Meaning and structure : structuralism of (post)analytic philosophers 9781351919043, 1351919040

Table of contents :
Structuralism and Analytic Philosophy --
Why not the French Structuralism? --
Contemporary (Post) Analytic Philosophy and Structuralism --
The Whys and Hows of Structuralism --
What is Meaning? --
Words and 'Mental Representations' --
Is Meaning Within the Mind? --
Is Language a Tool of Conveying Thoughts? --
Meanings as Abstract Objects --
Semantics and Semiotics --
The Case of Augustinus --
Language as a Toolbox --
What is Structuralism? --
Horizontal and Vertical Relations of Language --
Structuralism: Mere Slogan, or a Real Concept? --
Thus Spoke de Saussure --
But Also Thus Spoke de Saussure --
De Saussure and Frege --
Structuralistic Linguistics after de Saussure --
Structuralistic Philosophy --
Parts, Wholes and Structures: Prolegomena to Formal Theory --
Abstraction --
Part-Whole Systems and Compositionality --
Actual and Potential Infinity --
The Principle of Compositionality of Meaning --
The Birth of Values out of Identifies and Oppositions --
Appendix I: Mereology and 'Structurology' --
Appendix II: The Birth of the Structural as an Algebraic Fact --
Appendix III: Structure as a Matter of Relations and Operations --
Structuralism of Postanalytic Philosophers --
Translation and Structure: Willard Van Orman Quine --
The Indeterminacy of Translation --
The Indeterminacy of Reference and the Ontological Relativity --
Language and Thought --
Quine's Behaviorism --
Quine's Pragmatism --
Quine's Holism --
Translation and Structure --
Universe of Discourse and Ontological Commitments --
The Analytic and the Synthetic.

Citation preview

MEANING AND STRUCTURE In Meaning and Structure, Peregrin argues that recent and contemporary (post)analytic philosophy, as developed by Quine, Davidson, Sellars and their followers, is largely structuralistic in the very sense in which structuralism was originally tabled by Ferdinand de Saussure. The author reconstructs de Saussure 's view of language, linking it to modern formal logic and mathematics, and reveals close analogies between its constitutive principles and the principles informing the holistic and neopragmatistic'view of language put forward by Quine and his followers. Peregrin also indicates how this view of language can be made compatible with what is usually called 'formal semantics'. Drawing on both the Saussurean tradition and recent developments in analytic philosophy of language, this book offers a unique study of the ways in which the concept of meaning can be seen as consisting in the concept of structure.

ASH GATE NEW CRITICAL THINKING IN PHILOSOPHY The Ashgate New Critical Thinking in Philosophy series aims to bring high quality research monograph publishing back into focus for authors, the international library market, and student, academic and research readers. Headed by an international editorial advisory board of acclaimed scholars from across the philosophical spectrum, this new monograph series presents cutting-edge research from established as well as exciting new authors in the field; spans the breadth of philosophy and related disciplinary and interdisciplinary perspectives; and takes contemporary philosophical research into new directions and debate.

Series Editorial Board: David Cooper, University of Durham, UK Peter Lipton, University of Cambridge, UK Sean Sayers, University of Kent at Canterbury, UK Simon Critchley, University of Essex, UK Simon Glendinning, University of Reading, UK Paul Helm, King's College London, UK David Lamb, University of Birmingham, UK Stephen Mulhall, University of Oxford, UK Greg McCulloch, University of Birmingham, UK Ernest Sosa, Brown University, Rhode Island, USA John Post, Vanderbilt University, Nashville, USA Alan Goldman, University of Miami, Florida, USA Joseph Friggieri, University of Malta, Malta Graham Priest, University of Queensland, Brisbane, Australia Moira Gatens, University of Sydney, Australia Alan Musgrave, University of Otago, New Zealand

Meaning and Structure Structuralism of (post)analytic philosophers

JAROSLAV PEREGRIN Academy of Sciences of the Czech Republic and Charles University, Prague, Czech Republic

~ ~ ~~o~;~;n~~~up LONDON AND NEW YORK

First published 2001 by Ashgate Publishing Published 2016 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN 711 Third Avenue, New York, NY 10017, USA Routledge is an imprint ofthe Taylor & Francis Group, an informa business Copyright © J aroslav Peregrin 200 I The author has asserted his right under the Copyright, Designs and Patents Act, 1988, to be identified as the author of this work. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe.

British Library Cataloguing in Publication Data Peregrin, Jaroslav Meaning and structure : structuralism of (post)analytic philosophers. - (Ashgate new critical thinking in philosophy) !.Structuralism I. Title 149.9'6 Library of Congress Cataloging-in-Publication Data Peregrin, Jaroslav. Meaning and structure : structuralism of (post)analytic philosophers I Jaroslav Peregrin. p. em. -- (Ashgate new critical thinking in philosophy) Includes bibliographical references and index. !.Structuralism. 2. Analysis (Philosophy) I. Series. B841.4 .P45 2001 149'.96--dc21 2001027831 ISBN 13:978-0-7546-0411-2 (hbk)

Contents

1

Introduction 1.1 Structuralism and Analytic Philosophy 1.2 Why not the French Structuralism? 1.3 Contemporary (Post)Analytic Philosophy and Structuralism 1.4 Plan of the Book 1.5 Acknowledgements

1 1 2 6 8 10

PART I: The Whys and Hows of Structuralism 2 What is Meaning? 2.1 Words and 'Mental Representations' 2.2 Is Meaning Within the Mind? 2.3 Is Language a Tool of Conveying Thoughts? 2.4 Meanings as Abstract Objects 2.5 Semantics and Semiotics 2.6 The Case of Augustinus 2.7 Language as a Toolbox

15 15 18 22 26 28 31 34

3 What is Structuralism? 3.1 Horizontal and Vertical Relations of Language 3.2 Structuralism: Mere Slogan, or a Real Concept? 3.3 Thus Spoke de Saussure 3.4 But Also Thus Spoke de Saussure 3.5 De Saussure and Frege 3.6 Structuralistic Linguistics after de Saussure 3.7 Structuralistic Philosophy

37 37 39 40 44 48 50 53

4 Parts, Wholes and Structures: Prolegomena to Formal Theory

57 57 61 65 69

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9

Abstraction Part-Whole Systems and Compositionality Actual and Potential Infinity The Principle of Compositionality of Meaning The Birth of Values out of Identities and Oppositions Examples Appendix I: Mereology and 'Structurology' Appendix II: The Birth of the Structural as an Algebraic Fact Appendix III: Structure as a Matter of Relations and Operations

v

72

75 81 83 89

Meaning and Structure

VI

PART II: Structuralism of Postanalytic Philosophers

5 Translation and Structure: Willard Van Orman Quine 5.1 The Indeterminacy of Translation 5.2 The Indeterminacy of Reference and the Ontological Relativity 5.3 Language and Thought 5.4 Quine's Behaviorism 5.5 Quine's Pragmatism 5.6 Quine's Holism 5.7 Translation and Structure 5.8 Universe of Discourse and Ontological Commitments 5.9 The Analytic and the Synthetic 5.10 Holism and the Correspondence Theory of Language 5.11 Summary: Quine's Structuralism

95 95 96 99 102 104 106 108 111 114 117 120

6 Truth and Structure: Donald Davidson

123 123 125 128 131 134 137 140 142 144

6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9

Radical Interpretation and the Principle of Charity Tarski's Theory of Truth Truth and Meaning Meaning as a 'Measuring Unit' Davidson's Rejection of Empiricism Davidson and Pragmatism The "Third Dogma of Empiricism" Davidson's Naturalism Summary: Davidson's Structuralism

7 Inference and Structure: Wilfrid Sellars and Robert Brandom 7.1 Ascription of Meaning as "Functional Classification" 7.2 Sellars's Functionalism 7.3 Meaning as a Function 7.4 Sellars and Davidson 7.5 Normativity 7.6 Meaning and Inference 7.7 "Giving and Asking for Reasons" 7.8 The Nature of Language 7.9 Holism Again 7.10 The Nature of Reason 7.11 Summary: The Structuralism of Sellars and Brandom

147 147 149 153 155 157 161 163 167 172 173 175

Contents

Vll

PART III: Semantic Structure ofLanguage and of its Expressions 8 Meaning and Inferential Role 8.1

8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11

Inference Inference and Consequence Meaning as 'Encapsulating' Inferential Role Ontologico-semiotic View of Meaning Strikes Back? Why Meaning Can be Inferential Role The Extensional Model of Meaning Meanings as Products of the Truth/Falsity Opposition The Intensional Model of Meaning Intensionality as the 'Catalyst of Meaning' Semantic Models Reflecting Other Types of Inferences Syntax and Semantics

9 The 'Natural' and the 'Formal' 9.1 What does Having a Structure Mean? 9.2 Radical Translation Revisited 9.3

9.4 9.5 9.6 9.7

Geometry Structure as a Formal Prism The 'Realm of the Natural' and the 'Realm of the Formal' Formalization Bridging the Epistemic Gap?

179 179 181 186 188 191 195 201 202 206 208 211 215 215 216 220 224 227 229 231

10 The Structures of Expressions 10.1 The Semantic Structure of an Expression? 10.2 "Logical Form" of Chomsky 10.3 "Logical Form" of Logicians 10.4 Logical Form as Expressing Inferential Role 10.5 Logical Form as a Prism 10.6 Logical Forms as 'Universal Compensators' 10.7 The Dialectics of Structure

235 235 236 240 243 245 249 251

11 Conclusion

255

References

259

Index

269

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Chapter One

Introduction 1.1 Structuralism and Analytic Philosophy

If you open a book about language or about our knowledge of the world written by an analytic philosopher, it is quite probable that you will find repeated invoking of the concept of structure. The concept is essential not only for such classical works as Camap's Logical Structure of the World (1928) or Russell's Our Knowledge of the External World (1914), but also for writings of many contemporary (post)analytic philosophers, like Quine (see especially his 'Structure and Nature', 1992b). If the term 'structuralism' were up for grabs, it would be, I think, not too far-fetched to speak about a 'structuralism of (a part of) analytic philosophy'. No wonder: the concept of structure is of course intimately related to that of analysis we reveal structures by analyzing wholes into parts. However, the fact is that the term is not up for grabs: it has already been claimed by a philosophical stream stemming from the writings of Ferdinand de Saussure, flowing through all of this century's philosophy, especially in France, and deeply influencing contemporary philosophical atmosphere on the European continent. Levi-Strauss, Lacan, Foucault, Derrida and Deleuze figure as the key names. Is then this French structuralism in some way similar or parallel to analytic philosophy? Surprisingly, the contrary seems to be the case: these two philosophical movements are often taken as almost paradigmatic antipodes: French structuralism appears to be the exemplary example of the kind of 'irrational' philosophy which analytic philosophy was devised to extirpate. It is beyond doubt that the way philosophy is done by Foucault or Derrida is so different from that in which it is pursued by Russell or Quine that the two enterprises are almost incommensurable (Richard Rorty's and others' attempts to confront them notwithstanding). However, is this true also for de Saussure? Is his way of viewing language so different from the way language is usually viewed by analytic philosophers? In fact, it does not seem so: de Saussure's principal work, Cours de linguistique generale, is an austerely written scientific treatise, worlds apart from Derrida's stylistic jugglery. 1 1

This fact has caused Pavel (1989, p. vii) to accuse the French structuralists of completely misreading de Saussure: "They mistook the results of a specialized science for a collection of 1

2

Meaning and Structure

In view of this, I think it is interesting to confront de Saussure's own kind of structuralism with the ideas put forward by analytic philosophers. Given what we have just said, could it not be that some of the analytic philosophers are really closer to him than his avowed followers? In this book I will argue that this is indeed the case; namely that contemporary (post)analytic philosophy, particularly in the vein of Quine, Davidson, Sellars and Brandom, is in many respects congenial to de Saussure's teaching. 1.2 Why not the French Structuralism?

Is the aversion of analytic philosophers to the French structuralists substantiated, or is it the result of their inability to appreciate a different style of philosophical thinking? In developing an 'analytical structuralism', should we attempt to incorporate the results of continental structuralism? It is well known that the opinion of many analytic philosophers is stringent: the work of Derrida and company is sheer rubbish and has nothing to do with real philosophy. Recently this attitude has gained further support from the analyses of Sakal and Bricmont (1998), which demonstrate that the manner in which many of the French philosophers employ scientific concepts is often suspiciously close to the way such concepts are used by people who do not understand them but want to look learned. However, on the other hand, there are analytically minded philosophers who appear to take their French colleagues seriously, and even try to adumbrate points of convergence between them and the major exponents of analytic philosophy (see esp. Wheeler, 2000). It seems that what lies behind the elusiveness of a great deal of continental philosophy and what so irritates analytic philosophers is the implicit conviction of its exponents that truly philosophical questions are only those which do not allow for a rigorous, explicit answer; those which can be attacked only indirectly, 'metaphorically'. Here I am not going to argue that this attitude is misguided or capricious. Perhaps philosophy should attempt at attacking questions which are not answerable in the way required by the standards usually presupposed by analytic philosophers; perhaps sticking uncompromisingly to these standards we indeed rid ourselves of the possibility to deal with some problems with which we, as philosophers, should deal. (From the history of this century's philosophy we know that the reasonable demand that we should only use clear speculative generalities. They believed that breathtaking metaphysical pronouncements could be inferred from simple-minded descriptive statements."

