Cogitations: A Study of the Cogito in Relation to the Philosophy of Logic and Language and a Study of Them in Relation to the Cogito

COGITATIONS

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COGITATIONS A Study of the Cogito in Relation to the Philosophy of Logic and Language and a Study of Them in Relation to the Cogito

Jerrold J. Katz

OXFORD UNIVERSITY PRESS New York Oxford

Oxford University Press

Oxford New York Toronto Delhi Bombay Calcutta Madras Karachi Petaling Jaya Singapore Hong Kong Tokyo Nairobi Dar es Salaam Cape Town Melbourne

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and associated companies in Berlin I bad an

Copyright © 1988 by Oxford University Press, Inc. Published by Oxford University Press, Inc., 200 Madison Avenue, New York, New York 10016 Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Katz, Jerrold J. Cogitations : a study of the cogito in relation to the philosophy of logic and language and a study of them in relation to the cogito. Includes index. 1. Analysis (Philosophy) 2. Language and logic. 3. Descartes, Rene, 1596-1650. I. Title. B808.5.K37 1986 111 85-28421 ISBN 0-19-503744-8 ISBN 0-19-505550-0 (pbk.)

Printing (last digit): 9 8 7 6 5 4 3 2 1 Printed in the United States of America

This book is dedicated to the memory of my former colleague and friend JAMES F. THOMSON

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Acknowledgments The author thanks the following people for their help: David Auerbach, Jawad Azzouni, Martin Brown, Arthur Collins, Karen Evans, Harry G. Frankfurt, D. Terence Langendoen, Gareth B. Matthews, Fabrizio Mondadori, James Murphy, William Ney (who prepared the index), Peter Stamos, Amelie Rorty, Margaret D. Wilson, David Pitt (who proofread the paperback edition), and two anonymous referees for Oxford University Press.

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Contents

I. Introduction, 3 II. The Cartesian Scholar's Dilemma, 11 III. The Source of the Obscurity, 23 IV. Logical Form, Universality, Linguisticism, and Locke, 41 V. How the Concept Containment Notion of Analyticity was Lost, 52 VI. Regaining the Concept Containment Notion of Analyticity, 60 VII. The Analytic Entailment of Existential Sentences, 98 VIII. The Cogito as an Analytic Entailment, 118 IX. Cartesian Scholarship Revisited, 131 X. The Nature of Analysis, 144 XL The Cogito and Indubitability, 159 XII. On the Existence of a Thinker, 168 XIII. A Brief Revisionist History of Analyticity, 179 Notes, 186 Index, 199

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COGITATIONS

He who says, 7 think, hence I am, or exist,' does not deduce existence from thought by a syllogism, but, by a simple act of mental vision, recognises it as if it were a thing that is known per se. RENE DESCARTES

It seems to me that there are ever so many different cases of necessary connection. . . G. E. MOORF,

"You do not exist," said O'Brien. Once again the sense of helplessness assailed him. He knew, or he could imagine, the arguments which proved his own nonexistence; but they were nonsense, they were only a play on words. Did not the statement, "You do not exist," contain a logical absurdity? But what use was it to say so? His mind shriveled as he thought of the unanswerable, mad arguments with which O'Brien would demolish him. GEORGE ORWELL

I Introduction

The cogito is unique. No argument in the history of philosophy approaches its combination of importance for subsequent thought, controversiality, difficulty in comprehension, and utter simplicity in form. This unique combination poses the question addressed in the present study: how is it that so simple and important an argument has caused such difficulty in comprehension and such philosophical controversy? Since the cogito is so simple it ought to be easy to understand, arid since it is so important, numerous first-rate minds have, over the centuries, tried to understand it. Why, then, do we still not have an explanation of the nature of the inference that offers a satisfactory treatment of Descartes's writings on the subject and its role in his project? This book puts forth a radical answer to this question. It argues that the trouble lies where it is least suspected. The problem, on the view to be expounded here, lies, not with any obscurity or incoherence on Descartes's part or with any confusion or hard-headedness on the part of the scholars who have interpreted Descartes's work, but with a deficiency in the theory of language and logic that Cartesian scholars have brought to the study of the cogito. The problem, I shall argue, is that this theory falsely assumes that all formally valid inference depends on subsumption of the step(s) from premiss(es) to conclusion under a sequence of laws of logic. In order to count the cogito as formally valid on the basis of this theory, Cartesian scholars have had to recast it as a complex argument, with the consequence that the argument no longer fits either Descartes's own account of the cogito in his writings or the role he assigns it in his project. In this book, I argue that the cogito is not a logical inference in the sense of depending on laws of logic, but is formally valid nonetheless. The first part of my argument will distinguish the notion of

4

Cogitations

formally valid inference from that of logical inference and exhibit a class of inferences whose conclusion follows without subsumption of the inferential step under a law of logic. This class is the analytic entailments, the inference counterparts of analytic statements in the narrow sense of statements, like "A bachelor is an unmarried man", whose truth rests on sense structure alone. The second part of my argument will show that the cogito is an analytic entailment. My argument as a whole provides an account of the cogito which shows it to be valid as it stands, and hence, provides an account that squares with what Descartes says about the nature of the cogito, its relations to other principles, and the role it plays in his reconstruction of knowledge. At first blush, the cogito does not seem to be an anlytic entailment. "I think, therefore, I exist" will not be found among the customary examples of analyticity in the literature, and it does not appear to resemble familiar examples such as "John is a bachelor, therefore, John is an unmarried man". On consideration, there might seem also to be a philosophical argument against claiming that the cogito is an analytic entailment, since there are well-known objections to construing "exists" as a predicate and the claim seems to construe "exists" in just this way. Thus, I recognize that, at this early stage, it will be quite natural for the reader already to have doubts about the central claim of this book. At this stage, I offer two observations. First, a radical claim, in the nature of the case, must seem doubtful at the outset, and second, prior to and in the early stages of the systematic study of a linguistic structure, only the most obvious examples are conspicuous—more recondite ones becoming prominent only after substantial progress has been made. The present book is thus a study of the cogito in relation to the philosophy of logic and language and a study of them in relation to the cogito. Much of the argument in the book focuses on the questions of what analyticity is, whether there is an analytic—synthetic distinction, and, if there is, why, as a consequence, there is a form of validity that requires no subsumption under laws of logic (or mathematics). Three conclusions are reached: first, that Frege was mistaken in treating analyticity as a species of logical truth; second, that Quine was mistaken in thinking that there is no analytic—synthetic distinction; and third, that Carnap was mistaken in trying to fuse analytic, logical, and mathematical truth into a uniform notion of L-truth. The cogito functions as the principal case at issue in the arguments for these conclusions.

Introduction

5

Now it is widely recognized that doing systematic philosophy makes direct contributions to the history of philosophy. Everyone is familiar with examples of philosophical investigation coming up with something new that removes obscurities or difficulties in the thought of a major figure or classical position. The use that logical empiricists made of Frege's and Russell's work in logic to reconstruct Humean empiricism's account of 'relations of ideas' comes readily to mind. Moreover, the mechanism of such contributions is easy to understand. Major philosophers are major because they are far ahead of their time. It thus stands to reason that the thought of major philosophers will sometimes contain obscurities or difficulties because the ideas needed to make their thought fully clear or as clear as we'd like it to be were not available when they wrote. Hence, it is easy to see how systematic philosophy can clarify historical questions by developing ideas that were not available when a historical figure wrote. There is, then, no special discussion required to set the stage for my thesis that the development of certain ideas in current philosophical semantics can provide an interpretation of the cogito that is fully satisfactory from the perspective of the history of philosophy. On the other hand, it is not so well-recognized that the history of philosophy can contribute directly to systematic philosophy. But it will be one of my principal claims that, in removing the difficulties in our understanding of the cogito and those of Descartes's writings which bear on it, the interisionalist position in the philosophy of logic and language is corroborated. Thus, some special discussion is required here to explain how it is that the history of philosophy can contribute to systematic philosophy. The fact that exegetical success can corroborate a position on a substantive philosophical question is obscured by how we tend to think about the history of philosophy and systematic philosophy. We tend to think of them as being pursued independently by specialists with little to say of relevance to their counterparts in the other field. We do not rule out contributions from one field to the other, but think of them as rare, catch-as-catch-can affairs. But, although this is how things may often be, it is not how they need be. For the relation between philosophy and history of philosophy is not like that between fields such as biology and history of biology. Doing systematic philosophy is part of doing history of philosophy, and doing history of philosophy is part of doing systematic philosophy. This does not mean that there are no differences between them, but only that the differences should be attributed to the special focus of each field.

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Cogitations

The reason for the overlap between systematic philosophy and the history of philosophy is that the basic problems which occupied great philosophers of the past are the same problems which occupy philosophers today. Unlike other fields in which historical research concerns problems that are no longer at the cutting edge of systematic research, in philosophy, historical research concerns problems that, in one form or another, continue to be at the cutting edge. Some people see the continuity of the basic philosophical problems as an alarming sign that philosophical progress proceeds at a snail's pace, while others see it as an indication of the depth of the problems themselves. Be this as it may, the fact remains that, unlike other fields, philosophy does not outgrow its dependence on the thought of the great figures of its past: the Kantian revolution does not remove figures like Hume or Leibniz from a position of systematic importance in the way that the Einsteinian revolution removed Newton from a position of systematic importance in physics. Moreover, it is quite natural for Wittgenstein to set the problem with which he begins the Philosophical Investigations in terms of a quotation from St. Augustine, and later in the book, to illustrate the logical atomist position he wants to criticize not, as one might expect, by quoting Russell or his own Tractatus-Logico-Philosophicus, but by quoting Plato's Theaetetus. To claim that systematic philosophy and history of philosophy are integrated is not to say that systematic philosophizing does not often significantly extend philosophizing of the past, but just to say that attempts to say something new and attempts to say what has been said clearly are both part of the attempt to say what ought to be said about the basic problems of philosophy. Sometimes when the thought of a major philosopher is obscure the fault is not the philosopher's but lies closer to home. The problem may be with the framework within which contemporary scholars are trying to understand the philosopher's thought. In such a case, particularly when the framework is familiar and long accepted, the actual source of the obscurity is especially hard to recognize. Like New Yorkers who are so accustomed to traffic noise that they no longer hear it, contemporary scholars may not notice the framework they are working within. As a consequence, the obscurity will be mistakenly attributed to inadequacies in the major philosopher's thought, in its expression, or in one or another piece of scholarly interpretation. In such a situation, new ideas developed outside the philosophical mainstream can enable scholars to notice something that they have

Introduction

7

tacitly been accepting all along, and perhaps even to begin to question its acceptance. Sometimes, such ideas can provide an alternative diagnosis, attributing the exegetical problems to the framework that scholars have been taking for granted, and as a consequence, provide a clear arid satisfying understanding of the major philosopher's thought. If a set of ideas can affect such a significant historical clarification, the ideas must ipso facto be corroborated within systematic philosophy. Of course, the ideas will ultimately have to offer reasonable answers to the systematic questions for which the framework has so far been serving as the orthodox answers and provide grounds for being better satisfied with the new answers. But if history of philosophy and systematic philosophy overlap as I have suggested, it is hard to imagine how ideas which produce such significant historical clarification could not but offer reasonable alternative answers and justification for them. The trouble that history of philosophy has had in understanding the cogito fits this scenario. The fault lies not with Descartes, but with the logical framework within which Cartesian scholars have tried to explain the inference. The source of the obscurity of the cogito is that the framework makes no place for formally valid inferences whose validity depends on language rather than on logic. In addition to familiarity and long acceptance, a special factor contributed to a belief in the reliability of this framework. The controversy between intensionalism and extensionalism which should have brought the lacuna in the framework to light failed to do so because intensionalists as well as extensionalists conflated language and logic. The original sin of explicating sense and analyticity in terms of logical apparatus was Frege's, but Church, Carnap, and all the other major intensionalists maintained this explication. None of these logicians ever asked themselves whether sense and analyticity in natural language corresponds to the account of them in this explication. Indeed, these logicians took no interest in the nature of sense and analyticity in natural language until extensionalists, particularly Quine in his attack on the analyticsynthetic distinction, put linguistics to use against intensionalism. Even then, the weight of tradition was so great that most of the theories of sense and analyticity in natural language that have been constructed were constructed on the original Fregean model. My own work in the philosophy of language was motivated, in part, by the question of where the boundary between language and logic should be drawn. I was quite surprised by the complete neglect of this question when the other half of the question about the boun-

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Cogitations

daries of logic, the question of where the boundary between logic and mathematics should be drawn, had been of such great interest. I explored semantic theories of natural language without any assumption beyond what the science of linguistics could say about their form on the basis of their role in grammatical theory. As this work went on, it became clear that a version of intensionalism was possible in which sense is explicated without appeal to reference (i.e., abandoning Frege's conception of sense as mode of referential presentation) and in which analyticity is explicated without appeal to logical laws (i.e., abandoning Frege's conception of analyticity as consequences of logical laws plus definitions, but nothing else). The explication of analyticity systematized the conspicuous cases of analyticity independently of cases of logical truth and in a way that met Frege's objections to earlier attempts to explain analyticity without appealing to logic. Then, as is often the case in theory construction, systematization of the conspicuous cases revealed underlying similarities between these cases and certain superficially dissimilar ones. In this way, the systematization lead to the discovery of new types of analyticity. The cogito turned out to be such a new type. This meant that the cogito could be understood as formally valid as it stands, and hence, in a way that squares with what Descartes says about it. We automatically have an alternative diagnosis of why the cogito has posed such difficulties for Cartesian scholars and a clear and satisfying account of Descartes's thought in the parts of his corpus relating to the cogito. Given the nature of the argument I have just sketched, it is clear that this book must discuss a number of very basic issues in the philosophy of logic and language. To mention a few of the more central issues, there is Quine's criticisms of the analytic—synthetic distinction, his indeterminancy thesis, the general issue in the intensionalist/extensionalist controversy about whether the notion of sense is required in the study of language. Related to these issues, there are the somewhat different arguments of Putnam and Kripke in which the possibility of cats turning out to be robots or demons is used to challenge the intensionalist's conception of sense. Here the discussion will focus on the question of which intensionalism and which concept of sense are challenged by these arguments. Furthermore, there are issues internal to intensionalism, principally ones about the nature of the representation of semantic structure in natural languages. The most important of these for us is whether Carnap's conservative approach to handling the contribution of mean-

Introduction

9

ing to inference, i.e., simply extending the stock of constants and the list of postulates in a predicate logic, is adequate. Such a conservative approach can be opposed by a more radical one that handles the contribution of meaning to inference outside of logic on the basis of purely grammatical apparatus. This is another form of the issue already mentioned of where the boundary should be drawn between logic and language. Tied in with this issue are many issues raised by proposals to provide lingustic answers to questions about logic and vice versa. A host of issues within the history of philosophy arise in the course of setting out the argument just sketched. These include the relation of the accounts of analyticity in Locke, Kant, and other historical figures, the controversy between Locke and Leibniz on first truths, Descartes's distinction between intuition and deduction, Kant and subsequent philosophers' criticism of existence as a predicate, G.E. Moore and Wittgenstein on analysis, Cartesians and Wittgensteinians on the nature of first person statements, the long-standing allegation that the cogito commits a petitio principii, and so on. The number of historical and philosophical issues that must be taken up, and the complexity of each issue, explains how an entire book can be written about an inference as simple as the cogito. We are accustomed to think of philosophical stature being exhibited in grand flights of metaphysical imagination like Plato's theory of forms, but there are less grandiose things that still dramatically reveal philosophical stature. I have tried to show in this book that Descartes's handling of the cogito, when it is understood outside the standard logical framework, is such a revelation of stature. Descartes's overall handling of the cogito is seen as an instance of a great philosopher rising to the occasion in a situation where the ideas and apparatus required to develop and clarify a thought are unavailable but the thought is too important to be left undeveloped and unclarified. Recognizing the cogito to be fundamentally different from the types of syllogistic inference studied in the logic of the day, recognizing that he lacked an alternative way of explaining the nature of this inference, and recognizing that there were serious and easily anticipated objections against which his cogito had to be defended, Descartes did everything that could be done in the circumstances. He explicitly and vigorously denied that the cogito is a complex argument. To compensate for the lack of a logical theory to account for simple arguments, he turned from logic to epistemology, calling attention to the simplicity of the intuition by which we come to know

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Cogitations

"I exist" follows from "I think" and contrasting this with the complexity of the intuitions in cases of typical syllogistic inferences. Further, he went as far as anyone at the time could have to spell out the priority relations among the various principles that are in various ways involved in the cogito reasoning. Although Descartes has come in for much criticism in this connection, nearly everything he says on the question of priority relations turns out to be coherent and correct as far as it goes. Finally, Descartes recognizes that the cogito enjoys a special security against invalidity, that is, one not enjoyed by logical and mathematical inferences. He does not identify the source of this special security as linguistic structure, since he has no positive account of the cogito. He does, however, identify the special security as resistance to the strongest suppositional doubt. This to my way of thinking is perhaps the most remarkable aspect of Descartes's philosophical insight in this situation. For once we have a positive account of the cogito as inference exclusively based on language, we discover that resistance to the strongest form of suppositional doubt is possible only in the case of inferences exclusively based on language.

II The Cartesian Scholar's Dilemma

As Descartes first expressed the cogito, it runs: I noticed that while I was trying to think everything false, it must needs be that I, who was thinking this, was something. And observing that this truth "I am thinking, therefore, I exist" was so solid and secure that the most extravagant suppositions of the skeptics could not overthrow it, I judged that I need not scruple to accept it as the first principle of philosophy that I was seeking.1 Descartes, however, was riot the first philosopher to argue for his existence in this way. Aristotle has something like the cogito in the Nicomachean Ethics: . . . to perceive that we perceive or think is to perceive that we exist (for existence was defined as perceiving or thinking)2 It is also found in Augustine's The City of God: Concerning these truths [that I am, that I know it, and that I love it] I fear no arguments of the Academics in which they say, "What if you should be mistaken?" For if I am mistaken, I am. F'or one who does not exist cannot be mistaken either. And so I am, if I am mistaken. Because therefore I am, if I am mistaken, how am I mistaken about my existence when it is certain that I am if I am mistaken? Because therefore I, who would be the one mistaken, would have to exist to be mistaken, there is no doubt I am not mistaken in knowing that I am.3 Locke writes: If I doubt of all other things, that very doubt makes me perceive my own existence, and will not suffer me to doubt of that. For if I know I feel pain, it is evident I have as certain perception of my own existence, as of the existence of the pain I feel: or if I know I doubt, I have as certain perception of the existence of the thing doubting, as of that thought which I call doubt.'

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Cogitations

Thus, although philosophical attention has been focused on Descartes's cogito, something like this argument has been put forth by a number of other great philosophers.-1 do not make this observation to detract from Descartes's originality, but rather to indicate the historical scope of the present study. In one sense, the cogito is the least obscure of philosophical arguments: it is so simple and clear that one can immediately grasp that it is valid. Yet, in another sense, the cogito is one of the most obscure arguments in philosophy: it is extremely difficult to obtain a satisfying explanation both of the formal structure on which its validity rests and of the statements that Descartes made about the nature of the inference. Witness the many and diverse explanations of the cogito that keep being proposed. Witness also the range of disagreement among Cartesian scholars about what Descartes says concerning the nature of the cogito and its relations to other principles. And finally witness some of the surprising things many scholars have said about Descartes. I shall argue that the obscurity of the cogito is due to a problem in the framework within which Cartesian scholars have tried to explain the formal validity of the inference. To bring the problem into clear focus, I will present a dilemma that faces Cartesian scholars who wish to do justice to the inferential structure of Descartes's argument and to Descartes himself. To exhibit this dilemma in the context of contemporary Cartesian scholarship, I will begin with the treatment of the cogito in Margret Wilson's book on Descartes.5 I choose her treatment of the inference because it is extremely reasonable relative to the prevailing assumptions about inference among Cartesian scholars and because her treatment forms part of a fine overall account of Descartes's philosophy. In taking up the cogito, Wilson writes: . . . the cogito reasoning is intended to present 'I exist' as a truth known by inference to be indubitable; its indubitability is inferred from the indubitability of 'I think' . . . The indubitability of 'I think' itself is construed as a sort of datum. 6

This interpretation, which Wilson calls the "naive interpretation," seems quite reasonable. The cogito is an inference. It is valid. Its conclusion inherits the indubitability of its premiss in the manner suggested. These claims have, of course, been criticized by some philosophers, but not so as to seriously challenge the naive interpretation. That the cogito is an argument seems plain enough. It not

The Cartesian Scholar's Dilemma

13

only has the form of one, with clearly marked premiss and conclusion tied together by the sign of inferential connection, but also Descartes is forever using the idiom of logical argument in relation to the cogito, e.g., expressions like "follows from," "infer," and so on. Chevalier claimed that the cogito represents an appeal to intuition rather than an argument, 7 but there is no reason to think that these are mutually exclusive, particularly since within Cartesian philosophy and often outside as well we are encouraged to understand intuition as, in part, the apprehension of inferential structure. Ayer claimed that "There was . . . no need for Descartes to derive 'sum' from 'cogito'; for its certainty could be independently established by the same criterion".8 Ayer thinks that the same condition makes both the premiss and the conclusion indubitable, namely, ". . . their truth follows from their being doubted by the person who expresses them."9 But this is hardly an argument for the noninferential character of the cogito. It is simply to observe, as Descartes observes also, that another mental activity, viz., doubting, also entails the existence of its agent. That the cogito is valid seems plain, too. The intuition that if / am thinking then the I who is doing the thinking cannot be nonexistent at the time is undeniable for those who take "I" to be straightforwardly referential in these uses. There are, of course, some who do not, but I think their position can be shown to be false (as I will explain in chapter VIII). Furthermore, if one were to deny the intuition of validity, one would have to accuse Descartes of committing a logical blunder of staggering proportions in a situation of the utmost importance for his whole philosophy. The accusation against Descartes would, moreover, also have to be repeated against Augustine, Locke, and Aristotle. The position that such a denial puts one in is embarrassing to say the least (unless one has an accompanying story to tell about the reference of the first person pronoun). But Wilson goes on to claim that the naive interpretation requires that we read Descartes's own major presentations of his position as erithymatic, 10

and also that we need some principle to licence the inference of 'I exist' from 'I think'—otherwise it will lack formal validity. 11

These two claims are not required by the naive interpretation, but only by the naive interpretation coupled with the doctrine that all

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Cogitations

valid inferences depend on subsumption of the step(s) from the premiss(es) to the conclusion under a sequence of logical (or perhaps mathematical) laws. Given the wide acceptance of this doctrine among philosophers of logic and language and the tendency of historians of philosophy, like the rest of us, to go along with the opinion of recognized experts on matters outside their specialty, it is no surprise to find that Cartesian scholars construe the cogito as an enthymematic argument in order to construe it as a valid argument. Thus, the Cartesian scholar faces a dilemma. Descartes presents the cogito as an argument of the form P, therefore, Q. The Cartesian scholar assumes that a valid inference requires laws of logic to connect the premiss(es) and conclusion. Given that there is no law of logic connecting a proposition P with another Q, the Cartesian scholar either has to say that the cogito is invalid and accuse Descartes of a logical blunder or say that Descartes's presentation is deficient. In the latter case, the Cartesian scholar has to supplement Descartes's formulation by adding an alleged suppressed premiss in order to bring the argument under a law of logic. But, although this reconstruction saves the Cartesian scholar from the very unattractive first horn of the dilemma, it poses two difficulties which constitute a very unattractive second horn. Arguments are individuated by their premisses, conclusion, and sequence of intervening steps (if any). Thus, the premiss and conclusion pair "I think" and "I exist" which Descartes gives is not the same argument as the triple "I think", "If something thinks, it exists" (or some variant thereof), and "I exist" which the Cartesian scholar gives as an enthymematic reconstruction. Hence, Cartesian scholars who take this way out of the first horn must say that the real cogito is a different argument from the one Descartes himself presents. The difficulty with saying this is that it accuses Descartes of blundering in failing to give the right argument for his existence. The Cartesian scholar is forced to say that Descartes has somehow managed to express himself wrongly in a situation where nothing would have been easier than to express himself rightly. The Cartesian scholar is in the position of having to say that a philosopher of the first rank either blundered into giving the wrong argument in a case where giving the right one would have been child's play at a point where he is setting the cornerstone of his entire philosophical edifice, or if he didn't blunder, gave the wrong argument wittingly. But if wittingly, Descartes was either being duplicitous or else had good reason. What reason could there have been for duplicity or intentional obscurity?

The Cartesian Scholar's Dilemma

15

The second difficulty is that there is hard textual evidence for thinking that the argument for which the Cartesian scholar has secured validity is not Descartes's cogito. The enthymematic reconstruction is rejected by Descartes in explicit protests that his cogito is not syllogistic: When we observe that we are thinking beings, this is a sort of primary notion, which is not the conclusion of any syllogism; and, moreover, when somebody says: I am thinking, therefore I am or exist, he is not using a syllogism to deduce his existence from his thought, but recognizing this as something self-evident, in a simple mental intuition.12 On an enthymematic account of the cogito, there would be a complex mental process, first a step of taking the introduced proposition "If something thinks, it exists" together with Descartes's "I think," and second a step of applying a logical principle to them to deduce the "I exist." This, clearly, goes beyond "a simple mental intuition." Descartes is here contrasting recognizing his existence as "self-evident" in a thought with recognizing his existence as following from an application of a logical principle to the thought. The self-evidence of existence in the thought is absent in the latter case. Attempts have been made to save a reconstructive interpretation in the face of Descartes's explicit protests that his cogito is not a syllogistic inference. For example, Bernard Williams tries to reconstruct the cogito as an inference resting on a logical principle outside Aristotelian syllogistic logic. Thus, he distinguishes between . . . the syllogistic major premiss 'everything that thinks exists', and the statement of impossibility 'it is impossible to think without existing' (or, what comes to the same thing, the statement 'in order to think, it is necessary to exist'). . . . Thus the point is that 'in order to think, it is necessary to exist' does not make any reference to anything existing in the world: it is a bare statement of necessity which can, on Descartes's view, be intuitively grasped. . . . What is wrong with the syllogistic premiss 'everything that thinks exists' seems to be that it does make an existential claim; and while Descartes does not explicitly say this, it can perhaps be elicited from the denials and admissions already quoted. Moreover, this would be entirely in line with the traditional logic of the syllogism, since that logic does ordinarily presuppose that general propositions of the form 'All A's are B's' should refer to A's that actually exist. On this doctrine, to assert anything of all thinking things would be to presuppose that there actually were some thinking things in existence, which Descartes is clearly in no position to presuppose. 13 The first thing to note is that this reconstruction does not save the naive interpretation from conflict with Descartes's protests because

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Cogitations

the reconstruction construes the cogito enthymematically, and hence, as a complex inference, and Descartes protests that the cogito is recognizable as "something self-evident, in a simple mental intuition." A second difficulty with this reconstruction is that it only considers one case of syllogistic reasoning, whereas Descartes protests that his conclusion in the cogito "is not the conclusion of any syllogism." There is no rationale for treating the rejected 'everything that thinks, exists' as a universal affirmative major premiss of a standard syllogistic argument rather than, say, as a conditional premiss of a compound syllogism. Descartes does not identify the source of the problem here as a matter of existential import or existential presupposition. Furthermore, the alleged extra-syllogistic argument that Williams suggests could easily be expressed as a syllogistic argument with the principle 'in order to think, it is necessary to exist' functioning as a premiss of the compound syllogism. Thus, Descartes's protests against construing the cogito as syllogistic apply to Williams's reconstruction, too. Indeed, use of the term "syllogism" at Descartes's time was not restricted to the narrow range of cases Williams has in mind. The term applied to compound arguments with hypothetical premisses carrying no existential import. Such cases are discussed in the PortRoyal Logic.u Although Descartes could not have been familiar with that particular work, he must have been familiar with the logic it codified. Thus, attempts to save the enthymematic interpretation by distinguishing syllogistic from nonsyllogistic complex arguments in the way Williams does are undercut by the fact that the term "syllogism", as Descartes would have used it, refers to complex arguments of each sort. If the Port-Royal Logic can be taken as a reasonable codification of logical knowledge at the time, and surely it can, then Descartes has to be taken as protesting any such case of turning his actually stated argument into a complex argument by supplying a further premiss. To put a fine point on it, the Port-Royal Logic defines the enthymeme as "a syllogism which though complete in the mind is incomplete in expression."15 Making the reasonable assumption that Descartes would have been familiar with this conception of the enthymeme, we can take his use of "syllogism" in his protests to cover "syllogisms of the mind," and hence, we can take these protests to rule out enthymetic interpretations from the word go. Those who wish to avoid this natural way of taking Descartes's use of "syllogism" need to explain why he never addresses the question of enthyrnatic construals

The Cartesian Scholar's Dilemma

17

of his stated argument. On my view no such discussion is necessary, but those with a different view owe us an explanation. Are we being asked to suppose that Descartes had never heard of enthymemes, or that he had, but that it never occurred to him that his cogito was really one, or that it ought to be spelled out fully? There are other writings of Descartes's which support the view that Descartes's protests that the cogito is not a syllogism should be taken as denying that there is any more complete form of the argument than is found in the argument as stated. In the Rules for the Direction of the Mind, he writes, . . . intuition is the undoubting conception of an unclouded and attentive mind, and springs from the light of reason alone; it is more certain than deduction itself, in that it is simpler, though deduction, as we have noted above, cannot by us be erroneously conducted. Thus each individual can mentally have intuition of the fact that he exists, and that he thinks; that the triangle is bounded by three lines lines only, the sphere by a single superficies, and so on. Facts of such a kind are far more numerous than many people think, disdaining as they do to direct their attention to simple matters. Then Descartes goes on to contrast intuition with deduction: . . . we distinguish this mental intuition from deduction by the fact that into the conception of the latter there enters a certain movement or succession, into that of the former there does not. Further deduction does not require an immediately presented evidence such as intuition possesses; its certitude is rather conferred upon it some way by memory.17 Aside from the light that such passages shed on Descartes's use of the notion of a simple mental intuition in the hrst quotation, the passages show that Descartes distinguished between "facts of such a kind" which are static and known by "the light of reason" and deductive facts which are dynamic and known in "some way by memory." "Facts of such a kind" are ones for which the clearness and distinctness of an intuition in and of itself can establish certainty. Deductive facts are otherwise. There is other related evidence supporting the view that Descartes treated the cogito as nondeductive (in the special sense understood here), as a kind of fact that can automatically be "read off" in an act of intuition. For example, the distinction above recurs in Descartes's Reply to the Second Objections: When I said "we can know nothing with certainty unless we hrst know that God exists" 1 said expressly that. I was referring only to the science

