattern independent of those of other expressions (like ‘∧’ does), nor that the patterns for more complex expressions will always be derivable from those for their parts. The only restriction is the ‘finite generatedness’. However, a traditionally minded semanticist will probably not accept this kind of model as satisfactory. Where is truth?, where is consequence?, and indeed, where is meaning?, may well be asked. And, why call a purely syntactical structure like the above one explication of language? Although I am convinced that to call this kind of structure “purely syntactical” is misguided, I think these questions do require attention; so it is reasonable for the inferentialist to develop the structure further. First, can an inferentialist make sense of consequence as distinct from inference? I think that to some extent, she can. A paradigmatic example of such an enterprise can be found in Carnap’s (1934) Logical Syntax of Language. What Carnap undertakes in the book is a purely inferentialist enterprise; but surprisingly, what he declares to be his ultimate aim is not to delimit the relation of inference (Ableitbarkeit), but the relation of consequence (Folgerung). And indeed he tries to define consequence—as distinct from inference—using his purely inferentialist means. Now, having consequence, we can proceed to truth. For a traditional semanticist, consequence is in fact truth-preservation; and I see no reason for an inferentialist to disagree. The only thing he cannot agree to is to construe this as saying that the concept of consequence is reducible to that of truth. But if he wants to have consequence (or inference, if he thinks he can substantiate the denial of a gap between the two) as a concept more basic than truth, he can try to use the above relationship between truth and consequence as means of reducing the former concept to the latter one, rather than vice versa. He can say that truth is what is preserved by consequence. We are now approaching the last, and the most important, concept of the semantic battery—that of meaning. From the inferentialist viewpoint, meaning is

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usually said to be something like an inferential role, but as the concept of role is somewhat vague, we need an explication. I think that we can implicitly delimit the concept of inferential role by the following sets of constraints: (a) Inferential roles uniquely determine inference; that is the inferential roles of A1, . . . , An and A uniquely determine whether A1, . . . , An Í– A or not. (b)The inferential role of a complex expression is uniquely determined by the inferential roles of their parts (this follows from the fact that inferential roles are identified with meanings and that the concept of meaning involves compositionality—as I have argued for elsewhere). (c) Inferential roles are a matter of nothing else than (a) and (b); that is, the inferential role is ‘the simplest thing’ that does justice to (a) and (b). Do (a)–(c) answer the question of what an inferential role is? If we compare the concept of inferential role to that of number, it is not an answer on a par with von Neuman’s saying that a number is the set of its predecessors (with zero being the empty set), but it is an answer in the sense of Quine’s saying that a number is what is specified by the axioms of arithmetic. And given that on closer inspection von Neuman’s answer turns out to be not really an answer to the question what is number?, but rather one of many possible explications of the concept, I think that (a)–(c) do offer us a way of answering the question about the nature of inferential roles. Of course, just as in the case of numbers, it makes sense to go on explicating inferential roles. How is this to be achieved? The most straightforward way is to provide a mapping of expressions on some kind of entities that would do justice to (a)–(c). Before doing this, we should probably prove that such a mapping exists at all—but this is easy. It is clear that there is a relation of intersubstitutivity salva inferentiae—let us write E ª E¢ iff for every inference A1, . . . , An Í– A iff A1[E/E¢], . . . , An[E/E¢] Í– A[E/E¢] (where X[E/E¢] is the result of replacing zero or more occurrences of E by E¢ in X). Now it is not difficult to see that mapping E on the class [E]ª of all expressions that are equivalent with E does justice to (a)–(c). Hence we can use the equivalence classes as explications of the inferential roles; but this does not lead to an illuminating explication. Let us call the downstream inferential potential of a sentence the set of all sentences from which the sentence follows and let us call the upstream inferential potential the set of all sentences which follow from it together with various collateral premises: A¨ = {S | S Í– A} AÆ = {<S1, S2, S> | S1,A,S2 Í– S}

The inferential potential of A then can be seen as composed of these two parts. AIP = {A¨,AÆ}

An inferential role of an expression E can be now taken as a function mapping sentence contexts (appropriate for E) on inferential potentials, where a sentence context

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of a type appropriate for E is a sentence with one or more occurrences of an expression of the grammatical category of E replaced with three dots. (Thus, “. . . is an inferentialist” is a sentence context appropriate for “Bob,” and “Bob . . . an inferentialist” is one appropriate for “is”.) The inferential role of E maps a sentence context on the inferential potential of the sentence which results form the substitution of E for the three dots of the context: EIR (SC( . . . )) = SC(E)IP

Now the inferentialist’s claim is that two expressions have the same inferential roles (in this sense) iff they are intersubstitutive salva inferantiae. The obvious drawback is that, explicated in this way, the inferential roles do not comply with (a)–(c) above; indeed the inferential roles of any two different expressions come out as different. This is because the explicates are made up of linguistic expressions, distinguishable, as they are, one from another, whereas we now want to avoid distinguishing between inferentially equivalent ones. This poses a problem, though only one of a purely technical nature. Just as with all explications, to find the truly handy solution may take some ingenuity (for we seem unable to say in advance what exactly is meant by handy), but there are, I think, no deep philosophical problems involved.

IV. INFERENCE AND INCOMPATIBILITY We claimed that the other basic concept an inferentialist could use as an ‘unexplained explainer’ is incompatibility (or incoherence). Can we develop our inferential model of language to accommodate it? If we were to accept that incompatibility is reducible to inference, then there is one obvious way, a very traditional one: to say that two sets of sentences are incompatible if every sentence is inferable from their union. In this way, incompatibility becomes dependent on the expressive richness of the language in question. Something, it would seem, might come out as incoherent only because the language lacks, by pure chance, all sentences that would not be inferable from it. And though I think that in the case of a natural language we are entitled to presuppose some kind of ‘expressive saturatedness’, this feature of the reduction of incompatibility to inference makes it a little bit suspicious. There is also a way of making room for the concept of incompatibility by generalizing the concept of inference: by saying that inference is not a relation between finite sequences of statements and statements, but rather that it is a relation between finite sequences of statements and finite sequences of statements of length zero or one. The extension is natural in that the resulting relation would comply with the Gentzenian structural rules and can be seen as halfway to the multi-conclusion version of inference as we know it from the sequent calculus.

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The way chosen by Brandom consists in taking incompatibility as the ‘unexplained explainer’, explicating inference as compatibility-preservation: claiming A1, . . . , An Í– A is construed as claiming that whatever is incompatible with A is incompatible with A1, . . . , An, i.e. that whatever is compatible with the former is compatible with the latter. (This indicates that there is a sense in which compatibility assumes the role of truth in his system; we will return to this later.) Is there a difference between basing the formal semantics on inference and basing it on incompatibility? We have seen that the concepts may be thought of as interdefinable; but the interdefinability is not unproblematic. Starting from inference we can take incompatibility in stride, we saw, only with some provisos. Conversely, basing inference on incompatibility might seem more straightforward; but it contains a notable snag. The reduction of inference to incompatibility contains quantification over all sentences, hence the inference relation based on a finitary incompatibility relation might not be itself finitary. This may be more important than first meets the eye. Recall that when we considered the general structure of a formal language we distinguished between axiomatics (proof theory) and semantics (model theory) and we held for important which one of them is the ‘point of contact’ between the model and a real language. Now what is the crucial difference between these two components? After all, both of them aim at a specification of a relation among sentences (inference resp. consequence), or a set of sentences (theorems resp. tautologies) and we know that at least in some cases (classical propositional logic) even their outcome is the very same. The basic difference, I think, is that while the proof-theoretic enterprise is principally a matter of finite generation, there is no such restriction for the modeltheoretic specification. As a result, this specification may happen to be finitary (as in the case of classical propositional logic), but in general need not. Now the point is that if we have a finitely generated relation of incompatibility and use it to define the relation of inference, the resulting definition may no longer be finitary. This means that a proof-theoretical delimitation of incompatibility may yield a definition of inference that is, by its nature, more model-theoretic than proof-theoretic. In this sense, starting from incompatibility may lead us, in a way that is easy to miss, into the realm of formal semantics. It is also worth noticing that this definition of inference leads us, almost inescapably, into the realm of classical logic. Defining inference as containment of a set associated with the conclusion in the intersection of sets associated with the premises amounts (independently of whether the sets are sets of incompatible sets of sentences or of anything else) to giving the resulting logic a Boolean semantics— i.e. to having it semantically interpreted in a Boolean (rather than, say, Heyting) algebra. This interpretation, then, leaves us almost no other possibility than to define the logical operators in the Boolean, i.e. classical way. I find this problematic, because, as I argued elsewhere (see Peregrin, to appear), I find intuitionist logic more natural than classical from the inferentialist viewpoint.

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We have said that having an inferential model of language, the reason for going on to develop a formal semantics may be the desire to explicate the concept of meaning (which we may or may not submit to); but now we see that we might be driven into semantics in a sense against our will, by deciding to start from incompatibility rather than from inference.

V. INCOMPATIBILITY SEMANTICS AND POSSIBLE WORLD SEMANTICS Now we are finally homing in on our initial question (3). Does basing a semantic model on the concept of incompatibility, rather than on inference, or indeed on a more traditional concept, like that of a possible world, give us any advantage? Clearly, by granting ourselves the concept of incoherence, and hence coherence, we grant ourselves all we need to introduce the concept of possible world. It is well known that a possible world can be seen as a maximal coherent set of sentences; for the sake of perspicuity, let us distinguish, as is sometimes done, between a possible world as such, and a possible world story, the corresponding set of sentences (true w.r.t. the possible world). What we can take to be a possible world story is any set of sentences that is not incoherent, but any of its proper superclass is incoherent. The problem with turning incompatibility semantics into a possible world semantics then seems to consist in the fact that we do not have the concept of truth, hence we cannot talk about a sentence being true w.r.t. a possible world. This problem, however, is easily overcome. It is enough to realize that a possible world is complete in the sense that it leaves no possibilities open. Either something is the case, or it is not; there is no room for something being open in the sense that something could be coherently added. Hence to be true w.r.t. a possible world is to be compatible with the corresponding world story, i.e. to be part of the world story. (This explains the hint we made above—namely, that within the Brandomian setting, there is a sense in which compatibility assumes the role of truth.) This means that if we call any maximal coherent set of sentences a possible world story and if we say that a sentence is true w.r.t. the corresponding possible world iff it is compatible with the set, we have a recasting of the incompatibility semantics into a possible world semantics. Given what Brandom calls an incompatibility frame, i.e. a set (of sentences) and a subset of its powerset (of incoherent theories) closed to supersets, let us denote the set of all maximal coherent sets of sentences W and let w range over its members. Let us write w ||= p for p is true in w (which, as we already know, amounts to pŒw). Note also that w ||= p iff w |= p, i.e. iff w incompatibility entails p. (w |= p iff every q incompatible with p is incompatible with w, i.e. iff every q compatible with w is compatible with p. i.e. iff every element of w is compatible with p i.e. iff p is compatible with w i.e. iff p is true in w.) Hence p is true in w iff it is entailed by w iff it is compatible with w iff it is an element of w.

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This also gives us all the resources needed to define the simplest (S5-) kind of necessity: as we have possible worlds, we can say that p is necessary iff it is true w.r.t. all the possible worlds and that it is possible iff it is true w.r.t. at least one of them. To introduce any other kind of necessity, we would need, moreover, something amounting to the Kripkean accessibility relation among worlds; and it is important to realize that we have nothing of this kind. The point is that the accessibility relation spells out as a kind of ‘second-level compatibility’: though any two worlds are incompatible (in the sense that the union of their stories is incoherent) some worlds are ‘less incompatible than others’ (for example, by sharing the same physical laws etc.). In view of this, it seems puzzling that Brandom introduces a notion of necessity that appears to be more complicated than the simplest one. His definition of the necessity operator is the following: X∪{Lp} Œ Inc iff X Œ Inc or $Y[X∪Y Œ Inc and Y|≠{p}]

This says, in effect, that p is necessary w.r.t. a world iff p is not entailed by anything that is compatible with this world: (*) w ||= Lp iff ∀Y(if w ||= Y, then Y |= p)

But it is not difficult to show that this unperspicuous definition reduces to a very simple one: (**) w ||= Lp iff |= p

(To get from the right-hand side of (*) to that of (**) it is enough to instantiate Y as the empty set. To get, vice versa, from (**) to (*), it is enough to realize that for every Y, |= p entails Y |= p.) This means that basing semantics exclusively on the pure, ‘first-level’ concept of compatibility gives us resources to make sense of merely the most common-orgarden variety version of necessity. (See Appendix for an illustration of how an additional level can elicit different logic.) In contrast to this, it seems that the logical vocabulary of natural language is far richer and diverse. We have various kinds of necessity words—words explicitating varieties of material inferences from causal necessity or epistemic necessity to something very close to the S5-kind of logical necessity. A response to this might be But this is as it should be—perhaps Brandom’s is the only purely logical version of necessity—others being contaminated, in such or another way, by materialness. It might be argued that other versions of necessity correspond to such things as physical necessity that are surely not purely logical matters. But I do not think this answer, though partly true, should be fully embraced. It is obvious that a natural language never comes with a border neatly separating its logical vocabulary from the rest of its words. (Hence just as it is futile, as Quine taught us, to look for a seam between the analytic and the synthetic, it is equally futile to look for one between the logical and the material—for natural language is generally seamless.) Moreover, I do not believe that this should be seen as

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a shortcoming and make us search for the purely logical in ways bypassing natural language altogether. I think that the reason behind the apparent inextricability of the logical from the extralogical, just like that of the analytic from the synthetic, is that these distinctions are of our own making—that they are in the eye of the beholder rather than in language itself. To avoid any misunderstanding: there is no doubt that these distinctions are extremely useful and they help us understand the functioning of natural language. But we must not forget that they are a matter of the Bohr-atom kind of idealization—a kind of idealization that is, beyond doubt, an important (if not indispensable) means of our understanding things like language or the structure of matter, but an idealization nevertheless. To see the idealized model as an exact copy of the thing modeled and to believe that whatever is displayed by the former, but does not seem to be displayed by the latter, must therefore be somehow ‘hidden under its surface’, is to misunderstand the whole enterprise of model-aided understanding. What are the implications of all this for the question of whether there is the set of logical operators and hence the logic? I do not think the answer is in the positive. Apart from there being some leeway in how we explicitate inference, there is the question what inference exactly is. Most usually it is taken as a relation between finite sequences (or finite sets) of statements and statements; but after Gentzen’s (1934) seminal work it is not unusual to take it alternatively as a relation between finite sequences (or finite sets) of statements and finite sequences (or finite sets) of statements; and we may also consider some possibilities between the two extremes. Besides this, it is usual to assume that inference is to comply with the Gentzenian, structural rules; but even this assumption is sometimes alleviated (witness the research done in the field of the so-called substructural logics). It turns out that when we take inference to be single-conclusion and complying with the structural rules, the most natural tools for its explicitation are the intuitionist operators; whereas when we allow for multiple conclusions, what we gain will be classical logic (see Peregrin, 2008, for details). And as I am convinced that there are good reasons to believe that it is the single-conclusion variety that is more basic, I think that it is intuitionist logic that is the ‘most basic’ logic from the viewpoint of an inferentialist. The reason why I think that the single-conclusion inference is more basic is that inference may exist (according to the Brandomian picture to which I fully subscribe in this respect) only in the form of the inheritance of certain social statuses, prototypically commitments. It may exist through the fact that members of a community hold a person to be committed to something in virtue of her being committed to something else—even prior to their being able to say this. (This is essential, for it is only the need for making this explicitly sayable that is the raison d’être of the existence of logical particles and other expressive resources of natural language that do make it sayable.) And while it is clear what it could take practically to hold someone to be committed to doing something (above all, but not only, to be prepared to sanction him, when he does not do it), and hence also what it is to

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hold someone to be committed to doing something in virtue of being committed to doing other things, it is far from so clear what would it mean to hold somebody committed to doing one of a couple of things—or at least this would not seem to be a candidate for a perspicuous communal practice underlying, rather than brought about by, the occurrence of the explicit ‘or’ and other logical particles.