Introduction

3

concepts can be easily turned into the unreasonable demand to use only concepts which are explicitly defined in a way concepts can be really defined only within mathematics). However, what I am going to argue for is the converse thesis: that there are interesting philosophical questions which are answerable more or less explicitly and with respect to which the 'continental attitude' is simply inadequate. And one cluster of such questions is, in my opinion, precisely that which is centered around the concept of structure, especially of the structure of language. It is not the purpose of this book to give a systematic critique of French structuralism, but perhaps I should explain in greater detail why I think these philosophers fail to cope with the problem adequately. Let me, therefore, briefly discuss general principles of structuralism as envisaged by one of the key figures of the movement, Gilles Deleuze (1974). In the seven chapters of his text, Deleuze offers what he claims to be seven criteria definitive of structuralism. In the introduction he explicitly states that what he is after are "formal criteria of recognition" (p. 259). Unfortunately though, as I see it, the book actually contains no criteria worth the name altogether (let alone formal criteria). Let us look at Deleuze's account more closely. In the first chapter Deleuze claims: "The first criterion of structuralism ... is the discovery and recognition of a third order, a third reign: that of the symbolic. The refusal to confuse the symbolic with the imaginary, as much as with the real, constitutes the first dimension of structuralism" (p. 260). Well, this may seem to resemble a criterion- but only at first sight. Could the claim that besides the realm of the real and the realm of the imaginary there exists a third realm of the symbolic be taken as a criterion? Certainly; however, only as long as it is clear what characterizes such a 'world of the symbolic'; and this is what Deleuze fails to clarify. The point is that the existence of some 'third reign' would be accepted by the great majority of philosophers of all times (with the exceptions of those who, like William Ockham, made their philosophical living out of its rejection). Many of them, from Plato to those inspired by modem mathematics, would even defend its existence with a vengeance. Are all of them supposed to be structuralists? And if not, what distinguishes the structuralistic acceptance of 'the symbolic' from the wide acceptance of something like 'objective abstracts'? Of course that symbols are supposed to symbolize something; so does Deleuze implicitly assume that a structuralist not only accepts a 'third reign of being', but also takes its elements to be somehow related to some other entities? Or is he characterized merely by the fact that he calls his 'third reign' the 'reign of the symbolic'? These are questions the answers to which I find nowhere in the chapter.

4

Meaning and Structure

In the second chapter Deleuze attempts to explain what it is to be a "symbolic element of a structure." (p. 262) He states that "the elements of a structure have neither extrinsic designation, nor intrinsic signification", that they "have notliing other than a sense [... ]: a sense that is necessarily and uniquely 'positional"' (ibid.). Of course it can be intuited what he is after: however until he explains what makes the difference between his "designation" and "signification", on the one hand, and "sense", on the other, his pronouncements are unclear to the point of uselessness. And this is again something he never does. Neither of the further formulations to be found in the chapter offer much help in promoting a novice's understanding the concept of structuralism. "Structuralism cannot be separated from a new transcendental philosophy, in which the sites prevail over whatever fills them. Father, mother, etc., are first of all sites in a structure ... " It seems to be evident that philosophy is not to aspire to deal with individual fathers and mothers, but at most with the corresponding 'abstract' roles (or concepts). It seems also evident that such roles are in multiple ways inseparably interconnected (thus the role of father clearly involves, e.g., that of man and is unthinkable without the roles of mother and child), i.e. constitute a certain structure. However, this by itself does not seem to be something which would appreciably enhance the common way of thinking about relationships among people and social structures, and what would thus be capable of grounding a new, path-breaking philosophical direction. And what does it mean that "sites prevail over whatever fills them"? Does it mean simply that for an individual to be, e.g., a father, there must exist the role or the property or the concept of father? If so, then it is clearly again nothing original; if not, then it remains unclear what more it is supposed to mean. I fear that an adherent of Deleuze would call my objections pedantic or uncharitable, and say that my criticism stems from my taking Deleuze's pronouncements out of context - simply that the problem is my inability to tune myself to the author's frequency. Perhaps there is some truth in this; maybe my objections to the first two chapters are indeed somewhat dogmatic. However, I would be very unwilling to concede this for the objections I am now going to raise against what the author writes in the third chapter: there Deleuze invokes examples from mathematics, and he does so in a way which does not seem to me to make any intelligible sense. Let me quote: "We can distinguish three types of relations. A first type is established between elements that enjoy independence or autonomy: for example, 3 + 2 or 2/3. These elements are real and these relations must themselves be said to be real" (p. 264). What kind of relations is meant? "3+2" is a numeric expression, in a certain sense it can be seen as the name of the number 5, in a different sense as the expression of something as a

Introduction

5 2

'construction' of the number out of the numbers two and three - however, in no sense is it an expression of a relation - at least if we stick to how we normally talk in mathematics. (A relation in which 3 and 2 stand would be, e.g., greater than; the corresponding statement would be "!3>2"). I see only two possible alternative explanations of what Deleuze could mean by the term "relation" here. It seems that either (1) he uses the term "relation" for what is normally called operation (i.e. addition, subtraction, multiplication etc.) and says "relations obtain among elements" instead of the usual "operations are applied to elements"; or (2) he talks not about numbers, but rather about numerals and means the relation to be connected by the symbol"+" or"/". To find out which of the two hypotheses would be more adequate, let us look at how he continues: "A second type of relationship, for example, x2 + l - R 2 = 0, is established between terms for which the value is not specified, but that, in each case, must however have a determined value" (p. 265). An equation, such as "x2 + / - R2 = 0", can indeed be seen as a delimitation of a certain relation, in this concrete example the relation which holds among three numbers if and only if the difference between the sum of the quadrates of the first two of them and the third one is zero. 3 However, this is a relation among numbers, and we have just concluded that this is not what Deleuze could possibly have in mind. What he says now, though, seems to pre-empt also the possibility that his talk about relations is to be understood as a talk about operations; for there seems to be no substantiation for saying that the second case involves different operations. Equations are designedly built up from the very same operations which can be encountered within numerical expressions. So we seem to be left with my interpretation (2), i.e. the idea that Deleuze speaks about symbols: now he explicitly invokes "terms for which the value is not specified". The problem, however, is that if what is in question are relations among symbols, then it is utterly unclear what constitutes the difference between the two 7pes of relationships. The symbols "x", 'Y' and "R" within "x2 + / - R = 0" are in the same relationship (i.e. in the relation to be connected by a symbol of an arithmetical operation) as the symbols "3" and "2" within "3 + 2". The upshot is that before I can move to what, according the Deleuze, is the third type of relations, I am already lost - for what he says does not make any sense to me. I suspect that here the only available conclusion is 2 3

See Tichy (1986).

It is the relation in which the coordinates of a point on a circle (with center in the origin of the coordinate system) are to the radius of the circle.

6

Meaning and Structure

that Deleuze's way of treating mathematical concepts is merely another case of the kind of "abuse" dia~nosed by Sakal and Bricmont. The difference between "3 + 2" and "x + / - R 2 = 0" is twofold, neither of which seems to be a matter of "two kinds of relations". The first difference concerns the grammatical category of the expressions: "3 + 2" is, grammatically, a name (a term, in the jargon of logic); whereas "x2 + lR2 = 0" is a sentence (formula). The second difference is a matter of the fact that the expression "3 + 2" is closed, that it is a 'fully-fledged' expression (we can see it as yielding a definite number, namely 5), whereas the expression "x2 + / - R 2 = 0" is open, it is thus in fact a schema (it does not express anything about any particular numbers and is, by itself, neither true nor false). Hence it seems misleading to say that in the latter case we have "terms for which the value is not specified"; it is a relation among numbers, and this relation is specified by means of certain "terms for which the value is not specified" (if we want to introduce such a new name for what is usually called variable). The corresponding relation can be seen as a set of triples of numbers and the equation in question as the specification, the delimitation of the set: it specifies it as the set of all such triples which satisfy the equation. And in this way I could proceed all through Deleuze's book. Is my analysis, along with those of Sakal and Bricmont, inadequate in the sense of taking at face value something which has only an indirect, metaphoric meaning? Perhaps - though it is always possible to counter any arguments of the kind of those I have presented above by saying: "What you call 'abuse' is actually an enlightening metaphor". There is, to be sure, no criterion for what is, or what is not, a good metaphor; so there can be no knock -down argument to prove that something is a real instance of 'abuse'. (And the fact that Deleuze and his colleagues are so widely read and discussed corroborates the view that calling what they do an "abuse" would be at the very least an oversimplification). In view of this, I do not want to press my protests against what Deleuze says; what I protest against is what he does not say. What I miss is a more explicit clarification of the crucial concepts and a consequent formulation of satisfactory criteria of structuralism. My opinion is that his attitude does not provide for the kind of theory which is needed, and for which we will search in this book. 1.3 Contemporary (Post)Analytic Philosophy and Structuralism

What, then, if not the French way? Does analytic philosophy offer us a better lead? The thesis of this book is that it does, although couched in a

Introduction

7

jargon so different from the Saussurean one that it is not easy to see that it is a kind of structuralism. The only explicit discussion of Saussurean structuralism within the context of contemporary analytic philosophy of which I am aware is given by Michael Devitt and Kim Sterelny in their Language and Reality (1987, Chapter 7). 4 In their brief exposition of the Saussurean approach to language, the authors make two points which are important for our current project. First, they point out that the structuralistic approach is essentially holistic. "The meaning of each term," as they put it (ibid., p. 213), "is defined by its place in the entire structure; it has no identity except in that structure .... We cannot coin a term, giving it a meaning, and simply add it with its meaning to the language." This is an aspect which differentiates de Saussure from some analytic philosophers, but by far not from all of them. In fact, it constitutes the affinity between de Saussure's teaching and the views of that part of contemporary analytic philosophy which draws on the writings of Quine (and, also, Sellars): needless to say that holism is one of the pillars of Quine's view of language. And as holism and a certain kind of structuralism are indeed two sides of the same coin (as we will try to show later), Quine's structuralistic inclinations are not so surprising. However, Devitt and Sterelny object to de Saussure's version of holism for the reason that it is part and parcel of a counterintuitive view of language as a self-contained game, isolated from the extralinguistic world, and "to be explained entirely in its own terms without any reference to anything outside its structure" (ibid., p. 214). They point out that the favorite analogy of de Saussure, the comparison of language to chess, itself invites this view of language: chess is self-contained; but language, according to Devitt and Sterelny, is not. I think Devitt and Sterelny are correct here. However, what is the consequence of this for a theory of language? Devitt and Sterelny diagnose the source of the counterintuitive Saussurean 'autonomy oflanguage' as the failure of de Saussure and his followers to recognize that the central function of language is to refer to objects. "The rejection of reference," they write (ibid., p. 215), "is central to the relational, holistic and autonomous view of language that is definitive of structuralism." And their verdict is unambiguous (ibid., p. 218): "structuralism's rejection of reference is not well based and is thoroughly implausible". Whereas I agree that the 'self-containedness' of language which looms from de Saussure's picture is implausible, I do not think that the only 4

It was pointed out to me by Kevin Mulligan.

8

Meaning and Structure

response is the rejection of holism and the (re)installment of the concept of reference in the center of language theory. What is the basic difference between language and chess? While the moves of chess aim only at each other (a chess move 'makes sense' only conceived of as a response to other chess moves or as prompting further moves), 'language games' are somehow 'open to the world'. Frequently we either make an utterance in response to something non-linguistic or we respond to an utterance by a non-linguistic act. Language indeed is no self-contained game, it is one of our means of coping with the rest of the world. However, I think we can account for this kind of 'openness' of language without abandoning the basic holistic and structuralistic insights. One version of such a theory was proffered by the late Wittgenstein; 5 however, in this book I would like to examine another (although in many respects parallel) approach, the approach opened by Quine and Sellars and continued by Davidson, Brandom and others. 1.4 Plan of the Book

The book is divided into three parts, each consisting of three chapters. In the first part I introduce those aspects of the Saussurean legacy which I find crucial and which can be seen as congenial to the views of language entertained by the 'postanalytic' philosophers of the kind just mentioned. In this part's opening chapter, What is Meaning?, I sketch my reasons for being interested in the perhaps prima facie implausible structuralist view of meaning. I briefly review the standard, non-structuralist accounts of meaning and indicate how problematic they become on closer examination; and I suggest that structuralism might be a viable alternative. In the following chapter, called What is Structuralism?, I outline the crucial theses of de Saussure's structuralism and indicate that his insights need not be incompatible with those constitutive of analytic philosophy. In particular, I compare de Saussure's account of what he calls "linguistic reality" with Gottlob Frege' s account of the nature of abstract entities and I conclude that these two theories exhibit surprising similarities. I suggest that what de Saussure lacked and what prevented him from entirely disentangling his structuralist theory of language from the snares of pre-structuralistic mentalism was a theory of abstract objects of the kind proposed by Frege and later developed by the twentieth century logic and mathematics. 5

It is not without interest that the chess metaphor was central for Wittgenstein no less than for de Saussure (see Peregrin, 1995a, §8.3).

Introduction

9

In view of this I make an attempt to reconstruct de Saussure's key theses in mathematical terms. This constitutes the last chapter of the first part of the book, called Parts, Wholes and Structures: Prolegomena to Formal Theory. I claim that as structure is a way in which some parts are organized into a whole, we need a theory of systems of parts and wholes; and I consider the theory proposed for this purpose by Stanislaw Lesniewski and elaborated by his followers. I conclude that this theory is not exactly what we would need and offer a sketch of a more suitable mathematical theory. With its help I try to make a mathematical sense of the Saussurean idea of the birth of 'the structural' out of oppositions. In the second part of the book I tum my attention to the postanalytic philosophers whose views of language I want to portray as continuous with de Saussure's teaching. The first of its chapters, Translation and Structure, is devoted to the views of Willard Van Orman Quine. I argue that Quine's widely discussed indeterminacy theses can be read as simply pointing out the structural nature of language. In general, I claim that Quine's holism, with which he replaces the atomism of his analytic predecessors, is nothing else than a form of structuralism. In the next chapter, Truth and Structure, I discuss the views of Donald Davidson. I argue that Davidson can be seen as complementing the Quinean variety of structuralism with an important new insight revealing couched in Saussurean terms - that the opposition which is crucial from the viewpoint of meaning is that between truth and falsity. I review the way in which, on Davidson's account, truth gets projected into individual meanings and I consider consequences which this picture of language has for Davidson's philosophical views. The last chapter of this part of the book is called Inference and Structure and deals with the view of language originally put forward by Wilfrid Sellars and recently developed by Robert Brandom. I argue that this view can be seen as elucidating the rationale behind the structural character of language. According to Brandom, language is first and foremost our means of engaging in the practice of giving and asking for reasons; and hence its statements are useful only insofar as they are interrelated with other statements, as they can be used as reasons for other statements or be justified by means of other statements. The third part of the book is devoted to the discussion of some consequences of the acknowledgement of the structural nature of language. In the first chapter of this part, Meaning and Inferential Role, I summarize the outcome of the previous considerations by claiming that the structure of language that is constitutive of its semantics is the inferential structure, and that the meaning of an expression, as Sellars suggested, is most adequately