18

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depending on such conclusions as can recur in memory without my attending further to the proofs that led me to assert them [for] knowledge of first principles is not usually called a science . . . But when we become aware that we are thinking beings, this is a primitive act of knowledge derived from no syllogistic inference.18 This passage was a reply to Mersenne's objection that, until God's existence is proved, it is not possible for Descartes to claim, as he does, that he has proved his own existence. The point of the reply was already made at the end of the Fifth Meditation.19 As far as I can tell, there is only one place where Descartes fails to keep the cogito apart from deductive inference. In the Meditations, he lumps the cogito together with pure mathematics and there talks as if the absence of a reason to believe God is not a deceiver were a reason to entertain metaphysical skepticism about the cogito as well as about pure mathematics.20 The lapse is, however, quite explicable. Descartes is viewing these cases as ones whose denial is "a manifest contradiction,"21 that is, as necessary truths. This they all are, and, of course, establishing a necessary truth by the route of deducing a contradiction from its denial would involve the features of deductive process that raise the possibility of metaphysical doubt. What Descartes overlooks here is something that he himself has argued, that there are different cases of necessary truth and that knowledge of some does not require this round-about route. Descartes's single inadvertence in treating different necessary trviths as essentially the same in virtue of their being not deniable without contradiction is not surprising when, as we shall see in the subsequent chapters of this book, this mistaken treatment has been the fundamental error in philosophical attempts to understand analyticity from Descartes's time down to the present. In this connection, it is interesting to note that the cases that Descartes gives of divinely creatable eternal truths are deductively established truths of geometry: his example for Mersenne is the equality of all radii of a circle, arid his example for Mesland is the equality of the three angles of a triangle to two right angles.22 The examples in the quotation above about intuitive knowledge are, in contrast, merely analytic truths, deriving from the definition of "triangle" as a plane figure formed by three lines intersecting by twos at three points and the definition of "circle" as a closed plane curve, all of whose segments are of the same curvature. 23 We note also that the question at issue is whether God can make the denial of an eternal truth true. 21

The Cartesian Scholar's Dilemma

19

One further reason for thinking that the enthymematic construal of the cogito conflicts with Descartes's own conception of the inference is Descartes's response to Burman when the latter questioned him about whether his claim that the cogito is not syllogistic is consistent with things he said elsewhere about the nature of the cogito. Descartes answered that the generalization "Whatever thinks is" is "implicitly . . . always presupposed and prior," but that it does not follow that I am always expressly and explicitly aware of its priority, or that I know it before my inference. This is because I am attending only to what I experience inside myself—for example, 'I think therefore I am': I do not pay attention in the same way to the general notion 'whatever thinks is'. As I have explained before, we do not separate out these general propositions from the particular instances; rather, it is in the particular instances that we think of them. 25

There is surely a question what Descartes means by "presuppose" and "prior." I shall return to this question in chapter IX. I will argue that the relation he is pointing to (but, of course, cannot explicate) is the same as the relation between "whatever is having a nightmare is dreaming" and "I had a nightmare, therefore, I had a dream". But this question to one side, it is clear that, for Descartes, the validity of the cogito does not depend on the "general notion." As Descartes saw it, the cogito exemplified the generalization and is the basis for our coming to know the generalization. The case is assimilated to that in which we come to know a geometrical generalization in virtue of it being the case that the particular instance we have before us differs in no significant way from any other exemplification.26 Let us take stock. Descartes's discussions of the cogito pretty much rule out the possibility of an account of the inference which both secures its formal validity enthymematically and fits Descartes's characterization of it. So the choice with which Cartesian scholars seem to be faced is either to live with unease about how the Cartesian texts have been treated or to live with unease about how the Cartesian inference has been treated. In this respect, the Cartesian scholar's dilemma is typical of troubling dilemmas: neither horn presents an attractive prospect. But the Cartesian scholar's dilemma has a special unpleasantness. The desire to accord Descartes the respect he obviously deserves as one of the great philosophers, mathematicians, and scientists in Western history is an important consideration in choosing either horn. Thus, this desire must be frustrated no matter which horn is chosen: whichever alternative in the dilemma Cartesian scholars choose, they will have to paint essentially the same

20

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unflattering picture of Descartes that, in their original choice, they tried to avoid. I do not wish to claim that there is no difference in degree. It may well be that it is less unflattering to Descartes, and hence, less embarrassing to the Cartesian scholar, to paint Descartes as somehow having expressed himself wrongly than to paint him as having committed a logical howler. One strength of the enthymematic reconstruction, no doubt, has been that it is seen as the lesser of the two evils. On the one hand, the reconstruction, although it concedes that Descartes was confused enough to give the wrong argument, still presents him as giving an argument that most people would think isn't too far removed from the right one. On the other hand, this reconstruction avoids putting one in the position of saying that the founder of modern philosophy and one of the foremost mathematicians of all time over and over again presented an obviously fallacious argument for the fundamental tenet of his philosophy. It might be added, in the spirit of making do with small mercies, that the reasons that have been given by philosophers for saying that the cogito is a fallacious argument are quite poor. Carnap, perhaps the most eminent contemporary philosopher to accuse Descartes of a logical blunder, claimed that the fallacy resulted from two mistakes: The first lies in the conclusion "I am". The verb "to be" is undoubtedly meant in the sense of existence here; for a copula cannot be used without a predicate; indeed, Descartes' "I am" has always been interpreted in this sense. But in that case this sentence violates the . . . logical rule that existence can be predicated only in conjunction with a predicate, not in conjunction with a name (subject, proper name). An existential statement does not have the form "a exists" (as in "I am", i.e. "I exist"), but "there exists something of such and such a kind". The second error lies in the transition from "I think" to "I exist". If from the statement "P(a)" ("a has the property P") an existential statement can be deduced, then the latter can assert existence only with respect to the predicate P, not with respect to the subject a of the premise. What follows from "I am a European" is not "I exist", but "a European exists". What follows from "I think" is not "I am" but "there exists something that thinks". 27

The "first error" is that Descartes's inference predicates existence in conjunction with a name, but the rules of logical inference demand that "existence can be predicated only in conjunction with a predicate." True enough, existential statements take the form 'there exists something of such and such a kind', where a predicate is required to specify the such arid such kind. But, even assuming no other rules

The Cartesian Scholar's Dilemma

21

involving the notion of existence, what right does Carnap have to use "only"? How does Carnap know that all meaningful existential sentences can be expressed in the form 'there exists something of such and such a kind'? Carnap is wrong to say it is a matter of "I exist" violating a logical rule in virtue of its logical form. The question is not about the rules, but about the relation between the rules and the meaningful sentences of a language. The question is whether all meaningful sentences of a particular class are properly symbolized on the basis of the rules as so far formulated. Carnap begs the question when he assumes, without argument, that the fault lies with the Cartesian construal of the logical form of "I exist" rather than with the ability of the logical rules in question to properly symbolize the sentence. The "second error" begs the same question, but it also makes a mistake about what transitions are available in predicate logic. One can, contrary to Carnap, go from "f think" to "I am" by subsuming the inference under 'P(a) implies (3x) (x = a)'. This, in fact, is an approach taken by a number of Cartesian scholars in their attempt to reconstruct the cogito within the framework of standard logic. This possibility gives rise to a construal of the cogito that represents Descartes's formulation of the inference without enthymematic reconstruction and presents the cogito as a nonsyllogistic but nonetheless valid argument. For example, Frankfurt writes that in an argument of the form 'B(a) implies (3x) (x = a)', . . . the mere fact of predication suffices to make the transition legitimate; the content of the predication plays no essential role. The transitions are straightforward inferences of the form "B(a) implies (3x) (x = a)".28

There are a number of implausible things about this as an account of the cogito. One is that it is false that "the mere fact of predication suffices to make the transition legitimate"—not even true predication can do this. Let 'B' be the predicate 'is the legendary king whose riches many sixteenth century Spaniards wished to lay their hands on', and 'a' be the name 'El Dorado'. Then, 'B(a)' is true, but '(3x) (x = a)' is false. The problem is, of course, that the predicate in this case creates an opaque context. A further problem with the construal of the cogito is that '(3X) (x = a)' says something different from "a exists". The former says that there exists at least one thing such that it is identical to the object "a" names, whereas the latter says merely that the object "a" names exists.

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Cogitations

Thus, the former does not assert that the Cartesian ego exists but asserts something which logically entails it exists: if I am identical to something which exists, then, since whatever is true of it is true of me and it is true of it that it exists, it follows that I exist. This difference in logical form between the conclusion in this construal and Descartes's conclusion is brought out by the fact that the former, containing the identity relation, is open to the objection that Wittgenstein once raised that it is nonsense to say two things are the same and empty to say something is itself,29 while the latter is not open to this objection. Therefore, the construal under consideration is not offering us a formalization of the cogito but a formalization of an argument equivalent to the cogito, and furthermore, an equivalent argument on which the inference to the Cartesian conclusion is a complex inference as in standard enthymematic reconstructions. Consequently, the construal under consideration does not have an advantage over enthymematic ones in respect to not conflicting with Descartes's protests that his is a nonsyllogistic, simple inference, and hence, the construal leaves us still facing the Cartesian scholar's dilemma. To put the finishing touches on the Cartesian scholar's dilemma, it remains to point out that the enthymematic reading of Descartes's presentations isn't the lesser of the two evils by all that much. This reading paints nearly as unattractive a picture of Descartes as the one on which he is supposed to have committed a logical howler. Look at the picture of Descartes that we are given. He bungles the simple task of presenting the proper argument for his position, never notices this, and stubbornly keeps insisting on the wrong argument. What of the conflicts between the enthymematic reading and Descartes's protests against syllogistic construals or insistence on the cogito being known on the basis of a simple intuition? More muddle on Descartes's part. He must be painted as having failed to say enough where it is obvious that a fuller explanation is called for, as having said various conflicting things about the nature of his reasoning and the significant principles that enter into it, and as having expressed himself in highly confusing and unclear ways.30 When we step back and look at this portrait, it is hard to recognize the subject as Descartes. The portrait bears more of a likeness to Hegel or Heidegger. In the case of Descartes, we have a philosopher who had one of the clearest and most logical minds in human history, who was always painstaking in explaining his views, who was highly sensitive to the significant issues his views raised, and who was a master of simple, elegant prose.

Ill The Source of the Obscurity

If the unattractiveness of each horn of the Cartesian scholar's dilemma is grounds for resisting each individually, isn't the unattractiveness of both horns grounds for resisting the position of having to choose between them? If it is desirable not to portray a great philosopher as making so foolish a mistake as arguing from P to Q and it is desirable not to portray him as unnecessarily expressing a perfectly good argument in the form of such an obviously fallacious one, then surely it is desirable to avoid the dilemma itself. But no matter how desirable escaping the dilemma might be, escape has been blocked by what seems to be the logic of the situation. Given that the connection between the premiss(es) and conclusion of every formally valid argument is sanctioned as truth-preserving in virtue of falling under laws of logic, Descartes either argued fallaciously or put forth the wrong argument. But suppose for a moment that we trust the insight of a great philosopher more than what seems to us to be the logic of the situation. Then, the reasoning which blames Descartes for the obscurity of the cogito can be turned around. Assuming that Descartes presented the right argument for his existence and that the argument is formally valid, the cogito is just the argument from "I think" to "I exist" and it is valid as it stands. But, if the cogito so construed is valid as it stands, there is at least one argument that is formally valid without the sanction of subsumption under laws of logic (since no law of logic sanctions the transition from P to Q). Therefore, subsumability under laws of logic is not a necessary condition for formal validity. I shall argue that this trust is justified, that Descartes is not at all at fault for the obscurity of the cogito, and that the actual source of the obscurity is the assumption that subsumability under laws of logic is

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a necessary condition for formal validity. This assumption is made by virtually all Cartesian scholars, but it goes unrecognized, and hence, unchallenged. But the assumption introduces a limitation into the logical framework within which Cartesian scholars attempt to understand the cogito: the framework provides no place for cases of formally valid inferences that do not depend on laws of logic. Thus, when scholars attempt to explain the obscurity of the cogito within this framework, they must adopt one of the two highly unflattering pictures of Descartes. Historians require a logical framework to give them a general conception of what logical form and inferential structure are. They require a general conception to bring to bear in explicating particular inferences they encounter in texts. Historians have little choice but to adopt the framework that orthodox opinion in the philosophy of language and logic offers them. Rarely is the historian in a position to independently evaluate the logical framework recommended, and still more rarely is the historian in a position to embark on the construction of an alternative conception of logical form and inferential structure. Thus, orthodox opinion is usually taken as secure doctrine on which scholarship can safely rely. If the framework happens to contain a limitation that leads to obscurities in the scholarship that is done within the framework, then their source goes unnoticed. Cartesian scholarship obtains its logical framework from the venerable Fregean tradition: inference and logical form in natural language are seen as presented in standard treatments of predicate logic. I will refer to this framework as the "standard conception." There is no need to try to make our characterization more precise yet, since the conception is found in almost every logic text and most books on the philosophy of logic. It is so deeply entrenched in twentieth century philosophy of logic and language that to suggest, as I have done, that it is inadequate in some respect is to risk loss of philosophical respectability. For, as a result of Frege's enormous achievement, logic has earned so impressive a reputation that to suggest that it is inadequate would call one's own qualifications into question. Thus, I hasten to say that my criticism does not concern logic itself. In saying that the standard conception is inadequate, I am not challenging either predicate logic per se or even the standard conception's picture of the laws of logic. Rather, what I wish to challenge is simply the standard conception's claim to be a complete theory of the nature of inference in the use of natural Ian-

The Source of the Obscurity

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guage. What I think is mistaken is the standard conception's restriction of the ways in which the premiss(es) and conclusion of valid arguments can be connected to the argument-forms of predicate logic. I want to argue that such a restriction does not account for all cases of formally valid inference. To make clear what I am going to argue, let me pause to explain how I am using the critical notions. By the term "inference", I shall mean nothing more than is customarily meant, viz., an act of passing from one statement or statements to another whose truth is taken to follow from the truth of the former. I will also follow the practice of dispensing with the behavioral element and speak of statements, or sentences expressing them, as "inferences". By the term "valid", I shall again adopt the customary, nontechnical usage: an inference is valid just in case there is no counter-example to it, i.e., there are no possible circumstances under which the premiss(es) of the inference are true and the conclusion false. More technical formulations for the notion do not need to concern us. By "accounting for the validity of an inference", I mean nothing more than explaining why there is no counter-example to it. For example, I might account for the inference from "If Socrates is a man, then Socrates is mortal" to "If Socrates is not mortal, then Socrates is not a man" by taking it as an instance of the law of contraposition. This would be to say that no counter-example exists because the inference is an instance of a particular relation between statements under which truth is invariably preserved. Alternatively, I might explain why there is no counter-example to the inference from "N is an integer greater than one" to "N can be factored into a product of primes in one way only" by citing Euclid's proof. Accounting for validity, on my use, means providing a suitable justification for the claim that no counter-example exists. The nature of the justifying considerations is left open. The justifying considerations may be logical, mathematical, or perhaps even metaphysical (e.g., in the inference from "An event occurred today" to "Something caused occurred today"). Finally, by "adequate justification" I mean, at present, no more than that the considerations in question satisfy the requirements on the justification. Any conception of inference specifies a fixed set of inference-types under which particular inferences are to be subsumed in accounts of their validity. Thus, a conception of inference limits the possible ways in which the premiss(es) and conclusion of a particular inference can be validly connected. The standard conception limits all

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Cogitations

valid inference-types to ones in which the conclusion of a particular inference is reached by a sequence of derivational steps, each sanctioned by laws of logic. I want to argue that this limitation is too restrictive to give us an adequate conception of inference. Undoubtedly, all inferences via derivational steps sanctioned by laws of logic are valid inferences, but why suppose that all valid inference (below the levels of mathematics, metaphysics, and other theoretical domains) is inference via derivational steps sanctioned by laws of logic? Why couldn't the absence of counter-examples in some class of cases have nothing whatever to do with derivational steps sanctioned by laws of logic? Why couldn't the truth-preserving nature of one class of inferences be a matter of language per se? Here is where analytic entailments like the inference from "John has a sister" to "John has a sibling" present a prima facie challenge to the standard conception. Pretheoretically, they appear to rest on nothing more than a relation between the meanings of the words in the premiss and conclusion. I shall argue that this prima facie challenge turns out, in the final analysis, to be a counter-example to the standard conception, showing it to be too restrictive to be an adequate conception of inference. I shall try to show that what has concealed the fact that the standard conception is not a complete theory of inference is a confusion about the nature of the justifying considerations and the adequacy requirements on them in the case of analytic entailments. There are two possible responses to presenting analytic entailments as prima facie counter-examples to the standard conception. One is to adopt the strategy of denying that the presented cases are really valid inferences, and the other is to adopt the strategy of denying that the presented cases cannot be accounted for within the standard conception. The first response would come from those who have been influenced by Quine's criticism of the analytic—synthetic distinction.1 The second response would come from those who have been influenced by Carnap's theory of meaning postulates which enlarges the stock of inference-types in the standard conception so that there is a way of handling analytic entailments as inference by derivational steps based on laws of logic.2 Thus, Quine and Carnap, their philosophical differences notwithstanding, can be seen as having the common aim of trying to preserve the standard conception in the face of possible counter-examples from the domain of linguistic meaning. Much has been said about their philosophical differences, but, as I see it, the fact that they have the common aim of

The Source of the Obscurity

27

defending the standard conception of inference is, ultimately, of far more philosophical importance. Their differences are merely a matter of choice of means, expressing, I think, Quine's break with the Kantian philosophy underlying Frege's semantics and Carnap's basic sympathy with it. Their common aim expresses one of the fundamental ideas behind this century's so-called linguistic turn, namely, the idea that matters of logic and philosophy cannot be distinguished in any principled way from matters of language. Let us consider Quine's response first. His attack on analyticity meets the challenge to the standard conception by attempting to show that analytic entailments are not genuine inferences in the first place. He argued that there is no domain of analytic fact distinct from that of synthetic fact: there is no fact of the matter about meaning and analyticity outside the domain of synthetic fact (and there the facts are facts of stimulus meaning and stimulus analyticity). That the analytic is no more than the synthetic, falsely described, can be shown, he believes, by a comprehensive examination of the concepts of meaningfulness, synonymy, and analyticity on which the theory of meaning is based. Quine proposes to demonstrate that these concepts, and the notion of a proposition that underlies them, cannot be coherently explained, no matter where we look for an explanation. As Quine himself has succinctly put it: My objection to recognizing propositions does not arise primarily from philosophical parsimony—from a desire to dream of no more things in heaven and earth than need be. Nor does it arise, more specifically, from particularism—from a disapproval of intangible or abstract entities. My objection is more urgent. If there were propositions, they would induce a certain relation of equivalence or synonymy between sentences themselves: those sentences would be equivalent that expressed the same proposition. Now my objection is going to be that the appropriate equivalence relation makes no objective sense at the level of sentences. This, if I succeed in making it plain, should spike the hypothesis of propositions.3

Quine's argument in "Two Dogmas of Empiricism" tries to show that synonymy and the other concepts in the theory of meaning make no objective sense by surveying the domains where explanations of them might possibly be found. He supposes, quite plausibly, that if there is a way of explaining them, it will be found in one of the three domains which are supposed to concern themselves with meaning, namely, definition, logic, and linguistics. Quine looks at each of these domains in turn. He examines carefully the methodo-

28

Cogitations

logical approach taken to the explanation of concepts in each, and finds that none is, in principle, capable of explaining concepts in the theory of meaning. Definitions, both in the ordinary and the technical philosophical or mathematical sense, are hopeless because they either assume prior synonymy relations or have nothing to do with meaning at all. Logic, too, is hopeless. Here the approach, worked out by Carnap, sheds no light on the question of what synonymy and analyticity consist in. Finally, the methods for explaining concepts in linguistics do no more than circularly define one semantic concept in terms of others. Given that the areas of definition, logic, and linguistics are the only areas where one might reasonably expect to find an explanation of concepts in the theory of meaning, it follows that, since the concepts are not explainable in any of these areas, no explanation of them is possible. Quine's argument is thus misunderstood by appraisals like Grice's and Strawson's.4 Such appraisals treat "Two Dogmas of Empiricism" as an attempt to refute the analytic—synthetic distinction on the basis of the argument that all previous attempts to clarify the distinction haven't worked. The argument is seen as an induction. But Quine's argument is more sophisticated than this. Quine's argument is an argument by cases. There are only three places where an explanation to clarify the distinction might be found: definition, logic, and linguistics. In each of these cases, it can be demonstrated that no explication is forthcoming, and hence, there is, in principle, no way to explain the concepts on which the analytic—synthetic distinction rests. It is, therefore, just an "article of faith." The real trouble with Quine's argument is that the demonstration in one of the cases, the case of linguistics, fails. Quine argues that any attempt to construct an explanation of synonymy and analyticity in linguistics is inevitably circular. But an argument of this kind requires that the notion of explanation that it employs be the proper one for the science of language. What is the notion of explanation that Quine employs and why does he think it the proper one? Quine writes, So-called substitution criteria, or conditions of interchangeability, have in one form or another played central roles in modern grammar. For the synonymy problem of semantics such an approach seems more obvious still. However, the notion of the interchangeability of two linguistic forms makes sense only in so far as answers are provided to these two questions: (a) In just what sorts of contextual position, if not in all, are the two forms to be interchangeable? (b) The forms are to be

The Source of the Obscurity

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interchangeable salvo quo? Supplanting one form by another in any context changes something, namely, form at least; and (b) asks what feature the interchange is to leave invariant. Alternative answers to (a) and (b) give alternative notions of interchangeability, some suited to defining grammatical correspondences and others, conceivably, to defining synonymy. 5

Quine's argument against there being a fact of the matter in semantics depends on his claim that explanation in linguistics consists in providing substitution criteria that specify the extension of concepts in the theory of meaning on the basis of an independent concept which remains invariant when one linguistic form replaces another in the chosen contextual position. Assuming that such substitution criteria are the proper form of explanation in linguistics, Quine shows that explanations of synonymy and analyticity cannot be extensionally correct without being circular. Quine exploits the fact that substitution criteria explanation can fail either because the independent concept chosen to be invariant does not correlate with all and only members of the extension of concept to be explained or because the independent concept or the contextual position cannot be characterized without using the concept to be explained. Quine argues, correctly to the methodology of substitution criteria, that the only way to specify the extensions of analyticity and synonymy is to employ these concepts themselves. Consider the attempt to explain synonymy. Either we choose a context like "Necessarily, ", which is intensional, and employ truth as what remains invariant on substitution, or we choose a nonextensional context and then have to employ analyticity as what remains invariant on substitution. Either way, something in the explanation is itself defined in terms of the concepts that are supposed to be explained: either the operator 'necessarily'6 or the concept of analyticity (defined, on Quine's account, in terms of synonymy). Establishing this circularity, even conceding Quine's arguments in cases of definition and logic, is a far cry from establishing that the concepts in the theory of meaning cannot be explained. This conclusion follows only if it is also assumed that the proper form for the explanation of concepts in linguistics is via the use of substitution criteria. Quine assumes this because, as he himself tells us in the above quotation, substitution criteria were considered the proper way of explaining concepts in linguistics at the time he looked to see what the science of language might have to say on the linguistic questions of interest to him. At the time, the American structuralist

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school of linguistics (i.e., the "modern grammar" in the above quotation) ruled the roost. It held a strongly anti-mentalist conception of linguistics which it implemented on the basis of its operationalist methodology of substitution criteria. There is no problem about why substitution criteria would appeal to Quine. But what good reason is there for going along with Quine in making the assumption that substitution criteria are the way to explain linguistic concepts? Surely not that one school of thought in linguistics took them to be the proper way. Schools of thought come and go. Surely not that we have confidence in anti-mentalism and operationalism. Such confidence eroded long ago. Surely not that we are unable to find examples of other ways to explain concepts. Logic, mathematics, and natural science provide examples. The American structuralist school was overthrown in the sixties, in what has come to be called the Chomskyian revolution. Chomsky introduced a radically different conception of linguistics, generative grammar, on which explanation in linguistics is genuine theoretical explanation. Concepts in an area of linguistics are explained, not by correlating them with concepts outside this area, but by being given a place in a network of relations within a theory. An understanding of the concepts in question thus comes from their systematic connections to other concepts within the theory, on the one hand, and from the connections of the theory as a whole to the phenomena in its domain, on the other. Indeed, it was precisely to replace substitution criteria that Chomsky introduced theoretical explanation into linguistics.7 Once theoretical explanation proved successful in phonology and syntax, theoretical explanations were available to serve as models for the explanation of concepts in semantics. For example, Chomsky's explanations of syntactic well-formedness and syntactic identity as, respectively, syntactic generability and sameness of syntactic representation, could serve as models for explaining the corresponding semantic concepts: meaningfulness could be explained as semantic generability, and synonymy as sameness of semantic representation. Such explanations presuppose erecting a level of formal semantic representation, but this too can be carried out on the model of syntactic and phonological representation. A notation system for the elementary components of senses could be developed on the basis of which semantic representations are constructed for the lexical items of a language, and generative rules could be formulated for combining semantic representations to form other se-

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mantic representations that reflect the compositional structure of syntactically complex expressions. In such theoretical semantic explanation, concepts are defined in terms of particular configurations of symbols in semantic representations. These definitions are generalizations over the class of semantic representations of expressions exhibiting a specific semantic property or relation. For instance, the concept of redundancy exhibited in expressions like "free gift" might be defined in a generalization about the structure of the senses of such expressions, e.g., an expression consisting of a modifier and its head is redundant just in case the semantic representation of the modifier is a part of the semantic representation of the head. When similar definitions are given for other concepts in the theory of meaning, the explanation of each concept is achieved through a formal statement of its pattern of connections with the other concepts. Here the form and degree of connection with the members of the same family of concepts is a measure of the richness of the explanation. This contrasts sharply with explanation in terms of substitution criteria where the degree of connection indicates the viciousness of the circularity. Quine simply overlooked the possibility of theoretical explanation. It does not matter whether or to what extent such a theoretical explanation has actually been worked out for semantic concepts; the very possibility of such an alternative way of conceiving of the explanation of linguistic concepts, by itself, is enough to show that Quine has no argument against meaning or against there being a fact of the matter in semantics. Given the possibility of theoretical explanation, the circularity that he is at such pains to exhibit can no longer be taken as a sure sign of a troubled family of concepts. It can just as well be taken as a sign that the family of semantic concepts is like normal families of theoretical concepts in logic or mathematics. Suppose we were to impose Quinian standards of explanatory success on logic or mathematics? Suppose we insist, as Quine does in semantics, that the acceptability of logic and mathematics depends on showing that logical equivalence and mathematical identity can be defined on the basis of substitution criteria? Since here, too, there is no noncircular feature that is invariant in all and only substitutions of logically equivalent propositions in the one case and numerical identities in the other, the demand that logical equivalence and mathematical identity be explained on the basis of substitution criteria would lead us to conclude that there is no logic and mathematics as well as no semantics. This reductio shows that the circularity which

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Quine takes to damn semantics is in reality simply a sign that we have mistakenly treated a case of theoretical connection as a case of the kind of correlation to which operationalist definitions apply. These reflections dispense with Quine's semantic skepticism. They do not explicitly deal with his indeterminacy thesis, but, as I shall show in chapter XII, the thesis depends on this skepticism. But, even without Quine's arguments, there are still an influential set of arguments that, if adequate, would provide a reason for thinking that analytic entailments are not genuine cases of valid inference. These are the arguments presented by Donnellan and Putnam in the early 1960s, and subsequently developed by Putnam in a series of important papers.8 They are directed against traditional intensionalist semantics. Intensionalism claims that there is sense as well as reference, that senses can be complex, and that, as a consequence of sense inclusion, there is a special form of necessary truth, analyticity, and a special form of valid inference, analytic entailment. Intensionalists commonly hold that sense determines reference, so that, as with C.I. Lewis's view, senses of words provide, as he put it, "criteria of application".9 This view is Frege's conception of sense as mode of referential presentation construed from the perspective of the language user. On the view, an analytic sentence like "Cats are animals" expresses a necessary truth because inclusion of the sense of "animal" in the sense of "cat" means that anything to which "cat" applies is something to which "animal" applies. Putnam's argument runs as follows. He claims that intensionalists must assert both (P), which, for the sake of argument, is taken as a (P) "Cat" expresses a concept (has a sense) that includes the concept of being an animal. representative analytic relation, and also that (P) implies (Q). Put(Q) The referents of "cat" in statements could not be non-animals. nam points out, quite rightly, that (Q) is false, since the referents of "cat" in our various past statements about the world could, for purely contingent reasons, turn out to have been robots planted by Martians to spy on us. Putnam concludes, by modus tollens, that (P) is false, i.e., that there are no analytic sentences in the traditional intensionalist's sense. This, in a nutshell, is the argument which is found in all of Putnam's papers criticizing intensionalist semantics. Philosophers have been right to think it proves something significant, but wrong in

The Source of the Obscurity

33

thinking, along with Putnam, that it proves intensionalist semantics is not possible. As an argument against Fregean intensionalism, the argument is sound, but not all intensionalists assume with Frege that sense determines reference.10 Some of them do not make sense responsible for all the information which fixes the reference of expressions in our uses of language, but only make sense one of the factors on which reference depends. But Putnam's argument requires the strong, Fregean relation between sense and reference, since without it, the position against which he is arguing does not hold that (P) implies (Q). This cuts the connection on which examples like Putnam's robot cats have the force of counter-examples. Such examples are, of course, genuine possibilities, and indeed, they show that (Q) is false, but they show nothing about (P). There is now no basis for using modus tollens to infer the falsehood of (P). The existence of versions of intensionalism which are weaker than Frege's in not connecting reference to sense directly is based on the distinction between the reference of linguistic types and the reference of their tokens. In the former case, the referring expressions are the words and phrases of the language, and in the latter, the referring expressions are utterances or inscriptions of words and phrases which are produced in the use of language." On this distinction, we obtain a weaker intensionalism by replacing Frege's strong principle with the principle that sense determines "type-reference" but not "token-reference."12 This weakening does not imply that type reference plays no role in fixing token reference. Obviously, the speaker's knowledge of the meaning of expressions is a principal factor in his or her use of them, but the weakening does allow for many other factors to influence token reference. On such a weaker intensionalism, Putnam's premiss that the intensionalist is committed to (P) entailing (Q) is false. This commitment is precisely what the weak intensionalist denies. The weak intensionalist is quite happy to say that, for example, uses of "witch" by, say, Cotton Mather, succeed in referring, even though the type-reference of "witch" is null. Likewise, uses of "cat" succeed in referring to robots in the Putnam case even though the type-reference consists of feline animals. Such cases of successful token-reference in which the token-referents are outside the type-reference are seen as reference under a false description. The Salem witch hunter's reference to ordinary women with the word "witch" is a reference to them under the false semantic description 'woman in league with the Devil', and our reference to robot spy devices with

34

Cogitations

the word "cat" is reference to them under the false semantic description 'feline animal'. The weak intensionalist believes that factors beyond meaning have brought it about that the speaker's token-references are as they are in these cases, and identifies the major factor as the speaker's false belief that the robots (the objects picked out in such token-reference) have the biological properties that make them feline animals. Hence, the weak intensionalist denies that (P) entails (Q), and as a consequence, the contingent possibility of "cats" turning out to be robots is irrelevant to the question of whether the sense of the word "cat" involves an analytic connection to the concept of being an animal. The same criticism applies to Putnam's other versions of the argument involving blue lemons, organic pencils, etc., and to Kripke's versions of the argument involving blue gold, demon cats, etc.13 These versions vary the example but the structure of the argument remains the same: the contingent possibility that certain things could be different in nature from what we have taken them to be is the premiss from which these philosophers conclude that the term we use to refer to such things does not involve an analytic connection to the concept which expresses what we have taken them to be. But, as observed above, such a conclusion does not follow without the strong intensionalist's conception of the relation between sense and reference. The existence of weak intensionalism blocks any general conclusion about intensionalism. Putnam, Kripke, and their followers overlook its existence because they are fixated on Fregean intensionalism. 14 My criticism also applies to Putnam's famous twin-earth argument. This is nothing but the robot-cat argument against analyticity transformed into an argument against synonymy. 15 But, if anything, the fixation on Fregean intensionalism on Putnam's part is even clearer and more explicit in the case of the twin-earth argument. Putnam explicitly states that the argument rests on the assumption that "the meaning of a term (in the sense of intension) determines its extension (in the sense that sameness of intension entails sameness of extension)."16 Given this strong Fregean conception of the relation between sense and reference, it is easy for Putnam to impugn synonymy on the basis of the contingent possibility that water is H2O on earth but XYZ on twin-earth. But when the alternative of weak intensionalism is brought up, the argument is seen to be a good argument against the "traditional concept of meaning," as Putnam puts it, only if by that term we understand the Fregean concept of meaning. The argument is no good against the concept of meaning

The Source of the Obscurity

35

in weak intensionalism. On this concept, what water is (on earth or on twin-earth) is no basis for saying what "water" means (in earth-English or in twin earth-English). Water might be H2O on earth and XYZ on twin-earth, and "water" might mean 'an odorless, colorless, tasteless liquid that descends from the sky as rain' in both languages. "Anesthetic", which once referred to just ether, now refers to novocaine, xylocaine, etc. Visitors from the past who supposed it had changed meaning would be mistaken. "Anesthetic" still means 'substance which causes the temporary loss of sensation in a part of the body'.17 I can foresee the following objection to the above line of criticism: Frege introduced senses to fix reference. This function is their raison d'etre. Now Putnam and Kripke have shown that senses do not perform this function. Hence, senses do not perform the function for which they were introduced, and consequently, they lose their raison d'etre. They are idle. Therefore, the argument that Putnam and Kripke give does work against intensionalism per se. This objection, too, is a case of reading Fregeanism into every intensionalist position. On the weak intensionalism adopted here, the posit of senses is not based on their function in fixing reference (even type-reference) but rather on their function in explaining purely grammatical properties and relations of sentences. Senses are introduced as the locus of the grammatical structures responsible for meaningfulness, ambiguity, synonymy, antonymy, superordination, redundancy, and so on. Senses have their role in the explanation of why linguistic forms are meaningful, ambiguous, synonymous with certain other forms, etc. From this perspective, it is an independent question whether and how senses are related to the objects in the world to which we refer in uses of language. Only on a Fregean conception of intensionalism are senses conceived of as essentially connected with reference (in virtue of sense being defined as the mode of presentation of the referent). It will be recalled that, besides skeptical arguments which try to discredit analyticity and analytic entailment, there was another possible response to the challenge they pose to the standard conception. This response takes analytic entailment as a bona fide case of formally valid inference, but argues that it is not a case in which logical laws play no role. This response argues that an account of analytic entailment is within the power of predicate calculi acceptable to the standard conception. It sees the obstacle to accounting for analytic entailment as a failure to exploit the resources of logical systems.