VI. LOGICAL VOCABULARY OF NATURAL LANGUAGE VS. LOGICAL VOCABULARY OF FORMAL LANGUAGES I take it that Brandom’s stance is that a force behind the development of natural language is the tendency of its users to ‘make it explicit’—i.e. to introduce means which would allow them to formulate, in the form of explicit claims, what was only implicit in their practices before. Hence if they endorse the inferences such as from This is a dog to This is an animal, or from Lightning now to Thunder shortly, they are to be expected to develop something of the kind of if . . . then to be able to say If this is a dog, then this is an animal or If lightning now, then thunder shortly (and later perhaps more sophisticated means which would allow them to further articulate such claims as Every dog is an animal or Lightning is always followed by thunder). I take it that this is the point of logical vocabulary of a natural language like English. Now, besides natural languages we have formal languages with their logical constants, such as the language of Brandom’s incompatibility semantics with its N, K, and L. What is the relationship between such expressions and the logical vocabulary of natural language? I must say I am not sure what Brandom’s answer is supposed to be. There seem to be two possibilities. On the one hand, there is the view that what logic is after is something essentially nonlonguistic, some very abstract structure which can be identified and mapped out without studying any real language (be it a structure of a hierarchy of functions over truth values, individuals, and possible worlds, or a general structure of incompatibility). This is a notion of logic, in Wittgenstein’s (1956, §I.8) words, as a kind of “ultraphysics.” In this conception, any possible language is restricted by the structure discovered by logic (for it is only within the space delimited by the structure that a language can exist), and hence there is a sense in which philosophy of language is answerable to logic. On the other hand, we may hold that the primary subject matter of logic is the logical means (words and constructions) of our real languages (especially those that seem to be identifiable across languages and which something must possess in order to qualify as an element of the extension of our term “language”). It is, then, only derivatively that logic studies certain abstract structures—they are structures distilled out of natural language similarly to how the Bohr atom model is distilled out of our empirical knowledge of the inside of the atom. (Of course, this does not make the study of such structures unimportant—this kind of ‘mathematization’ has

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become the hallmark of advanced science.) Hence there is a sense in which logic is answerable to the philosophy of language rather then vice versa. Given these two options, I vote for the latter; for I am strongly convinced that the former one is not viable. In my opinion, formal languages of logic are not means of direct capturing of abstract logical structures, but rather simplified models of natural language—as I have already pointed out, they provide for Wittgensteinian perspicuous representation. They abstract from many features of natural languages, idealize the languages in many ways, but let us see something as its backbone quite clearly. Their logical vocabulary explicates that of natural language and though there may be some feedback, it is not in competition with it. I do not believe that any artificially created logical symbol, be it the traditional ‘⊃’ or Brandom’s ‘K’, ever gets employed by the speakers of English in such a way that it can viably compete with if . . . then or and. True, logical theories based on such symbols have helped us see the workings of our natural logical vocabulary in a much clearer light, and in some exceptional cases, as in the texts of some eccentrically meticulous mathematicians (such as Giuseppe Peano or Gottlob Frege), can even assume their role; but I do not believe that they can be generally seen as viable alternatives, or even successors, to the natural logical vocabulary. Now Brandom does not seem to concur with me on this point. He tries to extract the logical operators directly from the structural features of incompatibility. This would indicate that he goes for the option I reject. But the truth, probably, is that his understanding of his operators coincides with neither of my two options. If this is true, then I would be eager to learn what his option is.

VII. CONCLUSION To sum up, I think that formal semantics may be a very illuminating enterprise; and this is the case even when we subscribe to pragmatism and to the inferentialist construal of the nature language. Of course, if you are a pragmatist and an inferentialist, you must understand the enterprise of formal semantics accordingly—not as an empirical study of the ways in which words hook on things, but rather as a way of building a ‘structural’ model of language explicative of its semantic (and hence eventually inferential) structure. From this viewpoint, excursions into the realm of formal semantics as exemplified by Brandom in his Lecture V, seem to me very useful. However, I think we need a deeper explanation of why they are useful and what they can teach us. I believe not only that the logical analysis of natural languages without the employment of logical structures is blind, but also that the study of logical structures without paying due attention to the way they are rooted within natural languages is empty.

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APPENDIX Let me first summarize the basic conceptual machinery of Brandom and Aker (however, I will deviate from their terminology wherever I find it helpful; and I will also use the more traditional signs for logical operators). Given a language L (understood as a set of sentences), a set Inc ⊆ Pow(L) is called an incoherence property iff for every finite X,Y⊆L, if X⊆Y and XŒInc, then YŒInc. will be called a standard incoherence model. We write I(X) as a shorthand for {Y | X∪YŒInc}

and we write X |= p as a shorthand for ∀Y: if Y∪{p}ŒInc, then Y∪XŒInc.

Given L is the set of sentences of the modal propositional calculus (based on ∧, ¬ and ■), Inc is, moreover, supposed to fulfill the following postulates (¬) X∪{¬p}ŒInc iff X |= p. (∧) X ∪{p∧q}ŒInc iff X∪{p,q}ŒInc. (■ ) X ∪{■p}ŒInc iff XŒInc or there is an Y such that X∪YœInc and Y|≠p.

POSSIBLE WORLDS AND INTENSIONS AS BASED ON INCOHERENCE Given an incoherence property Inc, we define a set PWInc (of ‘possible worlds’) and, for every class X of statements, its intension ||X||Inc (the class of all those possible worlds w.r.t. which it is true). Definition. PWInc ≡Def. {X | XœInc and there is no YœInc so that X ⊆ / Y} (possible worlds) ||X||Inc ≡Def. {Y | YŒPWInc and X∪YœInc} (the intension of X)

(The index will be left out wherever no confusion will be likely.) We will use the letters w, w¢, w¢¢, . . . to range over those sets of statements that are possible worlds. Now we prove some auxiliary facts about possible worlds and intensions. Lemma. 1. wŒ||X|| iff X⊆w 2. XœInc iff there is a w so that X⊆w, i.e. so that wŒ||X|| 3. XŒInc iff there is no w so that X⊆w, i.e. ||X||= ∆ 4. ||X∪Y||= ||X||∩||Y|| 5. if I(Y) ⊆I(X), then ||X||⊆||Y|| 6. if I(Y)⊆/ (X), then ||X||⊆/ ||Y||

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Proof. 1. According to (1), wŒ||X|| iff X∪wœInc, which, given that nothing that is not a part of w is not compatible with it, is the case iff X∪w⊆w and henced iff X⊆w. 2., 3. obvious 4. wŒ||X∪Y|| iff X∪Y⊆w, that is iff X⊆w and Y⊆w, and hence iff wŒ||X|| and wŒ||Y||. 5. Suppose I(Y)⊆I(X). This is the case iff I(X)⊆I(Y), and hence only if I(X)∩PW⊆I(Y)∩PW, i.e. only if ||X||⊆||Y||. 6. Suppose that I(Y)⊆/ I(X), i.e. that there is a Z such that ZŒI(X) and ZœI(Y). In other words, Z∪XŒInc and Z∪YœInc, which, according to 2. and 3., is the case iff there is a w such that wŒ||Z∪X|| and there is no w such that wŒ||Z∪Y||. This implies that there is a w such that wŒ||Z∪X|| and wœ||Z∪Y||. This in turn implies that wŒ||Z|| and wŒ||X|| and (wœ||Z|| or wœ||Y||) and hence that wŒ||X|| and wœ||Y||.

Having proved this, we can prove that the assignment of intensions is isomorphic to the assignment of incompatibility sets; hence that the possible worlds semantics based on PW and || . . . || is a faithful representation of the underlying incompatibility semantics. Theorem. I(X) = I(Y) iff ||X|| = ||Y|| Proof. The direct implication is trivial, as ||X||⊆I(X). The indirect one follows from the last two clauses of the previous lemma. This shows that as in the case of ordinary modal logics, the semantic value of a sentence can be identified with the set of all those possible worlds in which it is true.

INCOMPATIBILITY SEMANTICS AND THE MODAL LOGIC S5 Let us call the logic to which this incompatibility semantics gives rise (i.e. the resulting relation of consequence) standard incompatibility logic (SIL), and let us investigate its relationship to the standard systems of modal logic. (B&A have already proved that SIL is equivalent to S5, but I present a proof which is more suitable for what will follow.) Lemma. Given (■), it is the case that X∪{■ p}ŒInc iff XŒInc or |≠p. Proof. It is obviously enough to prove that provided XœInc, |≠p iff there exists a Y such that X∪YœInc and Y|≠p. The indirect implication follows from instantiating Y as the empty set; the direct one follows from the obvious fact that if |≠p, then Y|≠p for any Y. Theorem. wŒ||■p|| iff ∀w wŒ||p||; hence ||■p|| = {w | for every v: if wRv, then vŒ||p||), where R = PW×PW Proof. According to the theorem just proved, w∪{■p}ŒInc iff wŒInc or |≠p,

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hence iff |≠p. Moreover, w∪{■p}ŒInc iff wœ||■p||; and |≠p iff p is incompatible only with incoherent sets, which means that it is compatible with every possible world and hence that wŒ||p|| for every w. Corollary. Let be a standard incompatibility frame.incoherence model. Then there exists an equivalent Kripkean model <W,R,V> with R = W×W, i.e. there exists a (one-one) mapping i of PWInc on W such that for every pŒL: pŒw iff V(p,i(w)) = 1. Proof. In view of the theorem we can simply take W = PWInc, i as the identity mapping, R = PWInc×PWInc and V(p,i(w)) = 1 iff pŒw. Corollary. S5-validity entails SIL-validity. Theorem. Let <W,R,V> be a Kripkean model with R = W×W. (We will use the variables v, v¢, v¢¢, . . . to range over elements of W.) Define Inc = {X | there is no v such that V(p,v) = 1 for every pŒX} Then Inc is an incoherence property and there exists a (not necessarily one-one) mapping i of W on PW such that V(p,v) = 1 iff pŒi(v). Proof. Let us call X impossible iff there is no vŒW such that V(p,v) = 1 for every pŒX (thus, Inc is the set of all impossible sets). Let us write V(X,v) = 1 a shorthand for V(p,v) = 1 for every pŒX .That Inc is an incoherence property is obvious. It is also obvious that for every v there will be an element i(v) = {p | V(p,v) = 1} of PW such that V(p,v) = 1 iff pŒi(v). Thus the only thing that must be shown is that Inc fulfills (¬), (∧) and (■ ). If we rewrite the postulates according to our definition of Inc, we get (∧*) X∪{p∧q} is impossible iff X∪{p,q} is impossible (¬*) X∪{¬p} is impossible iff ∀Y(if Y∪{p} is impossible, then Y∪X is impossible) (■ *) X∪{■p} is impossible iff X is impossible or $Y(Y∪{p} is impossible, whereas Y is possible) Whereas (∧*) is obvious, (¬*) and (■*) are slightly more involved. Let us start with (¬*): To prove the direct implication, assume that Y∪{p} is impossible, i.e that V(p,v) = 1 for no v such that V(Y,v) = 1. It follows that V(¬p,v) = 1 for every v such that V(Y,v) = 1, i.e. that V(X,v) = 1 for no v such that V(Y,v) = 1, and hence that V(Y∪X,v) = 1 for no v. To prove the indirect one it is enough to instantiate Y as ¬p. As for (■*): To prove the direct implication, observe that if V(X,v) = 1 for some v, then V(■p,v) = 0, and hence that there must be a v¢ such that V(p,v¢) = 0. But then, i(v¢)∪{p} is impossible, whereas i(v¢), being the set of all sentences true in v¢, is possible. To prove the indirect implication, observe that if V(X,v) = 1 for some v, there must be a v¢ such that V(p,v¢) = 0; hence V(■ p,v¢¢) = 0 for every v¢¢; and hence X∪{■p} is impossible. Corollary. SIL-validity entails S5-validity (and hence they coincide).

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AN EXTENDED INCOMPATIBILITY SEMANTICS AND THE MODAL LOGIC B Now we indicate how the addition of one more level of incompatibility may lead to a logic different from S5. Definition. An extended incoherence model is an ordered triple , where is a standard incoherence model and QInc⊆Pow(Pow(L)) such that: (a) if UŒQInc and U⊆U¢, then U¢ŒQInc (b) if ∪UœInc, then UœQInc (c) {Xi}iŒIœQInc iff there are possible worlds {wi}iŒI so that Xi⊆wi for every iŒI and {wi}iŒIœQInc If {Xi}iŒIœQInc, then the sets {Xi}iŒI are called quasicompatible.

(The intuitive sense behind this definition is the following: (a) simply states that QInc is an incoherence property; (b) states that it is a weakening of Inc in the sense that every two compatible sets are quasicompatible; and (c) states that to be quasicompatible is to be parts of quasicompatible possible worlds. It is obviously this last clause that makes QInc suitable for emulating a Kripkean accessibility relation.) Definition. Let be an extended incompatibility model. We say that a possible world w¢ from PWInc is accessible from the possible world w¢, wRIncw¢, iff {w, w¢}œQInc. Lemma. The accessibility relation is reflexive and symmetric; i.e. every world is accessible from itself and every world is accessible from every world that is accessible from it. Proof. Obvious. Definition. We replace the above (■ ) by (■ ¢) X∪■ pœInc iff for every Y: if <X∪■p,Y>œQInc, then Y∪pœInc.

The modal logic based on this kind of incompatibility semantics will be called extended incompatibility logic (EIL). Theorem. wŒ||■p|| iff for every w¢ such that wRw¢ it is the case that w¢Œ||p|| Proof. It is clear that w∪■pœInc iff for every Y: if <w∪■p,Y>œQInc, then Y∪pœInc, and as w∪■pœInc iff w∪■p = w, that w∪■pœInc iff for every Y: if {w,Y}œQInc, then Y∪pœInc.