10

Meaning and Structure

identified with its 'inferential role'. (And I indicate that this is compatible with the claim that semantics is grounded in the truth/falsity opposition, for inferential role is what the truth/falsity opposition becomes when it is 'compositionally projected' to the elements of language). However, I also try to show that this construal of meaning does not necessarily imply the rejection of 'formal semantics'. Formal semantics, I claim, is not to be dispensed with, but rather only understood as the means of envisaging the inferential structure. In the chapter, The 'Natural' and the 'Formal', I consider the general relationship between the realm of formal structures and models (such as those dealt with by formal semantics) and that of real phenomena (such as our natural language). I suggest that the situation is best seen in terms of our using the former as a prism to perceive (and to 'make sense' of) the latter. This, in my view, leads to a certain kind of 'dialectics': formal structures which we study when we do formal logic or formal semantics are non-empirical entities which are to be handled by mathematical means, but the question which of them are relevant for our understanding non-formal entities (which of them are structures of these entities) is an empirical question. The last chapter of this part, Semantic Structure of Language and of its Expressions, challenges some common wisdoms regarding 'semantic structures' or 'logical forms' of expressions. I try to show that from the vantage point presented in the book, both the concept of 'logical form' as developed by Chomsky and his followers, and that as developed by the logicians following Russell, are problematic. 1.5 Acknowledgements

This book is a completely reworked version of a text which appeared in Czech under the same title (Vyznam a struktura, OIKOYMENH, Prague, 2000). The revisions stem from two sources: they partly reflect the fact that the Czech edition had to be much more explicit on many points which for an 'international reader' are a matter of course; and partly hopefully also from a better grip I have gotten on the subject matter since finishing the Czech version. In any case, the work can be seen as a synthesis of various projects I have pursued during recent years, so in this sense it is indebted to the institutions sponsoring the individual projects: Alexander von Humbold Stiftung, Research Support Scheme and especially the Grant Agency of the Academy of Sciences of the Czech Republic, which directly sponsored my work on the Czech text. I am grateful to the colleagues and friends who commented on various parts of earlier versions of the manuscript and thus

Introduction

11

have helped me to bring it to this (I hope better) form, especially (but far from exclusively) to Tomas Marvan, Vladimir Svoboda and Pavel Cmorej. I am also grateful to Clare Britton for her effort to make the language of this work look more like English.

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PART I: The Whys and Hows of Structuralism Language is a form, not a substance. Ferdinand de Saussure

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Chapter Two

What is Meaning? 2.1 Words and 'Mental Representations' In this book we will pursue the idea that the concepts of meaning and structure are intimately interrelated, indeed that meaning is, in a clearly explicable sense, a matter of structure. Despite the fact that this thesis has been entertained in various forms by a number of different linguists and philosophers, it continues to sound controversial - perhaps even absurd and I am afraid its promotion could be decried as an exhibition by one of those academic Geisteswissenschaftler who depend on creating pseudoproblems for their existence. To pre-empt such a verdict I will attempt to show, in this chapter, that meaning is more problematic than it may, prima facie, appear. In particular, I will indicate that the usual straightforward theories of how language works and what is meaning, which might appear so natural and so explicative to an uncritical eye, become dubious when subjected to critical scrutiny. Those readers who are clear about the untenability of such simplistic theories are begged for patience: they will find this chapter largely dispensable. Where should we start getting a grip on meaning? Meanings are what expressions of our language are said to possess; and in fact it is only the having of meaning which makes an expression into an expression worth the name. We say that an expression has meaning or that something which looks like an expression lacks meaning, that it may acquire, change or lose its meaning, that somebody may discover, grasp, or forget the meaning. Thus it seems that meaning is a thing which is associated with an expression (and which must be associated with it, if it be an expression) and which whoever learns the corresponding language must somehow 'absorb' into his or her head. 6 However, what is this meaning? What kind of entity can be associated with a word in this way? The first idea which is likely to come to mind of a layman when she thinks about relationships between linguistic expressions and extralinguistic entities is the relation between a name and its bearer. A bearer of a name is a person (or an animal or another kind of entity) and the word which is her name is 6 Reddy ( 1979) pointed out that the basic metaphor underlying our treatment of meanings is that "ideas are objects and expressions are containers into which they can be filled". For a detailed discussion see Lakoff and Johnson ( 1980).

15

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Meaning and Structure

assigned to her via some specific act, the paradigmatic example of which is christening. Christening establishes a link between a word and an individual; and this might suggest itself as a paradigm for thinking about the relations between an expression, or at least a word, and its meaning in general: we, it might seem, simply have elected to give names to various things to be able to talk about them. From this angle, meanings would appear as just those ordinary things which we have chosen to christen by our words. Needless to say this idea proves untenable, even for the layman, once he gives it a second thought. What kinds of things could those named in this way be? What kind of thing is named, e.g., by the word "dog"? It is clear that it is not any one particular dog, so the only viable option seems to be that "dog" names some kind of 'doghood' or a 'concept of dog'. However, it is important to realize that this is by itself no real answer: until we explain what a concept is, the word "concept" is no more perspicuous than the word "meaning", so to say that the meaning of "dog" is the concept of dog is to say next to nothing. It may become a real answer only if supplemented by a clear explanation of what concepts are. A common view, then, is that such an explanation should be left to psychologists; for concepts are some creatures of human mind, and the mind constitutes the domain of psychology. In this way we reach the conception of meaning which could be dubbed psychologico-semiotic. Such a conception is characterized by understanding expressions as names or 'designators' (hence semiotic), and in particular as names of some psychic entities (hence psychologico-). This notion of language is often taken for granted, for it seems to be a direct consequence of the apparently self-evident fact that language is a tool of expressing and communicating thoughts (and/or other 'mental contents', such as mentalistic concepts, images etc.). According to this view, the principle of operation of language can be envisaged in terms of transferring 'mental contents' between the minds of individual communicants: a speaker, so the story goes, conveys a content to a hearer in such a way that she designates it by an expression, and by displaying the expression she makes the hearer 'absorb' the content in his own mind (viz. Figure 1). Under the influence of such a picture expressions are taken simply as names of 'mental contents'; and the particular contents named by an expression is taken to be the meaning of the expression.

What is Meaning?

17

Figure 1 This renders the gist of the 'folk philosophy of language', taken for more or less granted by most of those who do not think about it too much; but also of its sophisticated elaborations, based on what is usually called the representational theory of mind. What, by such theories, makes it possible to talk about an entity is an expression which expresses the mental representation of the entity. Thus there are dogs within the world, there are representations of dogs within human minds, and there are expressions expressing the representations - thereby enabling us to talk about dogs. We have stated that we see such psychologico-semiotic theories as resulting from the intersection of two independent ideas, the semiotic idea that an expression designates its meanings in the way in which a name designates its bearer, and the psychological idea that the meaning is something which exists within the minds of those who employ the expression. Our aim now is to present some arguments indicating that this response to the question What is meaning? brings, in its wake, a number of problems. We will divide our argumentation into three steps: first, within the next section, we will show that the psychological understanding of meaning does not follow from accepting that language is a means of conveying 'mental contents' (i.e. from what is envisaged in Figure 1), and, moreover, that such understanding is essentially problematic in itself. In the following section we

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will then challenge the idea that what we have caricatured in Figure 1 could really indicate the principle of operation of language. Then, in Section 2.5, we will try to show that it is the very understanding of meaning as something which is designated by an expression that may be misleading (and hence that the difficulties with the psychologico-semiotic understanding of language arise not only from its being psychological, but rather also from its being semiotic).

2.2 Is Meaning Within the Mind? The psychologico-semiotic notion oflanguage can appear to follow from what may seem to be an obvious fact: namely that what we use language for is expressing thoughts. Sentences appear to 'verbalize' thoughts, while parts of sentences, words, seem to 'verbalize' parts of thoughts, 'concepts' or perhaps 'ideas'. However, is this picture feasible? To clarify the situation, let us first accept, without discussion, the assumption that an expression is a designator of its meaning (i.e. something like a label which the users of language 'fasten on the meaning') and also the assumption that language serves the task of expressing thoughts or other 'mental contents'. Thus, let us assume that Figure 1 does indicate the genuine principle of communication, i.e. that we utter, e.g., the word "dog" just when our mind comes to contain a specific content (a concept or an idea of (a) dog) and we utter it in order to make the content appear also in our hearer(s)'s mind(s). Would it follow that the contents thus transferred from one mind to another are meanings of the corresponding words? Imagine there is a content within your mind (whatever it might be). If you want to convey this content to somebody, you use, according to our assumption, an expression. Could this mean that what you do in the moment is make the expression into a designator of the content? Surely not: if you were able to do this, if it were in your powers to make an expression into a designator of your mental content (in the way in which we make, by means of christening, a name into the designator of a particular individual), you could make do with any expression. If you thought, say, about a dog, you could take, e.g., the word "elephant", or the 'word' "xyz", make it into a designator of your 'mental content' and then use it to express the content and convey it to a hearer. However, this would hardly work: uttering "elephant" or "xyz" would hardly make anybody think about a dog. How, then, can you really convey what you think of to somebody else? Clearly by finding an expression which is 'suited' for the very purpose, i.e. which does have the meaning which is somehow related to what you are thinking of. It follows that meaning must be something which is here before the act of expressing a thought or a 'mental content' and which makes the

What is Meaning?

19

expressing possible in the first place. 7 There is no way to make something mental into the meaning of an expression; the only thing one can do is to find an expression which already has a suitable meaning; and the act of expressing the 'mental content' may be successful to the extent, and only to that extent, to which the attempt to find a suitable expression is successful. It is thus plainly wrong to conclude that the assumption that we use language to express and to convey mental contents entails the conclusion that these mental contents are meanings of the corresponding expressions, for the meaning of an expression and that which the expression conveys is not one and the same thing. Ifi say "My neighbor has a dog", I surely do not convey the meaning of the sentence I utter- on the contrary, I can convey something by it only to the extent to which my audience understands it, i.e. knows its meaning, in advance. This means that what is conveyed is not meaning and if we assume that language serves to convey mental entities, it does not follow that the mental entities are meanings of the expressions which are used to convey them. If I tell somebody "My neighbor has a dog", then what I am conveying to him is something factual, something about the status of my neighbor; while for the meaning of the sentence this status is irrelevant: we can surely know the meaning without knowing whether the neighbor in fact owns a dog, or even without knowing who the neighbor is supposed to be. (Not to mention the fact that if I tell somebody "My neighbor has a dog", what I convey to him is that the neighbor of Jaroslav Peregrin has a dog, while the meaning of "My neighbor has a dog" obviously differs from that of "The neighbor of Jaroslav Peregrin has a dog"). Therefore, the conclusion that meanings are mental entities does not really follow from the assumption that language serves to express and convey thoughts or other kinds of 'mental contents'. Moreover, the above discussion has indicated that the conclusion is problematic in itself: expressions cannot be designators of mental entities for the very reason that they can successfully serve communication ('conveying thoughts'), and for this purpose they have to be intersubjective. The point of meanings lies precisely in that they, unlike mental contents, can be shared by different participants of communication. Semantics thus cannot be a matter of psychology (in the sense of the theory of the subjective); on the contrary, semantics begins where subjectivity ends and hence where psychology 7

It is also important to realize that expressions of language as such do not display, in contrast to pictures, any 'natural' similarity to what they mean or to what they refer to (with the marginal exception of pictorial scripts). This is a fact which is, on one hand, plainly obvious, but which is nevertheless, often as if ignored when language is explained in representational terms or in terms of something like the early-Wittgensteinian picture theory of language.

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ends; it is intersubjectivity which is constitutive of it. As Dummett (1978, p. 217) puts it, "an individual cannot communicate what he cannot be observed to communicate"; hence as Davidson (1990, p. 314) urges, "that meanings are decipherable is not a matter of luck; public availability is a constitutive aspect oflanguage". 8 However, does this not contradict the obvious fact that we can talk about things which somebody simply fancied and which thus appear not to exist elsewhere than 'in thought'? How can we talk about Mickey Mouse, about Batman or about hobbits? Does this not mean that the statements treating of such beings cannot express anything but mere thoughts or ideas - that the name "Mickey Mouse" cannot stand for anything else than a 'mental content'? The answer to this objection is that we must avoid confusing two essentially different senses of "thought": in the psychological sense, in which we have employed the word so far, "thought" refers to an act of an individual mind which is, by its nature, subjective; however, there is also a different sense, in which it can be taken as referring to something intersubjective, something which exists apart from any individual mind. The crucial point to realize is that something can exist independently of any particular mind - and thus be essentially intersubjective - despite not existing independently of the very existence of minds (and thus not being 'tangible' in the way in which rocks or stars are). Mickey Mouse surely exists independently of the mind of Walt Disney or indeed any other particular mind - not in the sense that you could run into him on your way to the office, but in the sense that he has some objective properties independently of whether any particular person thinks he has them. This follows from the fact that one can be mistaken with respect to him: if you claimed that, e.g., Mickey has a bat-like suit, rides the Batrnobil and fights evil within the city of Gotham, you would be justly corrected that you mistake Mickey Mouse for Batman. (The problem of the 'real', 'non-fictive' existence of Mickey Mouse is then a purely empirical 'problem which has - similarly to the problem of the existence of, e.g., yeti - nothing to do with language and its semantics). All of this seems to suggest that the picture snuggling in the foundation of the common idea that meaning is something mental is far less plausible than it might prima facie seem. We have seen that even if we admit that language works in the very way presupposed by the picture, it would not follow that meaning is hidden somewhere within the human mind. Moreover, such an understanding of meaning, as we have also seen, is problematic in itself- for meaning is essentially intersubjective. 8

The most popular case for the "public availability" of meanings is made by Wittgenstein, in the course of what has become known as his anti-private language argument (see Wittgenstein, 1953, §243ff.; see also Kripke, 1982, and Baker and Hacker, 1984 for a discussion of the nature and import of the argument).

What is Meaning?