36

Cogitations

To understand the nature of this response, it is necessary to begin with Carnap's attempt to construct a uniform notion of logicomathematical truth that could be used philosophically to mark the boundary of factual truth. Carnap thought that the "old empiricist view" that logical and mathematical truths are contigent is mistaken, and accordingly, he wanted a notion of logico-mathematical truth which would provide a principled restriction on the application of the new empiricist thesis that kept it from applying to logic and mathematics.18 Carnap wrote, To me it had always seemed to be one of the most important tasks to explicate [the distinction between logical and factual truth], in other words, to construct a definition of logical truth or analyticity. In my search for an explication I was guided, on the one hand, by Leibniz' view that a necessary truth is one which holds in all possible worlds, and on the other hand, by Wittgenstein's view that a logical truth or tautology is characterized by holding for all possible distributions of truth-values. Therefore the various forms of my definition of logical truth are based either on the definition of logically possible states or on the definition of sentences describing those states (state-descriptions).19

Thus, Carnap pursued the construction of a notion of L-truth whose central concept of truth in all possible worlds gave the notion the potential to cover all varieties of nonfactual (i.e., nonempirical) truth but did so at the expense of eliminating the differences between them. Carnap saw that realization of this potential of the notion of Ltruth required that predicate calculi be extended in two ways. First, their logical vocabulary had to include all expressions of the language on whose meaning an L-implication depends. Second, the inference-types of standard predicate calculi had to be extended to include "meaning postulates" which express the extensional structure of the new items of logical vocabulary. Carnap's idea was at once both highly radical and highly conservative. It was highly radical in treating what had been thought of as extra-logical vocabulary as logical vocabulary, contributing to the logical form of sentences on a par with, and exactly parallel to, the standard logical particles. The idea was highly conservative in formulating the contribution using the familiar postulational approach of predicate calculus. That is to say, he simply introduced postulates expressing the extensional structure of words in the former extra-logical vocabulary on analogy to the introduction of postulates expressing the extensional structure of words in the logical vocabulary. The effect of introducing mean-

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37

ing postulates into a predicate calculus was to further restrict the admissible models for the calculus in just the way that introducing additional logical postulates into an incomplete calculus restricts its admissible models. The upshot is that analytic entailments can now be handled in predicate calculi as a case of L-implication. Given an analytic entailment like that from "Mary is a sister" to "Mary is a sibling", we simply shift the predicates "is a sister" and "is a sibling" from extra-logical to logical vocabulary and introduce a meaning postulate like "For all x, if x is a sister, then x is a sibling". Now, the conclusion of the entailment can be derived in the calculus. The meaning postulate functions like logical postulates to constrain the definition of an admissible model for the system: the addition of the above meaning postulate insures that the sentence "Sisters are siblings" is true on all admissible models, and that the sentence "Mary is a sibling" is true on all admissible models on which the sentence "Mary is a sister" is true. Given that there is no restriction on the use of meaning postulates, it is natural to think that, whatever analytic entailments may turn up in natural language, we can always help ourselves to appropriate logical vocabulary and meaning postulates to account for them. It is no wonder then that many have come to think that, although there may be practical problems, there is no longer any theoretical problem in accounting for analytic entailments: Carnap's invention of meaning postulates shows us how every analytic entailment can be accounted for as a logically derivable truth in a predicate calculus. But now things are beginning to look too easy. Although it is true that, on the basis of meaning postulates, any analytic entailment can be fit under some inference-type, and hence, be represented as an instance of a logical law, it is not clear why such an account should be considered fully adequate. Brute-force solutions always achieve a measure of success. The question that needs to be raised is whether the meaning postulate way of explaining the formal validity of analytic entailments is adequate. As yet, we have no reason to believe that, just because analytic entailments can be accounted for as formally valid on the basis of meaning postulates, the account identifies the considerations that are really responsible for their formal validity. To see better what is meant by suggesting that adequacy might go beyond the existence of a logical derivation, consider a parallel case from linguistics. Chomsky developed an approach to theories of natural languages which formulates them as generative grammars.

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Cogitations

These are formal devices which generate sentences in the way that logical systems generate theorems.20 Chomsky distinguishes two forms of adequacy for such grammars, "weak generative capacity," which concerns what strings are generated in the grammar, and "strong generative capacity," which concerns what descriptions of grammatical structure are assigned to generated strings. Chomsky then characterizes the principal condition of adequacy for grammars in terms of strong generative capacity: A grammar is descriptively adequate if it strongly generates the correct set of structural descriptions.21 [italics mine]

Chomsky goes on to observe that weak generative capacity is only "of rather marginal linguistic interest."22 Although this may be putting the point too strongly, it is clear that the adequacy of a grammar cannot be simply a matter of weak generative capacity. Using Chomsky's distinction as a model, we can distinguish between weak and strong generative capacity for systems describing inferential structure: weak generative capacity concerns what formulas are derivable as theorems and what sequences of formulas are marked as valid inferences, and strong generative capacity concerns what structures are assigned formulas in derivations as an account of theoremhood or formal validity. This distinction permits us to define the principal condition of adequacy on theories of inference: a theory of inference is adequate if it provides the correct set of structures. Now a grammar can generate all and only the well-formed sentences of the language but still be inadequate if it assigns incorrect or incomplete descriptions. Similarly, a meaning-postulate account of a class of inferences might enable us to derive all and only the valid inferences but still be inadequate if it assigns incorrect or incomplete descriptions of the structure underlying them. In such a case, we would have a specification of all the class of inferences but we do not have an acceptable explanation of what makes them valid. We do not understand what structure precludes the possibility of a counter-example. Let us take stock. The issue of whether the standard conception is correct has been narrowed down to that of whether the descriptions of inferential structure assigned to analytic entailments on a meaning-postulate approach are adequate in the sense of strong generative capacity. This is because, as we have seen, the principal arguments that can be used to eliminate the range of cases that might cause trouble for the standard conception, i.e., the arguments

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39

against analydcity of Quine and Putnam, have been shown to fail. But the issue is narrowed in this way also because, except for matters of detail, Carnap has done all that can be done to handle analytic truth and analytic entailment within the standard conception. He provided the idea of extending the logical vocabulary of predicate calculi to include constants for all meaningful nouns, verbs, adjectives, and adverbs of the language, and he introduced the idea of adding further postulates to calculi to express the extensional relations among the new constants of the logical vocabulary. There is nothing else to do to increase the generative capacities of predicate calculi beyond extending the logical vocabulary to the whole of the vocabulary of the language and introducing an appropriate set of meaning-postulates for the new logical vocabulary. Hence, if the standard conception is to prevail, Carnap's attempt to show that analytic entailments are based on laws of logic must prove to be, in principle, both weakly and strongly adequate. Let us look ahead. I will next explain how it is possible for the standard conception to be wrong in equating formally valid inference with inference via laws of logic. The explanation will show how the description of analytic entailments as resting on laws of logic misses the grammatical structure on which their validity actually rests. Then, I will trace this mistake from its source in Kant and Frege to the form it takes in the work of present-day philosophers of logic and language, showing how the tradition from Kant to Frege to Quine has caused philosophy to lose the purely grammatical, nonderivational notion of inference. After this, I will show that the formalization of analytic entailment in current semantics restores this lost notion. The next step in the overall argument is to show that inferences having existential conclusions, such as the cogito, are a species of analytic entailment. In this connection, I shall take up the question of whether "exists" is a predicate. I will explain why it is, what kind of predicate it is, and how treating it as such a predicate is both philosophically satisfactory and able to resolve controversies in recent Kantian scholarship. An important component of my argument is showing that the nonderivational notion of inference from linguistic semantics fits together with the derivational notion in predicate logic. I will try to show that there is, as it were, a place in predicate logic waiting for the formalization of analytic entailment to be put. If all these things can be shown, we will clear the philosophy of logic of the mythology of the standard conception without sacrificing the achievements of logic itself.

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Cogitations

We will also put Cartesian scholarship in a better situation. Without the standard conception, the naive interpretation can be maintained without an enthymematic construal of the cogito, since it can be counted as valid as it stands under the interpretation of the inference as an analytic entailment. It will be sanctioned on the basis of a fine-grained analysis of the senses of "I think" and "I exist" which reveals the sense of the latter to be a part of the sense of the former. Descartes thus appears in a light far more appropriate to a great philosopher. He is no longer accused of a logical blunder or confused expression. His protests that the cogito is not a syllogistic inference can be taken at face value, as straight denials that it is a complex inference involving steps based on laws of logic. Indeed, these protests can now be seen as insightful anticipations of our explanation of the cogito as an analytic entailment. Finally, the small part of the obscurity of the cogito which does originate with Descartes is revealed as necessary under the circumstances, a product of his having had no linguistic theory within which to explain how grammar could be responsible, by itself, for formally valid inferences.

IV

Logical Form, Universality, Linguisticism, and Locke

The fact that Cartesian scholarship would be better off if the standard conception were proven false is, of course, no argument that it is false. Indeed, the standard conception has so strong a grip on philosophical thinking about inference that it is about as hard for philosophers to imagine the conception false as it is to imagine a law of logic false. Thus, the immediate task is to show how it is possible for inferences not mediated by laws of logic to be formally valid. Validity is the absence of counter-example. Formal validity is absence of counter-example arising from aspects of the logical form of the premiss(es) and conclusion. There are, however, two notions of logical form. One is prepositional structure as determined by features of the logical vocabulary of the language. Since what makes something qualify as logical vocabulary is, roughly, its being required for the statement of the conditions that determine the application of laws of logic to sentences, what has no role in inferences based on logical laws has no role in logical form in this sense. Some, forgetting there is another sense, are encouraged to argue that it is impossible, by the definition of logical form, for there to be formally valid inferences not mediated by laws of logic. But such an argument is undercut by the other notion of logical form, namely, the aspect of the grammatical structure of sentences which determines their role in inferences. This sense begs no question about the kinds of inferences there are. On this broader notion of logical form, the inferences that count as formally valid are a function of what counts as logical form and what counts as logical form is a function of the inferences that count as formally valid. There is nothing wrong with this interdependency. We have here something like an equation in two variables. A systematic formaliz.ation of inference in natural language provides rnutu-

42

Cogitations

ally adjusted values for them. Philosophy of logic enters when, in specifying the unknowns, we try to avoid arbitrary stipulation, that is, when we try to justify choosing one range of values rather than another more or less inclusive one. Some choices would yield too exclusive or too exclusive a logical vocabulary to satisfy anyone, but there is a very wide range of choices between these extremes. Within this range falls the narrow range of choices that constitute logical vocabulary as most logicians see it. The role of the philosophy of logic here is to justify one set of choices as better than others for an account of inference using sentences from natural language. Logicians have need of the philosopher of logic once they step outside the area of artificial languages where they may stipulate as they like. Quine's philosophical critique of the analytic—synthetic distinction was important because it promised to provide a justification for specifying logical form exclusively in terms of the customary notion of logical vocabulary. If his critique had succeeded, there would be no air of arbitrariness about specifying logical form in terms of the customary enumeration of logical particles. These define the area where there is a fact of the matter, where translation is determinate. In contrast, the nouns, verbs, etc. of the so-called "nonlogical vocabulary" is the area where there is no fact of the matter, where translation is indeterminate. Thus, the semantic structure of words like "sister" and "sibling" (on Quine's view, their stimulus meaning) play no role in the logical form of sentences, and as a consequence, the inference from "John has a sister" to "John has a sibling" is not to be counted as a formally valid inference. But, as we have seen, Quine's critique of the analytic—synthetic distinction fails, so that the customary notion of logical vocabulary is left without a justification to save it from the charge of arbitrariness. From this perspective, Carnap represents a way out of the situation of having to draw an arbitrary line between logical and nonlogical vocabulary. He simply denies there is a line to be drawn. He specifies logical form in terms of an enlarged notion of logical vocabulary in which every meaningful expression of the language counts as an item of its logical vocabulary. Indeed, in enlarging the logical vocabulary to include the previous nonlogical vocabulary on the basis of meaning postulates, he is able to collapse the two notions of logical form. For now an account of the extensional structure of every meaningful expression of the language is required for a full statement of the conditions under which logical laws apply to its sentences, and every valid inference is accounted for on the basis its extensional structure.

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43

On Carnap's approach, it is possible to account for inferences in natural language like the inference from "John has a sister" to "John has a sibling" on the basis of meaning postulates like "(x)(SISTERx D SIBLING X )" and other logical laws like the familiar modus ponens.1 (Here the capitalized expressions represent predicate constants in the expanded logical vocabulary, and as such, they occur essentially in representations of logical form as much as the horseshoe for material implication.) The predicate constants in meaning postulates name a class of objects in the domain of the language, and the postulates employing them state an extensional relation among appropriate sets of objects. Meaning postulates thus express constraints on the admissible models of the language, insuring that, for example, "John has a sibling" will be counted as true on every model on which "John has a sister" is counted as true. Such constraints are completely on a par with those expressed by the more familiar logical postulates. Is this approach adequate in the sense defined in the last chapter? I claimed that it is not because an account of analytic entailments based on meaning postulates fails to exhibit the grammatical source of their validity. Here, then, is the alternative position to Carnap's. Keep the two notions of logical form separate. Assume the logicians have the right notion of logical form for their conception of inference via logical laws, even if they are unable to say exactly what it is. Thus, let us recognize their notion of logical vocabulary in spite of the fact that, without Quine's semantic skepticism, the notion is, at least for the time being, arbitrary. Assume also that the logicians' notion of logical form does not exhaust the inference supporting structures we have on the broader notion of logical form. Thus, let us recognize the possibility that their nonlogical vocabulary is relevant to formal validity in a nonlogical way. Let us hypothesize further that this nonlogical way is grammatical. That is, let us suppose that some truth-preserving connections are solely a matter of the sense structure of the premiss and conclusion, and that a formal theory of sense structure could be developed within the study of grammatical structure in linguistics. We might even have hope that the development of such a theory will introduce considerations which justify the separation of logical vocabulary in the logician's sense from logical vocabulary in the broader sense. Now, aside from the fact that, thus far, our alternative is largely assumptive, what can be said in favor of Carnap's approach in comparison with this alternative? The principal thing that can be said is

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Cogitations

that Carnap's approach secures weak adequacy in the treatment of analytic entailments. Carnapian predicate calculi are universal in this sense: for any analytic entailment which is not marked as formally valid in such a calculus, there is an essentially trivial extension of its logical vocabulary and meaning postulates that makes it possible to mark the entailment as formally valid on the basis of a derivation. This universality is, of course, not as yet established, and there are easily forseeable problems in the way of actually establishing it, such as how meaning postulates, which are finite, can be recursively combined to assign semantic structure to the infinitely many compositionally meaningful expressions of the language. Rather, we are conceding universality for the sake of argument. But, then, we ought also concede that the alternative approach can achieve weak adequacy. There is no reason to think it can't. Suppose, therefore, we focus on strong adequacy. The first thing to note is that, in fact, there is nothing at all in Carnap's approach to make us think that it will secure strong adequacy and something which ought to make us skeptical, namely, the brute force character of the way in which the approach handles formal validity. If one brings up an analytic entailment like that from "John has a sister" to "John has a sibling", the Carnapian slaps down a meaning postulate restricting the admissible models to those in which the extension of "sister" is included in the extension of "sibling". The treatment marks the inference as valid, but not in terms of anything having to do with the meaning of these words. The same treatment would be accorded to valid inferences from mathematics and metaphysics where word meaning is not principally responsible for validity. The treatment leapfrogs the intensional structure that is responsible for the extensional structure being what it is. One sign that intensional structure has been ignored is that a new pair of meaning postulates would be needed to state the intimately related semantic fact that both "John has a sister" and "John has a sibling" analytically entail "John has a parent" and "John's sibling has a parent". Earlier I argued that Quine's criticism of attempts to explain analyticity in linguistics is far less important than it has been taken to be. Now I wish to argue that Quine's other principal criticism, his criticism of attempts to explain analyticity in logic on the basis of Carnap's approach, is far more important than it has been taken to be. I will try to show that there is a depth to the criticism that has gone unnoticed because the criticism is looked at as a component of the case against the theory of meaning. This depth is revealed when

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45

the criticism is looked at as a component in the case one theory of meaning presents against another theory of meaning. To put the criticism in a nutshell, Quine claimed that Carnap's meaning postulates specify what sentences of a natural language are to be counted as analytic but not what analyticity is.2 A semantic rule such as (R) contains one of the terms "meaning", "analytic", or "syn(R) S is analytic for the language L if, and only if, S can be derived from the logical postulates and a non-null set of meaning postulates in the predicate calculus associated with L.3 onymous" in its defmiens, and hence, the rule does not help us to understand these terms. As Quine put the point: Semantical rules determining the analytic statements of an artificial language are of interest only in so far as we already understand the notion of analyticity. 4

Let us now commandeer this argument and make it part of the argument for our alternative approach against Carnap's meaningpostulate approach. The nature of the failure we are accusing Carnap's approach of may be brought out by asking a question Carnap himself might well have asked. Recall that Carnap modelled his meaning postulates directly on logical postulates. Thus, Carnap might well ask why it is that the standard logical-postulate accounts of logical truth do not fail, too, if Quine's argument shows the meaning-postulate account of analyticity fails. Carnap might press this point by arguing that, by parity of reasoning, (R'). (R)'s logical counterpart, (R') S is a logical truth for a language L if, and only if, S can be deduced from the logical postulates of the predicate calculus associated with L. contains the term "logical" in its definiens, and hence, the rule doesn't help us to understand the notion 'logical truth'. What would we say? Quine said, We may. . . view the so-called rule as a conventional definition of a new simple symbol 'analytic-for-L 0 ' which might better be written untendendously as 'K' so as not to seem to throw light on the interesting word 'analytic'.5

So, we should say the same in the case of (Rzt>): it is a conventional definition of a new simple symbol 'logical truth-for-L 0 ' which is bet-

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Cogitations

ter written as 'K' so as not to seem to illuminate the interesting notion of logical truth. The problem filters down to the level at which we try to explain particular logical inferences. Such inferences are represented as formally valid in calculi, and on this basis we say the inference is logical (the conditional expressing it is a logical truth). But why logical? Couldn't we also have arranged matters in the calculi so that certain mathematical or metaphysical truths are represented as formally valid too? We do not want to say that all truths that can be marked as formally valid in this manner are logical truths, but the metatheory does not tell us what a logical truth is. Just as the mere fact a formula representing "Sisters are siblings" can be derived from socalled meaning postulates is no basis for saying that it is analytic, the mere fact that logical truths are derivable from so-called logical postulates is no basis for saying that they are logical truths. I am not, of course, advancing a skeptical thesis about logical truth. Indeed, it is part of my point that logical truth is secure in the face of such a transposed Quinean argument. The point of turning Quine's argument against logical truth is to show that what makes logical truth secure is not an explanation of the kind embodied in (R'). I want to show, first, that we shouldn't even expect an explanation of logical truth to be forthcoming on the basis of sheer recursive specification in a calculus, and second, that, because logical truth is secure, there is something further in virtue of which it is secure. What I am leading up to is the claim that it is the semantic counterpart of this further thing in logic that Carnap's approach lacks and our alternative approach has. Quine completed the last quotation with the remark that Obviously any number of classes K, M, N, etc., of statements of L^ can be specified for various purposes or for no purpose; what does it mean to say that K, as against M, N, etc., is the class of the "analytic" statements of L,,?6 This is the question. It cannot be answered by the device that recursively specifies class K. The device either generates the set or not. Weak adequacy applies to such devices, but strong adequacy does not. Strong adequacy applies to the metatheories for such generative devices. In both the case of logical truth and analyticity, an explanation of the property can only be given as an interpretation of the formal structure in virtue of which the membership of the class of sentences is determined.

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Thus, we can introduce a sense of universality corresponding to strong adequacy. We can define a theory to be strongly universal with respect to a class K of truths or implications generated in a calculus C if, and only if, (i) the formulae assigned to the members of K represent their logical form, (ii) each truth or implication in K is marked as formally valid on the basis of the formulae assigned to it, and (iii) the metatheory for C interprets the structure in the formulae assigned to the members of K in such a way that we understand what it means to say that a member of K is, in the pretheoretic sense, a /^-sentence or a /^-implication. I want to pause at this point to sharpen the objection I am making to the standard conception. The standard conception's theory of predicate calculi is not strongly universal with respect to the class of analytic sentences and analytic entailments. The theory fails condition (iii). This is because, in treating mediation by laws of logic as a necessary condition for formal validity, the feature of unmediated sense inclusion which distinguishes analyticity from logicality cannot be explicated in the metatheory and employed as the basis of its interpretation of the class of analytic sentences and the class of analytic entailments. The recursive specification of these classes on the basis of meaning postulates precludes an interpretation of what it means to say that they, as against, say, the classes of logical truths and logical implications, are the classes of analytic truths and analytic entailments. No answer to Quine's question is possible. An answer would explain what it means to say K, in contrast to M, N, etc., is the class of analytic sentences or analytic entailments, but meaning postulates and logical postulates both mark formal validity in the same way. They constrain the model theory for the language so that nothing counts as an admissible model in evaluating inferences unless it conforms to all postulates. A meaning postulate like '(x) (SISTERX D SIBLING,,)' guarantees that there can be no counter-example to the inference from "John has a sister" to "John has a sibling" by excluding from the range of admissible models anything which contains a sister that is not a sibling. Since this is precisely how logical postulates guarantee the absence of counter-example, there is no peg on which the metatheory of the standard conception can hang an answer to Quine's question. Meaning postulates are extensional in all but name. The modifier in the term "meaning postulate" reflects the intention behind the use of the formalism; it does not denote anything in the formal explanation itself. The intention behind the use of meaning postulates is to

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capture pretheoretical sense relations like that between "sister" and "sibling". But the formal explanation represents the sense relation as a set-theoretic relation between the extensions of these syntactic forms. Since this is the same way in which other necessary connections are represented, there is nothing in the formal explanation of such a sense relation corresponding to senses or sense relations themselves. A formalism which expresses no difference between the various sorts of necessary connection achieves a uniform treatment of a wide range of necessary truths at the cost of losing the special features of each sort. This is why Carnapian possible-worlds semanticists find themselves committed to claiming that necessarily equivalent sentences express the same proposition, and hence, to claiming that there is one necessary truth. 7 These semanticists criticize Davidsonians for committing themselves to the claim that all true sentences express the same proposition (since all true sentences could be assigned the same truth condition, e.g., that snow is white, and a theory of truth conditions for a language is a theory of meaning for it on the Davidsonian approach). But these possible-worlds semanticists are open to the same criticism in connection with sentences expressing necessary truths. If there is nothing to propositional identity beyond extensional structure, then a Carnapian theory of meaning, although it would not claim that there are only two different meanings for all English sentences, would claim that there are only two for all of them which express necessary connections. On this basis, one could make a case for logicism. Few philosophers would be tempted to use Carnap's notion of L-truth to argue against there being a line dividing the upper bound of logic from the lower bound of mathematics, but very many happily use the notion to argue against there being a line dividing the lower bound of logic from the upper bound of language. Indeed, the view that linguistic truth is logical truth is so popular that the thesis parallel to logicism has never even received a name! Let me call this thesis "linguisticism". This name is so contrived and ungainly that it may help prevent the thesis from continuing to be ignored. As we shall see, Frege was responsible for linguisticism as well as for logicism. The standpoint from which we proceed is this: linguisticism is false, just as logicism is false. The standard conception gives us a correct picture of inference for logical inference, but an incorrect picture for inference generally: above the lower bound of logic, truth and inference involve subsumption under laws of logic, but

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below the upper bound of language, truth and inference involve no such subsumption. There we find an inference-type which sanctions inferences falling under it on the basis of purely linguistic considerations. Such considerations, without reference to logical laws, explain why there can be no case in which the premiss of an analytic entailment is true but its conclusion false. What is required now is some hypothesis about what such linguistic considerations might be. We want a hypothesis about semantic structure which tells us how truths and inferences can obtain their validity from the language itself. The history of philosophy provides first approximations to such an hypothesis. Locke's conception of trifling propositions is, as far as I can tell, the best of them. Locke says there are two cases of such propositions, first, . . . all purely identical propositions. These obviously and at first blush appear to contain no instruction in them. For when we affirm the said term of itself, whether it be barely verbal, or whether it contain any clear and real idea, it shows us nothing but what we must certainly know before.8

and second, Another sort of trifling propositions is, when a part of the complex idea is predicated of the name of the whole; a part of the definition, of the word defined. Such are all propositions wherein the genus is predicated of the species; or more comprehensive of less comprehensive terms: for what information, what knowledge, carries this proposition in it, viz., 'Lead is a metal', to a man who knows the complex idea the name lead stands for? 9

Locke then goes on to explain that We can know then the truth of two sorts of propositions with perfect certainty. The one is, of those trifling propositions which have a certainty in them, but it is a verbal certainty, but not instructive. And, secondly, we can know the truth, and so may be certain in propositions which affirm something of another, which is a necessary consequence of its precise complex idea, but not contained in it: as that 'the external angle of all triangles is bigger than either of the opposite internal angles'; which relation of the outward angle to either of the opposite internal angles, making no part of the complex idea signified by the name triangle, this is a real truth and conveys with it instructive real knowledge.10

In these short passages, Locke comes closer to the truth about analyticity than any philosopher until G.E. Moore. He returns the discussion of analyticity from Descartes's expedient epistemological

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disgression to its proper focus, the nature of analyticity itself. Instead of treating the topic from the perspective of how we come to know analytic truths or analytic entailments, Locke treats it from the perspective of the structure of the propositions. The kind of knowledge we gain is appropriately seen as a function of the structure of the propositions known. But not only is Locke's distinction between trifling and nontrifling propositions the basis for the distinction between verbal certainty and substantive certainty, it is, basically, the true distinction between linguistic necessity and extralinguistic necessity. He is very clear that, although "verbal certainty" and "instructive real knowledge" concern necessary consequence, necessary consequence is a common effect of quite distinct causes in the two cases. In the former case, he identifies the cause of necessity with an idea being contained in a complex idea, and in the latter, he identifies the cause with the nature of the reality that the proposition is about. Locke not only locates the source of linguistic truth and linguistic inference in the sense structure of the language ("a part of the definition, of the word defined"), but he even makes a concrete proposal as to what such sense structure is ("a part of the complex idea is predicated of the name of the whole"). Apart from the fact that Locke's discussion is informal and brief, it contains one serious defect. Locke thinks about the structure of propositions from the viewpoint of their use rather than the other way around, and this leads him to overemphasize the verbal in his discussion. His very term "trifling" reflects this viewpoint and overemphasis. It puts the focus on certain particular uses of the sentences in question, namely, the ones in which people trifle with or play with words. He does mention one other case, viz., "where a man goes to explain his terms to one who is supposed or declares himself not to understand him,"11 but this does not go far enough. It leaves out the most philosophically significant cases, such as where "trifling propositions" are put in the service of giving analyses of concepts expressed in the words of a natural language. The viewpoint that I shall adopt focuses on the structure of the proposition expressed by analytic sentences. It shifts the emphasis to the structure of the concepts and away from the use of the words expressing them. 12 This, I think, is not only a safeguard against a terminology that obscures the philosophically most significant cases, but is also more consistent with Locke's deepest insight that differences at the intensional level are more significant than uniformities at the extensiorial level.