This can be rewritten as wŒ||■p|| iff for every Y such that {w,Y}œQInc there is a w¢ such that w¢œ||Y∪p||.

Hence what we must prove is that (*) for every w¢ such that wRw¢ it is the case that w¢Œ||p||

is equivalent to (**) for every Y such that {w,Y}œQInc, there is a w¢¢ such that w¢¢Œ||Y∪p||.

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That (*) follows from (**) is obvious: restricting the Y’s of (**) to possible worlds yields us for every w¢ such that {w,w¢}œQInc, there is a w¢¢ such that w¢¢Œ||w¢∪p||, where {w,w¢}œQInc is the same as wRw¢ and w¢¢Œ||w∪p|| iff w¢¢ = w¢ and w¢¢Œ||p|| (as ||w¢∪p||⊆ ||w¢||∩||p||, w¢¢Œ||w¢∪p|| only if w¢¢Œ||w¢||, which is possible only if w¢¢ = w¢, and w¢¢Œ||p||).

Let us prove that, conversely, (**) follows from (*). Hence assume (*) and assume that {w,Y}ŒQInc. According to (c) of the definition of the extended incoherence model, there is a w¢ such that Y⊆w¢ and {w,w’}œQInc. In other words, there is a w¢ such that wRw¢ and Y⊆w¢. According to (*), {p}⊆w¢; hence Y∪{p}⊆w¢, i.e. w¢Œ||Y ∪p||. Corollary. Let be an extended incmpatibility model. Then there exists an equivalent Kripkean model <W,R,V> with R reflexive and symmetric, i.e. there exists a mapping i of PWInc on W such that for every pŒL and every wŒPW it is the case that pŒw iff V(p,i(w)) = 1. Proof. In view of the previous theorem we can simply take W = PWInc, i as the identity mapping, R = {<w,w¢> | <w,w¢>œQInc}, and V(p,i(w)) = 1 iff pŒw. Corollary. S4-validity entails EIS-validity. Theorem. Let <W,R,V> be a Kripkean model for a language L with R reflexive and symmetric. Define Inc = {X | there is no v such that V(X,v) = 1} QInc = {U | U œInc}∪{<X,Y>| there are v and v¢ such that V(X,v) = 1,V(Y, v¢ )=1 and vRv¢}

Then is an extended incoherence model and there exists a (not necessarily one-one) mapping i of W on PW such that V(p,v) = 1 iff pŒi(w). Proof. That Inc is an incoherence property is obvious. Let us check that QInc is a quasiincoherence property. The definition says that the sequence of sets is quasicoherent iff either the union of the sets is coherent, or it consists of a pair of accessible possible worlds. In both the cases (a) is obviously fulfilled. Also due to the first part of the definition, (b) is fulfilled. And also (c) is obviously fulfilled in both cases. So what is left to be proved is that the postulates for logical connectives are fulfilled, and of those (∧) and (¬) are the same as before. So we are left with (■¢): (*) X∪■ pœInc iff for every Y: if <X∪■p,Y>œQInc, then Y∪pœInc.

What we know is that given w and w¢ range over W, V(■p,w) = 1 iff for every w¢ such that wRw¢ it is the case that V(p,w¢) = 1.

hence (**) w∪■pœInc iff for every w such that if <w,w¢>œQInc it is the case that w¢∪pœInc.

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Thus we must prove (*), given (**). Let us start with the direct implication: assume X∪■pœInc and <X∪■p,Y>œQInc and head for proving Y∪pœInc. <X∪■p,Y>œQInc entails that there are w¢ and w¢¢ such that X∪■ p⊆ w, Y⊆ w¢ and <w,w¢> œQInc. However, X∪■p⊆ w entails that w∪■pœInc, and hence, according to (**), that for every w¢¢ such that <w,w¢¢>œQInc it is the case that w¢¢∪pœInc. Hence, as <w,w¢> œQInc, it is the case that w¢∪pœInc, and as Y⊆ w¢, that Y∪pœInc. To prove the indirect implication, assume that for every Y, if <X∪■p,Y>œQInc, then Y∪pœInc; and hence especially that for every w, if <X∪■p,w>œQInc, then w∪pœInc. As <X∪■p,w>œQInc iff <w¢,w> for some w¢ such that X∪■p⊆ w¢, hence X∪■pœInc.

ACKNOWLEDGMENTS This paper evolved from the commentary I gave to Brandom’s fifth lecture during his re-presentation of his 2006 Locke Lectures in April 2007 in Prague; however, the evolution was so rampant that the paper no longer quite resembles the original commentary—I hope I have managed to concentrate on what is really vital and left out marginal issues.

NOTES 1. In the sense of Carnap and Quine, in which an explicatum is “a substitute, clear and couched in terms of our liking” filling those functions of the explicandum “that make it worth troubling about” (Quine, 1960a, 258–59). 2. My urging of a ‘structural’, rather than ‘metaphysical’ reading of formal semantics goes even much farther back, to Peregrin (1995), a book whose subtitle was Formal Semantics without Formal Metaphysics. 3. It is also important to realize that such languages may be (more or less) parametric; i.e., they may be mere language forms rather than real languages. When, for example, we are doing logic, we are interested only in logical constants, and treat the rest of the vocabulary as parameters—we take into account all possible denotations of these expressions and thus gain results that are independent of them. But the boundary between constant, i.e. fixedly interpreted, expressions and those that are parametric, i.e. admit variable interpretations, can be drawn also at other joints. Hence it is always important to keep an eye on the extent to which the language we are considering is a true (fully interpreted) language and the extent to which it is only a language scheme. 4. A paradigmatic example of the discrepancy between the grammar of the regimented natural language and that of the regimenting language of logic is the case of variables of the languages of standard logic. Originally, variables were introduced as basically ‘metalinguistic’ tools; and it is well known that logic can make do wholly without them (Quine 1960b; Peregrin 2000). However, it has turned out that we reach a great simplification of the grammar of the logical languages if we treat variables as fully fledged expressions, on a par with constants, and hence if we base the languages of logic on a kind of grammar deviating from that underlying natural languages. (Regrettably, this essentially technical move has led some logicians to philosophical conclusions— such as that logic has discovered that natural languages contain variables in a covert way, etc.) 5. See Peregrin (2007). 6. Cf. McCullagh (2003).

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7. See Peregrin (2006b). 8. If this question is put into a form precise enough to be answered (which I tried to do in Peregrin 2006a), it turns out that what a relation must fulfill are precisely the well-known Gentzenian structural rules, stating that for all sentences A, B, and C and all finite sequences X, Y, and Z of sentences it is the case that A Í– A if X,Y Í– A, then X,B,Y Í– A if X,A,A,Y Í– B, then X,A,Y Í– B if X,A,B,Y Í– C, then X,B,A,Y Í– C if X,A,Y Í– B and Z Í– A, then X,Z,Y Í– B More precisely I assumed that what it takes, on the most general level, for a language to have a semantics is to classify its truth valuations into acceptable and unacceptable; and I have shown that an inference relation can be seen as effecting such a classification just in this case. The same holds, mutatis mutandis, for incompatibility. 9. See Peregrin (2006b). 10. See Peregrin (2005). 11. See Quine (1969, 45). 12. We follow Brandom’s terminology, according to which incoherence is simply self-incompatibility (and incompatibility is the incoherence of union). 13. Of course, in cases in which the accessibility relation is not symmetric it may be awkward to see it as expressive of ‘compatibility’, but we leave this aside. 14. In this way we have made a long story short. To tell the long story explicitly, we would have to say that to make the incompatibility semantics into a regular Kripkean one, we need an accessibility relation. That is, we need a relation such that Lp is true w.r.t. a possible world w just in case p is true w.r.t. all worlds accessible from w. The usual way to extract the accessibility relation from the world stories is to say that the world w¢ will be accessible from the world w iff whatever is necessarily true in the latter, is true in the former, i.e. wRw¢ iff {p | Lp Œ w}⊆w¢ This definition guarantees that a sentence necessarily true in a possible world will be true in all worlds accessible from it; but if it be the accessibility relation underlying our current necessities, we have to show also the converse, namely that a sentence is necessarily true in a possible world if it is true in all worlds accessible from it. Hence we must show that If pŒw¢ for every w¢ such that wRw¢, then LpŒw But given Brandom’s definition, this is easy; and it is also easy to show that R is an equivalence. 15. Pleitz et al. (to appear) have attempted to modify the definition so as to yield a less trivial modal logic, which they achieved by restricting the range of Y in (*) to singletons. This indeed yields them a logic weaker than S5. But the restriction they employed seems to me to be so unmotivated that I cannot see this result as of any other than purely technical interest. 16. In general, I think we should shy away from diagnosing natural language as ‘imperfect’. The millennia of natural selection responsible for its current shape are more likely to have streamlined and perfected it—though perfected it in its own way. It is probable that the imperfection diagnosis (a matter of course for many classical analytic philosophers, and the driving force behind much of their philosophy) results from language being expected to fulfill purposes different from its intrinsic ones—i.e. those for which it was selected. 17. I use the verb explicitate in the Brandomian sense of making explicit, whereas I am reserving the verb explicate for use in the Carnapo-Quinean sense of devising an exactly delimited substitute for a vague concept. 18. See Restall (2000). 19. It is important to realize that though this may seem unproblematic in some specific cases (for example to hold a person A, who accepted a thing from a person B, to be committed to either giving B another thing in exchange, or returning B the original thing, does not seem to be any more problematic than, and indeed no different from, holding A to be committed to giving B a

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thing), multiple-conclusion inference would require a wholly general notion of the disjunctive combination of commitments. And it is very difficult to imagine what it would take practically to hold a person to be committed to doing one of an assortment of unrelated things, without the means for stating the commitment explicitly. 20. I reflect the fact that the Appendix is the common work of the two authors (hereafter B&A). 21. I use the term model instead of B&A’s frame, for, as we will see later, the natural counterparts of these structures within Kripkean semantics are models rather than frames. (As incompatibility semantics is built directly from language, there is nothing that would correspond to the concept of frame of standard Kripkean semantics—i.e. the concept of a space of a possible world with the relation of accessibility, taken in isolation of any language.) Besides this, I base the definition directly on the incoherence property (rather than on the incompatibility function derived from it as B&A do).

REFERENCES Brandom, R. 2008. Between Saying and Doing: Towards an Analytic Pragmatism. Oxford: Oxford University Press. Carnap, R. 1934. Logische Syntax der Sprache. Vienna: Springer. Davidson, D. 1986. “A Nice Derangement of Epitaphs.” Truth and Interpretation: Perspectives on the Philosophy of Donald Davidson, ed. E. LePore, 433–46. Oxford: Blackwell. Gentzen, G. 1934. “Untersuchungen über das logische Schliessen I–II.” Mathematische Zeitschrift 39: 176–210. Haugeland, J. 1978. “The Nature and Plausibility of Cognitivism.” Behavioral and Brain Sciences 1: 215–60. Lewis, D. 1972. “General Semantics.” In Semantics of Natural Language, ed. D. Davidson and G. Harman, 169–218. Dordrecht: Reidel. Lewis, D. 1975. “Languages and Language.” In Minnesota Studies in the Philosophy of Science VII, ed. K. Gunderstone. Minneapolis: University of Minnesota. McCullagh, M. 2003. “Do Inferential Roles Compose?” Dialectica 57: 431–38. Montague, R. 1974. Formal Philosophy: Selected Papers of R. Montague. New Haven: Yale University Press. Peregrin, J. 2000. “Variables in Natural Language: Where Do They Come From?” In Variable-free Semantics, ed. M. Böttner and W. Thümmel, 46–65. Osnabrück: Secolo. Peregrin, J. 2001. Meaning and Structure. Aldershot: Ashgate. Peregrin, J. 2004. “Pragmatism und Semantik.” In Pragmatisch denken, ed. A. Fuhrmann and E. J. Olsson, 89–108. Frankfurt a M: Ontos. Peregrin, J. 2005. ‘Is Compositionality an Empirical Matter?” In The Compositionality of Meaning and Content, ed. M. Werning, E. Machery, and G. Schurz, 135–50. Frankfurt: Ontos. Peregrin, J. 2006a. “Meaning as an Inferential Role.” Erkenntnis 64: 1–36. Peregrin, J. 2006b. “Developing Sellars’ Semantic Legacy: Meaning as a Role.” In The Self-Correcting Enterprise: Essays on Wilfrid Sellars, ed. P. Wolf and M. Lance, 257–74. Amsterdam: Rodopi. Peregrin, J. 2007. “Consequence & Inference.” V. Kolman (ed.): Miscellanea Logica: Truth and Proof, ed. V. Kolman, 1–18. Prague: FF UK. (http://www.miscellanea-logica.info). Peregrin, J. 2008. “What Is the Logic of Inference?” Studia Logica, 88:263–294. Pleitz, M., and H. von Wulfen. 2008. “Possible Worlds in Terms of Incompatibility: An Alternative to Brandom’s Analysis of Necessity.” The Logica Yearbook 2007, ed. M. Peliš, 119–137. Prague: Filosofia. Quine, W. V. O. 1960a. Word and Object. Cambridge, Mass.: MIT Press. Quine, W. V. O. 1960b. “Variables Explained Away.” Proceedings of the American Philosophical Society 104: 343–47. Quine, W. V. O.. 1969. Ontological Relativity and Other Essays. New York: Columbia University Press.

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Restall, G. 2000. Introduction to Substructural Logics. London: Routledge. Wittgenstein, L. 1956. Bemerkungen über die Grundlagen der Mathematik. English translation Remarks on the Foundations of Mathematics. Oxford: Blackwell. Wittgenstein, L. 1953. Philosophische Untersuchungen. English translation Philosophical Investigations. Oxford: Blackwell.

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PHILOSOPHICAL TOPICS VOL. 36, NO. 2, FALL 2008

Infinite Explanation

Sebastian Rödl University of Basle

Brandom proposes, and this is the fourth of a sequence of claims he propounds in the sixth lecture of his John Locke Lectures, that we understand language and thought as “a development of and a special case of the sort of basic practical intentionality exhibited by the kind of feedback-governed transactions mentioned in the first three theses” (LL 6, 5). The transactions are tote cycles—test-operate-testexit—that link dispositions to respond in a certain way to a certain kind of stimulus in such a way that the effect of a given response is the next stimulus. “A creature’s practical engagement with its world exhibits practical intentionality insofar as it is feedback-governed, that is, specifiable [ . . . ] as having an algorithmic tote-structure in which each cycle is mediated by its differential responses to the effects of its own performances” (LL 6, 10). I argue in the first section that behavior does not manifest intentionality of any kind on account of exhibiting this structure. A fortiori, thought cannot be understood in terms of it. The second section is on Brandom’s account of objective validity. First, I question his motive. Brandom wants to explain thought in terms of responsive dispositions because he thinks comprehending something perfectly is being able to explain it in terms of something other. In truth, an account of this form is imperfect. Thought is an object of a higher form of comprehension. With Hegel, I call it infinite (2.1). Brandom explains objective validity by the unity of normative and modal vocabulary—two species of logical vocabulary, which can be elaborated from any autonomous vocabulary. I block the first step of this account by arguing that logical vocabulary cannot be elaborated from dispositions to respond to stimuli. The reason for this

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has a broader significance. As he conceives of acts of thought as acts of responsive dispositions, Brandom fails to register the defining character of thought: its representing the general (2.2). This suggests that we turn Brandom’s account on its head: the unity of normative and modal thought does not explain objective validity, but is explained by it. This is Kant’s view. It yields infinite comprehension (2.3).