21

However, could not the above distinction between the two senses of "thought" provide a clue for modifying the psychologico-semiotic theory of meaning into a tenable form? Would it not suffice to understand thoughts in the second of the above mentioned ways, namely not as something subjective, but rather as something which, although it may come to be contained within the human mind, is nevertheless capable of existing somehow independently (and which is only 'grasped' by a mind)? This move would indeed help us overcome the discrepancy between the subjectivity of minds and the intersubjectivity of meanings; however, it would amount not to saving the psychologico-semiotic notion of meaning, but rather to its obliteration. This is because a thought in the non-subjective sense is no longer something which could be considered a matter of psychology. 'Thoughts' existing outside of minds clearly fall within the legislation of those who inventorize 'what there is', i.e. ontologists or metaphysicians - or indeed semanticists, given that we agree to follow Frege and Wittgenstein in identifying thoughts of this kind with senses of sentences. This would quash the idea that we leave the explanation of meanings to psychologists- on the contrary, psychologists then would have to leave the explanation of the nature of such thoughts to us, semanticists. (If we construe the objectivity of the non-psychological thoughts in a Platonist vein, we would thus be subscribing to what we will later refer to as the ontologico-semiotic notion of meaning). For a psychologico-semiotic theoretician of meaning there may still be a defense line behind which to retreat- namely to claim, as Fodor (1998) does, that the thoughts relevant for semantics are nothing more than types of psychological thought-tokens. Hence they too would fall within the province of the psychologist (or a 'cognitive scientist')- just as the elephant, seen as an abstract type, still falls within the province of a zoologist. Both the psychologist and the zoologist, so the story may go, study their peculiar tokens (subjective thoughts, individual animals) and reach certain generalizations which can be taken as abstract universalia (non-subjective thoughts, animal kinds). However, notice that this parallel is flawed: a psychologist, unlike the zoologist, cannot be seen as arriving at thought-types by studying thought-tokens: there is no access into the minds to the tokens, so their existence is rather inferred from the (mostly verbal) behavior of people, and to understand a behavior as verbal and hence thought-expressing, we need to interpret it as meaningful; so to arrive at thought-tokens we need meanings, not the other way round.

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2.3 Is Language a Tool of Conveying Thoughts?

We have indicated that even if it were an indubitable fact that the function of language is to express and convey 'mental contents', it still does not follow that meaning is something mental. Let us now, moreover, indicate that even the notion of language as a tool of conveying thoughts is much less straightforward than might be assumed. Why do we think that we use language to convey 'mental contents'? This question might look, prima facie, silly - what else could a language be than a means of saying what we think of? What else could be the reason for the utterance of a sentence than the occurrence of a thought? If somebody says "My neighbor has a dog", then the reason obviously is that he has a thought about his neighbor's having a dog and he wants to communicate it to somebody! However, is the situation really so clear? What does it in fact mean that somebody has a thought, or that the thought occurs to her? What sense of "thought" is the one which fits into this context? One answer might be that a thought is simply something as a sentence made of a mental stuff, with something like 'ideas' or 'mental concepts' in place of words. The utterance of the corresponding sentence could then be seen as the result of replacing of the 'mental constituents' by the corresponding linguistic constituents, words. This is the idea fuelling the foundations of the "language of thought" theories developed most consequentially by Fodor ( 197 5). According to these theories, our overt language is meaningful because it expresses the covert language of thought, whereas the language of thought is meaningful somehow inherently. This idea, namely the idea that the semantics or 'intentionality' of language is reducible to the 'intentionality' of thought and that the 'intentionality' of thought is just something which we must accept, something irreducible to anything more primitive, is what Fodor's conception shares with the conception ofJohn Searle (1983). The glaring objection to this approach to language is that it leads us to what Blackburn (1984, §II.3) calls a "dog-legged theory"; a theory which does not solve the problem but rather only shifts it at one remove, namely from language to thought. Of course, the proponents of the approach may point out that explanations must come to an end somewhere and that the intentionality of thought is a good point at which to stop - the fact that our thoughts are about various things is experienced by everybody and therefore is in this sense perspicuous. However, even if we agreed that intentionality of thought is a perspicuous matter (which is far from noncontroversial)9 , to use this fact to explain the intentionality of language 9

I think that one of the important things indicated by Wittgenstein (1953) was that the alleged perspicuity is largely a matter of illusion.

What is Meaning?

23

would necessitate a story about how thoughts get expressed by language and this is the kind of story which we are now trying to cast doubt upon. So back to the proposal that an utterance of a sentence might be a matter of 'externalizing' a thought construed as an analogue of the sentence composed of a 'mental stuff. The first problem is the difficulty of finding any evidence capable of vindicating this. In particular, introspection does not appear to yield us such evidence: the point is that in this case having the occurrent thought My neighbor has a dog, which is supposed to underlie the utterance of "My neighbor has a dog", would amount to contemplating a complex made of several separate, distinguishable parts, namely the 'mental concepts' or 'ideas' corresponding to the five constituents of the sentence; and this is hardly something which we can claim happens in the course of our normal employment of language. 10 (Note that while we can plausibly say that we utter an articulated sentence without thinking of it as articulated, it would be much harder to maintain that we think an articulated thought without thinking it as articulated). 11 It might seem that to make this picture more realistic we should understand the occurrent thoughts which are taken to underlie our utterances as nothing so articulated as sentences, but rather as something in the spirit of 'pictures before the mind's eye'. Such an explanation would lead to the conclusion that the occurrence of the thought My neighbor has a dog would be a kind of imagining, rather than a kind of 'inner pronouncement'. However, if one imagines her neighbor and his dog - if she, that is, has a certain picture in her mind's eye- what causes her to express it as "My neighbor has a dog", and not as, say, "My neighbor's dog has four legs", or even "People keep animals"? Hence from this visual angle it would seem that the articulation of the sentence expressing a thought would have to be present already in the thought after all - for otherwise it would be scarcely explainable why a sentence articulated just in this way should express just this thought. However, we have concluded that to see a sentence uttered as a piece-to-piece translation into overt language of an occurrent conglomerate of ideas is not plausible. Could we, then, not solve the dilemma by assuming that the occurrent

10 Of cour e we could develop a more sophisticated version of the story, according to which not every expression expresses a self-contained idea. However, this kind of modification does not seem to make the story generally feasible. 11 That the picture of the stream of consciousness as consisting of recurring ideas is misguided was famously pointed out by William James (1910, p. 74): "A permanently existing 'Idea' which makes its appearance before the footlights of consciousness at periodical intervals is as mythological an entity as the Jack of Spades."

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thought taken to underlie the utterance of an overt sentence is literally a sentence uttered 'within the mind'? This too is an unsatisfactory solution to the problem in question- for if we understood thoughts in this, 'linguistic' way, the thesis that a person utters "My neighbor has a dog" when she has the occurrent thought My neighbor has a dog would boil down to the thesis that she utters "My neighbor has a dog" aloud when she utters "My neighbor has a dog" (or an equivalent of the sentence in another language) for herself beforehand. Obviously, situations exist when things like this happen; however, it would be hard to believe that this picture captures the general functioning of language. And besides this, in such a case it would no longer be the relationship between thinking and speaking which would be in question, but rather the relationship between speaking for oneself and speaking aloud - and instead of explaining speaking in terms of thinking it would amount to explaining, the other way around, thinking as a kind of speaking. If we consider the way in which we normally employ language, we can hardly fail to see that the case in which we first think of something and only subsequently 'dress it into words' is a highly specific case not representative of ordinary speaking. If I see a dog and say "There is a dog over there!", it is usually not the case that I would first think it, then find the appropriate words, and only then express the thought. An utterance and the thought expressed by it are generally not two subsequent and causally connected events. And this is the case whichever kind of mental activity we may assimilate the 'occurrence of a thought' to: observing our real usage of language does not seem to support the thesis that the overt utterance is the result of such a covert occurrence. Moreover, as Wittgenstein urged, 12 there is no uniform mental activity which could be claimed to generally accompany our utterances at all. 13

12

See Wittgenstein (1953, §153). The untenable picture of language as 'expressing thoughts' in this way must not be confused with the rather obvious fact that a linguistic utterances are accompanied by an intention (not in the sense of 'aboutness', but in the sense of 'purposing'). It is sometimes being argued that a speaker often feels that he has failed to express, by his utterance, what he wanted; and sometimes he even simply 'lacks words'. Is this not a clear proof that before the utterance there must be a thought which the utterance is to express and which it manages to express in a better or worse way, according to how faithfully it 'translates' it? Does this not mean that to make an utterance is to couch a thought into words? What this indubitably indicates is the presence of an intention, and the consequent possibility of assessing the utterance in its lights and finding it more or less satisfactory. It does not necessarily mean that this suitability has to involve a comparison of the utterance with its 'latent', mental form. Let us imagine we draw an abstract picture: we will probably find the result of our effort also more or less satisfactory - and this clearly need not mean that we had held, before starting to paint, an intended picture somewhere in our mind's eye. 13

What is Meaning?

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There is also another line of argumentation sometimes employed to show that language must be seen as a tool of expressing thoughts. This concerns the way language came into being. What else, so the argument runs, could have caused our ancestors to develop language other than the need to externalize their thoughts? And if we have developed language in order to be able to 'dress our thoughts into words', then we must regard its semantics as explainable in terms of the thoughts - otherwise we would be as someone trying to understand shoes whilst ignoring that they have been devised to cover human feet. However, this would presuppose that articulated thought existed prior to, and independently of, language; and this is a thesis which would be hard to accept. We have seen that to consider the articulation of thought independently of the articulation of language is a tricky matter; and in fact many outstanding linguists and anthropologists, as well as philosophers, have warned us against doing so: they claim that \our kind of) thinking and language are two inseparable sides of the same coin. 4 It is therefore dubious to claim that, historically speaking, language derives from (articulated) thought; and an attempt to give it such a position within the order of explanation, to explain language in terms of thought, would be an exemplary case of an obscurum per obscurius explanation. Language and its factual functioning is - in contrast to thinking - by its very nature easily intersubjectively graspable and relatively easily describable: so a far more promising vein is to explain thinking in terms of language and not vice versa. (Needless to say that this is one of the principal points of departure of the linguistic turn, which, as Dummett, 1988, p. 5, puts it, is based on the conviction "that a philosophical account of thought can be attained through a philosophical account of language" and "that a comprehensive account can only be so attained"). All of this seems to indicate that both the notion of meaning as something mental and the notion of language as a straightforward means of expressing pre-existing thought are fundamentally problematic. (Note that here we do not aspire to anything more than showing that they are problematic, i.e. much less straightforward and plausible than it is often taken for granted). In particular, any representational semantics in the sense outlined above will be problematic: even if we overlook the dubiousness of construing the human mind as

14

See, e.g., Dennett (1996) or Deacon (1998). De Saussure (1931, p.l56), whose views will be discussed in the following chapter, claims that it is only "the unity thought-sound" which implies any articulation of the hitherto amorphous mental substance. Many other outstanding linguists from Humboldt through Sapir, Whorf or Hjelmslev (see esp. Whorf, 1956) to Lakoff and Johnson (1980)- directly insist that the categories in terms of which our thinking grasps our world are largely a matter of our language.

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principally a representing device, 15 we cannot avoid the problems posed by the fact that it is essentially unclear in which sense mental representations could be relevant for a theory of meaning.

2.4 Meanings as Abstract Objects The upshot of the preceding sections is that the explanation of meaning in the psychologico-semiotic way, i.e. in terms of thoughts, images or psychologically construed 'mental contents', may raise more problems than it solves. However, if meanings are to be found neither among the denizens of the real, physical world, nor within the minds of thinking beings, then the only space left for them appears to be within a 'third realm of being', inhabited by some non-physical, and in the same time non-subjective, non-mental objects, a realm ofPlatonist ideas or 'objective abstracts'. The existence of such a realm has been urged by a number of philosophers from Antiquity until present times; but it has been also the target of many vigorous controversies which have multiplied with the establishment of modem naturalistic science. However, then Frege and his followers managed to lessen its controversiality by holding it subject to the legislation of mathematics, which continues to be a respectable science even for a naturalist. (And clearly this 'mathematization' of semantics was one of the important moments within the history of analytic philosophy). Subsequently, with the establishment of set theory as the universal metamathematical framework, it transpired that such a realm came to be seen as consisting of merely one kind of rather uncontroversial abstract entities, namely sets. The idea of Frege (1892) was original, and yet quite simple: while meanings of some elements of language, of names, are simply the objects named by them (and a bit surprisingly, Frege counted also sentences among names: he saw them as names of the two truth values), 16 those of the rest of the elements are reconstructible as functions, in the mathematical sense of the word, bringing us from objects to objects. Thus, the meaning of a predicate is 15

The case against such representationalism has been made most spectacularly by Rorty (1980), but it has been challenged, in various ways, by many recent postanalytic philosophers. (An equally spectacular, but much more succinct reaction to representationalism is reported by Brandom, 1994, p. 74. According to him, Rebecca West responded to the idea that we should be making copies of the universe with "One of the damn things is enough!") Let us stress that this is not to deny that various kinds of representations play important roles within human thinking - what we dispute is that thinking be reducible to, or be explainable solely in terms of, representing or manipulating representations. 16 Frege's story of how a name can come to name an abstract object is not quite simple; we will have the opportunity to discuss it in greater detail in Section 3.5.

What is Meaning?

27

simply what brings us from objects to truth values: the meaning of "dog" (or "to be a dog") is what brings us from Pluto to the truth (for "dog" combined with "Pluto" yields the sentence "Pluto is a dog" which is true), from Donald Duck to the falsity etc. Similarly the meaning of "not" brings us from truth values to truth values: in particular from the falsity to the truth and from the truth to the falsity. (Frege then supplements this story about meaning [Bedeutung] with a story about sense [Sinn], which amounts to the way meaning is "given" to us). Tarski (1933; 1939), Carnap (1942) and others then embedded these ideas into the framework of the modern, set-theoretic mathematics, within which functions are taken as specific kinds of sets, namely certain sets of ordered pairs. (Carnap, 1947, then indicated how this kind of treatment can be extended from Fregean meanings - or extensions, in Carnap's term - to Fregean senses - which he proposed to call intensions). In this way, the development of modern mathematics has provided for a certain vindication of the Platonist picture of meanings as ideas residing in some non-physical, but publicly accessible heaven, supplementing it with a non-mysterious explanation of how to enter this heaven to inspect the ideas: not by a mystical penetration, but by means of mathematical theorizing. CVV e will have the opportunity to say more about this approach in the course of the rest of the book, especially in Chapter 8). This has led some linguists and philosophers to an understanding of language and its semantics which might be called ontologico-semiotic. The expressions of language are still understood as designators, but now not as designators of mental contents, but rather as designators of objective, abstract entities (usually sets). For the reasons discussed above, this construal of language might be seen as a radical progress in the understanding of meaning; and it is indeed often extremely helpful to look at language in this ontologico-semiotic way. Nevertheless, if we take the ontologico-semiotic picture too literally, it too can lead us to a distorted way of thinking about the working of language and about the nature of meaning. The point is that the problem with the psychologico-semiotic construal, as we are now going to argue, lies not only in its being psychological, but also in its being semiotic and hence its replacement with the ontologico-semiotic notion is not a replacement enough. We are going to argue that problems arise from the very attempt to see an expression as the designator of its meaning.