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I have chosen Kant's term "analytic" over Locke's "trifling" because "analytic" puts the emphasis exactly where it belongs. The term "analytic" is also the standard term used in the literature of Anglo-American philosophy since the early part of the century. This is a mixed blessing, however, since in deriving from Frege's adaptation of Kant's term, the usage covers logical truth and inference as well as linguistic truth and inference. We could say that, from the perspective of this book, this extended coverage is a far worse defect than Locke's misplaced emphasis on the verbal. Be this as it may, given what has been said up to this point in the book, it is clear that the adoption of Kant's term should not be taken to be more than the terminological stipulation it is. If we now take Locke's proposal as a first approximation to the full, ultimately formal, explanation of the nature of analyticity and analytic entailrnent, we have the beginning of an answer to Quine's challenge to Carnap to explain what it means to say that "K, as against M, N, etc., is the class of 'analytic' statements". Carnap, as we saw, cannot meet this challenge because, under the influence of linguisticism, the possibility of a nonlogical inference-type is closed off. Locke's proposal opens up such a possibility: the sentences in K have a sense structure in which the idea expressing the assertion of an analytic sentence is contained in the complex idea expressing what the assertion is about. Of course, this is just a first approximation to a satisfactory reply to Quine's challenge. To go beyond it, we would have to construct a semantic theory in which sentences are formally represented in a manner that explicates their sense structure and in which the interpretation of such a representation system defines analyticity and analytic entailrnent in terms of the correct sense structures. This, it may be recalled, is the approach overlooked in Quine's argument that an attempt to explain synonymy and analyticity in the field of linguistics hits a dead-end of circularity. I think it is best not to go directly to the construction of such a semantic theory, but first to find out how Locke's proposal got lost in subsequent philosophizing about logic, language, and necessary truth. Great philosophers like Frege make mistakes, but they have well-considered reasons for the philosophical moves they make. Thus, by turning again to the history of philosophy we can perhaps find reasons for the disappearance of Locke's proposal that enable us to set conditions of adequacy ori the construction of a semantic theory.

v How the Concept Containment Notion of Analyticity was Lost

Frege introduced linguisticism into modern philosophy when he explicated Kant's containment notion of analytic truth as "truths deducible from general laws of logic and definitions without assumptions taken from the sphere of a special science."1 This explication, Frege claimed, was designed to overcome certain shortcomings in Kant's account of analyticity. The explication was not intended to "assign a new sense to [analytic], but only to state accurately what earlier writers, Kant in particular, have meant by [it]."2 This seems to be true, for Kant's account runs the concept containment notion of analyticity together with a logical notion. In the Prolegomena, Kant says that Analytical judgments express nothing in the predicate but what has already been actually thought in the concept of the subject, though not so distinctly or with the same (full) consciousness. When I say: "All bodies are extended", I have not amplified in the least my concept of a body, but have only analyzed it.3

But he goes on to say that All analytical judgments depend wholly on the law of contradiction . . . [the predicate of an affirmative analytical judgment] cannot be denied [of the subject] without contradiction.4

And in the Critique, when he is discussing the a priori character of an analytic judgment, specifically "All bodies are extended", he says, . . . before appealing to experience, I have already in the concept of body all the conditions required for my judgment. I have only to extract from it, in accordance with the principle of contradiction, the required predicate.5 The psychological formulation to one side, the first of Kant's notions of analytic judgments is virtually identical to Locke's notion of

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trifling propositions. Curiously, Kant never discusses Locke's contribution to analyticity. This was unfortunate because Locke is clear on the critical question of distinguishing necessary consequence relations based on sense inclusion in the language from necessary consequence relations based on extra-linguistic considerations. Kant was at least unclear, and as I read him, he conflates the concept containment notion of analyticity with the logical consequence notion. One might speculate that this conflation stems from the same hasty generalization which led Descartes at one point in the Meditations to talk as if the absence of a reason to believe that God exists were grounds on which to base metaphysical skepticism about the cogito as well as mathematical truth. Perhaps Kant was also tripped up by a perception of such truths as falling under the generalization that their denial is, using Descartes's expression, "a manifest contradiction." But there seems to be more than this behind Kant's conflation of the notions. Kant's conflation is not something that occurs once, buried in a paragraph of a discussion of another topic, and in opposition to many statements in more central discussions. Kant's conflation appears prominently: the logical extractability notion appears right alongside the concept containment notion in his presentation of analyticity. The conflation appears more than once. And it is unopposed by statements to the contrary elsewhere. Hence, we have to assume, in Kant's case, that it is a considered opinion that the two formulations express aspects of a single notion. Descartes's assimilation can be taken as a lapse, but Kant's must be taken as a matter of doctrine. This raises the question of whether there is any doctrinal motivation in Kant's case that might help to explain why he would think that the concept containment notion and the notion of extractability by means of the principle of contradiction are the same. One answer that immediately suggests itself is that here, as elsewhere, Kant was attempting to synthesize empiricism and rationalism: the Lockean concept containment notion is combined with the Leibnizian logical consequence containment notion. Indeed, there is hardly any difference between Locke's notion of trifling propositions and Kant's notion of analytic judgments as ones that add nothing through the predicate to the concept of the subject, but merely break . . . it up into those constituent concepts that have all along been thought in it,6

on the one hand, and between Kant's notion of containment as logical extractability and Leibniz's notion of the predicate being con-

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tained among the properties of the subject as something necessary and demonstrable from the subject notion, on the other.7 But this answer does not seem to be wholly right. Kant never gives any evidence of having considered Locke's thoughts in this connection, and further, there is nothing empiricist or rationalist per se about either of the two containment notions. There was, of course, a controversy between Locke and Leibniz over whether there were two distinct notions of containment that give rise to certainty or just one.8 Kant seems to have been unaware of the importance of the point in dispute, or for some reason, which is unclear, thought it could be ignored. It is ironic that the philosopher who posed the problem of how synthetic a priori knowledge is possible should somehow have missed the issue of whether there are two distinct notions of containment. For this issue is just the issue of whether our knowledge of logic is synthetic a priori knowledge. There is, then, a clear basis in Kant for Frege's contention that his explication only states Kant's meaning more precisely.9 Ralph C.S. Walker is historically correct when he writes that Frege's definition is a clarification of Kant's and not a departure from it. And it has the advantage of making clear that the truth of an analytic judgment . . . depends on two factors: the meanings of the words . . . , on the one hand, and on the other, the laws of logic.10

But, even if Kant was responsible for the initial conflation of the Lockean notion of concept containment with the Leibnizian logical consequence containment notion, it was Frege's explication of Kant that was the critical event in the eclipse of the Lockean notion in modern philosophy. Yet Frege was certainly aware that, in some sense, there are two distinct notions of analyticity in Kant's writings. Frege distinguished the concept containment notion from the logical consequence containment notion with the colorful metaphors of "beams in the house" and "plant in the seed".11 In the former case, the contained concept is part of the construction of the containing concept: take the containing concept apart, as you would a house, and you will find the contained concept, as you would find its beams. In the latter case, the contained consequence is not part of the construction of the proposition containing it, but something that grows from it according to logical laws, in analogy to the way a plant grows from a seed according to botanical laws. Buy a house and you have bought beams; buy a seed and you haven't bought a plant. Having this clear a conception of the difference between the two

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notions of analyticity, how did Frege come to produce an explication which takes no account of the autonomy of the concept containment notion? It is tempting to speculate about logicist ulterior motives, but the most plausible explanation is that he saw the beams-in-the-house notion as the locus of the shortcomings he identified in Kant's account. Kant's account of containment is informal, highly metaphorical, and expressively weak; the account offers nothing better than a psychological test for when one concept is contained in another; and the account is restricted to subject-predicate sentences, leaving us with nothing to say about analytic sentences of other syntactic types. These are, by and large, genuine shortcomings of Kant's account, and Frege's explication successfully eliminates them. That is to say, these shortcomings are not shortcomings of Frege's explication. But this, in and of itself, is no guarantee that it was correct to explicate analyticity as Frege does, getting rid of an autonomous concept containment notion by making definition a component of his logical explicatum. There is no argument in Frege's discussion to show that the concept containment notion is not an independent notion, as his metaphors suggest, and that the shortcomings of its initial formulation cannot be removed by less drastic means. To this day, no argument has been forthcoming, yet Frege's handling of analyticity is widely adopted by both its friends and foes. Quine writes, Kant conceived of an analytic statement as one that attributes to its subject no more than is already conceptually contained in the subject. This formulation has two shortcomings: it limits itself to statements of subject-predicate form, and it appeals to a notion of containment which is left at a metaphorical level.12

But any explicandum can be expected to have such shortcomings. One thus needs an argument to show that these shortcomings cannot be overcome without an explication based on the plants-in-theirseeds notion. Instead, Quine offers the following historical rationale for the Fregean explication: But Kant's intent, evident more from the use he makes of the notion of analyticity than from his definition of it, can be restated thus: a statement is analytic when it is true by virtue of meanings and independently of fact.13

Quine makes it clear that this "true by virtue of meanings" notion is the Fregean one. Quine writes,

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Statements which are analytic by general philosophical acclaim . . . fall into two classes. Those of the hrst class, which may be called logically true, are typified by: (7) No unmarried man is married The relevant feature of this example is that it is not merely true as it stands, but remains true under any and all reinterpretations of 'man' and 'married'. If we suppose a prior inventory of logical particles, . . . then in general a logical truth is a statement which is true and remains true under all reinterpretations of its components other than the logical particles. But there is also a second class of analytic sentences, typihed by: (8) No bachelor is married The characteristic of such a statement is that it can be turned into a logical truth by putting synonyms for synonyms; thus (8) can be turned into (7) by putting 'unmarried man' for its synonym 'bachelor'.14

I have quoted at length from Quine's characterization of analyticity to show how the logical consequence containment notion has eclipsed the concept containment notion. Truth by virtue of meaning is broadened to coincide with Fregean logical truth by stretching the notion of meaning to encompass the referential structures of truth-functional and quantification logic and then defining analytic sentences as a special case of logical truth. Quine's critical move in going beyond Kant's concept containment notion to Frege's notion is his construal of Kant's intent. Quine construes Kant as intending to put forth this broadened notion of truth by virtue of meaning. Quine claims that the correctness of this construal is evident from Kant's use of analyticity. Although there is some support for Quine's construal in Kant's secondary characterization of analytic propositions as ones whose denials violate the law of noncontradiction, Kant's use of analyticity is, in fact, the very opposite of what Quine supposes. Kant employed the analytic-synthetic distinction to cross-classify explicative and expansive truths with a priori and a posteriori truths. Kant's aim in cross-classifying them was to exhibit a limitation in the explanatory resources of Humean empiricism. On this position, we can explain how we know truths that rest on conceptual structure and we can explain how we know truths that rest on experience. Kant's point was that these explanations fail us when we encounter a priori knowledge which is not analytic. A priori truths that connect their subject concept with concepts that are not contained in its structure cannot be established in a thought experiment or on the basis of inductive extrapolation from observed

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events. Kant explains how we can know the truth of a sentence like "Triangles have three angles" without appealing to experience, namely, thinking through the concept of a triangle and finding the concept of a three angled figure as a component concept; but this method fails in explaining how we know an a priori truth like 7 + 5 = 12. The reason for the failure is that the concept of the sum of 7 + 5 contains merely their union in a single number, without its being thought what the particular number is that unites them. The concept of twelve is by no means thought by merely thinking the combination of seven and five.15

If Kant's intent did not involve just the concept containment notion of analyticity, he could not have argued in this way to show that we do not understand how we can know synthetic truths like "7 + 5 = 12" a priori. Kant uses the concept containment notion to carry out his intention of showing that Humean empiricism faces the problem of how we can have a priori knowledge of synthetic, i.e., expansive, truths. In taking the term "meaning" as broadly as he does, Quine eliminates the distinction between explicative and expansive truths on which Karit had erected his formulation of this problem. Quine's "restatement" of Kant's intent subverts it rather than conforms to it. The philosophical tradition of distinguishing the beams-in-thehouse notion of analyticity as a special, linguistic form of truth ends with Locke.16 The tradition from Kant and Frege to Quine drops this notion, presenting Frege's explication as something that preserves everything of value in the beams-in-the-house notion while eliminating only the shortcomings in Kant's formulation of analyticity. It can readily be conceded that these shortcomings are not found in Frege's explication, but, as pointed above, this does not establish that what is of value in the beams-in-the-house notion is preserved. Moreover, there never was an argument that the concept containment notion of analyticity is not something quite different from the logical consequence containment notion. The Locke—Kant conception of analyticity takes analytic propositions to be ones where the predicate concept is one among the concepts making up the subject concept. Examples (l)-(3) illustrate this. (1) Nightmares are dreams (2) One who is convinced that Descartes is a philosopher believes that Descartes is a philosopher (3) Flawed gems are imperfect gems

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This conception provides an entirely language-internal account of linguistic truth and linguistic inference. The truth of an analytic proposition derives from the security that its semantic structure affords it against falsehood: because its predicate concept is one of the concepts out of which the subject concept is constructed, whatever falls under the latter ipso facto falls under the former, and hence, there can be no instance of the latter which is not an instance of the former. Since this security results entirely from sense inclusion, it is solely a matter of language. The case of analytic entailment is exactly parallel. Corresponding to the analytic sentences (1)—(3) are the analytic entailments (4)—(6). Because the sense of the conclusion in such inferences as (4) Descartes had a nightmare, hence, Descartes had a dream (5) Gassendi was convinced that Descartes is a philosopher, hence, Gassendi believed Descartes is a philosopher (6) The Star of Brooklyn is a flawed gem, hence, the Star of Brooklyn is an imperfect gem is literally one of the propositions that comprises the sense of the premiss, any state of affairs on which the premiss is true is ipso facto one on which the conclusion is true, too. Again, the language alone is the source of the security, this time against invalidity. This conception of analyticity yields a language/theory distinction directly: the language side concerns analytic truth, while the theory side concerns synthetic truth. The ill effects of having no such distinction are found in cases of linguistic truth which are approached as theoretical truth or cases of theoretical truth which are approached as linguistic truth. The cogito is here the prime example of the former. Although it is not yet clear how this inference is to be brought under analytic entailment, if it is, the sense of "I exist" will be shown to be included in the sense of "I think", and this will establish a truth-preserving connection independent of the inference falling under a law of logic. There are various examples of the ill effects of approaching cases of theoretical truth as linguistic truth, 17 but the one closest to home in connection with the present chapter is Kant's failure to notice a critical facet of his problem of how synthetic a priori knowledge is possible, namely, the problem of how it is possible to know logical truth a priori. If Kant had stuck strictly to the concept containment notion of analyticity, then he would surely have seen that what he

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says about mathematical truth in posing the problem of synthetic a priori truth in mathematics can also be said about logical truth. That is, he might have said: The concept of the conjunction of the propositions "All Cartesians are dualists" and "Some Cartesians torture helpless animals" contains merely their union in a single proposition, without its being thought what particular propositions follow from them. The consequence "Some dualists torture helpless animals" is by no means thought by merely thinking the combination of the premisses.

The reason for this parallel is that computation is involved both in obtaining an arithmetic sum and in obtaining a logical conclusion. In both, laws must be applied to work out a result that is not there intact in what is given at the starting point. Hence, if there is a problem about synthetic a priori knowledge of arithmetic because we do not yet have a satisfactory justification of the laws we follow in making arithmetic computations, then there is also a problem about synthetic a priori knowledge of logic because we do not yet have a satisfactory justification of the laws we follow in making logical computations. Kant's point in cross-classifying the categories analyticsynthetic with the categories a priori—a posteriori was to show that a priori truths whose subject concept contains merely the elements of the computation and the computational operation, but not the actual result of the computation, do not come under the known forms of justification. Such truths are not to be justified by showing that the result is beams-in-the-house-contained in their subject concept because they are not analytic, and in addition, they are not to be justified by showing that the result can be confirmed in experience because they are a priori and necessary. Since logical truths are computational in the manner of arithmetical truths, the same applies to them. Hence, there is a problem about synthetic: a priori knowledge in the case of knowledge of logical truth, and Kant failed to recognize it because he conflated Lockean concept containment with Leibnizian logical consequence containment. As a consequence of this failure, the generality of Kant's formulation of the problem of synthetic a priori knowledge, and the philosophical formulations deriving from it, were unnecessarily and, considering the consequences of the loss of the concept containment notion of analyticity, disastrously limited.

VI

Regaining the Concept Containment Notion of Analyticity

Frege found three shortcomings in Kant's formulation of the concept of analyticity; Quine found one in Carnap's. Frege pointed out that Kant's formulation of the concept containment notion of analyticity restricts its scope to subject-predicate sentences, that the criterion for containment is psychological rather than logical, and that there is nothing more than an expressively weak, informal account of what it is for one concept to be a part of another. Quine pointed out that Carnap does not explain what analyticity is. These criticisms are correct, but they have been taken to be far more damaging to analyticity than they are. I propose to take these shortcomings as defects of the sort which are natural, and only to be expected, at the very earliest stage in the explication of a concept. As such, they reflect nothing more than features of the first attempts which have to be transcended in a satisfactory explication. Hence, these shortcoming translate directly into conditions of adequacy on a satisfactory explication of the concept containment notion of analyticity, viz., (Ci) The explicandum must take the form of a generalization about the nature of analyticity that covers both subjectpredicate and non-subject-predicate analytic sentences, and the explicans must be a formalization of the generalization. (C2) The explicans must define "containment" on the basis of relations that are stronger than "a simple list" but weaker than those in predicate logic. (Cg) These relations must constitute a linguistic structure in some natural, appropriate, pretheoretic sense. (C4) The explication must make it possible to say not just which sentences are analytic but what analyticity is.

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The present chapter undertakes to construct enough of an explication of the concept containment notion of analyticity to meet (Ci)— (C4). It thus shows how a theory of analyticity develops naturally out of a response to the standard criticisms when these criticisms are seen, not as the basis for skepticism about the concept containment notion, but as identifying defects in the initial attempts to explicate it. The criticism of Locke's and Kant's formulation that has to be taken up first is that the formulation restricts analyticity to subjectpredicate sentences. This criticism is pivotal: whether the concept containment notion of analyticity can be regained will be decided in the choice of a set of non-subject-predicate sentences on which to target the extrapolation beyond the standard subject-predicate sentences. This is because this choice determines the nature of the generalization about analyticity that is to be formalized and systematized in a semantic theory. This point can be underscored by noting that Frege's choice of logical truths as his non-subject-predicate analytic sentences determines that his explicatum will be a logical consequence containment notion. Given the decision to encompass sentences like (9)—(11), there is only one generalization about analyticity (9) If all horses are animals, then all heads of horses are heads of animals (10) If John is a bachelor, then John is a bachelor or John is rich (11) If everybody loves my baby and my baby loves nobody but me, then I am my baby1 which all the cases naturally fit, namely, Frege's generalization, i.e., "truths deducible from general laws of logic and definitions without assumptions taken from the sphere of a special science." It is not hard to guess why Frege chose cases like (9)—(11). The choice exemplified the logical, and more encompassing, side of Kant's characterization of analyticity, it was in line with Frege's cherished logicist program, and it fit nicely into the comprehensive system of formal predicate logic he had developed. But such factors have nothing to do with the semantic relatedness of the chosen sentences to subject-predicate sentences which are analytic in the beamsin-the-house sense. Such factors represent an extrinsic and, for that reason, suspect influence on the choice of examples to serve as paradigms of non-subject-predicate analytic sentences. In order to decide whether the shortcomings raised by Frege and Quine are fatal Haws

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which block a satisfactory explication of the beams-in-the-house sense of analyticity or are merely defects on a par with ones that every pretheoretic notion will have, we need to approach the choice of non-subject-predicate sentences on the basis of intrinsic, semantic, considerations. Once we approach the choice in this way, we immediately see choices that are, intuitively, better than cases like (9)—(11), namely: (12) John marries those whom he weds (13) John walks with those with whom he strolls (14) John receives books from those who give him books Three features make these cases a more appropriate choice than cases like (9)—(11). First, they are semantically similar to classical examples of subject-predicate analytic sentences, e.g., "Lead is a metal", "Bodies are extended", "Bachelors are unmarried", arid "A vixen is a female fox". The predications in (12)—(14) are redundant in the same way that the predications in classical subject-predicate analytic sentences are. The sense of (12), (13), and (14) exhibit the same concept containment structure. For example, (13) exhibits the containment of the concept of someone walking in the concept of the person strolling, i.e., walking slowly, in just the same way that the concept of being a sibling is contained in the concept of being a sister, i.e., a female sibling. The predications in (9)—(11) are riot redundant in this way, and hence, (9)—(11) are not like classical subject-predicate analytic sentences. For example, the concept of horses being animals does not contain the concept of heads of horses being heads of animals, in the sense of the latter being one of the concepts out of which the former is built: the concept of being a head does not even appear in the former concept. One can, of course, call this containment, as Frege did, but, then, it is containment of the plant-in-the-seed rather than of the beams-in-the-house. The conclusion that all heads of horses are heads of animals grows by the laws of logic from a seed that does not involve the concept 'head of. The appearance of such novel conceptual content in the conclusion of cases like (9)—(11) distinguishes them from the bona fide cases of conceptual containment like (1)—(3) or (12)—(14). Philosophers have at times noted that conflation of them leads to absurdity, but they typically have not drawn the right moral from this absur-

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dity, i.e., that there are two different notions of containment. Wittgenstein lays the blame on the Kantian metaphor of thinking through the subject concept. He writes, But what is it supposed to mean to say "If one proposition follows from another, thinking the second must involve thinking the first", since in the proposition "I am 170 cm tall" it isn't necessary to think of even a single one of the negative statements of height, that follow from it? "The cross is situated thus on the straight line: I "So it is between the strokes". "It is 16!/2° here"—"So it is certainly more than 15°" Incidentally, if you are surprised that one proposition can follow from another even though one doesn't think of the former while thinking of the latter, you should consider that p v q follows from p, and I certainly don't think all propositions of the form p v ^ while I am thinking p. The whole idea that a proposition has to be thought along with any proposition that entails it rests on a false, psychologising notion. We must concern ourselves only with what is contained in the signs and the rules.2

But the problem does not depend on the Kantian metaphor. It continues to exist even when the metaphor together with the psychologizing is dropped because containment in the signs and containment in the rules are different. A second feature which makes cases like (12)—(14) a more appropriate choice as non-subject-predicate analytic sentences derives from the fact that their conclusion involves novel conceptual content. The fact that the consequent in (9) involves the relation 'head of which does not appear in the antecedent means, in Kant's terms, that (9) is ampliative. Hence, unlike the explicative cases (1)—(3) and (12)-(14) where truth depends exclusively on sense structure, (9) requires extra-linguistic principles to make the hypothetical connection on which its truth depends. What Kant says about 7 + 5 = 12 carries over to logical cases like (9). A third feature is that sentences like (12)-(14) are syntactically simple, i.e., they have no subordinate or coordinate clause structure. These sentences express truth-functionally atomic propositions, as do the sentences (1)—(3). In contrast, sentences like (9)—(ll) are complex sentences which express truth-functionally compound propositions. The analytic sentences (12)—(14), like (1)—(3), express propositions that take the form of a predicate with terms occupying

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its argument places and that contain no compounding of propositions using logical connectives.3 This new set of non-subject-predicate analytic sentences enables us to formulate a generalization about the nature of analyticity which, although still informal, cannot be criticized for being restricted to subject-predicate sentences. The generalization is based on the following considerations: (12) and (13) contain a two-place relation, with their subject and direct object supplying the terms for the two places; (14) has a three-place relation, with its subject, direct object, and indirect object supplying the terms. In all three examples, analyticity is a matter of one term being, as it were, a microcosm of the whole proposition. The same is true in classical examples of subjectpredicate analytic sentences like (l)-(3). Such sentences express a property ascription, and hence, involve a one-place predicate. The subject in such a sentence supplies the term for the predicate, and hence, the inclusion of the sense of the predicate in that of the subject is, again, a matter of one term being a microcosm of the whole proposition. Thus, Locke and Kant failed to see the property of analyticity abstractly enough. They concerned themselves with the special case of analyticity which involves a redundant one-place predicate. Given cases like (12)—(14), and further assuming no upper bound on the number of argument places a predicate might have, our generalization is: (G) A sense of a sentence is analytic in case the sense has the form of a predicate whose argument places are filled by terms and one of the terms contains the predicate with each of its argument places filled by the same term that fills it in the sense of the sentence. To extend our generalization to sentences, we add: (G') A sentence is analytic (on a sense) just in case it has a sense that is analytic. This is as far as we can take our discussion of the first shortcoming in isolation from the others. A more precise characterization of the class of non-subject-predicate analytic sentences depends on the way the forrnalization of semantic structure that is developed on the basis of the clear cases fixes the boundary of analyticity in less clear cases. This is a familiar feature of forrnalization and explication: the construction of formal principles to explicate the pretheoretically clear

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cases brings their description to a higher level of detail and thereby reveals similarities and differences between the clear cases and the unclear cases. We are then in a position to decide on systematic grounds which of the pretheoretically unclear cases belong with one or another kind of clear case. The second shortcoming can be dealt with quickly in the present context.4 A formal explication of (G) would eliminate the need for a psychological criterion, such as Kant's, on which analyticity is determined by our thinking through a mental construction. Once we have a formal explication of the concept containment notion, we will require neither a metaphor nor a mental act. The remaining Fregean criticism of Kant's account of analyticity is that conceptual structure is too impoverished on this account. Frege writes that Kant . . . seems to think of concepts as denned by giving a simple list of characteristics in no special order; but of all ways of forming concepts, that is one of the least fruitful. If we look through the definitions given in the course of this book, we shall scarcely find one that is of this description. The same is true of the really fruitful definitions in mathematics, such as that of the continuity of a function. What we find in these is not a simple list of characteristics; every element in the definition is intimately, I might almost say organically, connected with the others. A geometrical illustration will make the distinction clear to intuition. If we represent the concepts (or their extensions) by figures or areas in a plane, then the concept defined by a simple list of characteristics corresponds to the area common to all the areas representing the defining characteristics; it is enclosed by segments of their boundary lines. With a definition like this, therefore, what we do—in terms of our illustration—is to use the lines already given in a new way for the purpose of demarcating an area. Nothing essentially new, however, emerges in the process. But the more fruitful type of definition is a matter of drawing boundary lines that were not previously given at all. What we shall be able to infer from it, cannot be inspected in advance; here, we are not simply taking out of the box again what we have just put into it. The conclusions we draw from it extend our knowledge, and ought therefore, on Kant's view, to be regarded as synthetic; and yet they can be proved by purely logical means, and are thus analytic. The truth is that they are contained in the definitions, but as plants are contained in their seeds, not as beams are contained in a house. Often we need several definitions for the proof of some proposition, which consequently is not contained in any one of them alone, yet does follow purely logically from all of them together.5 Much of what Frege says here is true. Kant says nothing about the structure of the components of a concept, and hence, by implication,

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he seems to endorse the view that Frege here attributes to him that the components of a concept are "a simple list of characteristics." Frege is surely also right that listing is the "least fruitful" way of forming complex concepts. The critical question, as Frege saw, is how to obtain a more fruitful way of forming complex concepts— how to introduce relations among the component concepts that constitute a structure richer than a list. Frege's solution was to introduce the full power of logical structure. This solution must have seemed ideal to him. For one thing, it was sanctioned by Kant whom he greatly admired, since Kant had characterized analytic propositions as ones whose denial violates a law of logic. For another, the fruitfulness achieved is no puny thing. Furthermore, as Frege makes clear in the quotation, no objection of the sort that he brought against Kant is possible against his characterization of analyticity. Not only is it clearly the case that a complex concept formed from logical relations is one where what can be inferred from it "cannot be inspected in advance" (i.e., "we are not simply taking out of the box again what we have just put into it"), but it is also the case that, on Frege's view, concept formation out of logical relations covers mathematical concepts, too. Finally, this solution eliminates, in one stroke, the shortcomings Frege had found in Kant's account of analyticity. Non-subject-predicate analytic sentences come in for treatment, psychologism disappears, and a formal construction replaces a metaphorical one. Frege notes that, on his solution, analytic propositions "extend our knowledge, and ought therefore, on Kant's view, to be regarded as synthetic." Frege also observes that such propositions "can be proved by purely logical means, and are thus analytic." Here he uses "analytic" in the second of Kant's senses, viz., propositions whose denial violates a law of logic. Frege's use of "synthetic", however, does not correspond to this analytic-synthetic distinction, i.e., it does not mean 'neither a logical truth nor a logical falsehood'. Rather, it is used in the sense of the explicative/ampliative distinction. Here the problem with Frege's solution, of conflating two distinct notions, surfaces. Frege tries to get around the problem by introducing a new construal of Kant's notion of containment: "The truth is that [explicative conclusions] are contained in the definitions, but as plants are contained in their seeds, not as beams are contained in a house." This merely papers over the problem. Unless the beams-in-thehouse notion of containment is shown to be nothing more than the discredited Kantian notion of "a simple list of characteristics in no

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special order," the problem remains. But nothing has been said to show this. Frege has done nothing to preclude the possibility that there is notion of conceptual structure stronger than a mere list of concepts but weaker than a logical engine. Against such a notion, Frege's criticism of Kant would be inapplicable. Such a notion would, to exploit Frege's metaphor, be a structure of beams, with its own architecture, rather than either a pile of boards or a forestry project. And a structure of beams wouldn't be useless because it isn't a forestry project. We now proceed to explain how (C 2 )—(C 4 ) can be satisfied. To do this, we shall step back and take another look at how the meaningpostulate approach fails. The analyticity of (1) is not adequately ex(1) Nightmares are dreams

plained on the basis of a representation of (1) as (15) and a deriva(15) For everything there is, if it is a nightmare, then it is a dream tion of (15) from a suitable meaning postulate. Such a derivation would tell us that the sentence is counted as an analytic truth but not what it is about the sentence in virtue of which it so counts. This explanatory failure of the meaning postulate approach is in no way unique to semantics. Philosophers are accustomed to thinking of the approach as indigenous to semantics, but, in fact, it applies in other fields. It is only because philosophers respect those fields that they have never contemplated applying the meaning-postulate approach in them in the way it has been applied in semantics. But it will be illuminating to apply the approach in some respected field. This will exhibit the failure of the approach in a revealing way. I propose, then, to apply the meaning-postulate approach in logic in the way it has been applied in semantics, namely, to show that a familiar apparatus suffices for new inferential phenomena believed to require new apparatus. I will argue that, when it is applied in logic in this way, the reason why meaning postulates fail to explain analyticity is dramatically revealed. The reason is that the use of meaning postulates takes the place of the structural analysis required to explain the source of analytic truth and implication, and hence, no explanation can be forthcoming. Let us apply the meaning-postulate approach in sentential logic as a way of enabling it to handle quantificational inference. We beef up a sentential calculus with an infinite list of sentential constants Si, S 2 , . . . , one for each sentence of English (ignoring ambiguity), and

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with a set of meaning postulates formulated with these sentential constants. For example, we could have the postulate 'S117 D SBIS', where "Si 17" names the antecedent of (9) and "SSi8" the consequent. (9) If all horses are animals, then all heads of horses are heads of animals If the marking of necessary connection were all that were asked of an account of quantificational inference (as it is thought to be in the case of analytic entailment), then an applied sentential calculus such as the one we have described would handle quantihcational truths like (9). It would be unnecessary to introduce quantification theory because quantihcational truths could already be derived as formally valid in the sentential calculus. Of course, such a proposal to render quantification theory otiose is absurd. The reason is clear. A meaning-postulate account of valid quantificational inferences is no substitute for a proper quantificational account, because the former offers no analysis of quantificational structure to explain the source of their validity. 6 How does quantification theory achieve such an explanation? It eschews the use of sentential constants to represent quantificational sentences, and, instead, adopts a representation scheme that makes it possible to analyze the structure of quantifiers, predicates, and variables within sentences. Sentential constants mask the quantificational structure which determines the extensional structure of sentences, while the representational apparatus for quantifiers, variables, scope relations, etc., exposes such structure. Meaning postulate derivations are explanatorily vacuous in the case at hand because sentential constants are unable to expose the relevant sentential structure. Taking our clue about how semantics might go beyond a meaning-postulate approach in cases like (1)—(3) from how quantification theory goes beyond our hypothetical applied sentential calculus, we shall say that the fault with meaning-postulate accounts of analyticity lies in their use of predicate constants. Just as the use of sentential constants makes our hypothetical sentential calculus unable to expose the quantificational structure required to explain logical truths like (9), so the use of predicate constants makes Carnapian predicate calculi unable to expose the sense structure required to explain analytic truths like (1)—(3). Accordingly, just as predicate calculi have the representational apparatus to expose the quantificational structure required to explain logical truths like (9), so se-

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mantles must develop the representational apparatus to expose the sense structure required to explain analytic truths like (1)—(3). Hence, the direction we have to go in to satisfy (C 2 )—(C 4 ) is now clear: we should eschew the use of predicate constants and instead develop a representation scheme designed to formally analyze the sense structure internal to predicates, similar to the way that representation schemes in predicate logic formally analyze the quantificational structure internal to sentences. What makes the predicate constants of Carnapian systems incapable of exposing structure is that their orthographic and syntactic form is only related in an arbitrary way to grammatical structure in the language they are used to regiment. 7 The shape of these symbols only functions to separate tokens of different symbol types and to collect tokens of the same symbol type, e.g., the vertical line with a longer topmost horizontal line and a shorter middle horizontal line which make up the capital letter "F" function to distinguish the first and second predicate tokens in "(3x) (Fx D Gx) D (3x)Fx" and to identify the first and third. I shall refer to these symbols as "designations" because they directly designate sets of things in the domain of the language.8 Designations contrast with a category of symbols I shall call "descriptions".9 These symbols have an orthographic and syntactic form designed so that, under suitable interpretive principles, the structure of the symbols formally represents the structure of some class of objects. The principles set up an isomorphism between the structure of the symbols and the structure of the objects they formally represent. The symbols for quantifiers, variables, etc., in predicate calculi are to a certain extent descriptions. For example, "(3x) (Fx D G x )" is a description: it is a complex symbol whose formal structure represents the construction of a proposition out of quantifiers, predicates, and variables. Besides descriptions for quantificational structure, there are descriptions for syntactic structure, such as the phrase markers familiar in the study of syntax. Under principles of interpretation in linguistic theory, these labelled trees formally represent the constituent structure of sentences. (One such principle is that a substring of the terminal string in a phrase marker belongs to the syntactic category K if the substring is dominated by a node labelled "K" in the phrase marker.) The distinction between designations arid descriptions is a general one belonging to the study of the nature of formalization. The im-

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portance of the distinction derives from the fact that the point at which formal representations are restricted to designations is the point at which the theory's account of the structure of the objects in its domain terminates. Given two theories for the phenomena in a domain, T\ and T2, such that T2 successfully employs descriptions beyond the point at which T\'s use of them ceases, T2 will offer the more revealing account of the phenomena, other things being equal. Thus, in evaluating a theory with respect to its representation of a domain, the question is whether the theory resorts to designations before the entire structure of each phenomenon has been revealed. My objection to Carnapian theories of inference in natural language is not that such theories use designations, since representation, like explanation, stops somewhere, but that their use of designations begins well before all inferentially significant grammatical structure in predicates has been exhausted. Syntactic simples, or morphemes, are uniformly represented by designations, but they contain the sense structure on which the analyticities and analytic entailments in (l)-(6) and (12)-(14) depend. There are two philosophical doctrines that lead philosophers to resort to the use of designations at the level of syntactic simples. First, there is extensionalism which denies the existence of senses. If there are no senses, then the lower limit of inferentially significant grammatical structure is reached at the point where each syntactic simple is represented on the basis of a designation with a specified extension. To employ descriptions to represent syntactic simples would be a concession that there is inferentially significant grammatical structure to morphemes. Since it is not syntactic structure, what else could it be but sense structure? Second, there is the Carnapian doctrine of intensional isomorphism.10 This holds that there are senses but that there is sense structure only for syntactically complex expressions. For Carnap, two expressions are intensionally isomorphic just in case they have the same syntatic structure arid corresponding constituents in the expressions have the same intension or sense. On this doctrine, synonymous syntactic simples, such as "money" and "dough", "perhaps" and "maybe", "violin" and "fiddle", etc., are semantic simples, too. The natural representation scheme for such sense monoliths is a stock of designations (and a set of rules for assigning complexes of such designations to syntactically complex expressions). The stock could consist of the numerals "1", "2", . . . , each of which stipulated as the name of a particular sense. (Numerals, of course, are in no way special, and

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nothing hangs on our use of them.) Numerals would be assigned to syntactic simples on the conditions: (a) a numeral n is assigned to the morpheme m just in case m has the sense n names, (b) no numeral is assigned to a meaningless morpheme, (c) at least one numeral is assigned to a meaningful morpheme, (d) k distinct numerals are assigned to a A-ways ambiguous morpheme, (e) the same numeral is assigned to two morphemes if, and only if, they are synonymous.