I. PRACTICAL INTENTIONALITY A tote cycle is a sequence of acts of abilities. An ability is a stimulus-response pair: something that has the ability responds in a certain way to stimuli of a certain kind: when something does X to it (“stimulus”), it does Y in consequence (“response”). It does it in consequence of being acted upon, not just after it has been acted upon, which means that there is a causal nexus of action and affection. In their ordinary use, the terms “stimulus” and “response” apply only to animals; comprehension of these terms therefore presupposes a theory of the animal. But Brandom uses them in the austere way just explained. So he can speak of automata as responding to stimuli. In the present context, then, we do not deploy the concept of intentional action or animal movement when we say that something does something, and does it in consequence of being affected in a certain way. “Do” is a variable verb, and the schema “something acts on something, which does such-and-such in consequence” does not restrict its instances to verbs representing animal movement. The flame heats the water, which boils in consequence. The water, suffering the stimulus of heat, responds by boiling. We may think the following a prime example of a response to a stimulus: I clap my hands, and the cat shies away, hiding under the sofa. The following is just as good an example: I throw the cat into the fire, and she burns to ashes. The fire acts on a cat, providing a stimulus, to which she responds by burning. This shows that the idea of a responsive disposition does not help us understand the intentionality animals exhibit in, I quote, “dealing skillfully with the world” (LL 6, 3). It is not true that, I quote, “the most basic form of such activity is a tote cycle of perception, performance, assessment of results of performance, and further performance” (LL 6, 3). A tote cycle is an “algorithmic elaboration of responsive dispositions” (LL 6, 4): there is a stimulus (test), and a response (operate). The effect of the response is the next stimulus (test), to which there is a further response (operate), and so on, until there is no further response (exit). We must not be misled by the word “perception” when Brandom speaks of a tote cycle of perception, performance, and so on. Usually, “perception” signifies a form of intentionality, and a power distinctive of the animal, wherefore, again, we understand this word only to the extent that we know what an animal is. But just as above “do” did not mean animal movement, but any change, here “perception” means any case of something’s being affected by something. Now, the cat burning in the fire

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does not exhibit intentionality, not by burning. She does not skillfully deal with the world as she burns. The following is no account of animal intentionality: something exhibits intentionality in doing something in consequence of being acted upon by something else. But nothing changes if we require that there be a sequence: stimulus, response, further stimulus, further response, and so on. And nothing changes if later stimuli are previous responses. And nothing changes if at a certain point there is no longer any response (exit). What is algorithmically elaborated from responsive dispositions is a responsive disposition. If we do not find intentionality in the disposition to do a certain thing when acted upon in a certain way, then no amount of algorithmic elaboration changes that. Tote cycles, as such, have nothing to do with intentionality. Nor would anyone think they did, did he not imagine, imagining a tote cycle, an animal or a man skillfully dealing with the world. (This is how it must be with Brandom, when he describes building a house as a tote cycle.) So how is it when an animal or a man skillfully deals with the world? Consider this: I want to kill a man. I see him (stimulus), shoot him in the chest (response), walk up and look, and see he is still moving (next stimulus, effect of my response to the previous stimulus), shoot again (response), see that he is moving no more (stimulus, effect of my response to the previous stimulus), and walk away (exit). Here there is not just a sequence of stimulus and response. And not only is the effect of a given response the next stimulus. The responses are united as means to an end I represent. They are united as steps I take to kill the man. This unity is constituted by my representing it, by my deriving its elements, the steps, from it. Which explains the exit: I see I have reached my end; the man is dead. My killing the man exhibits a teleological structure that is constituted by my representation of this very structure. We may call this rational teleology. Here the stimuli are not the ultimate causes of my responses (which therefore it is misleading to call responses). A stimulus—I see the man still moving—lets me shoot again because I am inside this process: killing the man. Therefore this process cannot be explained as a sequence of stimuli and responses; on the contrary, it is the principle of the sequence. While the process exhibits intentionality (in the given case, it exhibits not only sentience, but sapience; it is an act of applying a concept in such a way as to realize an instance of it), its intentionality cannot be understood in terms of the tote cycle. The cycle, its unity, must be understood through it. A tote cycle may be governed by the practical application of a concept. It may also be governed by the natural teleology of vital processes. It is sometimes thought that one has left teleological explanation behind when one can describe the mechanisms by which a plant or organ does this or that. But describing a mechanism is describing a teleological process. Its end is the principle of the unity of its steps; only through the end, through what it is a mechanism for, is a mechanism apprehended. There is a more specific form of natural teleology that is the source of the concept of perception. It, too, may subsume tote cycles. A chimpanzee fishing for termites sticks the stick in the mound, gets it out, sees termites, licks them off, and so on. The unity of this sequence is the teleological process of extracting termites.

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The process is not explained by the tote cycle; the tote cycle, its unity, is explained by it. If we want to understand natural teleology in general, the special form of it signified by the concept of sentience, and the rational teleology signified by the concept of the will, then Brandom cannot help us because he erroneously thinks he has explained teleology, directedness, intentionality in terms of tote cycles. The basic concept of Brandom’s account of intentionality is the concept of a responsive disposition, a disposition to do such-and-such when being acted upon in such-and-such a way. In lectures two and three, he anticipates that, I quote, “the stimulus-response model might seem to impose a formal, narrowly behaviorist strait-jacket on what counts as a primitive ability” (LL 2, 6), which one might think precludes it from throwing light on language and thought. Brandom thinks he can lay this worry to rest by observing that the model does not restrict the terms in which the stimulus and the response are described. For example—these are Brandom’s examples—the stimulus may be lyrical poetry and the response painting a wellcomposed picture. The disposition to respond to the presentation of a poem with painting a well-composed picture is one that, presumably, only sapient creatures could exhibit. Brandom envisages other responsive dispositions that “only a sentient creature could exhibit” (LL 3, 17). These passages reveal the fundamental error that lies at the basis of Brandom’s approach. The idea of a responsive disposition designates a certain kind of unity of what affects something and what it does. If we call the unity the form, then the terms of the unity, the stimulus and the response, are the matter. Brandom thinks that any being—inanimate, living, sentient, sapient—is the subject of responsive dispositions. There may be differences in the kind of stimulus to which certain beings can respond, and in the kind of response that can come from them. And, Brandom thinks, “sentience” and “sapience” signify special terms of responsive disposition, that is, a special matter of this kind of unity of action and affection. He does not consider the possibility that “sentience” and “sapience” signify different forms, that is, different kinds of unity of what affects something and what it does. But this is what these terms signify, as the examples show. In a teleological process, the nexus of action and affection depends on the principle of the process, which therefore, on its part, cannot result from affection and be the act of a responsive disposition. I do not shoot whenever I see a man moving. I do so when killing that man is what I am doing. Then his moving shows me that I have not yet killed him and need to shoot again. What is true of my shooting again holds of my killing the man: its ultimate cause will not be a stimulus to which it is the response. Action and affection bear a different kind of unity when the action is a vital operation, an animal movement, or an intentional action. Within this form of unity, we can distinguish natural teleology or life, sentient teleology or the animal, rational teleology or thought. These are not ever more complex constellations of responsive dispositions, but different kinds of unity of action and affection.

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II. OBJECTIVE VALIDITY Brandom wants to illuminate objective validity through an inner nexus of normative and modal vocabulary. I think his idea can be presented as follows. Brandom’s incompatibility semantics does not associate sentences with something other than sentences; it represents the meanings of sentences as other sentences, or sets of them. Hence we may doubt whether sentences, in virtue of being meaningful in the way represented by this incompatibility semantics, represent an object. A possible answer is this. Think what it means that sentences are incompatible: it means they cannot be true together. It means not all of them agree with the object. Incompatibility is a relation between sentences, but they bear this relation to each other in virtue of the relation they bear to the object. Now, this is not Brandom’s answer. He sets great store by the fact that he can treat the concept of incompatibility as a semantic primitive and need not explain it in terms of truth. He can do this, he thinks, because he can give a pragmatic account of it and explain what it is to treat sentences as incompatible: it is to treat commitment to one as precluding entitlement to the other. If this is to show that the concept of incompatibility is independent of the concept of truth, then the concepts of commitment and entitlement used here must themselves be independent of the concept of truth. Commitment and entitlement are kinds of correctness, and talk of correctness refers to a measure. It may be thought the relevant measure is agreement with the object. But Brandom does not want to invoke that at this point. We are to understand the concepts of being committed and entitled to a claim independently of the notion of agreement of the claim with the object. It is not clear how then we are to understand them. In the Locke Lectures, Brandom gives no indication of what he means by “commitment” and “entitlement”. He does so in Making It Explicit, where he explains being committed in terms of what it is to take someone to be committed, and taking someone to be committed in terms of the sanctions he suffers in case he does not honor his commitment. Presumably the lectures presuppose this. So we are not to rely on the idea of relating to the object in thought or judgment when we describe sentences as incompatible. Rather, Brandom argues, we receive that idea from this description. Since we did not already invest it, this amounts to an explanation. We receive it in this way. Consider a vocabulary of sentences joined by inferential and incompatibility relations. We can say how sentences must be used to be such a vocabulary; their use must involve suitable consequential relations of commitments and entitlements (or lack of them). We can show that the ability to use such a vocabulary can be developed into an ability to use normative vocabulary and modal vocabulary, which in different ways describe or specify the very ability from which they are developed. Normative vocabulary expresses the idea of a subject of commitments and modal vocabulary expresses the idea of an object to which her commitments are responsible. So with normative vocabulary and modal vocabulary we possess the idea of a subject representing an object. But

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modal and normative vocabulary are in a certain sense contained in any vocabulary of sentences standing in inferential and incompatibility relations, that is, in any vocabulary that, according to a leading assumption of the inquiry, is used to say anything at all. Moreover, modal and normative vocabulary describe the use of the vocabulary in which they are contained. If we allow ourselves to be lyrical, we can say: any vocabulary using which is saying something describes itself as a practice of subjects representing objects. The form of my objection to this claim will be clear from the foregoing. It is not possible to describe the use of language by the formal concept of responsive disposition. Responsive dispositions do not constitute intentionality of any kind; the burning cat shows this. Joining dispositions to states and states to dynamic systems does not change this. We cannot comprehend vital processes through the concept of responsive disposition, much less animal movement or action or language. These acts are distinguished not by the complexity of the responsive dispositions from which they spring, but by the different kind of unity of action and affection that they exhibit. The highest form of unity is this: something affects a subject who, being so affected, represents it in a judgment. A judgment is, and is understood by its subject to be, valid of its object. So we may call this sort of unity objective validity. Objective validity is not understood through responsive dispositions. A judgment is not a response to a stimulus. It bears a different relation to affection. It follows that no light is thrown on objective validity by the unity of normative and modal language, if language is described in terms of responsive dispositions. Comprehension of normative and modal language and their unity must begin from objective validity as a different kind of unity of what affects something and what it does. In what follows, I argue that Brandom’s failure to realize that his topic is a unity of action and affection different from the unity of stimulus and response corrupts his account of logical vocabulary. Then I sketch how, according to Kant, whom Brandom wishes to follow, the unity of modal and normative thought does not ground, but is grounded in the objective validity of judgment. But before I do so, I want to bring out a methodological claim implicit in what I have said. Brandom often recommends his project by saying that, if it succeeds, it provides a superior form of understanding. So he tells us to wait and see how far he can get with his reconstruction of the abilities that constitute language use, to judge the theory by its fruits and let the proof be in the pudding. This reply does not register that the objection is also against the method: it entails that the form of understanding the theory would deliver, if it were possible, would be inferior. 2.1 INFINITE COMPREHENSION

Brandom proposes that we explain intentionality as a constellation of responsive dispositions. The explanation may deploy special concepts to describe the terms of the dispositions. We have to speak of commitments and entitlements. It is the privi-

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lege of thinkers to have dispositions whose description requires these terms. But thinkers do not have something other than responsive dispositions. We do not need to think differently of the unity of what affects them and what they do. That unity is the same everywhere: a stimulus calling forth a response. We explain animal intentionality by the condition that the responsive dispositions be linked so as to form a tote cycle. For discursive intentionality, we impose further conditions: there must be dispositions to attribute commitments and entitlements that institute inferential and incompatibility relations. Here we comprehend something by representing it as certain elements satisfying certain conditions; we independently understand the elements and the conditions. Brandom thinks this is the highest mode of comprehension, the gold standard, he says. This seems wrong to me. Comprehension of this form is, as such, imperfect. We explain X as certain elements’ satisfying certain conditions. But now we can ask why, in a given case, given elements satisfy these conditions and satisfy them all. The answer is not contained in the nature of the elements; they may or may not satisfy the conditions. So we must turn away from the elements and their unity to something other to explain why they have come together in the manner required for X. But then there is a sense in which it remains an accident that they have come together in this way. For, the other thing to which we now turn, although it, too, may be explained by something other still, need not have been present in the sense that the nature of X does not account for its presence. Consider this: a brick becomes loose in a storm, slides down the roof and falls. It hits someone who passes by and kills him. We can explain why he was killed: the brick hit him. We can explain why the brick fell: it became loose in the storm. It remains an accident that the man was killed. What explains the fall of the brick does not explain its further causality, its killing the man; it was not necessary that things came together in this way. Note that it is different when I have loosened the brick, calculating that the man will pass by at such-and-such a time, will be hit by the brick and be killed. Explanation of something by something other Hegel calls finite explanation. An infinite explanation, by contrast, explains the elements and the conditions in virtue of satisfying which they constitute X by the whole or unity they thus constitute. Here we need not turn to something other in order to comprehend why given elements satisfy the conditions and satisfy them all. The nature of X, which is internal to the elements that constitute it, accounts for that. In this way, the nature of X accounts for its existence. What is capable of this form of comprehension Hegel calls an idea. The first kind of idea, he thinks, is a life-form, then there is knowledge, theoretical and practical, and finally pure reason. If thought, or language, were such as to be understood in the inferior manner that Brandom thinks highest, then there would be no complete understanding of it. But the intellect cannot be such an unworthy object of the intellect. If anything can be understood perfectly, then the intellect. Indeed, our reflections show that Hegel is right in thinking that intentionality, natural or rational, is an object of infinite explanation. Intentionality is not explained by responsive dispositions, because