28

Meaning and Structure

2.5 Semantics and Semiotics A sign, as understood by semiotics, is the unity of two entities, the signifier (or designator) and the signified. If we say that the well known five circles symbolize the Olympic games, we are saying that there is an interrelationship between the figure (as the signifier) and the Olympic games (as the signified), i.e. that whoever is confronted, within a suitable context, with the former will thereby feel to be confronted with the latter. If we say that the red traffic light means stop!, we are saying that there is an interconnection between the light and the order to stop; again, whoever is confronted, in an appropriate context, with the former, will acknowledge the order to stop. The sign is thus a matter of the interconnection of two independently existing items, the signifier and the signified. The signifier, as such, is understood only as a kind of pointer to the signified. "The sign comprises of two ideas," as we read in the seventeenth century Port-Royal Logic, "one is the idea of the thing that represents, the other is that of the thing represented; its nature consists in that it evokes the latter by means of the former." 17 The only function of the signifier, qua signifier, is to point to the signified; just like the only function of a photo a soldier puts into his wallet when he is leaving home is to 'point to', i.e. to help him recall, his wife. The unity of the signified and the signifier is thus a contingent empirical fact, resulting either from some factual short-term action ('christening') or from a long-term process. We can call the establishment of such an unity, together with Morris (1966), semiosis. The fact that the Olympic games are associated with the circles is the result of an historical development and probably also of certain formal declarations and/or legal acts; the fact that the red traffic light is associated with the order to stop is a matter of the rules of traffic. In which respect is the association of an expression with its meaning analogous to the association of the signifier with the signified? Surely in that we can see the expression as something the point of which is to enable us to perceive its meaning through it, just as we perceive the Olympic games through the circles. It is precisely this which makes it tempting to see semantics, the theory of meaning, as a special case of semiotics, the general theory of signs. What we urge here, however, is that such a subordination of semantics to semiotics obscures more than it clarifies. Although there is a respect in which we can see a meaningful expression on a par with signs of the kind of those mentioned above, in another respect this assimilation can be severely misleading. It forces on us the idea that the meaning of an expression is some independently existing entity which has only happened to be associated with the expression; that expressions are kinds of labels which we 17

See Arnauld, and Nicole (1662, Iere partie, chap. IV).

What is Meaning?

29

use to name things otherwise independent of them (be it things of the mental world, of the physical world, or of a 'third realm'). This results into a picture according to which language is a mere means of naming things, which are there anyway independently of whether they have a name or not. 18 And this is a picture which, as we will claim, trivializes the role of language within our coping with the world: according to it we could think, act and live in the very same way as we do now quite well without language - the only thing we could not do in such circumstances would be to convey our thoughts. To avoid misunderstanding, let us stress that this is not to say that I consider semiotics silly or misguided. Signs play an important role within human conduct and a theory of signs is thus surely an important part of the humanities. What I reject is that semantics should be subsumed under semiotics, that language should be seen as an attachment of expressions, as signifiers, to some independently existing signifieds. However, would not the rejection of the semiotic conception of semantics contradict what we concluded above in Section 2.2, namely that an expression must have a meaning before it can be used to communicate? Did this conclusion not imply that the employment of an expression must be preceded by an act of associating it with the meanings - i.e. by a semiosis? And are we thus not forced to conclude either that language must have been established via a series of human agreements or conventions, or that it must be a strange gift of God or Nature or other superhuman power? 19 Of course not - at least not more than the fact that people buy and sell things only insofar as the things are worth something entails either that there must have been a point when people settled down to establish the prices of things (or at least the principles of settling the prices) or that prices are from God. Prices and the sense of 'something being worth something' have developed, together with the enterprise of buying and selling, progressively out of the enterprise of exchanging which, in tum, developed progressively from nothing; and similarly meanings developed, together with linguistic practices, progressively from the stage where there were no such practices. So the conclusion is not that communication was preceded by a conventional meaning assignment, but rather that meaning and communication must have co-developed in mutual interdependence; that although any particular 18

In Swift's Gulliver's travels we can even find a recipe how to communicate without words: "Since words are only names of things, it would be more convenient for all men to carry about them such things as were necessary to express the particular business they are to discourse on .... Therefore the room where company meet who practice this art, is full of all things ready at hand, requisite to furnish matter for this kind of artificial converse." 19 In fact, some of the avowed structuralists, with their claims to the subordination of 'man to structure', seem to come quite close to the last notion.

30

Meaning and Structure

act of communication presupposes the meaningfulness of the expressions employed, it, in tum, contributes to the establishment of their meanings and hence language cannot be seen as a tool adopted for the purpose of communicating pre-existing meanings. At this point, it may be objected that using the untenability of construing the expression-meaning relation in semiotic terms as the reason for abandoning the semiotic picture of language is preposterous: that language is a semiotic system on the level of reference, not on the level of meaning; and reference is just about everything we need to explain language? 0 According to this view, a word like "dog" is something like a designator, though not a designator of a meaning or a concept, but rather a 'promiscuous' designator of individual dogs: as we say, it refers to dogs. (If we then insist on using the term "meaning", we might consider saying that meaning is the ability to refer to a certain kind of things, e.g. dogs). This may lead to a kind of 'naturalized semiotics': the kind of relation of designation which amounts to reference seems to be suitable to be accounted for in naturalistic, causal terms (see Devitt and Sterelny, 1987). The trouble with this story is not so much that it is wrong, as that it is essentially incomplete. That there is a causal relationship between some words and some things of the real world (e.g. the word "dog" and dogs) far from explains the semantics oflanguage.lt comes naturally if what we have in mind is the explanation of pronouncements like "Dog!" or "There is a dog over there" in the presence of a dog; however, if we want it to explain also such locutions as "There are no dogs here" or "Dogs are mammals", we must complement it by an additional story. (I do not claim that such a story is inconceivable: we can surely, for example, explain "Dogs are mammals" as expressive of the fact that we have come to adopt a convention according to which we never use the term "dog" to refer to something to which we would not be willing to also refer by the term "mammal". What I point out is that the referential theory of meaning is not a story about semantics, but at best the beginning of a story). Moreover, we would have to supply a couple of stories about terms which appear not to be referential, or at least not so straightforwardly as "dog"; words like 'justice", "number", "better", "through", "who" etc. We would have to supply stories either to establish that these words, despite appearances, are referential after all (which I doubt would be very plausible), or alternatively to establish that our employment of straightforwardly referential words like "dog" engendered the need for the other, non-referential vocabulary (and in this case it would seem that the bulk

20

This kind of stmy has gained popularity especially since the seminal analyses of Kripke (1972), moving the concept of reference into the focus of semantic theory.

What is Meaning?

31

of the theory of language would have to consist in these additional stories, rather than in the initial idea about reference).

2.6 The Case of Augustinus How does this refusal to subsume semantics under semiotics square with our proclaimed adherence to de Saussure, who is assumed to be one of the founding fathers of semiotics? I want to argue that the assumption that de Saussure is a semioticist in the sense exhibited above is mistaken, or at least misleading. While it is true that de Saussure often speaks about an assimilation of his theory of language to a general theory of signs (his term for this theory being not semiotics, but rather semiology), his notion of such a general theory is not the one we wish to circumscribe. The point is that de Saussure resolutely rejects the understanding of language as a 'nomenclature', i.e. as a set of labels stuck to things. His conviction is that " ... language has neither ideas, nor sounds that existed before the linguistic system, but only conceptual and phonic differences that have issued from the system" ( 1931, p. 166). This means that if we are to take a linguistic expression as a sign, we must take it as a sign crucially different from the ones mentioned above: its signified (and, as we will see later, in a certain sense even its signifier) is not constituted until the constitution of this sign. The things which become meanings thus, according to de Saussure, do not exist before language and independently of language, they come into being through language. They are not things which would be only 'labeled' by expressions, they are values of expressions which result from the expressions' assuming their positions within the system of language and, as Wittgenstein would put it, taking part in the relevant "language games". This is to say that the Saussurean idea of semiology can be understood (and, as the case may be, developed) in various reasonable and less reasonable ways. What we reject is the assimilation, effected by many contemporary (express or implicit) semioticists, of the relation expression - meaning to the relations of the kind ofjive circles- Olympic games or red light- stop!. If a sign is, as Eco (1986, p. 14) says using Peirce's words, "something which stands to somebody for something in some respect or capacity", then a prototype of a sign appears to be just the snapshot which a soldier takes when he is to leave his wife. The photo stands to him for the wife, and the wife exists entirely independently of the fact whether somebody has her photo. Hence if an expression were to designate its meaning in this way, meanings would have

32

Meaning and Structure

to be entities represented by words only for 'technical reasons' ;21 and if what we are after is the 'real subject matter', we should forget about expressions and penetrate directly to the world of meanings. The delusiveness of this picture, i.e. the delusiveness of the idea that meanings are some (mental or other) things, the association of which with expressions is observable in some manner analogous to observing the association of the Olympic games with the five circles, was one of the central themes of Wittgenstein's Philosophical Investigations. (And it has been pointed out that his viewpoint has lot in common with the central tenets of de Saussure's doctrine)? 2 Wittgenstein (1953, §316) describes the situation as follows: In order to get clear about the meaning of the word 'think' we watch ourselves while we think; what we observe will be what the word means! -But this concept is not used like that. (It would be as if without knowing how to play chess, I were to try and make out what the word 'mate' meant by close observation of the last move of some game of chess).

This means that just as we cannot understand the sense of the chess pieces by their inspection or by searching out their links to other entities (e.g. by trying to find out whether the piece of wood which is called king is associated with a kind of an abstract 'kinghood'), but only by learning the rules of chess, we can understand the meanings of expressions not by searching for some acts of semiosis or by trying to find the things which are labeled by them, but rather by considering what we do with language_23 The basic difference between the approach of semioticists like Eco and that of Wittgenstein is evident when we consider their evaluation of Augustinus' attempt, in his De Magistro, to explain language as a set of labels stuck to things. While for Eco this is a path-breaking discovery (Augustinus, according to him, "definitely bring[s] together the theory of signs and the theory of language"; "fifteen centuries before Saussure, he will be the one to recognize the genus of signs, of which linguistic signs are species", 1986, p. 33), for Wittgenstein it is exactly this Augustinian picture which is the prototype of an 21

They have to be represented by words because they, in contrast to the things themselves, can be easily 'carried along'- just in the spirit of Gulliver's story (see footnote 18 above). 22 See Harris (1988). 23

Fodor has recently subjected the language/chess comparison to a devastating criticism: "[O]n reflection, it doesn't seem that languages are a lot like games after all: queens and pawns do not mean anything, whereas 'dog' means dog. That's why, though you can't translate the queen into French (or, a fortiori, into checkers), you can translate 'dog' into 'chien'. It's perhaps unwise to insist on an analogy that misses so glaring a difference." (See Fodor, 1998, p. 36). Too bad that nobody told this to Wittgenstein- he might have saved himself the effort of writing Philosophical Investigations!

What is Meaning?

33

utterly misleading way to think about language. The problem, according to Wittgenstein, is that "Augustine describes the learning of human lan~uage as if ... the child could already think, only not yet speak" (1953, §32)? And the trouble is that if we explain language as a mere 'extemalization of (ready-made) thought', we obscure the fact that our thought (and thereby in a sense also our world) would hardly be what it is if we did not have the language we have. A sign, as a contingent association of a signifier and a signified, presupposes a ready-made space of potential signifi~rs ('words') and the complementary space of potential signified's ('things'), which are, or are not, contingently associated. However, a real language is characterized by the fact that meanings (and, in a sense, also expressions) do not exist beforehand, but rather come to be constituted through the constitution of the system of language. In the writings of Willard Van Orman Quine (which will be discussed in greater detail in the second part of the book), such a semiotic notion of language is portrayed as the product of what the author calls the museum myth. In his own words (1969, p. 27), "Uncritical semantics is the myth of a museum in which the exhibits are meanings and the words are labels. To switch languages is to change the labels." Quine's objection is not that this myth involves seeing meanings as something mental (although, as he says, "that could be objection enough"). The main objection concerns the idea that the 'real' semantics is a matter not of the (linguistic) behavior of speakers, but rather of an interconnection between words and things somewhere within the minds of the users of language. This is the root, as Quine claims, of the "pernicious mentalism" which "vitiates semantics". According to Quine, semantics can only be the investigation into the "overt behavior" of the users of language (or, as the case may be, of "dispositions" to such behavior). Semantics, according to him, does not consist in searching out things, which are interlinked with expressions, it consists in investigating the structure of language and the 'logic' which governs the 'games' we play with it. And as the roles of the elements of the language within the games are essentially intermingled, the structure is a nontrivial one; and it has little to do with how the 'pre-linguistic' reality is 'in itself. Meanings, then, can be nothing over and above 'materializations' of the capability of the expressions to play roles within the games - as certain kinds of values of the expressions? 5 24

Cf. also Sellars (1956, pp.l61-162): "[U]nless we are careful, we can easily take for granted that the process of teaching a child to use a language is that of teaching it to discriminate elements within a logical space of particulars, universals, facts etc., of which it is already undiscriminatingly aware, and to associate these discriminated elements with verbal symbols." 25 The extent to which this brings about the erasure of the traditional boundary between semantics and pragmatics was discussed by me elsewhere (see Peregrin, 1999a).

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Meaning and Structure

2.7 Language as a Toolbox All of this seems to suggest that even if we were willing to sacrifice the concept of meaning, we could hardly regard the concept of designation as alone constitutive of the semantics of language. However, if we give up the idea that language is a 'semiotic system', that expressions are labels stuck either to ideas, or to things, what kind of notion are we left with? What kind of story do philosophers following Wittgenstein (or Quine) offer in exchange? Well, we have already indicated it: we should tum our attention to what we do with language, to which 'language games' we play, and hence we should stick to seeing language as a kind of toolbox. We should not see words as labels representing the world, but rather as our means of coping with the world. Wittgenstein (1969, p. 67) portrays language in the following way: Language is like a collection of very various tools. In the tool box there is a hammer, a saw, a rule, a lead, a glue pot and glue. Many of the tools are akin to each other in form and use, and the tools can be roughly divided into groups according to their relationships; but the boundaries between these groups will often be more or less arbitrary and there are various types of relationship that cut across one another.