There would have to be recursive rules for forming sets of numerals to represent the senses of syntactically complex expressions, but we may ignore this challenging task. The defect of such a representation scheme already shows up in connection with syntactic simples. Although one might represent the synonymy of "money" and "dough" by assigning them the same designation, say, the numeral "17", the synonymy of a syntactic simple and a syntactic complex, such as "sister" and "female sibling", could not be represented as intensionally isomorphic, since these expressions are not the same in structure, as required by the definition of intensional isomorphism. A fortiori, antonyms like "sister" and "brother" and redundancies like "female sister" go beyond the power of such a representational scheme. It is easy to see why. The scheme is only designed to keep count of the number of senses an expression has. The numerals assigned to an expression under (a)—(e) specify how many senses the expression has (i.e., no numeral, no senses; one numeral, one sense; the same numeral in the case of two expressions, the same sense). The assignment of numerals cannot express properties and relations which involve reference to the internal structure of senses like synonymy, antonymy, and redundancy. This is because numerals are designations, and the orthography of designations functions only to group tokens of symbol types as occurrences of the same or a different type. Thus, a designation says nothing about the internal structure of a sense, but, in order to handle the redundancy of "female sister", the formalism would have to analyze the sense of the morpheme "sister" into its component parts and identify one of them with the sense of "female". The same applies in the cases of antonymy and cases of synonymy considered.11 Let us now try to construct a representation scheme which analyzes the sense structure of syntactic simples in a way that handles such semantic properties and relations. Let us start by becoming clearer about why we think there is inferentially significant sense

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structure at the level of syntactic simples. What we want to know is what the nature of the argument for such structure is. This question breaks down into two questions: what is the argument for sense structure at the level of syntactic simples, and what is the argument for taking the structure to be inferentially significant. To answer the first question, we can develop the argument as an instance of a general form of argumentation in the study of grammar. In this study, the presence of grammatical properties and relations of a type which cannot be accounted for on the basis of levels of structure that have heretofore been recognized is a sign of the existence of a deeper level of structure. For example, the fact that surface syntactic structure fails to account for grammatical relations like 'subject-of' and 'direct-object-of' in sentences like "John is easy to please" and "John is eager to please" was a sign of, and eventually led to the discovery of, a level of deep syntactic structure.12 Now, the semantic factsjust brought up against Carnap's doctrine of intensional isomorphism constitute similar signs of the existence of sense structure at the level of syntactic simples. For example, expressions like "female sister", "free gift", and "naked nude" have the semantic property of redundancy; an expression like "female sibling" is synonymous with a single morpheme like "sister"; "sister" and "brother", "hot" and "cold", and "happy" and "sad" are antonyms; "father", "brother", "bachelor", "husband", etc., are semantically similar. Neither phonological structure (which is arbitrarily related to meaning) nor syntactic structure (of which there is none in such syntactic simples) nor semantic structure of the kind considered in our numeral representation scheme can explain these semantic properties and relations. Hence, like Chomsky's posit of deep syntactic structure, we must posit sense structure at the level of syntactic simples. Only on the posit that syntactic simples are semantically complex can we account for (i) the redundancy of an adjective-noun construction as due to the sense of the adjective being part of the sense of the noun, (ii) the synonymy of syntactically complex and syntactically simple expressions as due to the compositional sense of the former being the same as the lexical sense of the latter, (iii) the antonymy of morphemes as due to an opposition in meaning between sense components, and (iv) the semantic similarity of morphemes as due to a shared sense component. On the basis of these signs, it seems reasonable to say that the language has decompositional structure, i.e., the language contains a level of semantic structure at which the sense of a syntactic simple like "sister" decomposes into the sense of "sibling" and the sense of

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"female", and these senses perhaps analyze into more elementary sense components. Thus, we shall abandon the use of designations to represent syntactic simples, and instead, represent them using descriptions which are specially designed to formally represent the semantically complex structure of syntactic simples. How large a stock of descriptions will be required to account for semantic facts like those we have been discussing depends on how far analysis of decompositional structure can be taken before it encounters semantic simples. Could the stock contain more descriptions than English morphemes? Why not? This need not mean that explanation has been sacrificed. The size of the vocabulary of English increases without finite bound, and anyway, it isn't words that matter but their elementary semantic parts. Are the elementary particles fewer than the elements from Actinium to Zirconium? Decompositional analysis can clearly be taken very much further than works in semantics have taken it to the present time. But it is anyone's guess how far such analysis can be ultimately taken in the long run. The simples of the semantics of natural language, in contrast to the simples of artificial languages, are the very last thing we will be in a position to determine. Nonetheless, we can now state the principle for determining when we have reached the semantic simples, namely, we have reached the semantic simples of natural language when we cannot extend the power of decompositional analysis to account for semantic properties and relations by adding descriptions or extend the simplicity of the analysis by subtracting descriptions. This is to say, we have reached the simples when designations are forced on us by the success of our theory of sense structure. The second question was what the argument is for thinking decompositional sense structure is inferentially significant. This has, in effect, been answered at various points in the preceding chapters. The answer is that decompositional sense structure is the source of one kind of necessary truth and one kind of inferential validity: the fact that the sense of "sister" is a complex structure one of whose parts is the sense of "sibling" is the source of the analyticity of (16) (16) Sisters are siblings and the analytic entailment of (17) by (18). Other semantic prop(17) Mary is a sibling of Tom's (18) Mary is a sister of Tom's

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erties and relations that we have mentioned also illustrate the inferential significance of decompositional structure. Furthermore, synonymous sentences express the same proposition, and thus, to the extent that sameness of proposition determines sameness of role in inference, have the role in inference. 13 Ambiguous sentences express two or more different propositions, and thus have two or more independent roles in inference. Meaningful sentences express a proposition, and have a role in inference, while meaningless sentences express no proposition, and have no role in inference. I have thus far been speaking about decompositional sense structure as the source of semantic properties and relations in order to emphasize that this aspect of grammatical structure will be the basis for our answer to Quine's question "what [does] it ... mean to say that K, as against M, N, etc., is the class of 'analytic' statements in L0?" The gist of our answer will be that it means the sentences of K, but not those of M, N, etc., have the sense structure expressed in the definiens of (G). In order for such an answer to be stated in a theory which is strongly universal in the sense of chapter IV, three conditions must be met: (i) the semantic representations of the sentences of K must formalize the features of their sense which determine their inference roles, (ii) these representations must be the basis on which the validity of the members of K is marked, and (iii) the metatheory for the representation must interpret the structure of semantic representations in such a way that we can see why, in the pretheoretic sense, each member of K is a /^-sentence. The proper way to develop such a theory is to take steps at the very beginning to insure that (iii) will be satisfied. The first thing to do is to find a pretheoretically natural domain for the theory. We know the theory will concern itself with analyticity, analytic entailment, synonymy, ambiguity, meaningfulness, meaninglessness, redundancy, antonymy, and sense similarity. What makes it natural to group these properties and relations together as belonging to the same domain? The answer would seem obvious: each of these properties and relations concerns meaning in a straightforward, pretheoretic sense. This can be appreciated by noting that the questions 'What is truth by virtue of meaning?', 'What is inference by virtue of meaning?', 'What is sameness of meaning?', 'What is multiplicity of meaning?', 'What is meaningfulness and meaninglessness?', 'What is repetition of meaning?', 'What is opposition of meaning?', and 'What is similarity in meaning?' are components of the general question 'What is meaning?' Any answer to 'What is meaning?' will perforce

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contain answers to each of the former questions. Accordingly, the properties and relations asked about in these smaller questions comprise the domain marked out by the big question, 14 The next step is to collect our informal answers to these smaller questions which have been obtained thus far. This includes, besides (G), the generalizations (G,)—(G 6 ): (Gi) A redundant expression is one in which the sense of the modifier is a part of the sense of the head. (Ga) Synonymous expressions are ones that have the same sense. (G3) Semantically similar expressions are ones that have a sense with a common component. (G4) A meaningful expression is one that has at least one sense, and a meaningless expression is one that has no sense. (Gr,) An ambiguous expression is one that has more than one sense. (G6) Antonymous expressions are ones that have opposite senses. At this point, we can ask how the theory will explain such semantic properties and relations on the basis of its representations of senses. The example of the numeral notation discussed above embodies the right idea. It just works it out in terms of too wide a use of designations. The idea, as embodied in (a)—(e), is to express informal generalizations like (G) and (Gi)—(G 6 ) formally in terms of configurations of symbols in the semantic representations of expressions and sentences. Since such a configuration will specify what sense structure a particular semantic property or relation consists in, we can use these configurations to define the semantic properties and relations. The use of grammatical representations to provide the formal features for definitions of grammatical properties and relations is familiar in syntax. We can explain how we will define semantic properties arid relations in terms of a particular example of how syntactic relations are defined on the basis of phrase markers. The model we will use is Chomsky's definitions of the traditional grammatical relations of 'subject-of, 'predicate-of, 'direct-object-of, 'mairi-verb-of, and so on.15 Chomsky explains these relations in terms of configurations of syntactic category symbols in phrase markers. In using this explanation as a model illustrating the dependency of metatheoretic definitions on formal representations of grammatical structure, I do not wish to be understood as endorsing Chomsky's proposal. Any of

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the alternative proposals could have served my purposes, though not as well because they are not as widely known. Chomsky suggests that "grammatical functions" can be uniformly denned relative to phrase markers in the following manner. Given a phrase marker of the terminal string W with the subconfiguration (P),

Chomsky proposes that we say that the substring U of W bears the grammatical relation [B, A] to the substring V of W if V is dominated by a node labeled A which directly dominates YBZ, and U is dominated by this occurrence of B.16

Thus, in the phrase marker (PM), "sincerity" bears the relation [NP, S]

to the entire substring of (PM), "frighten the boy" bears the relation [VP, S], "the boy" bears the relation [NP, VP], and "frighten" bears the relation [V, VP]. These functions illustrate the general definitions: Subject-of: [NP, S], Predicate-of: [VP, S], Dircct-Objectof: [NP, VP], and Main-Verb-of: [V, VP]. 17 These definitions be-

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long to the theory of language, while the phrase markers to which they apply are syntactic representations of sentences belonging to the grammar of English. The correctness of the entire theoretical explanation of these grammatical functions depends on both the faithfulness with which phrase markers like (PM) reflect the particular facts of English (e.g., whether "sincerity" is both a noun and a noun phrase and so belongs to the same categories as "boy" and "the boy") and the faithfulness with which the formal features expressed in the definitions capture the grammatical functions in natural language. Semantic representations will correspond to syntactic representations like (PM), and definitions of semantic properties and relations will correspond to Chomsky's definitions of grammatical functions. Semantic representations will be called "semantic markers", in analogy to the term "phrase marker".18 Semantic markers mark semantic structure. Semantic markers are descriptions, as are phrase markers, but their orthography is designed to represent sense structure rather than phrase structure. As we have seen, semantic markers will be fundamentally concerned with describing the decompositional sense structure of syntactic simples, though, of course, they will also describe the sense structure of syntactically complex expressions and sentences. We shall use English words enclosed in parentheses as symbols for semantic markers, but it is to be noted that their use is motivated by mnemonic considerations entirely. Formally, such occurrences of English words are on all fours with numerals. The definitions of semantic properties and relations formalize informal generalizations like (G) and (G])—(G 6 ) on the basis of semantic marker notation. In this way, they serve also to interpret the formalism of the notation, in the way that, say, Chomsky's definition of 'subject-of serves to interpret the formal configuration [NP, S]. There will be other interpretive conventions which relate the components of semantic markers to the components of senses. For example, we might adopt the convention of using the semantic marker "(Human)" to stand for the concept of being human, the semantic marker "(Adult)" for the concept of being an adult, the semantic marker "(Male)" for the concept of being male, and the semantic marker "(Unmarried)" for the concept of being unmarried. Relative to these conventions, we could represent the decompositional structure of the sense of "bachelor" by the semantic marker (SM). (SM) ((Human) (Adult) (Male) (Unmarried))

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We can now formalize the generalization (Gi) in the definition (G/) (G/) An expression consisting of a modifier and its head is redundant if, and only if, the semantic representation of the modifier is a component of the semantic representation of the head. and with (G/), on the basis of the semantic representations proposed for "bachelor", "male", and "unmarried", predict the redundancy of "male bachelor" and "unmarried bachelor". We could also formulate definitions like (Gz) and (G$') and then, on the (G 2 ') Two expressions are synonymous if, and only if, their semantic representations are the same. (Gs') Expressions are semantically similar if, and only if, there is a semantic representation that is a component of each of their semantic representations. basis of (SM) and similar semantic representations, predict the synonymy of expressions like "bachelor" and "unmarried adult male" and the semantic similarity of "bachelor", "father", "uncle", etc. It is natural to add the definitions (G 4 '), (G4"), and (G5') to the (G 4 ') An expression is meaningful if, and only if, it has a semantic representation. (G/) An expression is meaningless (semantically deviant) if, and only if, it does not have a semantic representation. (G5') An expression is ambiguous if, and only if, it has more than one semantic representation. ones already given. Definitions like these interpret the formalism by relating it to intuitively recognizable semantic properties and relations, and, in so doing, they impose constraints whose satisfaction provides factual support for assignments of semantic representations. For example, the assignment of one semantic representation to an expression predicts that it is meaningful, the assignment of none predicts that it is meaningless (deviant), the assignment of more than one predicts that it is ambiguous, and the assignment of the same semantic representation to two expressions predicts that they are synonymous. If such predictions are confirmed by the judgments of fluent speakers of the language, the assignments receive evidential support. If such predictions are disconfirmed, the assignments have to be changed. The more properties and relations that can be de-

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fined, the richer the interpretation of the formalism and the tighter the constraints on the assignment of semantic representations. The development of a more comprehensive interpretation of the formalism goes hand in hand with the development of a more powerful formalism because only formalism and interpretation together comprise a theory.19 In the advancement of a semantic theory, the needs of each spur the development of the other. Here is a case in point. Since antonymy (opposition of sense) is a semantic relation, we will require a definition stating the sense structure that is responsible for antonymy. But a semantic representation like (SM) is not rich enough to formally distinguish senses that are antonymous from ones that are merely different (i.e., sernantically dissimilar in some respect). "Bachelor" and "spinster" are antonyms, but a semantic marker for "spinster" on the model of (SM), that is, "((Human) (Adult) (Female) (Unmarried))" would not help to differentiate this antonymy from a conceptual difference like that between "bachelor" and "eligible American". Formally, there is nothing to relate "(Male)" and "(Female)" in an appropriate way that would not also relate "(Male)" and "(American)" in the same way. What is required is a way of formalizing the concepts of being male and being female that exhibits their opposition in meaning. One way of doing this is to analyze the concepts of being male and being female into both a concept that expresses the kind of incompability involved, viz., gender rather than species or marital status, and concepts that express the particular opposition found with this kind of incompatibility, viz., having organs for begetting offspring or organs for bearing offspring. The kind of incompatibility could be formally represented by a base symbol and the particular oppositions by choices of superscript symbols associated with the base symbol.20 Kinds of incompatibility would then be distinguished by different base symbols, and the cases of opposition within a kind by different superscripts. For the present, we have to leave open the questions of how many kinds there are and how many oppositions can obtain within a kind. In this way, we can represent the concepts of being male and being female in a manner which formally displays their incompatibility, namely: (SM,)

((SeXUal Organs) (Begetting Function))

(SM 2 ) ((Sexual Organs)

(Bearing Fu

""'°'»)

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We can introduce a partial fbrmalization of (G6) as follows: (Ge') The senses of two expressions are incompatible if the semantic representation of one contains a semantic marker of the form ((M) and Cohen and Nagel argued that the deductive circle in science is virtuous because it is "so wide that we cannot set up any alternative to it.""' Virtuous circularity can thus be distinguished from vicious circularity on the dirnen-

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sions of width arid expectation. Since the cogito's circle is neither very large nor very surprising, Wilson's attempt to defend Descartes against Williams would seem to fail. Williams can adopt the distinction between virtuous and vicious circularity and then reformulate his criticism to charge that, because the cogito's circle is so small and unsurprising, it is a petitio principii if anything is. This revised version of Williams's objection could not be dismissed as something that "would cut against any valid deductive argument whatsoever." But Wilson is quite right to take the picture of the circularity of all deductively established knowledge to be unacceptable. Now, if the reasons for this unacceptability go deep enough, then the attempts of Hempel and of Cohen and Nagel to soften the blow will fail and then Wilson's original rejoinder may be made to work. So, let us look more closely and critically at these attempts. Against Hempel's attempt, one can argue that psychological reactions of surprise have no bearing on a logical question like what the status of scientific inference is. Suppose the psychology of human beings were to change radically tomorrow, so that, from then on, one-step arguments surprised us. This wouldn't turn sophisticated, multi-step arguments in mathematics and physics into viciously circular arguments, and it wouldn't turn stupid arguments in television commercials into virtuous arguments. Similarly, if human beings were to become emotionless, so that surprise no longer existed, this would not put all arguments on a par. Against Cohen and Nagel's attempt, one can reply that a bad situation does not improve when it becomes so widespread as to be inescapable. The epidemic spread of a deadly virus from one locale to the entire globe is hardly an improvement. The natural response to these replies is to say that circularity is a matter of degree, with minimal arguments like analytic entailments being maximally circular and others decreasing in circularity as they increase in number of steps. But there are difficulties with such a suggestion. In the first place, it would be necessary to relativize the choice of a comparative concept of circularity to a particular formal system, since, given a free choice among formal systems, any valid conclusion can be made out to be one step away from its premiss(es). It is not clear that there is a way of making the choice which does not leave quite a number of relevantly different formal systems. Second, number of steps is a highly dubious measure of deductive circularity, since, for example, an argument such as p to p 8 c p 8 c p 8 c p 8 c p 8c p 8c p&p&p&p&p&p&p&p&p&p&p&p&p&p&p&p&p&p&

p £ p Sc p & p is more circular than a subtle argument of a few steps,

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even though it is longer. Third, a move to go beyond counting steps to some structural measure of circularity undercuts the suggestion. Not that one couldn't work out a notion of degree of circularity in this way, but once structure is introduced as a parameter, the basis for assigning analytic entailments to the very bottom of the scale is sacrificed. For, on pain of begging the question, sense structure must be included in the structural measure, and it is quite plausible to suppose that some analytic entailments will depend on more structural complexity than many logical implications. At least, there is no apparent way for the defender of Hempel or Cohen and Nagel to show that there is a limit to the structural complexity underlying analyticity and that this limit is exceeded by just the logical inferences which are noncircular. Let us take stock. The attempt to make the vicious/virtuous distinction required at this juncture of the argument runs into trouble, and this saves Wilson's defense of Dcscartes's cogito from the original objection. But, unfortunately, Wilson's defense, viz., that Williams's version of the petitio objection "would cut against any valid deductive argument", does not go far enough. Her defense at best provides a reason why philosophers who use the objection ought to have some second thoughts, and perhaps why they ought to have something to say about what makes the petitio charge more serious when levelled against the cogito than it is when levelled against valid deductive arguments generally. But her defense does not explain what those of us who champion the cogito against this objection want to have explained, namely, why the objection does not apply to the cogito or to valid deductive arguments generally. In the remaining pages of this chapter, I will try to provide a full defense of the cogito against the petitio objection. The interpretation of the cogito as an analytic entailment takes us a step toward our goal: it explains why valid deductive arguments generally are not circular, namely, a major class of such arguments are logical inferences and they are ampliative. Thus, the distinction between beams-in-the-house containment and plant-in-the-seed containment explicated in my definition of analytic entailment provides a reason why the petitio objection should not be made against logical inference. But, at the same time, this distinction seems to strengthen the case for saying that the cogito is a petitio prindpii, since analytic entailment falls on the explicative side. However, the distinction by itself does not imply that the cogito is a petitio. A further premiss is necessary: we must, equate explicativily with circularity. One time I

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did just this: I defined a petitio principii as an argument whose conclusion is analytically entailed by its premiss. 1 ' This seemed a plausible account of the fallacy because, on the one hand, the conclusion of an analytic entailment is literally one of the propositions comprising the sense of the premiss, and on the other, such an account automatically exonerates logical arguments from the charge of circularity, thus eliminating the threat of having to say that the entire deductive structure of science is one big circle.18 Thus, it looks as if we have not only produced a form of the petitio objection to the cogito very much like the one Williams has given, but. we have also produced it in a situation where a rejoinder that raises the spectre of all valid deductive arguments being circular is no longer possible. That is, it looks as if it can still be objected that: If 'I think' analytically entails 'I exist', then the proposition expressed by the former contains the proposition expressed by the latter. Then, to know that 'I think' is true and certain, one must already know that 'I exist' is true and certain.

This objection does not go through because the definition of vicious circularity as analytic entailment is unacceptable. What is wrong with the definition is that it makes question-begging exclusively a matter of grammatical structure, whereas the sin in begging the question is that the point at issue in the controversy is taken for granted and it is typically an extra-grammatical matter what point is at issue. Hence, contrary to my definition, a petitio is principally a matter of pragmatics, not grammar. If, for example, the question at issue between a philosopher and a dramatist is whether Plato is a more profound thinker than George Bernard Shaw, then the question is begged if the philosopher justifies his or her support for Plato by saying that the opinion of anyone who denies that Plato is the more profound thinker can be ipso facto disqualified. But, on the other hand, if the question is not this one, there need be no fallacy in claiming that Plato is a more profound thinker than Shaw and any contrary opinion can be ipso facto disqualified. The definition of the petitio principii as an analytic entailment misses the essential relativization of question-begging to the question at issue. Once this definition is rejected, there is no longer grounds for arguing that the cogito is a petitio principii just because it is an analytic entailment. The topic of whether the cogito begs the question must be examined anew, this lime with respect to an initial determination of what question is al issue in the context where the cogito arises. What is

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taken for granted in the context where Descartes puts forth the cogito, and what has to be argued for? What is taken for granted in that context is the indubitability of the cogitatio and what has to be argued for there is the indubitability of the existo.19 It follows, therefore that the question at issue is this: Do we show that the existo gains the indubitability of the cogitatio by virtue of showing that the existo is analytically entailed by the cogitatio'? The petitio objection must, accordingly, be an objection to Descartes's affirmative answer to this question. The objection must be that he has taken for granted what he is supposed to be arguing for, since, in knowing that the cogitatio is true and certain, he already knows that the existo is true and certain. One consideration that could encourage one to think that this objection will apply if the cogito is an analytic entailment is the following: if Descartes's affirmative answer to the question is to be satisfactory, there must be some gain for him in drawing the existo conclusion, but there can be no gain for him, no extension of his initial knowledge, if his use of language is merely trifling with words. Locke's unfortunate characterization of analytic consequence is, to be sure, to some extent responsible for raising this consideration. But he also made a suggestion which undermines this characterization and provides a clue to the significant uses of analytic entailments that enable us to finally rebut the petitio objection. Locke suggests that the use of analyticity is not trifling with words where a man goes to explain his terms to one who is supposed or declares himself not to understand him.20 Now the cases Locke has in mind here are narrowly didactic. They are examples of helping a foreigner overcome a lexical gap, teaching a child new words, or supplying someone with the definition of an esoteric word. But there are significant cases. These are failures on the part of mature native speakers to understand the subtle meaning of a philosophically interesting familiar word. The nontrifling uses of analyticity that are relevant here are, then, the uses involved in meaning explications like Socrates's elenchos or G.E. Moore's analyses. The obstacle to overcome in these attempts to supply understanding is not lack of full fluency with the language, but a grammatical opacity that accompanies fluency. Thus, one could say that, because of such grammatical opacity, Descartes might know the cogitatio is true and certain without at the same time knowing that the existo is true arid certain, particularly when the certainty must be strong enough to withstand the best

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efforts of an omnipotent deceiving god. Indeed, prior to his reflection on his thinking, Descartes asks himself what he can still think true in the face of such a deceiver, and he first answers "perhaps nothing." 21 Then he realizes that he can say at least that he knows he is thinking, since, on his conception of thinking, the supposition that his omnipotent opponent has brought it about that the things he has believed in are "merely inventions of my mind" is a supposition that he is thinking. 22 This knowledge of thought is, as yet, knowledge of the occurrence of thought only, not knowledge of existence. For the moment, the knowledge might be Lichtenbergian. Knowledge of existence thus comes only with the inference to the existo: the transparency of Descartes's cognitive activity prior to and at the very point of the inference does not present him with indubitable knowledge of his existence. But, then again, the petitio objection claims that this cognitive activity presents Descartes with precisely this knowledge. The objection runs as follows: Descartes knows the cogitatio prior to the inference, and since the existo is analytically entailed by the cogitatio, the existo is one of the propositions that comprise the cogitatio; hence, Descartes must know the existo prior to the inference, too, and there is no extension of his initial knowledge. It is true that, in some sense, Descartes must know the existo prior to the inference, but, in order for there to be no extension of his initial knowledge, this must be the same sense in which he knows the existo subsequent to the inference. But there is a perfectly natural construal of the situation on which these senses are different: Descartes's knowledge of his existence prior to the inference is tacit knowledge, while in virtue of the inference he gains explicit knowledge of his existence (from his explicit knowledge of his thinking). On this construal, the petitio objection equivocates on the term "knowledge". The objection collapses the sense in which Descartes lacks knowledge of his existence prior to the inference and undertakes the inference to gain it, i.e., explicit knowledge, with the sense in which Descartes has knowledge of his existence prior to the inference and needs no inference, i.e., tacit knowledge. The sense in which Descartes knows he exists just in virtue of knowing that he is thinking is the sense in which speakers of a language who are ignorant of linguistics know the syntactic rules of their language. In this sense, speakers of English know the rule that a direct object agrees with its subject in number, gender, and case, even though they have no conscious awareness of the rule they

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know. But in spite of this knowledge being unconscious, its existence can be demonstrated in the ability of speakers to make grammaticality distinctions, e.g., between well-formed constructions like "He likes himself" and ill-formed constructions like "You like herself".23 Further, the sense in which Descartes knows he exists in virtue of making the inference is the explicit sense in which grammarians know the rule that a direct object agrees with its subject in number, gender, and case. In this sense, the knowers are aware of what they know: they have a reason for thinking the proposition true and recognize that it is a reason for thinking the proposition true. Given this distinction between the explicit and tacit senses of "know", the full answer to the petitio objection to the cogito is as follows: prior to drawing the inference, Descartes does not know explicitly that the existo is true and certain, though he explicitly knows that the cogitatio is true and certain and also tacitly knows that the existo is true and certain. So, he must carry out the cogito inference to arrive at explicit knowledge that the existo is true and certain. Hence, the cogito does not beg the question, for the question was how he could establish indubitable explicit knowledge of the existo in the face of an omnipotent deceiving god. This the cogito does by enabling him to consciously recognize that the indubitability of the existo is part of the indubitability of the cogitatio. One further thing remains to be explained in showing why the cogito is needed, namely, what it is that prevents Descartes from having explicit knowledge of his existence when he has explicit knowledge of his thinking. But if there is one thing that a semantic theory of the kind introduced in chapter VI is in a good position to explain, it is what blocks such explicit prior knowledge of the existo. For the principal feature of this theory is its claim that natural languages have a decompositional semantic structure, that is, that the syntactic simples of a natural language are semantically complex. Therefore, on such a semantic theory, there are two ways for syntactic structure to conceal logical form. There is the familiar case in which surface syntactic structure conceals aspects of logical form revealed in deep syntactic structure, but there is also the case in which both surface and deep syntactic structure conceal aspects of logical form revealed in sense structure. In this latter case, logical form is not concealed by syntactic relations but by syntactic simples: complex senses at the semantic level are mapped onto syntactically simple lexical items at the deep syntactic level. What blocks Descartes from having explicit knowledge of his existence while knowing ex-

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plicitly that he is thinking is, then, this masking of semantic complexity at the syntactic level. The syntactic simplicity of the verb in sentences like "I think", "cogitatio", and "je pense" masks the existo proposition in their sense. Since the existo proposition is not transparent on cursory inspection, it must be revealed by an intuition of analytic entailment. The absence of explicit knowledge of the existo prior to a clear and distinct intuition of analytic entailment is explained as another instance of how grammatical form disguises logical form.