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a sequence of stimulus and response manifests intentionality only if the whole of the sequence explains its members, which whole then is a teleological process. An explanation by responsive dispositions is finite, explaining one thing, the response, by another, the stimulus, which is not explained in the same act, while explanation of a manifold by a unity under which it is subsumed is infinite. I said that “life”, “sentience”, “sapience” signify a unity of what affects something and what it does that is different from that signified by the concept of responsive disposition. We now see that this means that life, sentience, sapience are the object of a higher account than one that satisfies Brandom’s gold standard. They are, in Hegel’s term, ideas, and an object of infinite comprehension. 2.2 LOGICAL VOCABULARY: INTRODUCTION OF CONDITIONALS

There is no reason to be disappointed that an account of thought and language in terms of special responsive dispositions is inadequate to its object. For, an account of this form yields only finite comprehension. Brandom’s wish to give an account of this form, motivated by his notion that it fits the gold standard of comprehension, leads him to a false account of logical vocabulary. He explains how logical vocabulary is contained in any vocabulary by reflecting on the conditional as the paradigmatic logical symbol. The conditional, he says, can be introduced by algorithmic elaboration from any inferential practice. This seems wrong to me. It is not possible to introduce conditionals by algorithmic elaboration from a given set of responsive dispositions. For, asserting that something follows from something is not responding to a stimulus. We can focus the issue by considering a parallel. Quine defines an observation sentence by its involvement in a responsive disposition: an observation sentence is tied to a set of stimuli that call forth assent to the sentence. He then introduces observation categoricals reporting the regular coincidence of two stimuli, each associated with a given observation sentence. If we use “j” and “y” as observation sentence schemata, then the schema of an observation categorical is “whenever j, y”. How might someone who can use observation sentences come to use observation categoricals? If the stimuli to which “j” and “y” are tied regularly come together, one will associate them, that is, one will, upon suffering the one, expect the other. One may be said to express this expectation in doing something appropriate to the expected stimulus. In the world of our cat, the sound “fleisch” and salami on the food plate come together regularly. So she expects salami on her food plate when she hears “fleisch”. She expresses this expectation by hurrying to her food plate upon hearing “fleisch”. When she hurries to the plate, she manifests behavior informed by the regular coincidence of “fleisch” and salami. This nexus of stimuli has sunk into her responsive dispositions. Thus we might say that her behavior expresses this regular coincidence. But her behavior is not a case of using an observation categorical. As Quine explains, “[an observation categorical is] a generalized expression of expectation”.1 Our cat expresses her expectation by hurrying to the food plate. This is not a generalized expression. A generalized expres-

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sion would express that, in general, she expects meat when she hears “fleisch”: “whenever ‘fleisch’, salami”. Quine suggests that the step from using observation sentences to using observation categoricals is small. But this cannot be true. If it were, why does not our cat take it? The small step is from being able to use the observation sentences to absorbing a regular nexus of stimuli to which they are tied in one’s responsive dispositions. This step our cat takes. It is a different thing to tie the use of a sentence, no longer to a stimulus, but to a regular nexus of stimuli. An observation categorical is used, not when this or that stimulus is suffered, but when this stimulus generally coincides with that. And here, “when” bears a different sense. In “the observation sentence is used when the stimulus is suffered”, it means “at the time when”. But this is not its meaning in “the observation categorical is used when this stimulus and that stimulus regularly coincide”. For, there is no time when this happens. It is not something that happens. In using an observation categorical, one responds to the fact that the stimuli regularly coincide. This is what Quine must mean when he says that the categorical expresses that in general one expects this stimulus upon having suffered that one. But here the response is to something general. So the response is no longer to a stimulus. For, the general is not a stimulus. The general does not affect the senses. Let us return to Brandom. He says a conditional describes or specifies the practice, the system of responsive dispositions, from which it is elaborated. If that is right, then its use is not an act of such a disposition. Responsive dispositions are described in statements saying what in general is done and when. And the conditions of the correct use of such a statement cannot be tied to a stimulus. The use of a conditional is not a response to a stimulus and cannot be introduced by response substitution. Brandom’s description of the stimulus to which a conditional is to be tied as a new response is ambiguous, but it must be read as describing something general, in which case it describes no stimulus. Brandom writes: By hypothesis, the system has the ability to respond differentially to the inference from p to q by accepting or rejecting it. It also must have the ability to produce tokenings of p and q in the form of assertings. We assume that since it can produce those assertions, we can teach it also to produce-assertively tokenings of the new form “if p then q.” What is required, then, is first that this new sort of response be hooked up responsively to the previously discriminable stimulus, so that it is asserted just in those cases where the inference from p to q would have been responded to as a good one. This is an exercise of the algorithmic elaborative ability I earlier called “response substitution”: responsively connecting a previously distinguishable stimulus-kind to an already elicitable performance-kind. (LL 2, 21)

This may be read as a rule for the use of a specific formula “If p then q”. The rule would be that the formula is used to greet someone’s moving from the assertion p to the assertion q, if that inference is a good one. It is then a form of saying “yes” to a move, a special form of “yes” that can only be used when the move is from p to q.

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There will be a different rule for, say, the sentences s and r: the formula “If s then r” is a special “yes” said only of a move from s to r. These rules share a common form. But one is not conscious of this form in virtue of following rules of this form. Hence, if Brandom’s description is read in this way, then the formula “If p then q” does not say that the inference from p to q is good; it does not express consciousness of a rule of the practice. Brandom’s description of the stimulus to which the use of a conditional is to be a response may also be read as saying how, in general, formulae of the form “If j then y” are to be used: such a formula is to be used, when the inference from j to y is good or, equivalently, when one would treat a move from j to y as valid. Here, there is not just a sameness of rules, a grasp of which is not internal to an act of following any of them, but the generality is inside the rule and must be grasped by someone who follows it. In consequence, the “when” in the formulation of the rule does not mean “at the time when”. There is no time when an inference is good, and there is no time when one would treat a move as valid. So the conditions under which it is correct to use a conditional do not specify a stimulus to which the use of the conditional is a response. It is not possible to introduce logical vocabulary by algorithmic elaboration from a system of responsive dispositions. For, the use of a conditional constitutes consciousness of something general. And while any algorithmic elaboration from responsive dispositions is a responsive disposition, consciousness of the general is not an act of responding to a stimulus, for the general is no stimulus. This does not mean that logical vocabulary is not internal to any autonomous vocabulary. It means that, if it is, then in no case is an assertion a response to a stimulus. This is anyway the insight behind the claim that a system of Quinean observation sentences is not a language, an insight Brandom spoils when he thinks it means that a language needs further responsive dispositions as opposed to something different altogether. But what? We can indicate the direction of an account that would not be of the inferior form Brandom thinks is the highest by returning to our reflections on the rational teleology of action. The unity of an intentional action is mediated by a representation of this unity, from which its steps are derived. So the action does not just exhibit a unity, but the unity is such as to be known by the acting subject. Intentional action is self-conscious. An assertion, insofar as it expresses a judgment, is not an action, but it may share this formal character: rules that govern assertion are such as to be known by the asserting subject. If these rules describe a practice, then this practice is such as to be known by her who participates in it. What general statements describing the practice represent is such as to be known by bearers of the practice. The practice is self-conscious. Then it is a small step from following the rules of the practice to representing them in speech. For the power to follow them is a power to represent them, which power, however, is not a responsive disposition, but a self-conscious spontaneous power. Of course this concept, the concept of a self-conscious spontaneous power, is obscure (for us, not in itself) and must be developed.2

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2.3 KANT’S ACCOUNT OF THE UNITY OF MODAL AND NORMATIVE THOUGHT

Brandom associates the thesis that modal and normative thought are internal to thought as such with Kant. This seems right. But Kant explains in a different manner why thought as such contains modal and normative concepts. He derives their necessity from the objective validity of judgment. Judgment as such is objectively valid. It is, and is understood by the judging subject to be, valid of the object. This defines the general form of a judgment, the unity of representations in a judgment: the unity of representations in a judgment is the unity in virtue of which the judgment relates to the object in this way. Kant argues further that this unity of representations, the objective unity of apperception, contains specific forms of unity, among them the unity of judgments designated by the concept of causality and lawful connection. This explains why Hume’s atomism is wrong. It is wrong because the objective unity of apperception contains a unity of representations that involves necessary connections. Representations’ being related in this way is the form by which they relate to an object. Modal concepts are contained in the power of judgment because a judgment is objectively valid and thus exhibits the unity in virtue of which it is so valid, which unity is the source of modal concepts. Kant argues further that the objective unity of apperception, the unity of representations in virtue of which the judgment they constitute is objectively valid, is the unity by which they are self-conscious. The subject knows herself to be the subject of representations not in virtue of any character of their content, but in virtue of their unity. And this is the same unity as the one by which they relate to an object. Now, as the unity in virtue of which judgments are objectively valid is such as to be represented by the subject, that unity may figure in the subject’s thought as an imperative. The imperative form of the representation manifests an imperfection in the subject. It comes on the scene when something has gone wrong, as when the subject judges something to be the case that, according to what the subject takes herself to know, cannot be the case. In this way, the self-consciousness of judgment is the source of normative concepts. The same formal character of judgment is the source of modal concepts and is the source of normative concepts. Not only are both modal concepts and normative concepts internal to judgment. They spring from the same source: the objective unity of apperception. Brandom’s and Kant’s accounts are finite and infinite respectively. Kant’s central term is judgment, Brandom’s assertion; this difference is not important now. Brandom introduces assertion as the act of a responsive disposition that is part of a system of such dispositions. (The dispositions are special in that their terms, stimuli and responses, require special vocabulary for their description.) Then he argues that such a system can be algorithmically elaborated so as to include dispositions whose acts can be recognized as acts of using modal and normative vocabulary. Finally he maintains that, through this vocabulary, the practice of assertion reveals itself to be a practice of subjects relating to objects. In this way Brandom thinks he

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has explained objective validity in terms of a constellation of responsive dispositions. This is an explanation, he thinks, because an account of the concepts that the explanation deploys, the concept of a responsive disposition and the concepts of commitment and entitlement that describe the terms of the relevant dispositions, does not rest on a prior understanding of the idea of objective validity. Formally, this explanation is finite and therefore imperfect. Kant begins with the nature of judgment, which is objective validity. This is the principle. It explains. We understand it when we see what and how it explains. It explains in this way: the objective validity of judgment requires that judgments exhibit a certain unity, the objective unity of apperception. This unity is the source of modal and normative concepts, which thus are revealed to be internal to the power of judgment. So objective validity is not understood through independent ideas of the modal and the normative. These are understood through it. Objective validity is the principle of modal and normative thought and the principle of their unity. Thus it is a source of infinite comprehension of itself. Even if we think we cannot follow the account of the intellect that Kant gives in the Critique of Pure Reason, we ought to aspire to an account of that form. I want to end with pointing out a consequence of Brandom’s account of the subject. Brandom says that, as incompatibility of determinations constitutes the identity of the object so determined, so does incompatibility of commitments constitute the identity of the subject so committed. I believe this is right. But it shows that Brandom and I are one subject. Brandom does not see this because he does not follow his theory, but a prior idea he has that he and I are not one. If it is said that this is red and green, then something must be wrong. But if it is said that this is red and that is green, then it may be that everything is right. As red and green are said of different objects, these judgments are not in tension. Brandom suggests the parallel is this: If I say it is red and green, then something has gone wrong. But if I say it is red and Brandom says it is green, then nothing need have gone wrong. As different subjects make the judgments, they are not in tension. But this is not true. When I say it is red, and Brandom says it is green, then something has gone wrong. I cannot say, everything is fine, after all it is Brandom who says it is green, not I. I cannot say this because, in judging, I claim universal validity. I judge for any judger. So does Brandom. There is a conflict in the judger, whom Brandom and I represent. If we follow Brandom’s theory beyond prejudice, we must say: that the disagreements between us are disconcerting proves that we are one subject of judgment.

NOTES 1. W. V. O. Quine, Pursuit of Truth, rev. ed. (Cambridge, Mass.: Harvard University Press, 1992), 24. 2. See my Self-Consciousness (Cambridge, Mass.: Harvard University Press, 2007).

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PHILOSOPHICAL TOPICS VOL. 36, NO. 2, FALL 2008

Responses

Robert Brandom University of Pittsburgh

I. RESPONSE TO JOHN MCDOWELL Thank you very much for your thoughtful comments, John. I see you as having raised three questions: an overarching methodological one, an issue specifically about Wittgenstein, and in closing, a point on the indexicals, so let me address things in that order. The methodological question, I think, is indeed inseparable from how we think about the prospects for analytic philosophy. When I was first writing these lectures, the first human being who read the early version of them was my Doktorvater Richard Rorty. His characteristic response was thematic for John’s remarks. He said, “Why would anyone set out intentionally to prolong the death-agonies of analytic philosophy by another decade?” which is what he thought I was trying to do here. That seems to me more or less the attitude John is taking. I want to say two things. First, I think that there is something to this tradition. I think that there is something that we, in an extended sense of ‘we’, have been on about during this period in Anglophone philosophy that is worth recovering from the wreckage of some of the paradigmatic core programs of it. As John says, I’m not empiricist, I’m not a naturalist, I’m not an artificial intelligence functionalist, either. I don’t think any of those core programs is actually going to work. He is then asking, reasonably, “Then, why do you think that there is something worthwhile here?” One thing to say about this is that there are two things I am trying to point to a new future for, breathe new life into. One of them is analytic philosophy; the other is pragmatism. This is supposed to be an analytic pragmatism. I don’t see this 135

as a one-way street. I think John thinks that pragmatism is alive and triumphant, so its organs are going to be transplanted into the corpse or near-corpse of analytic philosophy. I actually think pragmatism has been looking somewhat peeked these days, too, and that it is precisely the quietistic aspect of it that is the problem. “Don’t think, look.” The advice is to eschew theorizing and offer microdescriptions of potentially puzzling practices. But actually, we haven’t even been doing all that much microdescription of practices. In the pragmatist tradition, it is not so clear what we should be doing: tending our roses and not worrying about it, maybe. Again, it seems to me that there are really fundamental and important insights in the pragmatist tradition and actual, important work of understanding to be done from that perspective, and that what is needed to help us do that is to bring it together with some of the insights of analytic philosophy. So what is wrong with these core programs? I do think, as John suggested, it is a certain way of thinking about the privileging of one vocabulary over another. In my lecture, I didn’t say anything, for reasons that may become clear, about what reasons you might have for privileging one vocabulary as a base vocabulary over another as an empiricist, as a naturalist, as a functionalist about the mind. Mostly, I’m completely uninterested in that question. For it seems to me that the interest in understanding the relations between vocabularies and the extent to which it is possible to say in one vocabulary most, if not all, of what can be said in another vocabulary, perhaps by the use of logic, should not at all be held hostage to the question of why it is you are interested in those vocabularies, or any collateral views that you may have about how one of them is more important or privileged in some way rather than another. It seems to me that there is a kind of intelligibility, a kind of understanding, that comes from investigating these relations between vocabularies and that one precisely should not take the second step that I think was characteristic of traditional metaphysics. I think of traditional metaphysics in general as the attempt to find a vocabulary in which everything can be said. Its favored vocabulary is one that for some reason it is confident about. That is its base vocabulary. Now when we look at other vocabularies, it will never turn out that one was completely successful: that you can say everything else in the favored terms, even by whatever potentially controversial standards of success are in play. There are always going to be some things that you’ve got a good story about. One can say in the base vocabulary these things from the target vocabulary. But then there are always going to be these awkward things that you can’t say in the favored terms. My view at that point is that one ought to say that we’ve learned something when we see that, when we see that the expressive resources of this vocabulary suffice to express this much of what you could say in this other vocabulary, but not these other things. But the impulse characteristic of traditional metaphysics was to say, so those things aren’t real, or aren’t intelligible, or are in some other way deceptive or bad. What is real (or whatever the metaphysical honorific is) is what you can say with the expressive resources that the metaphysician has for some reason or other argued are particularly perspicuous or