Wittgenstein's claim that it is useful to see language in terms of the 'games' we play by its means, is, of course, again not a full story about semantics, but at best a framework for a story. As it stands, it merely liberates us from having to see language as a set of labels; but it does not even exclude the possibility of doing so. We could surely say that as a matter of fact there is one principal 'language game' we constantly play, and this game consists in labeling or naming, and subsequently representing, things. And indeed, the 'language game' stance is, by itself, hardly incompatible with any notion of semantics. However, Wittgenstein says more than that we should assume this stance: he suggests that the 'language games' we play are 'rule-governed' (although, in contrast to activities like chess, not governed by explicit rules), and that to understand them we should reveal their rules (which presupposes clarifying what does it mean to follow an implicit rule). More specifically, he claims that naming things cannot be the language game we play (for there is no single one such game), and that in a sense it is not even a language game. To illustrate this, let us consider the story he tells us in the beginning of Philosophical Investigations. He invites us to consider a rudimentary language which is very unlike our developed one: a language consisting of several single words used by a person building a wall to indicate to his helper what kind of brick he needs. Of course, even in this case we could

What is Meaning?

35

say that the words of this language designate the respective types of bricks; but now it is obvious that this would not explain what turns the sounds emitted by the builder into words (albeit rudimentary ones). To satisfactorily explain the nature of the language in question we must talk about how the helper reacts to the individual words - i.e. to say what purpose the words serve their utterer, what he manages, or wants, to achieve with them. (However, note that having explained the universal purpose of the words, namely that they are commands to pass various kinds of bricks, we can explain the functions of individual words by simply showing which particular bricks they are related to). Now, is the situation not similar to that of fully-fledged languages? Should we not ask, seeking for meaning, what the expressions are good for, in which situations and how they are employed? True, to describe the employment of some expressions we would probably have to talk about those objects which the words are usually said to 'refer to' (thus we could scarcely describe the function of "dog" without talking about, or pointing at, dogs), but, as we pointed out earlier, to say what a word refers to, first, is not the whole story about what its function is within language, and second, in cases of many kinds of words is simply not possible. Wittgenstein points out that giving a name to an object is not a genuine move within a language game, but in a sense only a preparation for saying something about the object, for playing a 'real' game. Imagine I want to explain to you a geometrical problem: I start by making a drawing and designating the objects I have drawn - but the designating is merely a preparation for the real thing, for the exposition of the problem. And, moreover, what, after all, is designating? To say that it is making sounds or scribbles into names, or into representations of objects, is clearly begging the question. Should it instead be taken as something like building conditioned reflexes? Wittgenstein's verdict is that the very act of naming is not intelligible save as a part of more inclusive linguistic practices: "Only someone who already knows how to do something with it can significantly ask a name." (1953, §31) Hence as Baker and Hacker (1984, p. 117) summarize his view on the matter, "to know what a word stands for is alone insufficient to settle its use, whereas to know how to use a word renders superfluous the enquiry into what it stands for (and provides an answer to this question in cases where it makes sense)". Now what is important for us here, is that many of those philosophers who accepted the view of language as a toolbox came to the conclusion that it is a toolbox of a peculiar kind: its tools are entangled and mutually interconnected to the point of not being separable from each other. This is what the semiotic view conceals: it makes language look as a collection of

36

Meaning and Structure

items quite independent of each other, each of which simply designates its meaning (or its referents). This was pointed out already by Wittgenstein, but elaborated especially by the American philosophers whose views we will investigate in the second part of this book. 26 As stressed so vehemently by Quine, if language is a toolbox, then it is a toolbox whose tools somehow require and support each other. The tasks we use these tools for are always fulfilled by them collectively (albeit it often seems that only one or only a few expressions are involved); 27 and hence we can primarily speak about the utility or the meaning of certain assemblies of sentences ('theories'), not of individual sentences or expressions in isolation. This is the holism Quine so vehemently urges: no expression has a meaning by itself, it only contributes to theories in which it occurs (which do possess meanings in the sense of being useful), and there is no way to extract its contribution uniquely. What I claim, and what I will try to show in the rest of the book, is that Quine's realization of the essential semantic entangledness of the elements of our language, his holism, has surprisingly much in common with Saussurean structuralism - but with the genuine structuralism outlined by de Saussure himself, not with its later ersatzes and mutations. To document this, we need to reconstruct what de Saussure actually had in mind when he talked about language and meaning. This is the theme for the rest of this first part of the book; then, in the second part, we will tum our attention to Quine, Sellars and their followers.

26

For a discussion of the way in which Wittgenstein can be seen as anticipating some of the theses of Quine and his followers, see Peregrin (1995a, § 10.5).

27

Thus, e.g., we only seem to be able to verify a single thesis; in fact we are always verifying a whole theory (see Quine, 1992a, §§4-6).

Chapter Three

What is Structuralism? 3.1 Horizontal and Vertical Relations of Language The theoretical approaches to language which can be encountered in the twentieth century are diverse. On the one extreme, there are approaches which are based on seeing language as a kind of mathematical structure and consequently on seeing the theory of language as an application of mathematics or logic. This kind of approach has been adopted by the mainstream analytic philosophers as well as by the majority of logicians and of linguists after Chomsky; and it has yielded, besides other, a number of mathematical and logico-mathematical theories of syntax and semantics. The characteristic credo of the approaches of this kind can be seen in Montague's (1974, p. 188) claim that there is no principal difference between natural and formal languages. On the other extreme, there are approaches which are characterized by the rejection of mathematics and of formalisms and by inclination to such articulations of the nature of language which are closer to works of art than to scientific treatises. An a~proach of this kind is common especially among continental philosophers; and among its most vehement exponents we can find also the heterogeneous collection of French thinkers who entered the history of philosophy as structuralists. For the thinkers in this tradition, Montague's claim would appear utterly misguided - they would be much more sympathetic with Roman Jakobson's proclamation that "only as poetry is language essential". 29 However, for our purposes, this classification, natural as it may be on sociologico-historical grounds, proves less important than the one based on the considerations sketched in the previous chapter, namely the considerations about how to view the nature of the relation between an expression and its meaning. This leads us to a different division, which need not copy the boundaries between standardly recognized philosophical schools. The division separates those thinkers who see language as a 'semiotic system' (i.e. simply a collection oflabels stuck to ready-made things) from those who prefer to see it as a toolbox, as a collection of tools with various functions. 28

29

Viz., e.g., Heidegger's (1959) notion of"language as the 'house ofbeing"'. Quoted by Holenstein (1987, p. 25).

37

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Meaning and Structure

The 'semiotic' approaches, as we saw, are characterized by taking the relation between an expression and its meaning as something which is a matter restricted to the two entities and which is entirely independent of whether the expression belongs to any system. An expression and its meaning are, according to this view, two independent things whose interconnection is the result of a 'semiosis', i.e. of an act or a process by means of which they become conventionally attached to each other - independently of the presence of a linguistic system. Thus, under such a view, language becomes what de Saussure calls nomenclature, i.e. a collection of proper names for the 'furniture of the Universe'. If we depict language by means of Figure 2 (cf. de Saussure, 1931, p. 159), presenting it as a matter of two types of relations (the horizontal relations, relations among expressions, and the vertical ones, connecting expressions to their meanings), the 'nomenclaturistic' approaches can be characterized as those which take the vertical relations as wholly independent of the horizontal ones and for which it is exclusively these vertical relations which are constitutive oflanguage.

Figure 2

The views alternative to this kind of 'nomenclaturism' are based on the conviction that the vertical relations, connecting expressions to their meanings, cannot exist apart from the horizontal relations, interconnecting meaningful expressions. For this approach, it is the structure oflanguage which makes the meaningfulness of its expressions possible in the first place. It would thus be quite natural to call such approaches structuralistic - but we must keep in mind that this sense of "structuralism" need not coincide with the usual sense of the term, which makes it into a label for the French philosophical school. According to this view, meaning is not a ready-made thing, which we would simply label by a corresponding expression. The meaning of an expression is, as we have already indicated in the previous chapter, something as a value of the expression, a value which has to do with the position of the expression within the system of language. In the previous chapter we tried to indicate that the semiotic, or 'nomenclaturistic', approach is more problematic than it may prima facie seem. We tried to indicate that to see a meaning as a thing which gets designated by an expression in the way in which an exhibit in a museum gets designated by a label - i.e. to fall with the Quinean museum myth - leads us

What is Structuralism?

39

into muddy waters. Hence we arrive at the hypothesis that if we accept the division just outlined, it is the structuralistic approach which is to be favored. (After all, as Sherlock Holmes once claimed, "when you have eliminated the impossible, whatever remains, however improbable, must be the truth"). 30 However, to make this hypothesis more intelligible, we must characterize this approach in greater detail and indicate why we are not content with the usual sense of "structuralism". 3.2 Structuralism: Mere Slogan, or a Real Concept? It is beyond doubt that the term "structuralism" is one of the key words in the

history of twentieth century philosophy. Structuralism, as a philosophical movement, is surely something which cannot be ignored if we are to understand current philosophy, especially continental philosophy. Moreover, the consequences of the structuralist movement overspill the boundaries of philosophy: they have greatly affected almost all of the humanities. What, then, does "structuralism" in this sense amount to? It is common that if the term is being explained at all, it is in the spirit of the definition presented by Caws ( 1988): "Structuralism is a philosophical view according to which the reality of the objects of the human or social sciences is relational rather than substantial." This claim appears to be a reasonable generalization of de Saussure' s (1931, p. 122) maxim saying that everything in language is based on relations. The problem, however, is how this can be taken as a real definition or as a nontrivial explication - for the meaning of the claim that the "reality" of an entity is "relational rather than substantial" is obviously every bit as obscure as the concept of structuralism itself. Some of those who write about structuralism thus seem to have to come to doubt that the term has any real meaning at all: the word, they indicate, is used as a summary term for a collection of thoughts, persons and activities (Merquior, 1986, says: "a bunch of crabbed academic pundits, mostly French, active in social science, philosophy and the humanities") so diverse, that we could hardly find anything which is their common denominator; or at least that such a denominator would not really be theoretically articulable (as Leach, 1973, p. 37, says, "structuralism is neither a theory, nor a method, but rather 'a way to see things"'). Some of the books about structuralism indicate that to acquaint oneself with structuralism is to acquaint oneself with certain thinkers who only share a vague respect for the _teaching of de 30

In A.C. Doyle's The Sign ofFour, 1889, Chapter 6.

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Saussure; other texts, like the one by Deleuze discussed in Chapter 1, try to present an essence of structuralism, but offer results which - for the reasons already indicated- we do not consider satisfactory. We have indicated that here we want to concentrate on a narrower and more down to earth, but thereby more coherent, concept of structuralism. We have already mentioned how we want to understand it: as a term for a certain specific view of the nature of language,31 namely for the denial that the 'horizontal' relations among expressions (i.e. the systemic relations making expressions into the system of language) are secondary to the 'vertical' relations between expressions and their meanings. Structuralism in this sense engenders the insistence that the 'vertical' relations somehow depend, for their existence, on the 'horizontal' ones; and that to understand the former is not possible without getting clear about the latter. We also want to document that this interpretation we propose for the term "structuralism" is largely in accordance with what can be found in de Saussure's writings - although it clearly fails to account for many of the things that the term appears to signify amongst de Saussure's proclamative followers. Historically speaking, it seems that in the hands of some French thinkers the legacy of de Saussure became used as a weapon against the phenomenology of the preceding generation of French philosophers (and sometimes even against the analytic philosophy of their Anglo-American colleagues - which is ironically inapt, since, as we will attempt to show later, the teaching of many analytic philosophers is quite close to that of de Saussure himself). In this way the French structuralists have embraced only some aspects of de Saussure's teaching (especially those which appeared to warrant the 'emancipation' of humanities from sciences), leaving other aspects of his work largely ignored. 32

3.3 Thus Spoke de Saussure In which sense is de Saussure himself a structuralist? We claim that it is precisely in the sense put forward in the previous section: his structuralism is first and foremost the matter of his conviction that the entities with which language theory deals (especially meanings, 33 but more generally 31 Saying that it is a view of the nature of language we do not mean to deny that it is possible to apply it also to other 'sign systems'- provided these have something as the 'horizontal' and the 'vertical' dimension.

32

For an extremely skeptical attitude to the relationship of the French structuralists to de Saussure see the book of Pavel (1989), quoted in footnote I above. 33 De Saussure ( 1931, pp. 158ff.) himself explicitly rejects the identification of the value of an expression with its signification; however, his signification cannot be identified with

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everything that de Saussure calls "linguistic reality" should be seen as 'values' stemming from certain 'oppositions' of language - and so no meanings are conceivable without the system of language, which furnishes the needed oppositions. To explain this in greater detail, we must first consider the concept of structure and concepts related to it. (A more detailed discussion will follow in the next chapter). An immediate point to notice is that to talk about a structure makes sense only where there are already parts organized into wholes - for structure is just a matter of the way in which parts are organized into a whole. Thus, the proper context for the concept of structure is a part-whole system; and if we want to use the concept as a foundation for a theory of language, we must see language as such a system. Here it is important to notice that the understanding of language as a part-whole system, which is relevant here, is far from being a trivial matter. True, expressions of language can also be seen as constituting a trivial part-whole system - since they are, in the written form, strings of letters divided by spaces, they consist of 'natural' parts, segments separated by spaces. (Thus the statement "Luthien loves Beren" is a string consisting of the parts "Luthien loves" and "Beren", or of "Luthien" and "loves Beren", or, ultimately, of "Luthien", "loves" and "Beren"). This, however, is not the structure which is crucial for understanding the nature of language. There are more important structures, especially the one (or perhaps the ones, for linguistic theories do not always quite converge) resulting from the work of generations of linguists and usually called grammatical which is based on seeing expressions not simply as strings, but rather as certain 'grammatical complexes'. According to it, the sentence "Luthien loves Beren" can most helpfully be seen as consisting of "Luthien" and "to love Beren" (the 'subject' and the 'predicate'), or from the words "Luthien", "to love" and "Beren". (Notice that not all of these parts are parts in the previous, trivial sense- viz. "to love". This is because the string "loves" is taken to be only a 'form' or a 'manifestation' of the unit "to love"). Notice further that even in the context of a part-whole system a talk about structures makes truly nontrivial sense only there where there can be different wholes composed of the same parts. The structure is then that which 'makes the difference'. We have proposed to analyze "Luthien loves Beren" into "Luthien", "to love" and "Beren"; and we can further propose meaning in the intuitive sense. The intuitive concept of meaning (in the sense of what one knows when one masters the corresponding expression) is, as it appears, closer to de Saussure's concept of sense. But leaving de Saussure's specific terminology aside, we insist that meaning in our common sense is a (specific) value in de Saussure's sense of the word.