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The Nature of Analysis

My defense of my analytic entailment treatment of the cogito against the petitio principii criticism exploited the fact that there are nontrifling, philosophically significant cases of what Locke called trifling propositions. As a source of such cases, I cited Socrates's elenchos and Moore's analyses. The assimilation of Descartcs's cogito to such cases, together with my account of the cogito as an analytic entailment, imply that many such philosophically famous explications of meaning involve analysis of the same sort as the more mundane explications used to illustrate decompositional semantics. This implication needs supporting argument, and the present chapter will supply it for Moore's paradigm cases of analysis. Although Moore carried out his analyses informally and without the aid of linguistics, his method of separating senses into their components, his conception of the objects to which the analytic method applies, and his notion of the aims of such applications are essentially the same as those in decompositional semantics. There are a couple of secondary reasons for this chapter. First, it provides a needed revision of Locke's account of analyticity on the one point where it is in error, viz., its narrow conception of the use of trifling propositions. Second, it responds to the easily foreseeable objection that the use of ideas and apparatus from linguistics to explain a philosophical topic like the cogito cannot provide bona fide philosophical understanding. I anticipate suspicion on the part of some philosophers that no foreign model of explanation can provide the genuine philosophical clarification that we are accustomed to from domestic models. But if it can be shown that the ideas and apparatus imported from contemporary linguistics arc simply an improved version of one of the best domestic models, such suspicion ought to disappear.

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Some philosophers will take the assimilation of Moore's conception of analysis to decompositional semantics as raising questions about decompositional semantics. There are two principal criticisms of Moore's conception of analysis prevalent in twentieth century philosophy. One is the so-called "paradox of analysis" that C.H. Langford raised concerning Moore's conception of analysis. 1 The other is Wittgenstein's criticism of analysis in the Philosophical Investigations (beginning with section 46 and running through section 63). I will try to show that when analysis is formulated as decompositional semantic analysis both criticisms can be convincingly answered. Part of my claim that Moore's analysis is essentially decompositional semantic analysis is that some philosophical reasoning is of a piece with certain varieties of grammatical reasoning. I have already given evidence for this in providing grammatical arguments against Lichtenberg's criticism of the cogito. The fact that these arguments mesh so directly with his philosophical reasoning shows that the linguist's arguments, on the one side of the issue, and the philosopher's arguments, on the other, are about the same grammatical structures, entertain the same range of hypotheses about their nature, and reason in the same way from judgments about the structures to confirm or disconfirm hypotheses. The linguist's arguments are, of course, aided by a grammatical theory, whereas the philosopher's derives principally from intuitions of sentential structure. But grammatical theories themselves are the product of just such linguistic intuitions as the philosopher is able to use in virtue of being a fluent speaker of the language. The only difference between the linguist's reasoning and the philosopher's is the trivial one that the former's tends to be more rigorous and systematic because it is part of an effort to construct a scientific theory of the language. The linguist is forced to formulate explicit principles relating initially isolated facts about sentence structure and to bring them together into a theory. At this point, 1 foresee an objection to my line of argument that should be dealt with before I turn to Moore's conception of analysis. It might be claimed that such relations between linguistic and philosophical reasoning show riot that there is a common form of explication in both fields, but that what we thought was philosophical turns out to be linguistic. Thus, assimilating Moore's conception of analysis to decompositional semantics only shows that the former was riot a bona fide domestic model of explanation in the first place. This objection is prima facie not very plausible, for it is pretty farfetched to

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claim that Moore was not really doing philosophy. But this objection might be backed up with the argument that since linguistic explanation is empirical explanation and philosophical explanation is a priori, if Moore's analysis is shown to give a form of linguistic understanding, then it does not give philosophical understanding. As Moore himself might say, the common-sense judgment that analysis, when successful, gives philosophical understanding is considerably more secure than the soundness of this argument. Be that as it may, the argument's premiss that linguistic: explanation is empirical is now quite controversial: the claim that linguistics is a branch of the empirical study of the mind or of behavioral science has been criticized as a contemporary form of psychologism.2 The criticism is that the claim that linguistics is empirical confuses the study of the grammatical structure of sentences with the study of the form in which knowledge of such structure is realized in the human mind, brain, or behavior—in just the way that the claim that logic is empirical confuses the study of logical structure with the study of the form in which knowledge of such structure is realized in the human mind, brain, or behavior. Moore did not spend time speculating on the nature of the analyses he came up with in doing philosophy. The principal source for his metaphilosophy is his response to Langford's request for clarification of the nature of his analyses.' Langford's request seems to have caught Moore off-guard, and Moore can offer no account of their nature. Instead, Moore lays down a number of conditions on analyses in his sense, which he characterizes as "plain facts" that "one must hold on to."4 The first condition is that the analysandum and the analysans be concepts. This condition appears in our theory of decompositional semantics in the identification of concepts as Moore understands them with senses/' The second condition is that the expressions for the analysandum and the analysans be different. This is Moore's attempt to rule out completely trivial analyses like those he illustrates by "To be a brother is the same thing as to be a brother". But this attempt does not go far enough, since difference of expression does not rule out uninformative analyses in which the analysandum and analysans are synonymous words like "money" and "dough". Moore's third condition, viz., that "the expression used for the analysans must explicitly mention concepts which are not explicitly mentioned by the expression used for the analysandum" ,b goes farther than the second, but still not far enough to guarantee a full analysis.

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We can reconstruct both of these conditions in a way that remedies their shortcomings. We reconstruct "explicit mentioning" as the correspondence between the compositional semantic structure of "the expression used for the analysans" and the decompositional semantic structure of "the expression used for the analysandum": the former expression explicitly mentions cjust in case the sense of one syntactic constituent of the expression is the concept c and c is a component sense in the sense structure of the latter expression. Accordingly, partial analysis takes place when one provides an analytic sentence in which the subject expresses the analysandum and the predicate explicitly mentions some but not all of the concepts in the sense of the subject. A full analysis takes place when one provides an analytic sentence in which there is a distinct syntactic constituent in the predicate for each distinct concept in the sense of the subject, and each of these concepts is explicitly mentioned by one of these syntactic constituents. This approach captures the spirit of Moore's, since he thought of analyses as complete explications of meaning, i.e., as having an expression for the analysans which is synonymous with the expression for the analysandum. The conception of analysis that comes out of decompositional semantics is more general than Moore's. It encompasses riot only analyses of the kind Moore envisioned, i.e., natural language paraphrase, but also the kind found in theories of grammatical structure, i.e., formal representation of a natural language in a theory. Semantic marker representations of sense structure are thus one kind of analysis. The fact that such representations count as analysis makes it possible to satisfy the fourth of Moore's conditions, too, viz., that the method of combination [the way in which the concepts comprising the analysans are combined in this concept] should be explicitly mentioned by the expression used for the analysans is, I think, also a necessary condition for the giving of an ana!

The purpose of introducing semantic marker notation was precisely to expose the structure of complex concepts, i.e., to exhibit such structure as deriving from compositional combination at the level of syntactically complex constructions and from decompositional combination at the level of syntactic simples. Formal representation is needed because natural languages lack the explicitness that Moore himself demands. Even at the hands of a G.E. Moore, natural language paraphrase cannot be relied on to avoid all ambiguity, vagueness, and misleading implication. On the

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basis of such paraphrase alone, it would never be clear how one is to precisely determine the conceptual structure of the analysandum from the expression conveying the analysans. Aspects of the surface grammar of the expression are bound to be misleading, insufficient, or unclear in one or another instance. Without a theory of grammatical structure relating surface to deep grammar, we have no good idea when to take surface grammar at face value and how to get at underlying grammatical structure that is inferentially reliable. The aforementioned differences notwithstanding, what makes it clear that my conception of analysis is essentially the same as Moore's is that both take meaning in natural language to be the subject of analysis, and both understand meaning in the Cartesian and Lockcan sense, where sameness of meaning is a significantly narrower relation than necessary equivalence. Moore writes, For a full discussion of [the term "analysis"] it would be necessary to raise the question why I ask that the concept "x is a male sibling" is identical with the concept "x is a brother," but. refuse to say that the concept "x is a cube with twelve edges" is identical with the concept "x is a cube", although I insist that these latter are "logically equivalent". To raise this question would be to raise the question of how an "analytic" necessary connection is to be distinguished from a "synthetic" one—a subject upon which I am far from clear. It seems to me that there are ever so many different cases of necessary connection . . .8 This statement echoes Descartes's distinction between truths known through intuition and those known through deduction. It also recalls Locke's contrast between "the truth of two sorts of propositions [that we can know] with perfect certainty", viz., "trifling propositions which have a certainty in them, . . . a verbal certainty but not instructive" and those which convey "instructive real knowledge". Moore's example of identity of meaning is a definitional case just like Locke's, and Moore's example of logical equivalence is exactly the same kind of case as Locke's: . . . propositions which affirm something of another, which is a necessary consequence of its precise complex idea, but not contained in it: as that 'the external angle of all triangles is bigger than either of the opposite internal angles'; which relation of the outward angle to either of the opposite internal angles, making no part of the complex idea signified by the name triangle, this is a real truth, and conveys with it instructive real knowledge.9 It is as if Moore is undertaking to revive the Lockean distinction between necessary truths based on conceptual containment and

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other necessary truths within ordinary language philosophy. But, as argued just above, a revival within ordinary language philosophy is limited by the unavailability of theoretically discoverable principles about underlying grammatical structure. Further, a revival within the Carnapian tradition of constructing calculi in accord with the principle of tolerance is not possible.10 The choice of formal linguistics as a framework within which to attempt a revival of the distinction thus seems mandated since it incorporates both scientific canons of discovery and a requirement of faithfulness to the linguistic facts. Thus, my conception of analysis agrees with Moore on the object of analysis, the facts to which analysis must be faithful and the importance of faithfulness to the facts; but it disagrees with Moore in taking semantic representations, rather than paraphrases, as the appropriate form for stating analysans. My conception sees informal description of linguistic facts in ordinary language as useful for various purposes, and perhaps a first approximation to a philosophically optimal formulation of them; but it denies that such description is itself a philosophically optimal formulation. It sees semantic representation going beyond the informal description expressed in paraphrases in the same way that phonetic representation goes beyond the informal description of pronunciation. It chooses semantic representation over paraphrase riot from scientism but because the former promises to be a better means to the same end that Moore put the latter. Other advantages of semantic representation are those of systematization in general. One such advantage is that semantic representation brings with it a methodology for handling cases where the determination of a gramrnitcal property of an expression is unclear, that is, cases where direct intuition does not give us an answer or where intuitions of different speakers give us conflicting answers. The methodology permits us to bring clear intuitions to bear in these cases. We can systematically connect the issue in the unclear cases to certain clear cases, and then reason back from our intuitions in these clear cases. For example, if we are unclear whether the word "chair" can be paraphrased as "seat with a back for one . . .", we have the option of looking beyond the unclear synonymy intuition, to the clear intuition that "chair" and "stool" are antonymous in order to provide evidence for the paraphrase. Such appeals are made possible because the semantic representation of a word fits into an overall system of semantic representations for the vocabulary of the language and must account for all the word's semantic properties and

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relations, i.e., its ambiguities, the analyticities to which it gives rise, the redundancies, its synonymy relations, its antonymy relations, and so on. Moore, with characteristic candor, confesses to being "unclear" about how "analytic necessary connection is to be distinguished from synthetic [necessary connection]". Moore could give no answer to this question because the ordinary practice of paraphrasing does not lead to a theory of grammatical structure that explains semantic properties and relations like analyticity and analytic entailment. The principal advantage of semantic representation is, then, that it makes it possible to construct and justify definitions like (A) and (AE) which distinguish analytic from synthetic necessary connection. Thus, the question Moore left open can be answered as follows: the connection between "x is a male sibling" and "x is a brother" is distinguished from the connection between "x has twelve edges" and "x is a cube" by the fact that, although both connections are necessary, the former rests exclusively on a sense inclusion relation in the language, while the latter rests on something extra-linguistic. Langford backs up his request for Moore to be clearer about analysis by posing the so called "paradox of analysis": . . . if the verbal expression representing the analysandum [what is to be analyzed] has the same meaning as the verbal expression representing the analysans [that which does the analyzing], the analysis states a bare identity and is trivial; but if the two verbal expressions do not have the same meaning, the analysis is incorrect.11

Moore tries to comply with Langford's request, and although he says many helpful things about analysis, he is unable to say enough to actually solve this paradox. Moore says: An obvious suggestion to make is that, if you say, "To be a brother is the same thing as to be a male sibling", you are making a statement both about the concept brother and also about the two verbal expressions used; which would explain why this statement is not the same statement as the statement "To be a brother is the same thing as to be a brother".12 Then he adds, . . .one must suppose that both statements are in some sense about the expressions used as well as about the concept of being a brother. But in what sense they are about the expressions used I cannot see clearly; and therefore I cannot give any clear solution to the puzzle. 13 A solution to this paradox follows directly from the reply we gave to the petitio criticism of the cogito in the last chapter. Like the petitio

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criticism, the paradox assumes that analyses say nothing significant if the verbal expressions for the analysandum and for the analysans are synonymous. But, as we have seen, triviality is not an automatic consequence of two expressions having the same meaning. Correct analyses run the gamut from highly trivial to highly significant cases, depending on how much of the conceptual structure of the analysandum is explicitly mentioned in the verbal expression representing the analysans. At the highly trivial end, there are analyses like Moore's example in which "brother" is used to analyze "brother", or my example in which "dough" is used to analyze "money". Slightly more significant is an analysis of the concept expressed by "brother" in terms of "male sibling". Well into the significant range is an analysis of the concept expressed by "chair" in terms of "piece of furniture with a seat and back that is designed to be or that serves as a place for one to sit". Significance is a function of the degree to which the surface syntax of the expression or sentence conveying the analysans grammatically marks the separate components of the analysandum. The standard cases of analysis are ones where the analysandum is expressed by a syntactic primitive, e.g., "brother", "bachelor", or "chair". In such cases, the greater the extent to which the conceptual structure of the analysandum (concealed by the surface syntax of the expression conveying it) is revealed by the surface syntax of the expression conveying the analysans, the more significant the analysis. The excellence of an analysis is, therefore, a matter of how much of the conceptual detail is hidden from us and how much of it is brought to light. The paradox of analysis dissolves, in spite of the fact that a correct analysis "states a bare identity", because it can be instructive in cases where our knowledge of the structure of the analysandum is incomplete prior to the analysis. This knowledge is completed by the information that can be read off from the surface syntax of the expression conveying the analysans. Saying that the analysans is the very same concept as the analysandum is riot making a trivial identity statement but an informative statement about the conceptual complexity of the analysandum obscured by the syntactic simplicity of its linguistic label. Thus, Locke's claim that trifling propositions are not instructive is misleading, though, of course, he meant that such propositions conveyed no "instructive real knowledge".14 Trifling propositions convey nominal knowledge which is instructive in virtue of the nature of the sentences expressing them. Moore was quite

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insightful to say that the statements in an analysis concern "the expressions (used as well as ... the concept". If I am right, it is clear why the paradox should have defied solution for so long. The principal elements in my solution are these: a syntactic simple can have rich semantic structure, such sense structure is continuous with and reflected in the sense structure of syntactically complex constructions, and accordingly, analyticity in the concept containment sense can be defined in terms of identities between senses and components of senses. Given the neglect of concept containment analyticity since Frege, and particularly as a consequence of Quine's skepticism, it is no surprise that the paradox should have remained unsolved. To some, however, Wittgenstein's criticism of the entire notion of analysis in the Philosophical Investigations refutes that notion once and for all. Wittgenstein begins his criticism with the observation that it makes no sense to speak of something as simple or composite absolutely. Proper use of these concepts requires that the user specify the aspect of the case in question with respect to which he or she intends to make a division into parts. Wittgenstein writes, To the philosophical question: "Is the visual image of this tree composite, and what are its component parts?" the correct answer is: "That depends on what you understand by 'composite'." (And that is of course not an answer but a rejection of the question.) (PI: 47)10

Wittgenstein also observes that almost anything can be a whole or a part, depending on the aspect chosen in relativizing the use of "simple" and "composite" in the case at hand. We do not have absolute concepts of simpleness and compositeness. Rather, We use the word "composite" (and therefore "simple") in an enormous number of different and differently related ways. (PI: 47)

These ways typically provide different divisions into parts, but all the divisions are on the same footing. Each division results from a different choice of an aspect with respect to which division is relativized. Each choice can be recommended as a means of achieving the intended purpose. There is no need to take issue with Wittgenstein here. Absolutism, in the sense he rejects, is not necessary to defend analysis as "digging out" sense structure. A defense requires no more than relativized notions of simpleness and compositeness. Relativized notions do not preclude a privileged relativization with respect to the aim in question: the defender of analysis can make do with a relativization of the

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notions of grammatical simplicity and compositencss to the scientific aim of discovering the truth about the structure of the language. To appreciate why such relativized notions suffice, consider the case of analysis in physics. Everything that Wittgenstein says about the analysis of language can also be said about the analysis of physical substances. Physical analysis cannot employ absolute notions of simplicity and compositeness, either, and for the same logical reasons. But physicists from Democritus to Dalton employed a notion of the components of matter that was relativized to the scientific aim of uncovering the truth about its behavior. As a consequence, what physicists said about the nature of matter on the basis of scientific investigation enjoyed a derivative privileged status with respect to counter claims made on other bases. One couldn't sensibly reply to the Democritean theory, "Matter? Well, it's composed of atoms and molecules, relative to findings based on investigations aiming at the truth, but, of course, it isn't relative to findings based on investigations with other aims." Returning to the case of language, we find the exact parallel. Linguistics is a scientific study of languages. It seeks to analyze the grammatical structure of their sentences. Such analysis is relativized to the scientific aim of discovering the truth about grammatical structure in language. Division in the case of physics is aimed at making it possible to state true laws about the properties of substances; division in the case of linguistics is aimed at making it possible to state true laws about the properties of sentences. Accordingly, the notions of grammatical simpleness and compositeness are relativized, but, as in the case of the study of matter, the relativization is privileged, so that no claims based on other aims can undercut what linguists say about the nature of sentential structure. Thus, as in the case of physics, the only relativity that enters the picture is that which defines the enquiry itself. Hence, all use of the term "relative" drops away, and we can quite sensibly pose "absolute questions", such as "Are the senses of expressions composite?" and "What are the components of the senses?" Decompositional semantic analysis addresses such questions. It divides senses into their components and does so in accord with both the scientific aim of discovering the truth and the scientific method of constructing theories to reveal structure that is not manifest at the surface. It divides a sense into components when further posits of components senses are required to explain semantic properties and relations. For example, the sense of "sister" must be divided into

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components in order to explain the redundancy of "female sister", the antonymy of "brother" and "sister", arid the synonymy of "sisters" and "female children of the same parents". Decompositional semantic analysis claims, in principle, to carry this division to its logical conclusion, thereby revealing the fundamental elements of sense. These would be the terminus of the division process, that is, the point at which the introduction of further divisions would mean a loss of simplicity without a gain in explanatory power, and the removal of a division would mean a gain in simplicity with a loss of explanatory power. In the following passage, Wittgenstein directs his criticism to just such claims to reveal something more fundamental: To say, however, that a sentence . . . is an 'analyzed' form of [another] readily seduces us into thinking that the former is the more fundamental form; that, it alone shows what is meant by the other, and so on. For example, we think: If you have only the unanalyzed form you miss the analysis; but if you know the analyzed form that gives you everything.— But can I not say that an aspect of the matter is lost on you in the latter case as well as in the former? (PI: 63)

Wittgenstein's argument here, as the rhetorical character of the final question of the passage makes clear, is that analysis can make no legitimate claim to superiority because both forms, the unanalyzed as well as the analyzed, miss some aspects of the matter and catch others. To evaluate this argument, we have to ask what Wittgenstein is referring to when he says that "an aspect of the matter is lost on you in the latter case as well as the former." The answer is, of course, that the matter in question is the use of the sentence. He has his interlocutor express high hopes for analysis in the remark, "if you know the analyzed form that gives you everything," since the everything to which he refers is everything about the use of the sentence. Given such hopes for analysis, Wittgenstein is surely right in pointing out that neither form can successfully realize them because any change in the grammar of an unanalyzed form will make a difference in use. Even so, this concession does nothing to undermine analysis in Moore's sense or in the sense of decompositional semantics. These less ambitious forms of analysis make no pretense to account for everything about use. As we saw in Chapter VIII, linguistic meaning is narrower than use. For instance, the English words "urine," "pee," "wee-wee," and "piss" have the same linguistic meaning but not the same use. No doctor would present clinical

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findings to medical colleagues by saying "We found that piss samples . . .", and no tough would snarl at a bartender, "That beer tastes like wee-wee." Moreover, the notion of linguistic meaning can be given without any reference to use. It can be denned as that aspect of the grammatical structure of sentences responsible for their semantic properties and relations, i.e., ambiguity, synonymy, antonymy, redundancy, and so on. Hence, a form of analysis whose pure and simple aim is to explicate linguistic meaning can ignore aspects of use that are determined extra-semantically. Because the form of analysis that both Moore and I have in mind was never intended to explain everything about use, it can have nothing to fear from Wittgenstein's criticism. Consequently, a response to the criticism can be given by defenders of this form of analysis arguing that the things about use left out in analyses are not "lost". It would be wrong for analysis with the modest aim of explicating the linguistic meaning of the unanalyzed form to try to include them. We cannot, for example, explicate the synonymy of "urine" and "pee" if our account of them has to count their differences in use as features of their meaning. We can say, then, that "if you know the analyzed form that gives you everything," for in our case "everything" ranges over only those features which make for sameness and difference of sense. Wittgenstein imagines a language game (a) in which composite things have names and another language game (b) in which only parts have names. He asks, In what sense is an order in the second game an analyzed form of an order in the first? Does the former lie concealed in the latter, and is it now brought out by analysis?—True, the broom is taken to pieces when one separates broomstick and brush; but does it follow that the order to bring the broom also consists of corresponding parts? (PI: 60)

The answers, respectively, are None, No, and No. Wittgenstein is right in each of these rhetorical questions because, relative to the language games (a) and (b), words are names, and names, Wittgenstein saw, are, in effect, labels. If names are just labels for things, what could be concealed if there were just two names for a broom, a simple name for the broom, say, "Sam", and a compound name for the stick and brush, say, "Mary-Joe"? Wittgenstein's criticism was, of course, aimed at Russell's logical atomism and his own Tractatus position, against which they work. But they work against them because these positions actually think of referring expressions as just names. The decompositional semantic theory on which I am basing lin-

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guistic analysis does not take all referring expressions to be names. Rather, it adopts a position like Mill's on which proper nouns but not common nouns are treated as names. It supports this position with arguments different from those Mill uses. The difference stems from the difference in our conceptions of meaning. Conceiving of meaning as the aspect of grammatical structure in sentences on which their semantic properties and relations depend, I must use arguments which concern sense rather than reference. Thus, to establish that common nouns have a sense while proper nouns do not, I must argue that the former have semantic properties and relations which depend upon sense (e.g., unlike the property of being meaningless). For example, one such argument is that the expression "the kings who are monarchs . . ." is redundant but the expression "the Goldsmiths who are goldsmiths . . ." is not redundant. 16 Therefore, there is a form of analysis quite different from the Russellian and early Wittgensteinian form in the essential respect that it does not treat all referring expressions as names. Given, then, that Wittgenstein modelled language games (a) and (b) on the Russellian and early Wittgenstein cases, (a) arid (b) are not appropriate cases to serve as a basis for a general evaluation of analysis. We must thus entertain two further language games (a') and (b') where the words which are candidates for analysis are common nouns and, on the basis of arguments like the one mentioned above, must be taken to have sense. We must reconsider Wittgenstein's three questions in the above quotation with respect to (a') and (b'). If we do this, we see that the first two can be answered in the affirmative. Consider the first question: "In what sense is an order in the second game [now (b') instead of (b)] an analyzed form of an order in the first [now (a') instead of (a)] ?" Answer: In the sense that the analysans expresses explicitly that there are component senses in the analysandum while the surface form of the analysandum gives no indication of their existence. In an analysis of "brother" as "male sibling", sense components which are concealed by the syntactic simplicity of "brother" are revealed in the analysans. The excellence of analysis is, then, a function of the degree to which sense structure is concealed in the analysandum and revealed in the analysans. Thus, the negative answer originally given to the first question was due to nothing more than assuming that the words in (a) and (b) do not have sense. "Does [an order in the second game] lie concealed in [an order in the first], and is it now brought out by analysis?" Yes, just as with the

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analysis of "brother" as "male sibling", we can say that the sense of "Kiss a sibling!" and the sense of "Kiss a male!" lie concealed in the sense of "Kiss a brother!" And, in addition, it seems fine to say that the order issued in a standard use of "Kiss a brother!" includes the orders to kiss a sibling and kiss a male. 1 ' The answer to the third question can be affirmative or negative, but which it is does not turn on anything to do with analysis. Rather, it turns on whether analysis is combined with the principle that language and reality are isomorphic. "True, the broom is taken to pieces when one separates broomstick and brush; but does it follow that the order to bring the broom also consists of corresponding parts?" If the language were constructed on the principle of isomorphism Socrates expresses in the passage from the Theaetetus in section 46, the answer would be affirmative. As long as the pieces are parts of the broom, the principle insures that there are corresponding parts of the sense of the word "broom". Unless the point of the question requires shifting from the proposition to an act of ordering which in principle has no corresponding parts, there is an appropriate question and its proper answer is "yes". But, on the other hand, if the language did not conform to this principle, it would not follow that analysis of the sense of "broom" revealed corresponding parts. But why would an approach committed to faithful description of natural language rather than to prescriptive reconstruction wish to endorse ths principle of isomorphism? My approach to analysis is not in the "subliming" tradition which thinks of a natural language as more perfect to the extent that it conforms to such a principle.18 On my approach, the only criteria of adequacy are the scientific criteria of faithfulness to the semantic facts, simplicity, etc. Departures from the facts of the language to remove what are thought of as imperfections are illegitimate because there is no higher purpose of perfecting the language. Thus, I side with Wittgenstein on the issue of description vs. prescription, and share his sentiment: . . .the word "ideal" is liable to mislead, for it sounds as if these languages were better, more perfect, than our everyday language; and as if it took the logician to show people at last what a correct sentence looked like. (PI: 81)

I agree with Wittgenstein's view that it is clear that every sentence in our language 'is in order as it is'. That is to say, we are not striving after an ideal, as if our ordinary vague sen-

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tences had not yet got a quite unexceptionable sense, and a perfect language awaited construction by us,—On the other hand, it seems clear that where there is sense there must be perfect order.—So there must be perfect order even in the vaguest sentence (PI: 98)

What is in question for me is whether the language is in fact based on this principle. I conclude that it isn't: the parts of the sense of a word do not correspond to the parts of the object to which the word refers. The sense of "trolley-car" does not contain component senses corresponding to the gears, panes of glass, screws, wheels, bushings, hand-straps, etc. of the objects to which "trolley-car" refers. As I see it, the principle is another artifact of the failure to properly distinguish sense from reference. Finally,19 I can also agree with Wittgenstein that someone who says that the broom is in the corner does not mean to speak of the stick or brush in particular (PI: 60). It is just as Wittgenstein says: Suppose that, instead of saying, "Bring me the broom", you said "Bring me the broomstick and the brush which is fitted onto it."!—Isn't the answer: "Do you want the broom? Why do you put it so oddly?"—Is he going to understand the further analyzed sentence better?—This sentence, one might say, achieves the same as the ordinary one, but in a more roundabout way. (PI: 60)

But the truth of these reflections does not count against analysis. If someone asks me to write a note to the candy store asking for sixty seven of the best quality lollipops for the party, and I write "(6 • 10)+ 7" instead of writing "67", the clerk in the candy store is not going to understand my note better than the one I was expected to write and will surely wonder why I put the request so oddly. Nonetheless, the "roundabout way" in which I put it does not count against the analytic representation which I used in my note. In both this case and that of the analytic representation of senses, the fact that there can be misuses or abuses does not call analysis into question. It calls the use of the analysis into question. The analysis itself has a legitimate use: to uncover the truth about sense structure hidden by syntactic structure.20

XI

The Cogito and Indubitability

Along with whatever else il may be, Descartes's project in the Meditations is an attempt to provide foundations for human knowledge so secure that they will withstand any doubt. To provide such foundations, Descartes employed the ingenious device of putting doubt in the service of its own defeat. He created the fiction of a maximally powerful god who bends every effort to make Descartes believe what is false. Whatever beliefs withstand doubt in the face of such a deceiver are absolutely indubitable, and hence, suitable for the foundations for human knowledge. Descartes's argument that his knowledge of his own existence is absolutely indubitable was the first step toward providing such secure foundations. In the present chapter, I want to show that the cogito's being an analytic entailment is essential to its playing this role in Descartes's project. I will try to show that the indubitability of the existo is sacrificed if the cogilo is construed as a logical inference. This will complement my earlier claim that Descartes did not think that the cogito should be construed as a logical inference by showing that he couldn't think it should be so construed and still hope to use it as he does to erect new foundations for human knowledge. I will also try to explain why, construed as an analytic entailment, the cogito's conclusion does possess the requisite indubitability to play the role that Descartes wants it to play in his reconstruction of knowledge. In both cases, I shall have to confine myself to simply stating the reason, for actually establishing these claims goes far beyond the present study. 1 To show that indubitability is sacrificed on a logical coiistrual, let us suppose that Descartes's presentation is enthymematic as the standard conception of inference takes it. We can now ask: Can Descartes's certainty of his existence, arrived at by an application of a law of logic, withstand the efforts of the deceiving god? Descartes

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himself makes it quite clear that he can be deceived into thinking that an eternal truth like 2 + 3 = 5 is untrue. Since such cases always involve the possibility of computational error, it ought to be child's play for so powerful a deceiver to fool Descartes. The function of Bourdin's example, as Frankfurt notes,2 is to show that someone can be deceived even in adding 2 + 3. Now, in the relevant respect, namely, presence of computation, the cases of mathematical and logical reasoning are the same. Hence, in applying logical laws, just as in applying mathematical laws, there is the possibility of a computational slip-up. Even the existence of one single inferential gap presents the possibility of such a slip-up in the application of a law of logic. Since there is such a gap in every logical inference, the omnipotent deceiving god has all the opportunity needed to fool Descartes. The god can confuse Descartes about the proper law to apply at a particular derivational step, confound Descartes in his attempt to apply a law of logic properly, delude him into thinking that a proper application is improper or an improper one proper, etc. If the cogito were a logical inference, as claimed in the enthymematic reading, the game would be up for Descartes right at the very outset. On the other hand, if the cogito is an analytic entailment, the omnipotent deceiving god cannot trick Descartes in these ways because there is no inferential gap, and hence, no computation. There is, then, no foothold for even so "consummately powerful and crafty [a] deceiver." The point may be illustrated by considering the story of another infamous deceiver, namely, the Tortoise in Lewis Carroll's fable, "What the Tortoise Said to Achilles."1 Achilles, as we recall, is accosted by the Tortoise while trying to justify his inference to Z by arguing that if A and B are accepted as (A) Things equal to the same are equal to each other (B) The two sides of this triangle are things equal to the same (Z) The two sides of this triangle are equal to each other true, Z must be accepted as true. The Tortoise is agreeable to premisses A and B, and also the logical principles that Achilles invokes, providing their credentials have already been accepted. The Tortoise refuses to accept steps of an argument justified by principles whose credentials have not first been accepted. When Achilles initially tries to infer Z from A and B, the Tortoise challenges him and explains the ground rules by which Achilles's

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attempt to meet the challenge will be evaluated. Absorbing the explanation, Achilles says, "I'm to force you to accept Z, am I?" Achilles said musingly. "And your present position is that you accept A and B, but you don't accept the Hypothetical—" "Let's call it C", said the Tortoise. "—but you don't accept: (C) If A and B are true, Z must be true "That is my present position," said the Tortoise. "Then I must ask you to accept C." "I'll do so," said the Tortoise, "as soon as you've entered it in that note-book oi yours."