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whatever; the rest of these, they’re not real. I think that is the step one should not take. Just learn the detailed lesson about the relative expressive powers of the vocabularies in question and move on. This relaxed, nonmetaphysical view is connected with my views about logic. The two traditional questions in the philosophy of logic were the question of demarcation (What is logic? Or, as I would prefer to put the point: What makes something a bit of logical vocabulary?) and the question of correctness (What is the correct logic?). But if you give my expressive answer to the first question—roughly, that the expressive role distinctive of logical vocabulary is making explicit proprieties of inference—then the second question lapses. The beginning of wisdom in thinking about logic is not to look for the right logic but to observe the different expressive powers of classical logical connectives, intuitionistic-relevance ones, and so on. Dummett notices some differences in the expressive power of intuitionism and classical logic and says, “So classical logic is unintelligible. It manages to confer no actual content on its things. Only what meets these particular conditions, has this particular expressive power can be correct.” That is the old bad metaphysical impulse. My picture is that understanding is knowing our way around in ultimately an inferentialist-expressivist network of different vocabularies, practice fragments, and so on, and practically learning what the relations among them are. So we can just pick some vocabulary—for all I care, because it is Tuesday, we pick this as a base vocabulary, and see what that is expressed in other target vocabularies we can find a way to express in this base vocabulary. And then on Thursday, we pick another one, and see what we can express in its terms. Eventually we are going to know our way around better, mastering the relations between these different kinds of vocabularies, which cut across each other in various ways. So I don’t think that what ought to be understood as essential and taken forward in a progressive way in analytic philosophy was the extent to which it was a metaphysical program. It would have horrified the founders of this tradition to have it described this way, but I think having this invidious, discriminatory notion of privileging just is the old metaphysical impulse. That is always what was unpleasant and thuggish about the analytic tradition. But it has never been what was important.1 I do not want to say, with the metaphysical naturalist, for instance, that one must be able to explain the significance of a signpost in a vocabulary that resolutely restricts itself to talking about pieces of wood and movements of people in the vicinity. The view that would say, “Well, if you can’t say everything about it in the language of pieces of wood and movements of primates in the vicinity, then it’s unintelligible, or there is something defective about it,” would be making that second, inappropriate, metaphysical move. But resisting that move leaves room for it still to be worth thinking about various naturalistic vocabularies and what expressive relations they stand in to various other kinds of vocabularies. That’s the spirit in which I am going to be talking about normative vocabulary, about modal vocabulary, about intentional vocabulary, in the lectures to come. So I think that there’s

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a way to draw a line that puts what is objectionable about the analytic tradition, its metaphysical impulses, to one side while still keeping what was right and genuinely contributing to our understanding of things within the analytic tradition. As to the discussion of Wittgenstein: my beloved colleague John is one of those who I think draws the quietist, particularist, semantic nihilist conclusions from Wittgenstein. He would, I think, say, “That’s not a conclusion from a general view on language because Wittgenstein wouldn’t have a general view of anything. The point is the particularism, the nihilism, and so on.” Well, maybe it is. I certainly agree that Wittgenstein does want us to think about the signpost in an environment in which there are persons and uses of it; I myself found John’s gesture at an account of the signpost-using-practice a little bit thin. “We have to think about it in an environment where there are signposts.” Well, yes, maybe in the end that’s right, but I also think that there are a lot more articulate things that can be said about it. I think that one methodologically promising—not merely tempting, but actually promising—way to fill in and articulate that picture is to try and think about the possibility of pragmatically bootstrapping accounts of that practice of using signposts that don’t use the concept of a signpost or knowing which way to go. Now, it is not going to be the language of wood and movements, but can we help ourselves to a normative language, but not yet a language of signposts and semantic content? How much of that practice—if we describe what you are doing, allowing ourselves to use a deontic vocabulary that talks about correctnesses of various doings but restricts itself from using semantic and intentional vocabulary— how much of a practice of using signposts can we express? How much of what we say in the signpost language can we say in a normative but not yet intentional and semantic vocabulary? I want to ask that question quite generally about discursive practices. Now, it may well turn out that we can say some things but not everything. I want to systematically resist the conclusion from that that there is something spooky or fishy about the stuff we can’t say in that way. But I think we’ll understand something if we do that. How much can we say in the language of alethic modality but not the normative? And so on. I took John to be claiming that we weren’t going to get a bootstrapping account, that going pragmatic isn’t going to help us get a bootstrapping account of the phenomena Wittgenstein most cares about. Maybe so. Let’s try it and find out. I didn’t hear, and surely he didn’t intend, a transcendental deduction of the impossibility of bootstrapping accounts of anything. Since I believe I have some bootstrapping accounts of some things in my back pocket, I propose to lay them out and see what we can do along those lines. I may be missing the Wittgensteinian point, but I still think that there’s that kind of stuff to find out, even if he’s entirely right about the conclusion we’re going to end up in. Now, the indexical point. There’s a longer discussion of this that I am only epitomizing and gesturing at here.2 It’s a very delicate issue. I do believe that one can say in an entirely nonindexical language—can formulate rules in an entirely

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nonindexical language—for the correct use of indexicals. That claim I am committed to, and John clearly denies that. I do not think that nonindexical language is an autonomous discursive practice and an autonomous vocabulary. I don’t believe it’s intelligible that there be creatures who speak only a nonindexical language. This is for reasons that will be familiar to readers of Gareth Evans, for instance. I think his account of the way in which one needs to be able to map egocentric space and public space onto each other in order to so much as have the concept of spatiotemporal continuance is right. So, when John says that what you have to be able to do to use nonindexical language is—I think this is a quote—“not intelligible entirely independently of the capacity to use indexicals,” I actually agree with that. I don’t think you can use nonindexical vocabulary unless you can also use indexical vocabulary. But that’s a separate claim from the question of whether someone who can use both kinds of vocabulary can formulate rules in the nonindexical language that specify sufficient conditions for correctly using the indexical vocabulary. It’s a delicate issue, and certainly, if one were engaged dialectically with the sort of made-up skeptic that I mentioned briefly, the one who says, “I don’t even understand indexical vocabulary,” the place to start would be with the argument that nonindexical vocabulary is not autonomous, so you can’t actually be in the position that the skeptic claims to be in there. But of course, that’s not the point that I’m after. So, I think the question about the independence of these two types of vocabulary is one thing, and I am not claiming that nonindexical vocabulary is autonomous. Nonetheless, someone who, partly in virtue of being able to use indexicals in fact, actually is the master of nonindexical vocabulary, only needs to use the capacities he is using to deploy the nonindexical vocabulary to state rules that determine the correct use of the indexical vocabulary. That’s the claim.

NOTES 1. I respond to McDowell’s (and Rorty’s) worries here in much greater detail in the Afterword to Between Saying and Doing (Oxford: Oxford University Press, 2008). 2. The full discussion can be found in the Appendix to Lecture 2 in Between Saying and Doing.

II. RESPONSE TO JOHN MACFARLANE I think I know what to say about two of John’s three thoughtful and challenging questions. That’s what I’m going to say first. I won’t say much about the middle one. The first question is this. I was pretty careful to describe being universally-LX as the genus of which logical vocabulary is the species. What is being left room for there, and why? Why not just identify this genus with logical vocabulary? I think

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you could do that, but doing it that way is more revisionary than doing it the way I would like to do it. Lots of stuff that people don’t normally think of as logical vocabulary would come in. What I have in mind is that of the features of discursive practice that seem plausibly to be really essential, some of them are semantic and some of them are pragmatic. The semantic ones, I think, generally have to do with the inferential articulation of things. That is the species that I think ought to be identified with logical vocabulary. Adding that restriction includes all of the classical logical vocabulary (including logical vocabulary), and not too much else. But recall that the original argument was that besides the inferential dimension in discursive practice, there is always also an assertional dimension. Nothing that doesn’t involve your capacity to commit yourself assertionally is going to count as a discursive practice. (This is something I talk about more in the fourth lecture.) That means that if there is a way of algorithmically elaborating vocabulary that attributes commitments to people, paradigmatically by using propositional attitude-ascribing locutions, then just from the ability to take people as having made claims and committed themselves (and though it is no part of what I am going to do in these lectures, I think there is—that is, I think there is a way of algorithmically elaborating the implicit ability in practice to distinguish somebody as having made an assertion and having committed himself into the capacity to say things like, “John claims that . . .,” “John believes that . . .,” “such and such”) then propositional attitude-ascribing locutions are going to come out as universally-LX. I think they are. And I think it is sensible to distinguish between the things that are universally-LX because they are elaborated from and explicative of, as it were, pragmatic features having to do with what you’re doing, the commitments that you’re undertaking, and so on, from the semantic, that have to do with the inferential relations among things. Since one very traditional way of thinking about logic is as the science of inference, one picks up that tradition by restricting the notion of logic to the universally-LX things that are elaborated from an explicative of inferential relations that are essential to any discursive practice. That’s what I had in mind there. For the third question, John offered a weak and a strong reading of the VPsufficiency condition as it holds in the meaning-use diagram that’s expressing the meaning-use analysis or construction—it’s the same thing—of the notion of being universally-LX, where the question is whether you can make all of the PV-necessary practice explicit or only part of it. Here, I actually want to say that I think it doesn’t matter what you say about that, because if you look at the diagram, the PV-necessary part, the contained rounded-rectangle there—that can contract. We’re not claiming that it’s the whole PV-sufficient practice that’s made explicit; it’s just got to be some element of it that’s necessary. It has to be sufficient to elaborate the vocabulary from, but other than that it doesn’t matter how big it is. So we can say that it is only an aspect of the inferential practices that is made fully explicit. The inferential practices are only one aspect of the PV-sufficient practices. And that is all that is made fully explicit in this case. But conditionals really are VP-sufficient to make

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that aspect of the PV-sufficient practices explicit. And that aspect really is a necessary condition of every autonomous practice. So the LX condition is met. I think of that as just shrinking down to whatever the vocabulary is actually sufficient for, subject to the condition that enough is left that you can elaborate that practice from it. In this case, I think one can do that. The other question was about the status of the algorithmic elaborative abilities. Granting that none of us actually has those abilities, since there are going to be some psychological restrictions on us, even if it is just the number of states we can be in—there is presumably some upper bound to that—how exactly do we draw the boundary around this, and how do we motivate drawing the boundary one place rather than another? In one sense this is not a critical issue because I am introducing a notion of one set of practical abilities being in principle sufficient for another. And I can give a clear notion of what “in principle” means. I suggested that these are the algorithmic elaborative abilities that really are constitutive of a Turing machine. (I also pointed out that, though people don’t talk about these as among the primitive algorithmic elaborative abilities, things like response-substitution and universal state formation are actually always assumed by automaton theorists.) What is the motivation for having that particular set of algorithmic elaborative abilities as the sense of “in principle” that matters here? Of course I have my eye over my shoulder at the core program of AI-functionalism as a way of thinking about what discursive practices are. So, for that one, it is the Turing machines that matter. That is a sort of low-strategic reason, having to do with what I am going to go on to discuss, to make that the right general conception to have in play. In fact, what I need in order to introduce the conditionals is something only very much weaker than that. The most substantive thing I appealed to was really just responsesubstitution. If you actually looked at how you would write the algorithm to do it, you would use some other abilities, but nothing nearly as sophisticated as a Turing machine is required to do that. I’m happy enough to have the different notions of algorithmic elaborability, indexed by what abilities you actually have in that, give us different notions of PP-sufficiency and so different notions of LX-ness. Because, however, what I ultimately care about is the possibility of giving an algorithmic decomposition of discursive abilities into individually nondiscursive abilities, which is what I’m going to say the claim about AI is, if you are going to worry about that you might as well have the full set of algorithmic elaborative abilities. That is the set that’s required for a Turing machine, that can compute everything that can be computed. We don’t know a stronger set than that, and we can build machines that can do that. So there’s nothing mysterious about that sense of algorithmic elaboration. It clearly would not be sneaking a ghost in the machine in somewhere at the back if you assume that full panoply of algorithmic abilities. I am eventually (in the third lecture) going to argue against that pragmatic version of artificial intelligence, and the argument against that ought to be addressing the most plausibly workable version of that which is going to allow the strongest set of algorithmic elaborative abilities.

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That all having been said, I don’t really know how to think about what turns on drawing the boundaries in one place or another, and I think that’s a really interesting question. For each way of filling in the “in principle” practical sufficiency of one set of abilities for another will yield a different notion of PP-sufficiency. There are clearly a lot of them available (“in principle”), and I can only pretend to have thought about this one.