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to see "Luthien is loved by Beren" as consisting of the very same parts, put together in a different way and thus instantiating a different structure. The view of language as such a part-whole system naturally leads to viewing expressions as kinds of building blocks, as potential components of more complex expressions. Sentences are relatively completed wholes ("completed" because a sentence can be used to convey something; and "relatively" because even a sentence can be a part of a more complex sentence). Each element of the system, each 'building block', is suitable for certain ways of building certain wholes, and is unsuitable for other ways and other wholes. Two elements may be usable in the same or similar ways, but also in wholly different ones. If they are usable in the same way, the elements are perceived, from this viewpoint, as equivalent- building any whole we can interchange one of them with the other and we always reach a result which is the same as the one which would be reached if we did not carry out the interchange (where "the same" is to be read as "equivalent with it in the currently relevant sense"). The usability of an element then can be seen as the value of the element; and similarity or dissimilarity of the usability as a matter of the measure of coincidence of the values. Doing this, however, we must remember that the situation is not that we have some abstract values and assign them to the elements of our system. The value of an item should rather be seen as a 'materialization' of the relative usability of the item for the relevant aim. It is thus not reasonable to see values as that which 'causes' the equivalence- we should rather see the values as engendered by the equivalences (or identities, in de Saussure's terminology). It is for this reason that de Saussure (1931, p. 154) can claim that "the notion of identity blends with that of value and vice versa." The principal structuralistic thesis which we ascribe to de Saussure can now be expressed in the form that all abstract entities with which the theory of language has to do are best seen as values, and hence as certain 'by-products' of certain identities (or oppositions, which are complementary to identities). It is clearly this which carried de Saussure to the conclusion that "in a language-state[= a language fixed to a particular time moment] everything is based on relations" (ibid., p. 170). De Saussure starts his exposition of the general principles of a language theory with an emphatic warning against understanding language as a kind of nomenclature, against the idea that words are associated with ready-made meanings by means of a simple operation of naming. It is precisely to counteract this idea that he puts forward his understanding of meaning as a value: language is, as he puts it, "system of pure values which are determined by nothing except the momentary arrangement of its terms." (ibid., p. 116) The value of an expression, such as its meaning, is thus always constituted exclusively by means of relations among expressions. This is effected by the

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fact that saying that two elements are (from a given viewpoint) equivalent ("identical") is tantamount to saying that they have the same value (from the viewpoint). Today's train going from Geneva to Paris at 8:25 is probably a physical object which is quite different from yesterday's train from Geneva to Paris at 8:25 - however, the two objects are functionally equivalent, both are the same 8:25 Geneva-to-Paris train (ibid., p. 151). The abstract object the 8:25 Geneva-to-Paris train is, in this sense, constituted purely by the (functional) equivalence between certain tangible objects; and in the same sense the values of expressions such as meanings are constituted purely by (functional) equivalences between the expressions. De Saus sure's structuralism thus consists first and foremost in seeing linguistic reality as a system of values reducible to identities and oppositions. However, it would be a mistake to assume that there are some basic concrete items (words) and some basic relations between them (functional equivalences), which are simply immediately given to us, and that the rest of the "linguistic reality" results from the 'materialization' of these relationships. The point is that, according to de Saussure, all items of language, including the most basic ones ("units"), are in a sense an abstract, derived matter. "Language," writes de Saussure (ibid., p. 146), "does not offer itself as a set of pre-delimited signs that need only be studied according to their meaning and arrangement; it is a confused mass, and only attentiveness and familiarization will reveal its particular elements." To say that the grammatical structure of language (i.e. the part-whole structure the embodiment of which language becomes for us when we try to capture it theoretically) is not immediately given is to say that to identify the basic 'building blocks' of language and the ways in which these building blocks can be composed together is a nontrivial task. This is why de Saussure states that it is not only the concept of value, but also that of unit, which coincides with the concept of identity. This means that the very units and relationships between them, which appear to be the basis of the "linguistic reality", are themselves theoretical, abstract constructs. "[T]he idea of value as defined," says de Saussure, thereby formulating the credo of his structuralistic methodology, "shows that to consider a term as simply the union of a certain sound with a certain concept is grossly misleading. To define it in this way would isolate the term from its system; it would mean assuming that one can start from the terms and construct the system by adding them together when, on the contrary, it is from the interdependent whole that one must start and through analysis obtain its elements" (ibid., p. 157). "The linguistic entity," writes de Saussure further (ibid., p. 145), "is not accurately defined until it is delimited, i.e. separated from everything that surrounds it on the phonic chain. These delimited entities or units stand in opposition to each other in the mechanism of language." There exists

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something 'tangible' which underlies language, viz. the factual utterances of speakers (i.e. certain kinds of sounds emitted by the people)- what, however, is of significance is not their 'substance', but rather their structure, which makes the episodes into linguistic utterances - and the task of linguistic theory is to identify the structure, to reconstruct the mass of utterances as a collection of constructs built from a basic set of building blocks according to some rules of composition. "Language then has the strange, striking characteristic," de Saussure (ibid., p. 149) continues, "of not having entities that are perceptible at the outset and yet of not permitting us to doubt that they exist and that their functioning constitutes it." This means that although language is primarily an incomprehensible mess or multiplicity, we must, in order to grasp and understand it, look at it as at a part-whole system. Language thus does not originate from naming ready-made objects- associating potential 'signifiers' with potential 'signifieds' - in an act of semiosis, for the signifiers and the signifieds are, in an important sense, constituted only together with the constitution of language. De Saussure' s semiology is therefore not semiotics in the sense of the previous chapter. Hence Saussurean structuralism does not consist merely in the reduction of 'abstract' entities to some 'concrete' ones ("units") and their oppositions- it proceeds to reduce also those entities which appear to us, from the viewpoint of the more abstract ones, as 'concrete units' or 'basic building blocks', to oppositions. "[T} he characteristics of the unit blend with the unit itself," says de Saussure (ibid., p. 168). This means that "in language there are only differences without positive terms" (ibid., p. 166); that "language is a form and not a substance" (ibid., p. 169). 3.4 But Also Thus Spoke de Saussure

I am not claiming that everything said by de Saussure fits nicely with the interpretation which I have proposed for the core of his doctrine. There are plenty of things he says and which may appear as not corroborating, or even as contradicting, the present interpretation (and thereby his own principles which we cited in its support). However, this should not be too surprising: I think that de Saussure, creating his brand new, structuralistic framework for a theory of language, simply could not but from time to time rest on the old framework, and therefore could not manage to avoid discrepancies in his argumentation. Which kinds of inconsistencies do we have in mind? Without aspiring to any systematicity, let us mention two of them. First, although de Saussure so vehemently rejects the understanding of language as a 'nomenclature', in more than one place in his treatise he talks as if he still somehow

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presupposes this rejected idea. (It would, however, have been almost superhuman were he to have performed his 'structuralistic tum' so flawlessly as to completely disentangle himself from that way of talking about language which, at the time when he initiated his path-breaking conception, was almost universal). Second, de Saussure often speaks about the semantic aspect of linguistic signs, about the "signifieds" of language, as if they were quite straightforwardly a matter of thought, thereby bringing himself dangerously close to the psychologico-semiotic notion of language which we rejected in the previous chapter and which was otherwise rejected also by him. (Here the reason, I suspect, must be that de Saussure lacked a conceptual apparatus which he could use as a foundation for his non-psychological theory of meaning, and he was thus sometimes obliged to resort to the mentalistic terminology). 34 Let us consider some examples. On page 28 of the Course we read (note, though, that this is one of the passages which is particularly disputable from the viewpoint of de Saussure's direct authorship): 35 Suppose there are two people, A and B, talking to one another. The circuit begins in the brain of one of them, say A, in which objects of consciousness, which we may call concepts, are located, associated with representations of the linguistic signs, or auditory images, that serve to express them. We may suppose that a given concept releases in the brain a corresponding auditory image; this is an entirely psychic phenomenon, followed in tum by a physiological process: the brain transmits an impulse corresponding to the image to the organs of sound production; the sound-waves are then propagated from the mouth of A to the ear of B: a purely physical process. Next, the circuit continues in B, in the reverse order: from the ear to the brain, a physiological transmission of the auditory image; in the brain, the psychic association of this image with the corresponding concept.

Such a description of communication strongly resembles that which we depicted in Figure 1 (on page 17) and which we subsequently rejected. We do not dispute that communication can proceed like this, that it may be based on some two centers within the brain, one connected with expressions as such and the other with what the expressions mean (indeed it 34

It is also possible that at least some of the inconsistencies of this kind were produced in the text of the Course by those who gave it its book form. The fact that the text, as we know it now, is reconstructed from de Saussure's personal notes and the notes of his hearers makes it obviously disputable how far the details of the thoughts expressed in it and of the formulation used there really can be ascribed to de Saussure himself. This is noted also by the editor of the new edition of the Course (see de Saussure, 1972, note 132). 35 This particular passage is not backed by anything in de Saussure's own notes.

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seems that recent results of neurophysiology corroborate such a picture). Our point is that this has little to do with meanings or concepts in the Saussurean sense - it surely cannot be said that the concept expressed by an expression is a region in the brain. And even if we interpret de Saussure so that it is in the mind, rather than in the brain, where concepts are located, we still have a scarcely tenable picture. The idea that concepts are mental images connected to mental signatures of words (reminiscent of the doctrine of the British empiricists) is clearly nothing else than the Quinean museum myth. As stated by Dummett (1988, p. 185), the passage cannot be correct for at least two reasons: First, "someone's understanding a word as expressing a certain concept cannot be explained as consisting in the word's calling up in his mind a concept with which he has come to associate it, since there is no such process as a concept's coming into anyone's mind: a tune, a name, a remembered scene or scent can come into the mind, but a concept is not the sort of thing of which this can intelligibly be said." 36 And second, "if to have a concept were to be like having an intermittent pain, in that the concept came to mind on certain occasions, we should still need an explanation of what it was to apply that concept. Someone incapable of applying it would ordinarily be judged simply to lack the concept, just as someone incapable of telling whether something was or was not a tree, or of saying anything about what trees are or do would be judged ignorant of the meaning of the word 'tree': it would be useless for him to claim that, whenever he heard the word, the concept of a tree came into his mind, although this happened to be a concept that he could not apply." The idea of concepts, meanings of words, as 'mental contents' is simply not tenable, as we concluded in the preceding chapter; and if we reject nomenclaturism, what is unacceptable is any idea of concepts being 'completed' before their linguistic expression. Let us consider another passage from the Course: "Without language, thought is a vague, uncharted nebula. There are no pre-existing ideas, and nothing is distinct before the appearance of language .... The linguistic fact can therefore be pictured in its totality - i.e. language - as a series of contiguous subdivisions marked off on both the indefinite plane of jumbled ideas and the equally vague plane of sounds." (de Saussure, 1931, p. 155) "[L]anguage works out its units while taking shape between two shapeless masses" (ibid., p. 156). Here de Saussure's criticism of the nomenclaturistic approach to language again fails to avoid resting on presupposing the framework of the very approach. As Hjelmslev ( 1966, p. 46) aptly remarks, the point is that de Saussure's own conception implies that "substance depends on the form to such a degree that it lives exclusively by its favor 36

We have reached the same kind of conclusion in Chapter 2.

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and can in no sense be said to have independent existence". And it is just because the substance about which de Saussure talks appears, from his viewpoint, to be so 'esoteric' that he feels compelled to take recourse to mind and to borrow a more 'respectable' substance there: in this way meaning becomes, for him, a mental entity. Thus, his exposition becomes contaminated by psychologism, in the guise of the implicit assumption that meaning cannot be but a mental matter. Similarly problematical pronouncements can also be found in places where de Saussure tries to analyze the oppositions which are constitutive of language. He distinguishes two kinds of such oppositions: syntagmatic and associative. The former concern such pairs of expressions which can be put together (into 'syntagms'), the latter concern those which can be substituted for each other. The syntagmatic oppositions are thus, we would say, a matter of the differences between expressions of different syntactic categories ('intercategorial' differences), whereas the associative oppositions concern differences between different expressions of the same category ('intracategorial' differences). Unfortunately, de Saussure characterizes the second kind of oppositions in terms of mental associations, and so invokes the impression that what is constitutive of the meaning of a word is that a person, on hearing it, recalls some other words. However, this obviously contradicts his own credo which takes bare oppositions to be the foundation of everything in language - for what is presupposed here is not opposition, but rather a mental mechanism. Viewed from a genuinely structuralist angle, this dimension of the meaning of an expression is the outcome of the opposition between the expressions and other expressions which are capable of replacing it - not the outcome of any mental associations. (I suspect that it is also for this reason that the term associative oppositions was later replaced by the term paradigmatic). Besides these inconsistencies, I feel that de Saussure' s doctrine is also problematic in another important respect, namely in respect to its strictly symmetric treatment of the relationship between the signifier and the signified. Both the two poles of the sign are constituted, according to de Saussure, in a symmetric interdependence, no one of them is in any way more primary. However, it seems hard not to allow at least a methodological asymmetry, placing the signifier 'before' the signified. (Notice that this amounts to the inversion of the usual asymmetry presupposed by semiotics, for which the signifier is only a secondary substitute for the signified). The point is that the phonic (or graphic) side of language is accessible for us in a more direct way than the semantic side. We can voice or put down a word disregarding its meaning (although it would in fact not exist as a word if it lacked meaning), whereas the meaning, being a value, cannot be presented other than via an