Then, while the Tortoise is dictating the propositions A, B, C, and Z for Achilles to copy into his notebook, Achilles objects "You should call it D, not Z," . . . "It comes next to the other three. If you accept A and B and C, you must accept Z." "And why must I?" "Because it follows logically from them. If A and B and C are true, Z must be true. You don't dispute that, I imagine?" "If A and B and C are true, Z must be true", the Tortoise thoughtfully repeated. "That's another hypothetical, isn't it? And if I failed to see its truth, I might accept A and B and C, and still not accept Z, mightn't I?" "You might," the candid hero admitted; "though such obtuseness would certainly be phenomenal. Still, the event is possible. So I must ask you to grant one more hypothetical." "Very good. I'm quite willing to grant it, as soon as you've written it down."3

Achilles writes it down and the debacle continues, and will continue as long as Achilles accepts the rules of the game. At each play of the game, Achilles will encounter a new inferential gap that has to be bridged by a new principle of inference to sanction the conclusion; but each new principle of inference will not have been written down in the notebook and hence, will not sanction the conclusion. Thus, the Tortoise can always challenge the inference, force Achilles to write the new principle down, and thereby change the inference to a new one containing a new gap requiring a new further principle to bridge it. Lewis Carroll's Achilles is a poor soul who doesn't realize that he is playing with the deck stacked against him. But with one change in the fable, we can cast Achilles in a role more appropriate to his

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legendary glory, and at the same time show why an analytic entailment interpretation of the cogito justifies the certainty of its conclusion. Change the inference in the fable from a logical implication to an analytic entailment. Now the slayer of Hector becomes the slayer of the Tortoise: the Tortoise accosts Achilles in the process of justifying the inference from A' to Z' with the same challenge from (A') Descartes had a nightmare (Z') Descartes had a dream Lewis Carroll's fable, but now Achilles replies "I'm to force you to accept Z', am I? And your present position is that you accept A', so that I may write A' down in my note-book?" "Yes," replied the Tortoise. "In that case, force will be unnecessary. For having written down A', Z' is written down, too. Before, when you asked me what else I had written down in my note-book, I was in the embarrassing position of having nothing else but memoranda of the battles in which I distinguished myself, but now I can say that I also have Z' written down. Surely, you won't balk at the fact that A' and Z' are written in markerese—which won't be invented for some two thousand years."

Achilles's triumph over the Tortoise is Descartes's triumph over the omnipotent deceiving god. The triumph results from the fact that, since there is no inferential gap to be bridged by a law of logic, there is no opportunity for Achilles to be frustrated or for Descartes to be deceived. In both cases, the analytic entailment affords the Tortoise and the deceiving god no chance to undermine the agent's confidence in his inference because the conclusion of an analytic entailment requires no justification beyond that for the premiss. But does the absence of computation insure that the omnipotent deceiving god has no opportunity to tamper with the justification? Couldn't the deceiving god still get Descartes by, say, confusing him about the true situation so that he thinks there is an inferential gap?6 From the viewpoint of Descartes's epistemological inquiry, isn't the issue whether Descartes thinks there is a gap, not whether there is one? If so, why couldn't he be fooled on this score? An omnipotent god could, of course, zap poor Descartes so that he entertains no beliefs, or confuses the truth conditions of the beliefs he was entertaining with other truth conditions, or is made to believe on command. But a god who used omnipotence in such ways would no more defeat Descartes at the deception game than someone who drugged or hypnotized chess opponents into making fatal blunders

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would beat them at chess. Winning in either deception or chess presupposes that one's opponent understands the rules, is able to apply them on the basis of his or her understanding, and makes his or her own moves. If the god tinkered with Descartes's grasp of the truth conditions of the propositions he was entertaining, so that Descartes thought there was an inferential gap to be bridged in the case of the cogito, the god would have succeeded in fooling Descartes, but fooling him in this way would not win the deception game. Therefore, when Descartes plays the deception game as he does, the omnipotent god must lose to him, for Descartes has indubitable knowledge of his thinking and he puts forth the existo on the grounds that it is analytically entailed by the cogitatio. Assuming the game is being played on the up-and-up, there would be no place for the god to begin to undercut Descartes's justification. Descartes cannot be somehow misled into thinking that he does not exist when entertaining the proposition that he is thinking because his intuition provides the understanding of the semantic structure of the proposition. For this understanding penetrates deeply enough into the conceptual structure of the proposition to see that one of the component propositions asserts that he, the agent of the activity of thinking in question, exists, and that, as a component of the premiss, the proposition shares the grounding that makes the premiss true and certain. Descartes must thus be credited with indubitable knowledge of his existence, just as Achilles must be credited with being able to see that, in the writing down of A' in the note-book, both A' and Z' are written down. Because Descartes can judge that he exists on the basis of his comprehension of the cogitatio, the game is over before the omnipotent deceiving god makes a move. In the Discourse, Descartes says, . . . I noticed that, while trying to think that everything was false, it was necessary that I, who was thinking this, should be something. And observing that this truth: / am thinking, therefore I exist was so firm and secure that all the most extravagant suppositions of the skeptics were not capable of overthrowing it, I judged that I should not scruple to accept it as the first principle of the philosophy I was seeking.'

I think this passage contains a remarkable insight into the nature of the special firmness and security of the cogito, and I would like to show this, even though I cannot give a full explanation of the insight here.8 The specialness becomes quite clear when we note that, whereas "extravagant suppositions" are capable of overthrowing other necessary truths (in the context of the supposition), "all

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the most extravagant suppositions of the skeptics were not capable of overthrowing [the cogito]". For example, we can overthrow logical and mathematical truths in the context of a supposition initiating a reductio proof; or, we can entertain the falsehood of such necessary truths in the context of a philosophical investigation (like Aristotle's) into the foundations of logical law; or, we can entertain their falsehood in considering possible ways out of a paradox. Philosophers and logicians have considered the falsehood of excluded middle in connection with Brouwer's constructivism, the falsehood of contraposition in connection with the Raven paradox, and the falsehood of modus ponens in connection with the paradox of the heap. Such contra-logical and contra-mathematical suppositions exist. The sentences expressing them are meaningful. In contrast, contra-semantic supposition does not exist. No meaningful sentence on the language expresses a semantic parallel to the contra-logical and contra-mathematical propositions expressed by sentences stating contra-logical and contra-mathematical suppositions. The reason is that the sense of such a sentence would rest on the very semantic relations that it would suppose not to obtain. Thus, the special security and firmness of the cogito and other analytic entailments and analytic truths derives from the fact that supposing them to be false would undercut the semantic relations on which the meaningfulness of the supposition itself depends. In the cases of contra-logical and contra-mathematical supposition, the relations that are undercut are extra-linguistic, and hence, not among those on which the meaningfulness of the supposition depends. Thus, an analytic proposition, such as the one expressed by "Bachelors are unmarried", is secured against falsehood even on supposition where logical and mathematical truths are false. No matter how extravagant the supposition of a skeptic, the fact of supposition guarantees that the analytical proposition is not false. Supposition must respect the semantic relations that make the analytic proposition true because these relations are the very ones on which the supposition itself rests.9 This, of course, is not to say that we cannot suppose bachelors to be married or that the sentence "Bachelors are unmarried" is false. The former is merely supposing that, contrary to fact, the men who never married did marry. This is a de re supposition about a class of people. The latter is merely supposing that the sentence/sense correlation in Modern English works differently from the way it does, in particular, that the sentence "Bachelors are unmarried" expresses

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some other sense than the one it does, say, the proposition that philosophers are paid better than lawyers. Neither of these cases, however, is supposing the falsehood of the proposition that bachelors are unmarried. Thus, the supersecurity of analytic: propositions and the vulnerability of logical and mathematical propositions to "extravagant suppositions" is due to the fact that the truth of the latter but not the former depends on extra-linguistic matters which can be the focus of the supposition and thereby allow the meaning relations on which its intelligibility rests to remain intact. Supposing the falsehood of the proposition expressed by "The square root of two is not a rational number" is possible because the supposition concerns an extra-linguistic fact about numbers. An ideal lexicographer can be a mathematical ignoramus, and hence, consistent with all lexicographical knowledge, think the fact about numbers other than it is. But in the case of analytic propositions, there is no extra-linguistic element. Since the truth of the proposition depends on meaning alone, there is nothing that can be denied in non-suicidal supposition. This secures analyticity against suppositional falsehood.10 Hence, Descartes was right in saying that the cogito is "so firm and secure that all the most extravagant suppositions of the skeptics were not capable of overthrowing it" because the cogito is an analytic entailment and, as such, its validity rests on relations that must be held fixed in supposition. What Descartes says about the cogito and the way in which he says it strongly suggest that he realizes in some sense the supersecurity of the inference is clue to the fact that supposition itself is undercut when one tries to entertain contra-semantic facts like thinking without a thinker, doubting without a doubter, or deception without a deceivee. This, it seems, is why Descartes believes that attempts to suppose them fail. 11 I do riot want to claim that Descartes sees things in the explicitly linguistic way that I do, for he surely doesn't. Nor do I want to claim that he has a sharp language/theory distinction in mind. It goes without saying that he has no inkling of the intensional semantics or the model theory that underlies the claim that such a distinction exists, f cannot even claim to know what exactly he had in mind in saying that the cogito is "so firm and secure that all the most extravagant suppositions of the skeptics were not capable of overthrowing it." But I think that he must have had enough of a glimpse of the considerations set out above to give him grounds for taking the cogito to be the kind of argument he took it to be and for taking its conclusion to have the kind of indubitability he took it to have.

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My own view of skepticism is close to Descartes's in that both hold that the relations on which the cogito rests are essential to supposition, so that any supposition the skeptic can construct will respect them. But Descartes does not see these relations in the semantic way in which I do, and as a consequence, his treatment of the philosophical issues arising in connection with skepticism are different from what would be reasonable on the basis of this book. As I see it, skepticism arises at precisely the point where we cross the line from language to theory. When we enter logic, mathematics, or some other theoretical domain, we must rest our statements on the facts in the domain. Since such facts do not have to be held fixed in supposition, the skeptic can construct suppositions in which they are otherwise than they are and ask us how we know such suppositions are untrue. Once we cross from the realm of language to that of theory, we have to face such questions. We have to accept the omnipresence of skepticism since suppositions raising skeptical doubts about even the best of our theoretical beliefs can always be entertained. Skepticism is the permanent possibility oj suppositional doubt in the realm oj theory. I am not claiming that skepticism is omnipotent, only omnipresent. It may be that the skeptic can be defeated, it may be that the skeptic can't. I take no stand on this. But it seems to me that failure to appreciate the nature of skepticism in relation to supposition, language, and theory has been partly responsible for the failure of some of the best known attempts to refute the skeptic. 1 cannot actually prove this claim here, but I can suggest how the one failure is linked to the other. Descartes tried to use the indubitable knowledge of his existence to prove the foundations for a wholesale reconstruction of knowledge that would establish matters of theory, both in metaphysics and theology, with the same certainty as he had established the matter of his existence. Later philosophers who have taken his starling point and embarked on his quest for certainty (for example, Husserl) have, like Descartes himself, failed to achieve the desired reconstruction. I think the basic problem is that the starting point, the security from suppositional doubts provided by language, does not give broad enough support for so ambitious a reconstruction. The defeat of the skeptic looks easy at the starting point, but the source of the skeptic's weakness at the starting point is the source of the skeptic's strength beyond it. The philosopher who fails to appreciate the nature of skepticism underestimates what is in store when the skeptic is

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faced outside the area of language. For if I am correct in drawing the language/theory distinction to coincide with the analytic—synthetic distinction, the area of language contains no suppositional doubt but also no synthetic truths about extra-semantic matters while the area of theory contains suppositional doubt for any synthetic truth and no linguistic means to defeat it.

XII

On the Existence of a Thinker

The last chapter leaves unclear exactly what is established in the cogito and how far it takes us philosophically. Since Kant's famous discussion of the cogito, philosophers have recognized that there is a metaphysical issue about the scope of Descartes's conclusion. The present chapter makes no pretense of examining this issue in any depth. Rather, it attempts to look at some contemporary thinking on the subject and to suggest a plausible resolution of the issue in light of the overall discussion in this book. Recently, Bernard Williams has argued that the exislo is so limited that it cannot even serve as a basis of the Cartesian reconstruction of knowledge. Williams claims to have put his finger on a fundamental flaw in Descartes's argument, which he refers to at one point as Descartes's "deepest error" and at another as Descartes's "basic error."1 The error is a kind of fallacy. There is nothing in the pure Cartesian reflection to give us [a thirdperson perspective]. The Cartesian reflection merely presents, or rather invites us into, the perspective of consciousness. Descartes thinks that he can proceed from that to the existence of what is, from the thirdpersonel perspective, a substantial fact, the existence of a thinker. 2

The error, if there is one, is not the simple fallacy of making an illicit leap from the cogitatio to the existence of a thinker. The inference from "1 (he, Jones, she, etc.) am thinking" to "A thinker exists" is a special case of analytic entailment. The analytic entailment obtains just in virtue of "think" being an activity verb, and hence, the inference turns on the same semantic fact as the inferences from "I am chasing (killing, etc.)" to "A chaser (killer, etc.) exists" do, namely, that the concept of an activity specifies the existence of its agent. But, although the existence of a thinker follows from the cogilatio, the derivation falls short of an answer to Williams's criticism. The

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derivation per se leaves open the question of substantiality. Substantiality is a fact about the agent, and as we have seen, nothing about the way in which the agent is characterized in the premiss plays a role in the inferential connection. As yet, there is no explanation of the sense in which the cogito might provide us with a "substantial fact" from the third-person perspective. Beyond the semantic fact on which the inference turns, there are other aspects of the cogito that contribute to the assertion its conclusion makes, viz., what exists and when, and where it exists. For example, there are valid inferences such as that from "A cop is chasing a robber in Boston" to "A chaser exists in Boston". It also seems plausible to say that the premiss and conclusion of the inference from "A cop is chasing a robber" to "A chaser exists" involve an indefinite location: the premiss says that a cop is chasing a robber somewhere and the latter, that a chaser exists somewhere. There is a question of whether such inferences are found in the case of psychological verbs, i.e., whether such verbs take qualifications of place. What does it mean to say "I was thinking it in Boston" or "I doubted it in Oslo"? Does it mean simply that I was physically in that place at the time the mental activity took place? Perhaps, but since it is dubious whether these location attributions work to specify the location of the activity itself, like location attributions in the case of physical activities do, I shall put the question of location aside. In many treatments of the linguistic expression of time relations,'5 the present tense constituent in the premiss of the cogito expresses the occurrence of the thinking over the temporal interval during which the utterance of the sentence takes place. The thinking referred to may overflow this interval, spreading over a portion of past or future, but some temporal stages of the thought process coincide with the initial and terminal points of this interval. There are, of course, interesting and subtle questions that can be raised about this characterization from the philosophical point of view, but the only point I wish to make is that the conclusion of the cogito is bound to the same temporal interval. That is, the conclusion asserts the existence of a thinker for only the period enclosed by the initial and terminal points of this interval. Hence, the guarantee of the existence of a thinker that comes from the truth of the premiss and the validity of the inference extends only for the time specified for the thought process. Given this, there is a form of insubstantiality that derives from the semantic analysis of the cogito we have developed, namely, that, insofar as it is established by the cogito, the thinking

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substance which is Descartes is not established as persisting through time in the sense in which we suppose the self, as the locus of one's thoughts and experiences generally, to. This point is a semantic version of one aspect of Kant's Cartesian paralogism. 4 Let us concede the others, too. Not only does the cogito not establish that the thinker exists beyond the limits of the period of the specific thought process referred to in the premiss, but the cogito does not establish that the thinker is the same thinker that thinks other thoughts or that the thinker is a self-subsistent substance. Given these limitations, the cogito, although it still stands as a good argument, is not as wide-ranging or philosophically promising as Descartes thought. Nonetheless, we cannot conclude that the cogito is as limited and philosophically unpromising as Williams thinks. Williams encourages us to suppose that his argument here is "only a development of Kant's in the Paralogisms of Pure Reason."'' Williams says further that starting solely from the point of view of consciousness, one cannot gain any objective conception of there being several such selves—nor, consequently, can one gain an objective conception of there being even one. b If gaining an objective conception of one self means establishing that it persists through time as the locus of other thoughts, whether or not this can be established from the point of view of consciousness, it cannot be established just by the cogito. However, these Kantian concessions leave open an important question about substantiality, namely, why doesn't the cogito at least establish the substantiality of the thinker at the moment of thought, as it were, an objective conception of one temporal slice of the metaphysical self? Such a conception, although narrow and constricted in philosophical promise by comparison with Descartes's concept of the ego, would still provide a jumping-off point for transcendental arguments to a fullblooded conception of the metaphysical self. One could argue that the semantics of the first person pronoun by itself, or in interaction with the selection restrictions on the agent argument place, determines such a conception of substantial existence within strict temporal limits. Williams, as I read him, is committed to denying even this minimal position, since existence in this sense would be a fact from a third person perspective. Williams does not address this point directly, but he says, . . . sticking solely to the point ol view of consciousness, we are forced back to a position in which there is, in e f f e c t , only one sue!) point of

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view: events either happen for it, or they do not happen, and there is no way of conceiving of such events happening, but happening (so to speak) elsewhere. But this is what . . . Descartes must need.'

But saying this is not enough. He needs an argument for his claim that "there is no way of conceiving of such events . . . happening (so to speak) elsewhere." Before looking to see whether an argument can be found in what Williams later says, let us flesh out the minimal position such an argument would have to meet. This position would claim that "A thinker exists" expresses an objective fact, transcending the metaphysical solipsism that Williams takes to be inevitable if we stick within the point of view of consciousness. The position distinguishes such metaphysical solipsism from epistemological solipsism. The former says that we can have no conception of the real that does not represent it as subjective (i.e., the self is the only existent). The latter says that we can know nothing beyond our own subjective states (i.e., skepticism about the outside world cannot be refuted). This allows that transcending metaphysical solipsism still leaves us with an inevitable epistemological solipsism, which could well be our common philosophical fate if the view of skepticism presented in the last chapter is correct. The minimal position claims that we can transcend metaphysical solipsism because a concept of objectivity can be constructed from within the point of view of consciousness. Thomas Nagel has articulated such a concept: We do not abandon the essential factor of a point of view when we conceive of the minds of others: instead we generalize it, and think of ourselves as one point of view among others. The first stage of objectification of the mental is for each of us to be able to grasp the idea of all human perspectives, including his own, without depriving them of their character as perspectives. It is the analogue for minds of a centerless conception of space for physical objects, in which no point has a privileged position.8

Nagel's point is that, "sticking solely to the point of view of consciousness," we can, nevertheless, form an objective perspective on which our experiences and those of others are viewed from outside any point of view, "as events in the world."9 To me, these reflections seem right, and show Williams is wrong in his criticism of Descartes: the statement that a thinker exists is objective, asserting that there is at least one mind in this centerless space at the time in question. We can now examine Williams's arguments against such a position.

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Williams raises two objections against the cogito that can be marshalled as criticisms of Nagel's "objectification of the mental." First: If there were a class of autonomous items in the world which were the contents of consciousness, then there would have to be a coherent conception of the world from which just those items had been removed, leaving all those other facts as they were. But, if we conceive a world determined just as ours is with regard to all the physical facts, then surely we have already included the facts of a person having pains and thoughts and being in other conscious states. (If not, then indeed it. is obscure why, even as things are, we have any reason to believe in the general occurrence of these things). 10 The first of these conditions may be accepted as true, but not the second. We can describe circumstances under which the antecedent of the second conditional is true and its consequent false. These circumstances are suggested in Descartes's famous hats-and-coats passage in which the world is just as ours is with respect to the physical facts, but contains no facts of conscious experience: So I may by chance look out of a window and notice some men passing in the street, at the sight of whom I do not fail to say that I see men, just as I say that I see wax; and nevertheless what do I see from the window, except hats and cloaks which might cover automata.11 [Italics mine] Williams cannot save his argument by making a physicalist rejoinder, to the effect that all physical facts would include all mental facts. This would beg the question since Williams rightly makes clear that his argument is put forth to support physicalism. 12 Thus, if his argument is to be saved, the rejoinder has to be based on the parenthetical comment at the end of the passage, viz., that if the facts of conscious experience are not already included, we have no reason, as things are, to believe in the general occurrence of conscious experience. I take it that the operative term here is "general", i.e, that Williams is not suggesting that Descartes's world of human-looking automata with "hats and coats" is impossible, or that we, each of us individually, do not have a first-hand reason for believing in the existence of such a thing as conscious experience. His point must be that we wouldn't have a reason for believing in a world populated with conscious persons. As his phrase "indeed it is obscure why" suggests, he does not state his denial outright, but as one horn of a dilemma, whose argument, seems to be this: either one agrees that a world like ours with regard to physical facts includes facts of conscious experience already,

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or else one does not agree and must accept obscurity in one's reasons for believing in a world populated with conscious persons. But the threat of obscurity which is supposed to make one agree with Williams is present on both horns. The obscurity in question can only be that of an unsolved problem of other minds: it is obscure what the grounds are for our ordinary belief that there are people outside the window and not merely automata with "hats and coats." But whether one is a physicalist like Williams or a Cartesian dualist, this problem has to be faced. Unless one is a behaviorist as well as a physicalist, one also has to explain how we justify our inference to the existence of an unobservable entity or state. Of course, for the physicalist, this inference is an inference to the existence of something physical, but this does not change the proportions of the problem. Such somethings are riot just anythings that direct behavior, but have to be precisely the sort of internal directing mechanisms that can be conscious. There is obscurity enough for anyone here. But it is hard to see that Williams has a rejoinder even if the opposition has to accept obscurity in their reasons (for believing in other minds). Just because someone's reasons in connection with a philosophical issue are obscure does not imply that they are wrong on the issue, anymore than having crystal clear reasons means that they are right. The second of Williams's criticisms is a very direct challenge to the Nagel proposal. Nagel generalizes the first-person point of view to obtain the conception of a centerless space in which points are occupied by a res cogitans. Williams seems prepared to admit that such a generalization could abstract away from the agent's own privileged point of view in virtue of the fact that "the contrast between having [a] thought and thinking about someone else's having it ... can vanish" in "the case of episodic thought in words."13 Williams says: [The contrast] totally vanishes where the thought is entirely verbal, and the one who conceives of it has a thought with exactly the same verbal content. In this ultimate case, thinking, speaking, hearing and understanding are entirely homogeneous in their content."

Thus, if facts about the language, particularly semantic facts, are entirely unproblematic, Williams would seem prepared to countenance Nagel's generalization. Continuing his thought from the above quote, Williams says, What this means is that a totally verbal thought-occurrence can he as fully determinate as a public utterance in its intcnsional aspects; and

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that means that it can be fully determinate relative to a shared understanding of the language. If A's thought is just these words, then we can be given the words, and being given them, we shall be given his thought just to the extent that we understand the words. The thought which we then all have will be determinate to the extent that, the meanings we all ascribe to those words are determinate. ls

But Williams thinks that the semantic facts in question are anything but unproblematic. He claims that Quine's indeterminacy thesis shows that the ascription of meanings is indeterminate because, as Williams says, quoting Quine,"' There is "no fact of the matter" in the case of deciding which of two translations is correct. Granting Quine's thesis, Williams concludes that fully determinate meanings of what we and these others say cannot figure in the absolute conception of things, that conception which is neutral between all observers; consequently, fully determinate content for verbal thoughts cannot figure there cither. 17

Williams rests his case with this bare appeal to Quine's indeterminacy thesis. The heart of Quine's thesis, as Williams observes, is the claim that there is no fact of the matter in an alleged scientific choice between conflicting semantic hypotheses. The critical test for this claim comes in showing that there is indeterminacy in semantics rather than mere tmderdetermination of hypotheses by evidence as is common in physics and other sciences. In his discussion of the comparison between semantics and physics in Word and Object, Quine does not present an argument against supposing "that translational synonymy at its worst is no worse off than truth in physics," 18 but merely asserts that there is no fact of the matter in semantics because there are no linguistically neutral meanings. For there to be a fact of the matter, there must be something to which a true semantic hypothesis corresponds, that is, the truth in semantics requires that the sentences which semantic hypotheses pair as instances of translational synonymy express the same linguistically neutral meaning. Instead of putting forth an argument for his claim that there is no "free-floating, linguistically neutral meaning which we can capture in 'Neutrinos lack mass' and the native cannot," Quine simply asserts that the discontinuity of radical translation tries our meanings: really sets (hem over against their verbal embodiments, or, more typically, finds nothing there.19 [Italics mine]

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Some have been tempted to charge that, in failing to argue for the nonexistence of linguistically neutral meanings, Quine is begging the question. This charge is based on an uncharitable reading of Quine which fails to take account of his criticism of meaning prior to Word and Object. I believe Quine thinks he has taken up the question in his earlier works, particularly, in "Two Dogmas of Empiricism,"20 and has shown that the analytic-synthetic distinction which is required to support a domain of linguistically neutral meanings is nothing more than an "article of faith." Accordingly, I believe that Quine now sees himself in a position to flatly assert that there are no linguistically neutral meanings. The argument against there being a parallel with physics starts prior to Word and Object with the attack on meaning, synonymy, and analyticity. There is evidence for this construal in Quine's discussion of translation in "The Problem of Meaning in Linguistics."21 This discussion shows that, at least at the time, he thought his criticisms of attempts to define synonymy (as part of an attempt to draw the analyticsynthetic distinction) as undermining the claim that there is a fact of the matter in connection with meaning. Harking back to his restatement of the arguments from "Two Dogmas of Empiricism" concerning the impossibility of defining synonymy on the basis of a substitution procedure (beginning of section 4), he says (in section 5) that the task of constructing a lexicon for translating a language whose speakers belong to a quite different culture suffers from a "paucity of explicit objective controls." He writes, The finished lexicon is a case, evidently, of ex pede Herculem. But there is a difference. In projecting Hercules from the foot we risk error, but we may derive comfort from the fact that there is something to be wrong about. In the case of the lexicon, pending some definition of synonymy, we have no statement of the problem; we have nothing for the lexicographer to be right or wrong about. 22

Hence, the earlier argument against attempts to define meaning, synonymy, and analyticity is intended to ground the thesis of the indeterminacy of radical translation. This would be accomplished if it is a good argument, but, as I have shown in chapter III, the earlier argument fails to establish that the concepts in the theory of meaning cannot be defined. The argument is an argument by cases, and it fails because it does not disprove the possibility of definition in linguistics. Quine's attempt to show that the concepts in the theory of meaning cannot be defined in linguistics depends on a pre-Chomskian notion of linguistic definition, namely, definition by substitution criteria.