III. RESPONSE TO PIRMIN STEKELER-WEITHOFER Let me say something briefly about the last point. It seemed to me striking that there is a parallel between what by the end I was calling executive algorithmic elaboration or decomposition, the one that matters for AI, and the other sort of PPsufficiency relation, the notion of practical elaboration by training. For the notion of algorithmic decomposition still has applicability even in that case, because it makes sense to talk about pedagogical algorithmic elaboration in the form of training regimens that are flow charts. The particular source of the interest there was the question of whether when we move with Wittgenstein to centering our attention on practical elaboration, extension of our practices by training, whether that means we have to give up on the idea of pragmatic analysis of anything and just say that all we can do is describe the practices that we have or the abilities that we have. So the question arises: is it still possible to see the sort of dependence of one sort of practice on another that meaning-use analysis was looking for, the sort that Sellars invokes for instance when he argues that what you have to be able to do in order to use looks- or appears-talk already presupposes what you have to be able to do in order to use is-talk? It seemed to me that seeing that even after we have decided with Wittgenstein to focus our interest on this other kind of PP-sufficiency, practical elaboration by training, there still is the possibility of algorithmic decomposition or elaboration there, in the form of thinking about completely solved pedagogical problems. And that then was my entry into the political issue. That is how I was thinking about these points as being related. There are a couple of other small things that I might say about StekelerWeithofer’s deep remarks about the framework in which people are thinking about AI. As he pointed out, we mostly don’t disagree about that. But he is setting up a richer background for the discussion. One of his points is to ask whether it really is true that context-free vocabularies are VP-sufficient to specify Turing machines. He points out that if we want to answer questions like whether a machine has broken down or not, we are going to have to step outside of the computer language, outside of the context-free language, in order to answer that question. That is true, and it is very important when we think about practical or, as he said, real AI rather than what he called utopian AI. But I really was only addressing the project of utopian AI. The automata that I am talking about are abstract machines; they are not physi-

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cal machines. So they are not machines for which the question of whether it has bugs in it arises, or where it is appropriate to ask: Does this chunk of machinery actually implement this finite-state automaton or this Turing machine? Those issues just don’t come up. I am thinking about a conceptual analysis of things. Why ought we not, in a certain sense, to be surprised that the weaker, context-free languages can say everything that a Turing machine has to do in order to do things, compute functions, that the automata that can deploy context-free languages cannot do? I think this is because of the very phenomenon that Stekeler-Weithofer pointed to: in the context-free language, all we have to be able to do is, in effect, describe what it is that the Turing machine has to be able to do. So, even things that in the context-free language you cannot do, you can still have terms that let you say what you would have to do to do that. In a way it is like the athletic coach, who can describe for the gymnast what she needs to do in order to be able to execute a certain maneuver. Even though the fat middle-aged coach couldn’t perform this maneuver to save his life, he still might be able to say what it is you need to do in order to perform the maneuver. That is what you can do in a context-free language: say what it is that the Turing machine has to be able to do. And it is because being able to say what it is and being able to do it are two different things that the Turing machine can be more capable. Another question is about the appropriateness of the Turing test. Here I think that there is really a deep issue, and it really has to do with the modality that is involved in the Turing test. The Turing test is a test for sapience. If you cannot tell, no matter how extended the conversation is, whether you are dealing with a machine or a human being, some real deployer of vocabularies, then the system passes the test. What is the force of that ‘can’? In one sense, of course, the conversation only lasts as long as it lasts. At a certain point, even if you’re only just, as Bertrand Russell said, medically limited by the fact that life only lasts so long, the conversation will come to an end. (I’ve had many conversations with Kambartel over the years that do not seem to have been medically limited—if conversations could go on forever, ours do. They are as close as you can get.) But the in some sense “in principle” medical limitation means that there is always the possibility that whenever you say, all right, I have said everything I can say, I have tried everything I could try to discriminate these things and I cannot tell whether it is a human or a machine, it always could be that the very next thing it would have said would have tipped you off, would have been the thing that would have let you discriminate. Does that mean that you can tell, or does it not mean that you can tell? If there is some path through the conversational labyrinth that you could have taken, if it had occurred to you, or it had just happened that you had taken that path, if you’d lived long enough to do that, that would have made the distinction, then in my understanding of the Turing test that means that you can tell the difference between them by engaging the system with conversation. The fact is that you cannot actually be sure that something has passed the Turing test, that there is no finite amount of

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conversation that can let you certify the negative existential claim that there is no discriminating conversational path, though there is a finite amount of conversation after which you may be in a position to say it has failed the Turing test. I am comfortable with the modality that says that nonetheless would count as your being able, as its being possible, to discriminate them—if there is some conversation that would have permitted the discrimination. So when I say that I think the Turing test is a fair test for what I want to call synthetic intelligence, that is, genuine intelligence that is created in this particular way, it’s that strong modality that I mean. StekelerWeithofer is pointing out in effect that that’s no use to us in actually assessing these things, at least if we want to certify something as deploying an autonomous vocabulary. We are never really in an epistemic position to do that. This is nontrivially connected as he at least hinted to the halting problem in more orthodox AI. But the semantic point I am after concerns when it would be correct to apply the concept deployer of an autonomous vocabulary, not the epistemic question of how we would find out.

IV. RESPONSE TO HUW PRICE I think this is a very difficult issue. Huw Price and I have been trying to hammer this out, Richard Rorty and I have been trying to hammer this out, and John McDowell and I have worried about the same issues. We all have deflationary impulses, and everyone except Price and Rorty has some kind of realistic impulses, too. Those two think that we should just get over all of these attempts to speak with the vulgar in the tradition, and we in the middle are stuck, torn both ways. I actually find metaphysics left in claims such as that we should just stay on the word side of the wordworld divide. I think that that sort of recoil is betraying that one hasn’t sufficiently freed oneself from the traditional way of thinking. It is moving from a one-sided objectivism to a one-sided subjectivism. But that is not to say that I know exactly how one should be in the middle. Rorty and McDowell and I once agreed to triangulate our positions like this. Rorty, in Philosophy and the Mirror of Nature,1 argues that the only way to avoid the pickle modern and contemporary philosophy have gotten into is to banish the concepts experience and representation. Any use of them, he thinks, will start us down a familiar slippery slope into the abyss. In Making It Explicit, I follow Rorty in carefully avoiding any appeal to or use of the term ‘experience’ in discussion of mind and language. And I do not appeal to representation as a basic concept in my semantics. But I do go to some trouble to show how to introduce representational locutions, and to understand what they express, on the basis of the twin notions of inference and assertion, which serve as the pragmatic bases on which the semantics is built. I claim that this sanitized notion of representation does not involve any of the objectionable commitments Rorty so tellingly diagnosed. McDowell, in Mind and World, is happy to use hygienic notions both of experience and of representa-

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tion. I do not think that McDowell’s version of experience involves commitment to the Myth of the Given, or that his (less explicit) embrace of representational locutions involves an objectionable sort of semantic foundationalism or reductionism. Rorty thinks that the abyss is so threatening that a fence must be erected a quartermile from the edge, to keep the unwary safe. I think that a hundred yards away is sufficiently prudent. McDowell is happy prancing surefootedly on the very edge of the precipice like a mountain goat. I don’t think McDowell falls in. But I want to say: “Kids, don’t try this at home. This man is a professional.” I wouldn’t myself recommend that anyone try to duplicate his performance. Nonetheless, Rorty objects to my intermediate view from as it were, the left, and McDowell from the right. Price is with Rorty on this one. Here is the sort of thing that I mean about not being sufficiently freed from the old ways of thinking. When Price says, “In effect, it would tell us why creatures in our situation would be led to develop a modal physics, even if they inhabited a nonmodal world”—I don’t understand what ‘a nonmodal world’ could conceivably mean. That counterfactual—what if we inhabited a nonmodal world—makes no sense if the expressive resources recruited by modal vocabulary are really part of the very meanings of the words that we use to describe the world. If the claims I am making in my fourth lecture about the expressive role characteristic of modal vocabulary are correct, then it is a necessary feature of modal vocabulary that it play that role. It is not an optional or contingent feature of modal vocabulary. The claim is that the very idea of empirical descriptive and explanatory talk involves this modal articulation. Price wants to say that it is a fact about talking, not a fact about the world. I don’t understand the game that we’re playing in assigning some features of what our only understanding of things could be, assigning responsibility of that to us and saying that that’s because of something about our conceptual activity, our talk, not some feature of the world. That enterprise, which Kant certainly encouraged (whether or not in the end he ought to be understood as practicing it himself), the enterprise of trying to assign responsibility for some of these features to one side or the other of a word-world divide, is what I don’t understand. One place where this comes out is this. Price says: “You seem to believe that there is some genuinely descriptive vocabulary, where that involves representing how things are.” I do. I think describing is something we do—well, Huw thinks that, too—but I think that it is right, not just in our ordinary talk, but even in our philosophical talk, to say that part of describing is representing how things are. Now Sellars says that in the dimension of describing and explaining, science is the measure of all things, of those that are that they are, of those that are not that they are not. (This is his famed “scientia mensura” remark.) He is clear that not everything that we do with the language is describing. He says also that the descriptive and explanatory resources of the language advance hand in hand. That is one of the thoughts that I have been developing in the lecture that we just heard, that explanatory resources are the ones that take explicitly modal form. Those are the ones that tell us how facts that we can represent stand in explanatory relations to one another, and how

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the very idea of a fact, indeed of a way the world could be, is unintelligible apart from the notion of explanatory connections that we make explicit with modality between those facts. The job of those modal expressions is not to describe something. So if by a nonmodal world we mean one where one does not use modal resources to describe features of the world, then I guess we do live in a nonmodal world. When I say that it is and must be one that we can only be aware of, describe, or understand in modal terms, Huw is going to say that we should not think of those modal features as features of the world. Well, if they are necessarily features of our talk about the world, if our talk about the world is necessarily modally articulated, I don’t really understand the point of saying that there is no objective feature of the world that corresponds to these things. If what we’re saying is that their job is not to describe, that they have a different job from that of the descriptive vocabulary, in particular because they are articulating these explanatory relations—well, I understand and accept that. I do not know what to say at this point. I do not know how to talk about what to assign responsibility for to the world and what responsibility to assign to us. I do not know how to play that game, and I am trying not to play that game. That is on the one hand wriggling and not taking sides on the opposition Huw offers; on the other hand, I think of it as trying to get beyond the framework that looks as though you need to come down on the word side or the world side. One of the things I am trying to do, no doubt clumsily, in the sixth lecture will be to give us some way of talking that gets outside of having to come down in a one-sided way. The questions then are, exactly what is involved, what is required, what is the best way to turn one’s back on metaphysics? Price wants to do that; I want to do that, too. But I think that assigning responsibility for some feature of our discursive practice either to us or to the world is doing metaphysics. It is just doing it in a subjectivist way rather than in an objectivist way. (But that is not to say that I know how to talk about these things.) Huw thinks that doing anthropology is doing a kind of biology. I don’t understand that. I think that social sciences are sciences, too—they are not reducible to natural sciences, even to biology—and that the last thing you want to do is be biological in the kind of anthropology you are doing, if it is discursive practice that you’re talking about. Discursive practice is essentially a kind of social practice. Biology gets to the verge of the social in things like population biology, but when it does it is not getting to the social in the normative sense that we need to talk about discursive practice. So I actually find that an unnecessarily reductive form of naturalism even if you are biological on the subject side rather than on the object side. (Ruth Millikan has offered the most sophisticated sort of bridge between evolutionary biology and the normativity essential not only to practical, but also to discursive intentionality. I do not pretend to have an a priori objection to her way of thinking about things.) Here is one last maybe confession, or form of the confession, about not knowing how to talk in this area, which is possibly responsible for the wavering that Price is seeing. He says that once representational relations become part of our substan-

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tial theoretical semantics (not just of an account of how these words are used in ordinary talk, but in our philosophical theorizing), so do their relata. We become committed to both ends of the relation. That means we must acknowledge the existence not just of words, but of all the things to which a representational semantics takes those words to stand in semantic relations: numbers, values, causes, conditional facts, and so on. I accept that. I do think there are numbers. I think there are norms. I do think that adopting representational talk toward basically declarative sentences commits you to the existence of facts corresponding to them and to the objects the facts are about. But a fact for me, as for Frege, is just a claim that is true (in the sense of a true claimable, whether or not there are corresponding claiming of it), and if there are true normative claims, then there are normative facts. If there are true modal claims, then there are modal facts. What I don’t have is a metaphysical account of the nature of facts in general, for instance, that requires them to be built up in tinker-toy fashion as spatial arrangements of objects or something like that, which is going to make you puzzle about what kind of a thing a modal fact or a probabilistic fact or a normative fact could be. I want to say that I’m using ‘fact’ in a much more deflated sense than Huw is when he is worried about us being committed to these things. When I say that there are numbers, I’m saying that some arithmetical claims are true and that numerals function as proper singular terms. That is all I’m saying. I think that is how Frege taught us to think about the question of whether there is a certain kind of object—it just is the question of whether a certain kind of expression, occurring essentially in the expression of truths, functions as a singular term. Huw wants us to say that we should stop talking after we say that an expression functions as a singular term. That much is okay, that is good pragmatist anthropology. Do not go on to say that because some of these claims are true—now understood in a properly deflationist sense—that means that there are arithmetic facts and numerical objects. But I do not see why not to say that, once we understand the suitably deflated sense of such claims. These claims are true; a fact is a claim that is true. Now what I am not sure about is this. I am not confident that the various remarks I’ve made about how to turn one’s back on metaphysics and have a relaxed view about the representational dimension of language, all actually hangs together and is coherent. I do feel the tension that Huw is diagnosing. But it does not seem to me necessary to go all the way over to the positive claim that all this stuff is happening on the side of the words and we have a non-Humean world that is . . . what? I do not know what is on the object side if I stop thinking about all of these facts and objects. That’s probably just a complicated confession of confusion, but those are the things I think I know how to say.

NOTE 1. Princeton University Press, 1979—to be reissued, with an Introduction by Michael Williams, in a thirtieth anniversary edition in 2009.

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V. RESPONSE TO JAROSLAV PEREGRIN Jaroslav Peregrin offers us a sophisticated discussion of the relation between formal and philosophical semantics and applies it to the incompatibility semantics I introduce in my fifth lecture. Two of his ideas that I find particularly helpful are stated very early on: 1. “We can say that where the model connects with reality is not semantics, but inference.” 2. “Semantics is simply our way of seeing the inferential roles as distributed among individual expressions.” If I understand him correctly, he is worried that the incompatibility semantics violates at least the spirit of both of these principles. I do not see that it does. To begin with, the incompatibility semantics is not offered as a replacement for an inferentialist semantics, but as a piece of one. It takes its place as part of a program of grounding semantics in pragmatics, of understanding meaning in terms of use. The inferentialist idea is that what makes something a discursive practice, one capable of conferring conceptual, paradigmatically propositional content on acts and expressions that play suitable roles in that practice, is that some performances have the significance of assertions and inferences. That is another way of saying that it must be intelligible as a practice of giving and asking for reasons. I argue on quite general grounds that to be a practice of giving and asking for reasons, participants must in practice distinguish two sorts of normative status: commitments (acknowledged in the first instance by assertings) and entitlements. There are then at least three basic sorts of inferential relations among assertible contents that can be distinguished: • Commitment-preserving inferences, • Entitlement-preserving inferences, and • Incompatibility entailments. I say that two claimable contents are incompatible in case commitment to one precludes entitlement to the other. And p incompatibility entails q in case everything incompatible with q is incompatible with p. Thus that Pedro is a donkey in this sense entails that Pedro is a mammal, because everything incompatible with his being a mammal is incompatible with his being a donkey. Commitment-preserving inferential relations are a generalization, to include the case of nonlogical, material inferences, of deductive inferential relations. Entitlement-preserving inferential relations are a generalization of inductive inferential relations. And incompatibility entailments are a generalization of modally robust, counterfactual-supporting inferential relations.