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Quine's argument simply failed to consider the possibility of theoretical definition, that is, constructing a theory in which grammatical concepts are denned by their relations to other grammatical concepts, and where theory and definition are jointly validated by predictions of grammatical facts about the sentences of the language. Given the possibility of theoretical definition for concepts in the theory of meaning, Quine's attempt to show there is no fact of the matter in the case of meaning fails. Nothing more than the possibility is required. It is unnecessary to show that progress toward theoretical definitions has been made. For Quine's is an a priori argument against the possibility of a theory of meaning, not an a posteriori argument that the prospects for such a theory look rather dim. Hence, given the possibility of a theoretical definition of meaning as elaborated in chapter VI, Quine's argument fails. With this failure, not only does the attempt to distinguish indeterminacy in semantics from inductive underdetermination fail, but the attempt to justify indeterminacy in terms of radical translation fails, too. There are two principal features of Quine's radical translations situation. 23 First, the situation is conceived as involving no presuppositions about the alien language on the part of the field linguist. Because Quine thinks that such presuppositions would beg the question, he designs the radical translation situation so that the linguist must construct a translation from scratch (or rather, very nearly from scratch, since somehow the linguist can presuppose knowledge of what assent and dissent is). Second, the queries that the linguist can direct to the natives are exclusively questions about whether a term in the alien language applies to something in their midst. The situation Quine constructs requires queries about referential relations and not meaning relations, again to assure that no question is begged. But the danger that without these features a question is begged is one that exists only if the situation of the field linguist must be constructed as one in which the linguist builds the translation up from the observational bottom, that is, only if the linguist restricts him or herself to the same methodology that underlies the use of substitution criteria in defining linguistic concepts. Given the possibility of theoretical definition, the linguist has the option of, as it were, dropping the theory of translation down from above. That is, the linguist can propose any sort of theory about the translation of the alien language which makes reasonably precise predictions about the grammatical facts concerning sentences in the two languages. It doesn't, matter how the linguist arrives at his theory. It could have

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come in a dream. All that counts is that its predictions be validated by the evidence about such facts. Therefore, there is no danger that, unless the linguist has no presuppositions and asks no questions about meaning relations, a question is begged. Any presupposition or answer to any question may be built into the translation theory and tested along with its other principles by their joint predictions. The converse of this is that the radical translation situation as Quine has designed it begs the question against intensionalisrn by restricting questions to purely referential relations. Of course, translation will be indeterminate in Quine's situation: the situation is set up so that analytical hypotheses that have exactly the same referential relations but differ in meaning relations cannot be separated evidentially. The critical point is this: given the possibility of theoretical definition, the radical translation situation is not a fair test of the thesis of the indeterminacy of translation. Translation can be fully determinate, and we can know it to be so, even if it. comes out indeterminate in Quine's radical translation situation. This situation would be a fair test if we had to construct concepts from referential data by appropriate substitution criteria, since, then, we could not assume abstract semantic concepts without begging the question of how they had been obtained from the data. But since we do not have to limit ourselves to just referential data, Quine's situation unfairly restricts our epistemic potential in a way that rigs the test to insure that theories of meaning will fail to pass. Field linguists may presuppose or ask whatever they like about alien languages. Such presuppositions may very well falsify the alien language, but are of no import in principle. Linguists may read any foolishness into alien languages; it will matter no more than the anthropomorphism of early physicists and biologists. Such false claims about the alien language can be eliminated in the way anthropomorphism was, by constructing theories without the dubious presuppositions that are simpler and yet predict the relevant facts equally well. Furthermore, the linguist's queries need not be restricted to referential relations. They can be about meaning relations like synonymy, antonymy, redundancy, ambiguity, etc., since there is no a priori argument to bar them. The use of queries about meaning relations significantly improves the test situation: evidence which decides between rival translation hypotheses now becomes available. Quine illustrates the indeterminacy of translation by observing that hypotheses which translate "gavagai" as 'rabbit', 'undetached rabbit part', and 'rabbit stage' cannot be distinguished by evidence from the radi-

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cal translation situation. But in our improved situation the distinguishing evidence is available. The linguist can query the native about whether "gavagai" is synonymous with "rabbit" or ask whether "gavagai" bears the same relation to an expression in the alien language that "finger of a hand" bears to "hand" in English. An affirmative answer to the latter question will be evidence for the translation hypothesis that correlates "gavagai" with "undetached rabbit part".24 There are indefinitely many such questions that bear on such issues in the translation of languages because there are indefinitely many expressions in which the terms occur. This, together with the indefinitely many speakers that can be questioned, entails that the evidence for a translation hypothesis can continue to mount until it is as strong as any evidence for any hypothesis in science. Though such questions assume bilingual fluency on the part of the linguist's informant, the use of bilingual speakers is a common feature of actual linguistic practice and poses no theoretical problem because any hidden deficiencies of our informant can, in principle, be uncovered in the long run by virtue of the fact that the theoretical approach we are imagining is self-corrective. We need neither initially discriminate who is a true bilingual nor assume that the bilinguals we choose will make no mistakes. Errors that enter our theory from our informants can be corrected in the long run on the basis of standard scientific method. In this sense, the problems posed by a deficient bilingual informant are no different in kind from those posed by a faulty meter in the physics lab.2a Given that the support for Quine's indeterminacy thesis collapses, Williams's criticism of an objedification of the mental along the lines that Nagel has suggested collapses, too. As a consequence, we can claim that the cogito establishes the existence of a thinker as a substantial fact in at least one appropriate sense. This sense is admittedly weaker than Descartes's, but, given Kant's arguments, it is not clear that one could hope for anything as strong as Descartes thought could be established. Moreover, it is surely open to philosophers who are sympathetic to the notion of a metaphysical ego to deny that the cogito by itself should provide the full sense of substantiality that the notion requires, and to seek, as Kant himself did, a metaphysical basis for full substantiality. From this perspective, Descartes's optimistic assumption vis-a-vis skepticism has to be acknowledged as a mistake, and it has to be accepted as enough for Descartes's cogito to have gotten things started.

XIII

A Brief Revisionist History of Analyticity

The present study presents a quite different picture of analyticity in modern philosophy from the usual ones. On this picture, it is the empiricist Locke rather than the rationalist Kant who was clearest about the nature of analytic a priori truth. Locke, together with Descartes, are the heroes of the story. Though Kant is popularly considered the hero, he introduced nothing that is not already found in Locke's account of trifling propositions and was responsible for the confusion between the semantic and logical notions of containment that has plagued subsequent philosophical thought. Except for one minor thing—the misleading suggestion inherent in Locke's term "trifling" that analyticity is entirely a matter of the expressive side of language—Locke's account of analyticity is a model of what a short informal account should be. Most importantly, the account makes a point of distinguishing between "necessary consequences" that depend on mere idea containment and ones that do not, i.e., those that, in Locke's words, "convey . . . instructive real knowledge." In contrast, Kant's account of analyticity was less clear. It doubly characterizes analytic propositions, first, as ones whose predicate is contained in its subject concept, and second, as ones whose denial is a contradiction.1 The false supposition that these characterizations are co-extensive had the internal consequence of undermining Kant's formulation of the general problem of pure reason: it led Kant to ignore both the question of whether logic is synthetic a priori and the question of why mathematics, whose propositions cannot be denied without contradiction, isn't analytic. The double characterization had the external consequence of setting the stage for the disappearance of the concept containment notion of analyticity. The fact that the concept containment characterization was no more than a metaphor, presented in psychological terms and

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restricted to subject-predicate sentences, made Frege feel that it was hopelessly flawed and should be abandoned in favor of the other Kantian characterization. Received history has it that, next to Kant, Frege is analyticity's truest friend. Actually, next to Kant, Frege bears the most responsibility for the loss of the sense containment notion of analyticity. Although he clearly saw the distinction between the beams-in-thehouse notion and the plant-in-the-seed notion, Frege dropped the former and put forth the latter as the notion of analyticity. Without much in the way of argument, he took the flaws in Kant's presentation of the beams-in-the-house notion to be insurmountable intrinsic defects instead of features of Kant's presentation. The prestige of Frege's great achievements in logic caused intensionalists and extensionalists alike to take his logical explication of analyticity as the only notion that need be taken into consideration. Frege is also hailed as the father of contemporary intensionalism. No doubt he deserves this position, but there are clear reasons for thinking that, even beyond his role in the loss of the sense containment notion of analyticity, he was not such a great parent. 2 Although I cannot review here all of his nurturing failures, it may suffice to remind the reader of his failure to distinguish the relation that sense bears to the reference of linguistic types from the relation it bears to the reference of linguistic tokens. The result of this failure has been the tribulations that intensionalism has unnecessarily suffered on the basis of the "counter-examples" of Putnam and Kripke. Frege's strong sense-reference thesis has led to undeserved doubt being cast on the basic intensionalist claims that words have senses in the language, that these give rise to analytic truths, and that such truths are a priori and necessarily secured from falsehood. Received history also has it that Carnap is the champion of analyticity in the twentieth century. G.E. Moore is rarely, if ever, thought of in this connection. But, in fact, it is G.E. Moore who deserves this title if anyone does. He preached the doctrine that "there are ever so many different cases of necessary connection." Carnap, by contrast, preached a doctrine that might be expressed in the slogan "there is only one case of necessary connection," and implemented the doctrine in a way that complemented Frege's elimination of the sense containment notion. Carnap's innovation was to reformulate Frege's definition of analyticity. Frege had denned an analytic proposition as one that is a consequence of logical laws and definitions with assumptions from a

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special science. Carnap took out the reference to definitions, thereby making the account uniformly logical. He did this by introducing a new kind of logical law, a meaning postulate, to cover the cases that came under definitions in Frege's logico-lexigraphical account. Carnap's definition of an analytic proposition is that it is a consequence of logical laws. With the later addition of mathematical laws, we get the familiar Carnapian notion of L-truth which expresses, on Carnap's logical empiricist viewpoint, the slogan, "there is only one case of necessary connection." Carnap's innovation had two significant effects. First, it made it easy for the foes of meaning to level an unanswerable objection to what was taken as the best explication of analyticity that its friends could provide, namely, Quine's objection that Carnapian meaning postulates tells us what sentences are to be counted as analytic but do not explain what it is for a sentence to be analytic. The second significant effect of Carnap's innovation was to remove the last vestige of Locke's important distinction between those necessary consequences which are linguistic and those which are extra-linguistic, reflecting an invariable connection in the world. Frege's explication retained a trace of this distinction between language and theory in its distinction between those analytic propositions which follow from laws of logic alone and those which follow from them plus definitions. Even Quine preserves this trace of the distinction in the way that he characterizes an analytical statement as one that "can be turned into a logical truth by putting synonyms for synonyms." 3 It was Carnap who took the final step in eliminating the linguistic element remaining in Frege's explication of analyticity by replacing reference to definitions with logical postulates. Received history has it that Quine, once and for all, proved that the concept of analyticity "makes no objective sense at the level of sentences". Even linguists today echo this piece of folklore.4 All Quine actually showed was that no objective sense can be made of analyticity within a methodological framework that linguistics has since discarded as inadequate to handle the level of abstraction required for grammatical concepts. Received history further has it that Putnam and Kripke have presented knock-down arguments showing that analyticity is not consistent with the possibilities in actual reference. But, although these philosophers have shown that the Fregean framework for theorizing about meaning and reference is refuted by what is possible in reference (by no means an insignificant achievement), they have not shown anything about analyticity per' xe. Their counter-

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examples show that reference cannot be determined by sense, but there are intensionalist frameworks for theorizing about sense and reference within which sense does not determine actual reference. Finally, there is a curious irony in this revisionist history. On one important question, I must reverse my position to agree with Quine's. The question is whether the logical vocabulary as customarily understood should be expanded to include each of the extra-logical words. Formerly I argued that it should be expanded, 3 basing my argument on two things. First, there was the observation that the distinction between logical and extra-logical vocabulary seems to be arbitrary at crucial points, that is, none of the attempts to draw the distinction offer a philosophically satisfactory basis for excluding so-called "extra-logical vocabulary" from contributing to logical form. Second there was the notion that only by including such vocabulary as logical vocabulary can we account for the validity of analytical truths and analytical entailments. Most discussions of the notion of logical vocabulary neither attack the problem at the fundamental point by explaining the sense in which the items in the customary enumeration of logical vocabulary are logical, nor say why the items in the customary enumeration of extra-logical vocabulary are not. This, however, is not to dismiss such discussions; many of them are quite important, but none, I think, would convince Tarski to change his skeptical stance on the distinction between the logical and the extra-logical: Underlying our whole construction is the division of terms of the language . . . into logical and extra-logical. This division is certainly not arbitrary. . . . If, for example, we were to include among the extra-logical signs the implication sign, or the universal quantifier, then our definition of the concept of consequence would lead to results which obviously contradict ordinary usage. On the other hand, no objective grounds are known to me which permit us to draw a sharp boundary between the two groups of terms.6 It. is to Quine's credit that he attacked the problem at the fundamental point: Quine proposed a principle strong enough to provide the desired explanation. In criticizing the analytic—synthetic distinction and advancing the indeterminacy thesis, Quine proposes a principled way of distinguishing the logical from the extra-logical vocabulary. His principle states that the only vocabulary that counts as logical is that which is free of translational indeterminacy. Quine thought that this principle would let in the items in the standard logical vocabulary,' but preclude the items in the standard exlra-logi-

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cal vocabulary, since the latter, on his account, are subject to indeterminacy. The trouble with this proposal is, as we have seen, that Quine's argument for indeterminacy does not hold up. Reflecting on the failure of philosophers and logicians to supply a distinguishing principle, it seemed to me that the problem was best solved radically, i.e., by taking the failure to find any difference between logical vocabulary and extra-logical vocabulary to mean that there is none. This radical solution implied the expansion of the logical vocabulary to include the entire vocabulary of the language, and this, in turn, seemed the appropriate basis for the explanation of the validity of analytic truths and analytic entailments. This, of course, was Carnap's influence. I failed to appreciate that, in resurrecting the purely linguistic notion of sense containment, I had in fact developed an alternative to Carnap's basis for this explanation. Thus, an option had been created: instead of going ahead from Kant's Janus-headed notion of analyticity to the Fregean and then the Carnapian notions, it was possible to go back to the Lockean notion. Once I recognized that the linguistic basis provided an explanation independent of the logical basis Carnap had used, it became plain that there is no motivation for an expansion of the logical vocabulary. Of course, the first thought on noting the absence of motivation is that we are back with the old problem of distinguishing the logical and the extra-logical vocabulary. But, then, we realize that what has put us back with this problem also solves it. Once we recognize that there is a linguistic basis for the validity of inferences coexisting alongside of the logical basis, we see that the notion of logical vocabulary itself is ambiguous. It can be understood either in the sense of vocabulary whose properties determine what follows validly from what, or in the sense of vocabulary whose properties determine the application of laws of logic. The desire to make extra-logical vocabulary into logical vocabulary comes from the knowledge that the nouns, verbs, adjectives, etc., are logical vocabulary in the former sense. Properties of "sister" and "female" determine that "Gretel is a female" follows from "Gretel is a sister". But when the ambiguity is unnoticed, the conversion of extra-logical vocabulary into logical vocabulary in the first sense leads automatically to conversion in the second sense, too. This is mistaken because "Gretel is a female" does not follow from "Gretel is a sister" in virtue of the application of laws of logic. Hence, there is no problem about distinguishing the logical and extra-logical vocabulary: we can have our cake and eat it. There is a fixed logical vocabulary apart: from the unwashed masses of nouns,

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verbs, adjectives, etc., just as the defenders of the distinction believed all along. The distinction marks the logical vocabulary as that whose properties determine what follows from what in virtue of the application of laws of logic. Thus, projecting logical form from the laws of logic as the simplest structural differentiation required for the application of logical laws is quite legitimate, even though simplicity may allow differentiation no farther than the structures of quantified modal logic. On the other hand, nothing in any of this prevents us from saying that the properties of every meaningful item in the so-called extra-logical vocabulary of the language play a role in determining what follows validly from what. I think it would be a mistake to create a second logical vocabulary in terms of the notion of what follows validly from what. Doing this would be saying that there is a legitimate sense in which not only are linguistic inferences logical, but so are mathematical and other necessary inferences (perhaps, e.g., "There is an event" to "There is a cause" or "This is yellow" to "This is lighter than brown"). It is best not to take "logical" to have any such broad sense, since this would encourage the already too strong tendency to assimilate cases of necessary connection to some notion other than necessary connection. Saying an inference is valid is just saying that its conclusion is true in every circumstance in which its premises are, but saying that an inference is linguistic, or logical, or mathematical, or metaphysical is saying something about why the necessary connection obtains. The why may have to do with the sense structure of language, the lawrs of truth, the nature of number, or the a priori conditions of being. The explanation of necessary connection is a different matter in each such case. The grave error made by Carnap and those who have followed him in trying to reconstruct all nonempirical truth on the basis of "Leibniz' view that a necessary truth is one which holds in all possible worlds" is just that they eliminate the why. Quine spotted the particular case of this error in Carnap's semantics: Quine complains that Carnap tells us which sentences are analytic but does not explain why they are. But with the current fashion of giving uniform possible-worlds accounts of basic concepts in language, logic, mathematics, and metaphysics, the number of particular cases of the error has multiplied to the point where it is now imperative to attend seriously to the why of necessities. Since analytic: truth and analytic entailment can be handled without eliminating the standard distinction between logical and extralogical vocabulary, 1 now find myself agreeing with Quine on how

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the logical vocabulary of a language should be specified. There is agreement because, in opposition to Carnap, we see logic as an autonomous subject. Of course, Quine and I arrive at this view in different ways. Quine thinks that there is no threat that logical structure might become entwined with linguistic meaning because he thinks there is no linguistic meaning. On the other hand, I think that there is no threat because I think linguistic meaning is independent of logical structure. As I see it, logic is a domain of synthetic laws, laws of truth, as Frege conceived them, while language is a domain of analytical laws, laws of the expression of the statements and theories that fall under the laws of truth.8 Surprisingly, then, establishing the existence of an analytic—synthetic distinction works just as well as showing that the distinction is mere dogma for the purpose of establishing the autonomy of logic. One does not have to be an extensionalist like Quine in order to draw the distinction between the logical and the extra-logical vocabularies at the place where logicians have felt it ought to be drawn. Extensionalists cannot, I think, provide a principled basis for drawing the distinction at this point without something like Quine's skepticism. This is because extensionalism reconstructs all necessary connection in the same way, eliminating the different whys in the different cases of necessary connection. The uniformity of treatment is, I think, the reason Tarski could see no "objective grounds . . . which permit us to draw a sharp boundary between the two groups of terms." One can no more identify the boundary between the logical and the extra-logical uninformed by knowledge of the sense structures in the language than one can identify the boundaries between nations uninformed by knowledge of geopolitics. Fregean and Carnapian intensionalists fare no better than extensionalists because their assimilation of linguistic meaning to logical structure puts them in the same position as the extensionalists.9 Although in the case of these intensionalists there is a more ramified organization of the objects in the domain of language into set inclusions due to the overlay of meaning postulates, still the scene is of a uniformity that exhibits no natural point at which to establish the desired boundary. Only an intensionalism based on decompositional semantics is able to provide a principled basis for the distinction between logical vocabulary and extra-logical vocabulary.

Notes

Chapter II 1. The Philosophical Works of Descartes, ed. and trans. E. Haldane and G. R. T. Ross (Cambridge: Cambridge University Press, 1969), Vol. I, p. 101. 2. The Basic Works of Aristotle, ed. R. McKeon (New York: Random House, 1941), p. 1090 (Nichomachean Ethics, 1170a32). 3. Arnaukl points out the parallel with Augustine's reasoning in Book XI of The City of God; ci. Philosophical Works of Descartes, Vol. I, p. 80. For an interesting discussion of Augustine's anticipation of Descartes's cogito, see G. B. Matthews, "Si Fallor, Sum," in Augustine: A Collection of Critical Fssays, cd. R. A. Markus (Garden City, N.Y.: Double-day, 1972), pp. 151-107. 4. J. Locke, An Essay Concerning Human Understanding, ed. A. S. Pringle-Patlison (Oxford: The Clarendon Press, 1924), pp. 309-320. 5. M. D. Wilson, Descartes (London: Routledgc & Kegan Paul, 1978). 6. Ibid., p. 55. 7. J. Chevailier, Descartes (Paris: Plon, 1921), p. 218. My account of Chevailier's position is taken from the discussion in A. Kenny, Descartes: A Study of His Philosophy (New York: Random House, 1968), pp. 41-42. 8. A. J. Ayer, The Problem of Knowledge (Harmondsworth, England: Penguin Books, 1956), pp. 46-47. 9. Ibid., p. 46. 10. Wilson, Descartes, p. 54. 11. Ibid., p. 55. 12. Philosophical Works of Descartes, Vol. II, pp. 38, 127. 13. B. Williams, Descartes: The Project of Pure hu/uhj, (Harmondsworth, England: Penguin Books, 1978), p. 91. 14. A. Arnauld, The Art of Thinking: Port-Royal Logic, (Indianapolis: Bobbs Merrill Company, Inc., 1964). 15. Ibid., p. 228. 16. Philosophical Works of Descartes, Vol. I, p. 7. 17. Ibid., p. 8. 18. Ibid., Vol. II, p. 38. 19. Ibid., Vol. I, pp. 183-185. 20. Ibid., Vol. I, p. 159. 21. Ibid., Vol. I, p. 159. 22. Descartes, Philosophical Letters, trans, and ed. A. Kenny (Minneapolis: L'niversity of Minnesota Press, 1981), pp. 15, 151. 23. This seems to me the proper sense of "circle" in natural language. The sense

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involving the concept of equal radii is one that is acquired in the formal study of geometry, as is clear from the fact that little children who have the concept of a circle have no notion of radii, or if presented with the notion, they need to see that, in the case of circles, the radii are all equal. 24. Descartes, Philosophical Letters, p. 159. 25. Descartes's Conversations with Burman, trans. J. Cottingham (Oxford: Clarendon Press, 1976), p. 4. 26. See Philosophical Works of Descartes, Vol. II, p. 127, where Descartes makes the geometrical analogy. 27. R. Carnap, "The Elimination of Metaphysics through the Logical Analysis of Language," in Logical Empiricism, ed. A. J. Ayer (Glencoe: The Free Press, 1959), p. 74. 28. H. Frankfurt, Demons, Dreamers, and Madmen Indianapolis: Bobbs-Merrill Company, 1970), p. 95. 29. L. Wittegenstein, Tractatus Logico-Philosophicus London: Kegan Paul, 1972), sections 5.53-5.5303. 30. E. M. Curley, Descartes Against the Skeptics (Oxford: Basil Blackwell, 1978), p. 73.

Chapter III 1. W. V. Quine, "Two Dogmas of Empiricism," in From a Logical Point of View (Cambridge: Harvard University Press, 1953), pp. 20-46. 2. R. Carnap, "Meaning Postulates," in Meaning and Necessity, 2d ed. (Chicago: University of Chicago Press, 1965), pp. 222-229. 3. W. V. Quine, The Philosophy of Logic (Englewood Cliffs, N.J.: Prentice-Hall, 1970), p. 3. 4. H. P. Grice and P. F. Strawson, "In Defense of a Dogma," The Philosophical Review LXV (1956): 141-156. 5. W. V. Quine, "The Problem of Meaning in Linguistics," in From a Logical Point of View, p. 56. 6. This point, unfortunately not enough taken to heart these days, is made in Quine's "Two Dogmas of Empiricism," p. 23. 7. N. Chomsky, Current Issues in Linguistic Theory (The Hague: Mouton & Co., 1964). 8. K. Donnellan, "Necessity and Criteria," arid H. Putnam, "It Ain't Necessarily So," The Journal of Philosophy, LIX (1962): 647-658, and 658-671, respectively; H. Putnam, "Is Semantics Possible?," Metaphilosophy 1 (1970): 189-201, and "The Meaning of 'Meaning'," Language, Mind and Knowledge, Minnesota Studies on the Philosophy of Science, Vol. VII., ed. K. Gunderson (Minneapolis: University of Minnesota Press, 1975), pp. 131-193. 9. C. I. Lewis, An Analysis of Knowledge and Valuation, (La Salle, Indiana: Open Court Publishing Co., 1946), pp. 135-152. 10. J.J. Katz, "Why Intensionalists Ought Not Be Fregeans," in Truth and Interpretation: Perspectives on the Philosophy of Donald Davidson, ed. E. LePore (Oxford: Basil Blackwell, 1986). 11. J. J. Katz, "A Proper Theory of Names," Philosophical Studies 31 (1977) 1-80, and "The Neoclassical Theory of Reference," in Contemporary Perspectives in the Philosophy of Language, ed. P. A. French, E. E. Uehling, Jr., and H. K. Wettstein (Minneapolis: University of Minnesota Press, 1977), pp. 103-124. 12. See my "Why Intensionalists Ought Not Be Fregeans." 13. Putnam, "Is Semantics Possible?," and S. Kripke, "Naming and Necessity" in Semantics of Natural Language, ed. D. Davidson and G. Harman (Dordrecht: D. Reidel Publishing Company, 1972), pp. 315-321.

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14. Such a fixation is not idiosyncratic to these philosophers but is a general feature of Anglo-American philosophy. See my "Why Intensionalists Ought Not Be Fregeans." 15. Putnam, "The Meaning of'Meaning'," pp. 131-193. 16. Ibid., pp. 135-136. 17. Putnam's twin-earth argument has given rise to a major industry in the philosophy of psychology. Fodor has used the argument to motivate his attack on naturalistic psychology and to justify his methodological solipsism. J. A. Fodor, "Methodological Solipsism Considered as a Research Strategy in Cognitive Psychology," The Behavioral and Brain Sciences 3 (1980): 63-109, and "Cognitive Science and the Twin Earth Problem," Notre Dame Journal of Formal Logic 23 (1982): 98—118. See my discussion of the first of these papers, "Fodor's Guide to Cognitive Psychology," The Behavioral and Brain Sciences 3 (1980): 85-89. 18. R. Carnap, "Intellectual Autobiography," in The Philosophy of Rudolf Carnap, ed. P. A. Schilpp (La Salle, Indiana: Open Court Publishing Co., 1963), p. 64. 19. Ibid., p. 63. 20. N. Chomsky, Aspects of the Theory of Syntax (Cambridge: M.I.T. Press, 1965), p. 60. 21. Ibid., p. 60. 22. Ibid., p. 60.

Chapter IV 1. Carnap, "Meaning Postulates," pp. 222-229. 2. Quine, "Two Dogmas of Empiricism," pp. 32—37. 3. Ibid., p. 33. 4. Ibid., p. 36. 5. Ibid., p. 33. 6. Ibid., p. 33. 7. Stalnaker seems to believe there is exactly one necessary proposition. See R. Stalnaker, "Propositions," in Issues in the Philosophy of Language, ed. A. F. MacKay and D. D. Merill (New Haven: Yale University Press, 1976), pp. 79-92. What does he take Godel to have proved? 8. Locke, An Essay Concerning Human Understanding, pp. 306—307. 9. Ibid., p. 307. 10. Ibid., p. 308. 11. Ibid., p. 308. 12. Note that the shift of emphasis to the structure of concepts in the sense of a sentence is a shift in the right direction. Emphasis on words, expressions, and sentences would be misplaced because analyticity and analytic entailment apply to them only indirectly. A sentence like "A father is a parent" is ambiguous in virtue of its subject meaning both 'a male parent' and 'a priest'. Such a sentence is thus not analytic absolutely but only on a sense, which is just another way of saying that it is senses of sentences that are analytic.

Chapter V 1. G. Frege, The Foundations of Arithmetic, trans. J. L. Austin (Oxford: Basil Blackwell, 1953), p. 4C. 2. Ibid., p. 3. 3. I. Kant, Prolegomena to Any Future Metaphysics ed. L. W. Beck (New York: The Little Library of Liberal Arts, The Liberal Arts Press, 1951), p. 14.

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4. Ibid., p. 14.

5. I. Kant, The Critique of Pure Reason, trans. N. K. Smith (New York: The Humanities Press, 1929), p. 49. 6. Ibid., p. 48. 7. See the informative discussion in "The Unity of Leibniz's Thought on Contingency, Possibility, and Freedom," in A. W. Collins, Thought and Nature: Studies in Rationalist Philosophy (Notre Dame: University of Notre Dame Press, 1985), pp. 123179. 8. See Margaret Wilson's informative essay, "Leibniz and Locke on 'First Truths'." On p. 366, she suggests two considerations supporting Leibniz and indicating that he has had the last word. First, " . . . Leibniz might well point out once more that he is primarily concerned with the logical relations among truths, not with questions of psychology; and that whether or not a given truth is "instructive" is a question of the latter sort." Second, ". . . the exalted status which Leibniz enjoys as the 'founder of mathematical logic' is in part a consequence of his refusal to admit on intuitive Lockean grounds an unbridgeable gap between serious mathematical propositions and the 'trivial' logical maxims." With respect to the first of these considerations, one can reply that there is no reason to take Locke to be expressing a psychological thesis. Locke can be understood to mean a conceptual containment in virtue of which the sentences expressing trifling propositions cannot be used instructively. With respect to the second of these considerations, it can be replied that the consequence relation to which Wilson refers can only be a historical matter, since admitting an unbridgeable gap does not in any way affect the debt that mathematical logic owes to Leibniz. Leibniz was just not the founder of semantics too. 9. Frege, Foundations of Arithmetic, p. 3. 10. R. C. S. Walker, Kant (London: Routledge & Kegan Paul, 1978), pp. 23-24. 11. Frege, Foundations of Arithmetic, p. 101. 12. Quine, "Two Dogmas of Empiricism," pp. 20-21. 13. Ibid., p. 21. 14. Ibid., p. 22; pp. 22-23. 15. Kant, Prolegomena, p. 16. 16. Some philosophers since Locke have had the beams-in-the-house notion in mind but haven't been as clear and explicit about the difference between this notion and logical containment. G. E. Moore is an example, and we will discuss his conception of analysis in some detail below. 17. See my "Semantics and Conceptual Change," The Philosophical Review 88 (1979): 327-365, for an example in the philosophy of science, and G. E. Smith and J. J. Katz, Intensionally Admissible Models: The Extensional Interpretation of Intensional Semantics (Harvard University Press, in press), for a discussion of the point in the philosophy of logic.

Chapter VI 1. The example is generally attributed to Richard Cartwright. 2. L. Wittgenstein, Philosophical Grammar, (Berkeley: The University of California Press, 1974), p. 248. 3. Cases like (l)-(3) and (12)-(14) are the basic cases of analyticity, but, since any account of meaning in natural language must also provide analyses of the meaning of sentences with "and", "or", etc., coordinating clausal structures, the question of the analyticity of cases like "If John leaves and Mary leaves, then John leaves" and the analytic entailment. of cases like the inference from "John left and Mary left" to "John

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It-it" arise once the basic cases are dealt with. These cases are systematically treated only in Smith and KM/., Intensionally Admissible Models. 4. The present context is one in which a psychological criterion is considered unacceptable. It might be argued, in line, say, with Chomsky's psychologizing of linguistics, that psychological criteria are in order, but this would take us outside the context in which these shortcomings have been discussed in philosophy. See my Language and Other Abstract Objects, (Totowa, N . J . : Rowman and I.ittlcheld, 1981). 5. Frege, Foundations of Arithmetic, p. 101. 6. J. j. Katz, "The Advantage of Semantic Theory over Predicate Calculus in the Representation of Logical Form in Natural Language," in The Monist Vol. 60 (1977): 392-398. 7. See Quine, W. V. Word and Object, pp. 157-190. 8. Katz, "Advantage of Semantic Theory over Predicate Calculus," pp. 380—405.

9. Ibid., pp. 380-405. 10. R. Carnap, Meaning and Necessity, enlarged ed. (Chicago: University of Chicago Press, 1956), pp. 56-59. 11. This is perhaps the place to say something about Carnap's disciples in psychology. J. D. Fodor, J. A. Fodor, and M.F. Garrctt, in "The Psychological Unreality of Semantic Representations," Linguistic Inquiry, IV (1975): 515—531, argue for meaning postulates on the assumption that linguistic semantics must be part of a psychological theory of the language user in the narrowest sense of being a component in the on-line performance model. In "The Real Status of Semantic Representations," Linguistic Inquirf V I I I (1977): 559—584, I observe that this assumption is completely gratuitous, since linguistic semantics might be taken as a component in a theory of competence or might not be taken as part of a psychological theory at all but thought of the way we think of mathematics. 1 also observe that, granting the assumption, the experimental argument is flawed and shows nothing. ). A. Fodor, M. F. Garrett, K. C. T. Walker, and C. I I . Parks, in "Against Definition," Cognition 8 (1980): 263367, respond to this last observation with a new experimental argument. But this new experimental argument is no belter than the old one; see my Language and Other Abstract Objects, p. 1544, n. 13. J. A. Fodor, et al. present one original nonexperimenlal argument (they make the usual genuflections to Quine's arguments in 'Two Dogmas of Empiricism" but fail to consider my replies to I hem in, for example, J. ]. Katz, "Where Things Stand with the Analytic—Synthetic Distinction," Sinthese 28 (1974): 283—319). These authors argue against the existence ol definition on the novel grounds that it has proven difficult to construct definitions that can't be faulted in some way. 'The argument assumes, bizarrely, that the test of a science is whether it can succeed in fully describing some particular object in its domain. Sciences seek principles, not complete descriptions of particulars: If their constraint were adopted in syntax, it would mean the end of the subject, as anyone who has ever taught bright students in the subject knows quite well. 12. Chomsky, Current Issues in Linguistic Theon. pp. 34—50. 13. The nicety here is necessary because of well-known problems about the substitution of an expression for a synonymous one in a opaque context. See J. J. Katz, "Why Intensionalists Ought Not be Fregeans." 14. Semantic Theory, pp. 1 — 10. 15. Chomsky, Aspects of the Theory of Syntax, pp. 68—74. 16. Chomsky, Aspects of the Theory of Syntax, pp. 70—71. 17. Ibid., p. 71. 18. Semantic Tlieor}