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The incompatibility semantics is intended to codify only this third class of inferential relations. It does not pretend to capture the full inferential roles expressions play, because it ignores the commitment- and entitlement-preserving inferential relations they stand in. But the subclass of inferential relations it does aim to capture, it aims to capture precisely in Peregrin’s sense of being a “way of seeing the inferential roles as distributed among individual expressions.” And the picture is indeed one according to which the model “connects with reality” via what practitioners actually do, the pragmatics, that is, in terms of inference and assertion. Incompatibility, and the semantics that captures a portion of inferential role by associating with a sentence the sentences incompatible with it, has no relation to actual practice that is not mediated by the consequential relations among normative statuses that it codifies. So I think the two principles Jarolsav formulates are fully complied with. He also raises a technical reason for concern along these lines. It can happen in some settings that an inferential consequence relation that can be formulated finitistically has only infinitistic representations in terms of incompatibilities. This leads Jaroslav to suspect that the camel of model theory is poking its nose into the tent of inferentialist semantics. This would be a problem if it meant, for instance, that we were obliged to appeal to the denotational relations fundamental to model theory antecedently to and independently of the inferences they support. But I do not see that they are. Both Peregrin and I see model theory as providing a rich metalanguage for codifying inferences—in some important ways, more expressively powerful than traditional proof-theoretic metalanguages for codifying inferences. Nothing stops us from still understanding them as “ways of seeing the inferential roles as distributed among individual expressions.” Indeed, Peregrin himself has done the most important work to show how that can be done for model theoretic semantics. So even insofar as infinitistic representations of inferences bring model theoretic considerations into play, I don’t think the inferentialist construal of what is going on is threatened. And, if one were more worried about this issue than I am, it is always open to us to say that the fact that some particular incompatibility codification is, as it were, gratuitously infinitistic just shows that this is not one of the inferences that should be represented that way. After all, the incompatibility semantics is not meant to represent all inferential relations. The next point is that there is a formal recipe for going back and forth between the incompatibility semantics and standard Kripke semantics for modal languages. All the information about incompatibilities is contained in the minimal incoherent sets. (Two sets of sentences are incompatible just in case their union is incoherent.) And possible worlds correspond to maximal coherent sets. You get S5 if you impose no further structure, and various other modal logics in the familiar way by adding a kind of second-order compatibility/incompatibility relation, corresponding to accessibility of worlds. (Kohei Kishida has shown how to represent a wide variety of other familiar modal logics in the incompatibility framework by adding

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neighborhoods.) If the two semantic schemes are just notational variants of one another, where is the philosophical payoff supposed to come from adding the incompatibility version? The philosophical motivations of the two schemes are quite different, and so are the philosophical lessons we can draw from them. Three results can illustrate this. First, incompatibility semantics treats modal and nonmodal logical vocabulary on a par. The Kripke framework understands classical logical vocabulary in terms of truth-at-a-world, and modal logical vocabulary as corresponding to quantification over worlds. By contrast to that two-stage procedure, incompatibility semantics offers the same kind of definition of possibility as it does for negation. Each makes explicit aspects of material incompatibility (non-compossibility). Since material incompatibilities are an essential feature of the meaning of any nonlogical vocabulary, they both show up as explicitating features of discursive practice in general. Second, the incompatibility semantics is fully recursive, in that the semantic interpretants of more complex formulae are entirely determined by the semantic interpretants of less complex formulae. But it is holistic at each level; changing the semantic value of any sentence can change the semantic values of all the rest. So it is not compositional. But it is projectible and systematic. This is a combination of features that Fodor, among others, have argued is not possible. Third, many consequence relations permit the imputation of an incompatibility relation, on which basis modal operators can be introduced to make explicit various features of the consequence relation. This notion of a logic intrinsic to a consequence relation is a distinctive feature of the incompatibility framework. I also think the way in which the semantic values available, and hence the formulae that are valid, depend on the expressive power of the language—since inferences are defeated by claims that are incompatible with the conclusion, but not with the premises, so a less expressive language will invalidate fewer inferences—is both technically and philosophically interesting. Technically, it means one is working in effect with variably multivalued logics. Adding new sentences to the language adds new semantic values, and can alter what follows from what, even among the old sentences. Philosophically, this set-up gives us a tractable test-bench for investigating the relations between the expressive power of a language as a whole and the meanings of its individual sentences. The final question Peregrin asks concerns how I am thinking about logic. He offers two alternatives. Either • “Logic is something essentially nonlinguistic, some very abstract structure, which can be identified and mapped out without studying any real language . . . [such that] any possible language is restricted by the structure discovered by language.” or

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• Logic is the study of the meanings of the logical words of actual natural languages. He suspects that I reject the supposed exhaustiveness of this classification, and I do. As I detail in the lectures, I think that logical vocabulary is elaborated from and explicative of the broadly inferential relations that characterize any vocabularies. The constraint on possible languages is definitional and pragmatic: if they don’t have sentences that stand in relations of material inference and incompatibility, then it is not discursive practices we are talking about. That constraint does not stem from logic, but underlies it. To be a bit of logical vocabulary, it must be the case that in being able to assess the material goodness, in various senses, of inferences, one already knows how to do everything one needs to know how to do to deploy the vocabulary in question. (That is the “elaborated from” part.) And the expressive role of the vocabulary must then be to let one say that various inferences are good, in the sense characteristic of the logical locution in question. Thus asserting a two-valued conditional is saying that the inference from its antecedent to its consequent is good in the sense that it does not have true premises and a false conclusion. Asserting an intuitionistic conditional is saying that the inference from its antecedent to its consequent is good in the sense that there is a recipe for turning a conclusive argument for its antecedent into a conclusive argument for its consequent. Asserting a strict implication is saying that the inference from its antecedent to its consequent is good in the sense that it is impossible for its antecedent to be true and its consequent not. And so on. It could be that every use of a natural language expressions such as “if . . . then__” corresponds to the use of some genuinely logical expression. But that certainly need not be the case. And it wouldn’t matter to the enterprise of logic, which is to introduce connectives whose inferential and expressive roles are clear, tractable, and surveyable, and use them to make explicit aspects of the inferential roles of nonlogical expressions. This broadly metalinguistic role fits neither of Peregrin’s proferred alternatives. The philosophy of logic traditionally revolved around two questions (I am thinking here of settings-out such as Quine’s little book The Philosophy of Logic). The demarcational question challenges us to say what it is that makes something a bit of specifically logical vocabulary. (So we know how to classify alethic or deontic modal operators, the set-theoretic epsilon, second-order quantifiers, functional expressions, and so on.) The evaluative question challenges us then to say what the correct logic is. The account of the expressive role characteristic of logical vocabulary that I offer in Between Saying and Doing (further developing the characterization in Making It Explicit) offers a detailed answer to the demarcational question, in the form of a meaning-use analysis of LX (elaborated-explicitating) vocabulary. And on that account, the evaluative question lapses. The question is not which logic is correct (classical or intuitionistic logic, for instance), but just what the expressive role of the different connectives is. From my

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point of view, Peregrin’s partisanship for intuitionism is retrograde: the result of asking a question we should have gotten beyond.

VI. RESPONSE TO SEBASTIAN RÖDL Sebastian Rödl is expressing a view that I think is genuinely deep, and delineating a difference in approaches in philosophy that I think is also genuinely deep. He is starting with a notion of form, of unity, of principle connected to explanation that has its origins in Aristotle, that also, as he suggested, animates the German idealists, and that he and my colleague Michael Thompson have been developing in the contemporary age.1 I actually think that the next twenty years is going to be the site of an epic confrontation between this way of thinking about things and the attitude of murdering to dissect that I represent here. Though I do not myself make much of the specialness of the organic case, and so do not usually rely on that class of metaphors. What I think is at issue is two forms of explanation. Rödl is quite right in seeing what I am doing as a kind of bottom-up explanation, by elements, by construction. He is opposing that to a kind of top-down explanation, where you explain the elements in terms of the form, the unity, the principle of the whole thing that one is talking about. I think it is very important to understand the difference between and the relations between these different kinds of explanation. It is Sebastian’s work and Michael Thompson’s work that begins to give me a glimmer about how Hegelian infinite explanations might contrast with the sort of finite ones that, it is true, I treat as the gold standard of understanding—not in the sense that I think everything can be understood that way, or that anything that we cannot understand that way must forever remain unintelligible. When I call it the “gold standard,” I mean that when I can get a bottom-up constructive explanation from elements, I feel I understand things better than when I am understanding the same things in the topdown way. Sebastian thinks that the most important things—the notions of life, of intentional agency, of language, of consciousness, of discursiveness—can in principle only be understood top-down, in terms of the distinctive form that different statements, for instance, about living things, get in virtue of the form of statements about the biological, and similarly for teleology, for agency, for discursiveness. I think that he is probably right that to discuss something living or intentional as such you’ve got to take into account this top-down way of thinking about it, to pick it out as something living, as something intentional, as something rational, that you have to pick it out in the kind of vocabulary that he is describing for us. I think he might be overlooking the possibility that though these forms of explanation are different, and though the home language game of talk of living, of acting, and of thinking beings might well be in the sort of idiom that he’s talking about, it is at least not obvious, and it may not be true, that you cannot explain the applica-

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bility of top-down explanatory vocabularies in bottom-up terms. I don’t know. Because I feel I understand things better when I can understand them in bottomup terms, I am aiming to understand the applicability of the very terms he is talking about, but to explain them in another vocabulary, in a bottom-up vocabulary. I think Sebastian might systematically underestimate the extent to which new stuff happens when you put lots of more basic things together in new structures. He is confident that because the poor cat that he threw into the fire responds by bursting into flame does not exhibit anything like the response of a living creature—never mind intentionality—therefore, no account that appeals to stimulus-response connections could ever exhibit the sort of phenomena that are described in the topdown vocabularies that he uses. When the bolt falls off of my automobile, I can hold the thing up and say, this is never going to take me to the airport in the morning. But that does not mean that putting together in the right way a lot of little things that will never get you to the airport in the morning doesn’t add up to something that can take you to the airport in the morning. Of course he is going to hasten to say that this might be true of mechanism, but that living things are not like that. Well, maybe so; maybe not. In particular, the sort of rational teleology that he’s talking about, the sense in which there is goal-seeking behavior is one case where it seems we have learned a contrary lesson. One of the striking things about automata that can execute conditional branch-schedule algorithms is that they are goal-seeking. The exit condition is not, as he characterized it, just ceasing to respond. It is sensible, and I think it is correct, to understand these systems as casting about, trying all sorts of things, until and unless a certain goal situation is brought about. I think that there is a kind of teleology that is exhibited by anything that is describable as having the structure of executing a test-operate-test-exit cycle, and in fact we see sophisticated goal-seeking behavior in robots that instantiate such things. Now again, he is going to insist that there is a big difference between what these artifacts do and what biological things do—and I do not mean to deny that. My account of what I call the level of practical intentionality and the way in which that might be practically elaborated (not now algorithmically elaborated but practically elaborated) into discursive intentionality, started off with living beings, the ones that really do have stimuli and responses, their skillful doings, what they are doing as part of the lived life of an animal, and the way in which objects are involved in that and goals are sought. But I am animated by an idea that I think was important to the American pragmatists: that there is a structure in that that we can see in living organisms, that we can see in evolution, that is common to the learning of individual organisms, to the evolution of species, that is common also—though this for obvious reasons was not a big theme for the classic American pragmatists— to these sort of goal-seeking machines, genuine functional machines, that are not simply stimulus-response engines, precisely because of the flexibility of conditional branch-schedule algorithms that are TOTE cycles. The idea was that although it is true that the details of these particular cases were quite different, living things do it

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differently, nonetheless they can all be described in a common vocabulary, the vocabulary of test-operate-test-exit cycles. The challenge is to see whether the fact that they can be described in this common vocabulary is something that we can use to explain ultimately the applicability of the kind of more sophisticated top-down explanatory vocabulary that Sebastian is interested in. I still think that is an enterprise that’s worth trying. And I think that the sorts of things that he is led to say— for instance, that an assertion is never a response to a stimulus—are not clearly correct. I think it can be enlightening to think about observation reports as inter alia responses to stimuli, to think of them as having a structure that involves exercising a reliable differential responsive disposition, something that we reporters of things can share with merely sentient creatures like pigeons but can also share with clanking artifacts like photo-cells hooked up to the right things, even though the instantiations of these things is different and much richer vocabularies are applicable to us than to the pigeon and to the pigeon than to the clanking artifact. For nonetheless, the reason colorblind people cannot noninferentially report the presence of red things is that they are not properly describable in terms of exercising reliable differential responsive dispositions to respond differentially to red things. That is an important thing to realize. Of course we also want to talk about the significance of the fact that reporters are applying concepts, and then we are using a different vocabulary. But the fact that that richer vocabulary applies, and must apply, for it to be an observation, does not, I think, undercut the intelligibility, the illumination, that we get from also observing that we can describe what they are doing in a much sparer, bottom-up vocabulary that already applies in other cases where the richer vocabulary does not. Let me end where Sebastian ended, with his proof that he and I are identical. We have a lot in common, I’m glad to say. His argument turns on the observation that if he says, “The ball is red,” and I say, “The ball is green,” there is something wrong. We’re not just okay normatively. Maybe we’re better off than if I say, “The ball is red, and the ball is green,” but it doesn’t mean that we are off the hook just because it’s the two of us. In talking about this, let me substitute something that we really do disagree about—since I don’t know what color he thinks the ball is actually. He says that if I offer anything other than top-down explanations, what I’m explaining cannot be a feature of life, of agency, of rationality. I say that I can explain the applicability of that terminology even though my explanation is couched in a different vocabulary. Now again, if I said both of those things, I would be contradicting myself—and so I would be in real trouble. I acknowledge that there is still some problem when he and I disagree. But it is a different kind of problem, and what defines us as different subjects is the difference between the normative pickle that I’m in if I contradict myself, and the normative pickle that we’re in if we contradict each other. All I need to claim, it seems to me, is that there is a normatively distinctive wrongness that is sufficient to distinguish the subjects. Now it is a basic Hegelian claim that self-conscious individual subjects and their communities are simultaneously synthesized by reciprocal recognition. A con-

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sequence of that is that in the end you cannot understand the two sorts of normative wrongness, the kind distinctive of the individual subject, the sense in which I repel incompatible commitments, apart from the sense in which we repel incompatible commitments and acknowledge an obligation to sort things out ourselves. Those are two sides of one coin. I did not talk about that second kind of normativity, intelligible in principle only as part of a package that includes the kind I did talk about and vice versa, that Sebastian rightly points to. Those differences are equally essential in this holistic structure. But, as the differences between Sebastian’s recommended methodology and mine call normatively for a fruitful dialogue between us, and may eventually lead to a better understanding, I can only applaud the sense (Hegel’s “identity in the speculative sense”) in which we are in the end identical. (In the Afterword to Between Saying and Doing, written after the Prague meeting, I respond at greater length to some of the comments presented there, especially to the methodological challenges of McDowell and Rödl. Readers interested in these debates are invited to consult that discussion.)

NOTE 1. Thompson’s views are now more widely available in his wonderful, path-breaking book Life and Action (Cambridge: Harvard University Press, 2008).

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