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expression. Even if language is exclusively a matter of oppositions, it always exists via a substance, something 'tangible' -and this substance is obviously more immediately related to the signifiers than to the signified's. This is what leads us to see meanings as values of expressions - although according to de Saussure the situation is in fact entirely symmetric, and thus nothing should prevent us from being able to see expressions as values of their meanings. 3.5 De Saussure and Frege

I thus suggest that de Saussure was hampered by the lack of a firm conceptual framework by which to support his path-breaking proposals, and thus was obliged to 'pour new wine into old vessels'. He failed to extricate himself entirely from the idea that what is not physical is bound to be mental, and thus to avoid mistaking the mental for the structural (and especially for the semantic). The fact is that to avoid this confusion was probably not possible without the help of a systematic, non-psychological theory of abstract entities. Does a theory suitable for this purpose exist? I think that it does, and that it is nothing else than modern abstract mathematics, in particular the so-called universal algebra and set theory. To elucidate this statement, which might seem a surprising traverse, let us consider, for a moment, another path-breaking event occurring contemporaneously with de Saussure's laying of the foundations of modern linguistics - namely the laying of the foundations of modern logic by Gottlob Frege. To document some interesting parallels between de Saussure and Frege, let us first consider a much discussed passage from Frege's book Foundations of Arithmetic (1884); a passage in which Frege explains how to understand abstract entities. Frege starts from an inquiry into the nature of such abstract objects as 'directions', and carries out the following consideration. We have the concept of being parallel, which has the character of an equivalence. We understand sentences of the type "The line a is parallel with the line b" and we know how to determine (at least in principle) the truth values of such sentences. At the same time, the statement "The line a is parallel with the line b" can be paraphrased as "The direction of the line a is the same as the direction of the line b", and this last statement can then be taken as a statement about a direction as an abstract object: about the fact that two lines 'realize' (i.e. have) the same direction. It is precisely the fact that statements about sameness and difference of directions make such clear sense to us that enables us to treat directions as abstract objects (we can 're-recognize' a direction in various different 'realizations' as one and the same); however, it does not tell

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us anything 'substantial' about what such a direction is. "The definition of an object does not, as such, really assert anything about the object, but only lays down the meaning of a symbol," says Frege (ibid., p. 78). Thus, the only thing we can say about the direction of a line is that it is what the line shares with all its parallels. The object direction of a is identical with the object direction ofb if and only if a and b are parallels; and in such a case also the extension of the concept parallel with a (which consists of all the parallels of a) is identical with the extension of the concept parallel with b (which consists of all the parallels of b). Hence what Frege suggests is to identify the object direction of a with the well-understood extension of the concept parallel with a, i.e., in effect, with the set of all parallels of a. It is hopefully needless to say that this train of thought is straightforwardly analogous to the one concerning the "8:25 Geneva-to-Paris train", entertained by de Saussure and discussed above. In both cases we have some basic objects (lines; trains as physical objects) and equivalences between them (being parallel; going the same route at the same time). These engender new 'abstract' objects (directions, trains as abstract objects), each of them arising as that which is shared by all of the equivalent original objects, as an e pluribus 37 unum. However, Frege then indicates a further step, which makes it possible to grant the object arising in this way a solid status: if a new object arises in this way out of a set of old equivalent objects, we can - at least for some purposes - simply identify it with the set. The abstract object the direction ofa line thus can be identified with the set of all lines parallel with the line in question, and likewise the abstract '8:25 Geneva-to-Paris train' could be identified with the set of all concrete trains, which depart on 8:25 from Geneva in the direction to Paris on individual days. 38 However, this ultimate step becomes fully possible only when modem mathematics with its sets, relations and functions establishes itself. And it is just this to which Frege significantly contributed.

37

This is a general mechanism which Quine (1950, p. 71) characterizes as that yielded by the maxim of "identification of indiscemibles": "Objects indistinguishable from one another within the terms of a given discourse should be construed as identical for that discourse. More accurately: the references to the original objects should be reconstructed for purposes of the discourse as referring to other and fewer objects, in such a way that indistinguishable originals give way each to the same new object." See Quine's paper for more details. 38 It is precisely this kind of explication which Quine (1960, p. 258-9) characterizes as follows: "We fix on the particular functions of the unclear expression that make it worth troubling about, and then devise a substitute, clear and couched in terms of our liking, that fills those functions. Beyond those conditions of partial agreement, dictated by our interests and purposes, any traits of the explicans come under the head of 'don't-cares"'.

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Nevertheless, I am not claiming that Frege and his analytic followers successfully accomplished what de Saussure tried to accomplish with smaller success. For indeed, although Frege and his direct continuators, such as Russell or Carnap, in comparison to de Saussure had the advantage of successful mastery of abstract entities, in the understanding of the 'structural' character of language which de Saussure so vividly propagated in his treatise, they fell significantly behind. I think that this handicap has been neutralized only by the very generation of philosophers which are better called postanalytic and on which we will concentrate in the second part of this book. Thus the fact that the paths ofFrege and de Saussure did not meet was, I think, regrettable from the point of view of both of them. 3.6 Structuralistic Linguistics after de Saussure We have seen that de Saussure's path-breaking approach to language, to a large extent, can be seen as counteracting the Quinian museum myth, i.e. the idea that expressions denote ready-made objects in the way that labels in a museum denote corresponding exhibits. If we dispense with the myth, semantics becomes (along with syntax, morphology, phonology etc). first and foremost a matter of certain underlying equivalences and oppositions among the units of language; and about the values engendered by these relations. Meanings (like the rest of 'linguistic reality') thus get supplanted from the physical or the mental world into the world of 'the structural'. Whereas syntax, morphology and phonology become rendered as different versions of a structuralist account for the opposition between a well-formed sentence and other strings of letters or phonemes (with syntax stopping at the level of words, mo~hology going farther to morphemes and phonology still farther, to phonemes), 9 semantics will be understood as accounting for the oppositions relevant from the viewpoint of what a sentence says (paradigmatically, as we will see later, the opposition between truth and falsity). The units of these 39

This is to say that decomposing the class of sentences we can probe into various depths. For instance, the sentence "Luthi en loves Beren", from the viewpoint of syntax, can be seen as composed of three primitive parts, namely "Luthien", "to love" and "Beren", whereas from the viewpoint of morphology, it can be seen as consisting of jour parts, viz. "Luthien", "love-", "-s", and "Beren"; and from the viewpoint of phonology it can be seen as consisting of a still greater number of phonemes. (And note that what can appear, on the level of syntax, as two different ways to compose the same units - viz. "Luthien loves Beren" and "Luthien is loved by Beren"- might appear, on the level of morphology, as compositions of different parts). Each of such decompositions may be interesting from a specific viewpoint and useful for a specific purpose. This gives substantiation to the theories of language which see language as a system of levels, each of which has its own theory syntax, morphology, phonology etc. See, e.g., Sgall (1987).

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theories - words, morphemes, phonemes, but also meanings - will then appear not as self-standing entities entering into certain relationships and thus constituting language, but rather as the means of analysis, as the means of our getting a grip on the vastness of sentences in their functioning. However, according to the view advocated here, de Saussure's revolutionary proposals required further support and further maintenance. The revolution he initiated could be completed, in our view, only when his 'structural' could be mastered theoretically and thus be rid of the air of 'esotericity' which surrounds it until its nature is sufficiently clarified. This was a task awaiting de Saussure's followers. Unfortunately, though, they did not quite accept it, and instead of the definitive fortification of the foundations of the edifice of the structuralistic approach to language they often rather set out to add further floors to it. Nevertheless, in linguistics the structuralistic view of language provoked a real upheaval: it prompted new ways to study language, for it showed that its 'structural order' can be studied independently of the 'causal order of communication' (i.e. of the naturalistic study of the processes underlying communication); and hence it freed linguistics to concentrate entirely on language itself - i.e. not be burdened by psychology, sociology etc. (On the negative side, it brought about the tendency to view language as something isolated from the rest of the world criticized in Section 1.3). However, none of de Saussure's famous followers managed to secure the approach a theoretical foundations sufficiently firm to unfold it in its full power. (As we have indicated before, our conviction is that this was not possible without a strategic alliance of linguistics with mathematics and logic - something which appeared inconceivable to linguists until Chomsky). Not even the two most prominent de Saussure's continuators, Roman Jakobson and Louis Hjelmslev, managed to stabilize and anchor the outcomes of the structuralistic revolution to the needed extent, although, as it seems, each of them for different reasons. Jakobson was influenced not only by de Saussure, but also by the Moscow 'neogrammarians' with their focus on the historical and causal view of language, and especially by what Holenstein (1987) calls the "Russian ideological tradition", which rests significantly on Hegelian dialectics. Although it is beyond doubt that his application of the structuralist program produced a number of extremely important contributions, his approach to language was constantly checked by a suspicion that the elusive phenomenon of language could not be approached in a scientifically rigorous way - as if he believed that language could surrender only to a poet, and not to a scientist. The result of this was that Jakobson, in the words of Waugh and

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Monville-Burston (1990, p. 9), "found the picture of language propounded by Saussure to be at the same time too abstract, too static and too simplified." Thus, in contrast to de Saussure's view oflanguage as a kind of 'mathematical structure', Jakobson viewed it more as a 'living organism', which inevitably escapes a rigorous description. And what holds of Jakobson, holds to a large extent of his colleagues from the Prague Linguistic Circle, of which Jakobson was a leading personality: they made many indubitably important contributions to the structuralistic program, but they did not fortify its foundations. From this viewpoint, the most congenial follower of de Saussure was Hjelmslev, whose unambiguous aim was a truly rigorous, systematic theory of language. 40 However, instead of reinforcing the foundations of de Saussure's edifice and making it more perspicuous, Hjelmslev further complicated the framework and thereby reached a stage where the theory became unperspicuous to the point of unintelligibility. The post-Saussurean structural linguistics thus comprised a loosely delimited collection of views rather than a rigorously articulated methodology or a conceptual framework. This fuzzy understanding of Saussurean structuralism is also responsible, in my opinion, for the embarrassment surrounding the problem of the relationship between the Saussurean program and the formalistic trends in linguistics initiated in the sixties especially by Noam Chomsky. It seems clear that Chomsky's approach is concerned with the structural aspects of language; however, at the same time it seems unlike a theory aimed at by de Saussure, Jakobson, or Hjelmslev. 41 From the viewpoint assumed here, Chomsky's approach is first and foremost a breakthrough which has initiated an approach to the structural aspects of language using the means most suitable for this purpose, namely those of modern mathematics. And the same holds for the subsequently proposed approaches to language which were inspired by modern formal logic.

40

See especially Hjelmslev (I 966). Hence I disagree with Pettit's (1975) claim that Chomsky's approach represents one of the possible directions of elaboration of Saussurean thoughts, namely the syntagmatic one; and that the alternative is the direction represented by Jakobson, called paradigmatic by Pettit. To see Chomsky and Jakobson thus, as two alternatives is, in my view, misguided: if we are right that the syntagmatic and the paradigmatic (associative) oppositions, as we stated above (viz. Section 3.4), can be understood as the intercategorial and the intracategorial ones, respectively, the two concepts are complementary and to tear them from each other for the purpose of using them as labels for different theories of language does not make a clear sense. (Although it might indeed happen that in some trivial cases one of these dimensions may turn out to be absent- we can, for example, make do with a single category, or make, t,he other way around, the categorization so fine-grained that we leave no room for any intracategorial differences). 41

What is Structuralism?

53

3.7 Structuralistic Philosophy De Saussure's approach to language and his conclusion that what is substantial is the form (structure) and not what fills the form ('substance') also obviously could not pass unnoticed by philosophers. De Saussure's approach reached the first philosophical blossom within the writings of the anthropologist Claude Levi-Strauss (whom they reached via Jakobson). In Levi-Strauss' mind the Saussurean considerations appeared to crystallize into the following challenging question: what if the nature of some of the things which people say or do escapes us precisely because we look at the substance, and do not see that what is genuinely important is the structure? We may, for example, hear that some natives tell stories in which bears kill people, and we are convinced that this must be the consequence of some bad experience the people or their ancestors had with bears. However, what if the bears are wholly irrelevant, what if the relevant thing is the structure of the story, in which the bears play the role of a dispensable filler? The perspectives which were opening for the humanities through the considerations of all kinds of possible roles of structures then appeared to be immense. Levi-Strauss and other, mostly French, pioneers of structuralism were so fascinated that, as we said above, instead of paying attention to the theory's foundations, they added further and further floors to the edifice; and they soon appeared to approach the heavens. Moreover, the next generation of structuralists, or better poststructuralists, especially Derrida and Deleuze, started a new revolution within the structuralistic revolution.42 They were alarmed that the concept of structure, which represented for them the hope for an ultimate erasure of what they called "logocentric metaphysics", appeared to be grounding a new kind of metaphysics (which in fact quite resembled the old one, now only in a structuralistic disguise). This has led them to the philosophy of a permanent subversion (or "deconstruction") of everything which threatened to become stable, to a philosophy which refuses to state anything actually graspable and which thus becomes a kind of a 'permanent metaphor'. As a matter of course, French structuralism became an integral part of the stream of continental philosophy, for which the patriarch of twentieth century philosophy was not Frege, but rather Edmund Husserl.43 Jakobson endorsed 42

See Frank (1984).

43

It is not without interest to realize that Husser! and Frege were much closer to each other

than it might appear from the current perspective: both reached their path-breaking philosophical conceptions partly via considering the foundations of mathematics (both pondered, at the outset of their philosophical careers, the question what is a number?); and also the ways in which both tried to secure new foundations for philosophy display many

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Meaning and Structure

Husserl's phenomenology explicitly; and likewise most of the structuralist philosophers were strongly affected by Husserl's views - be it positively (Ricoeur, 1974) or negatively (Derrida, 1972). The parallel between the efforts of de Saussure and those of Frege thus remained not only unexplored, but rather even unnoticed. Interestingly, within the writings of early analytic philosophers, Frege's followers, we can find many things which are also relevant from the viewpoint of de Saussure's teaching. It is not difficult to see that the concept of structure is crucial for such classical works of analytic philosophy as Russell's Our Knowledge of the External World (1914), Wittgenstein's Tractatus logico-philosophicus (1922), or Camap's Der Logische Aujbau der Welt (1928; the title of the English translation is, not without substantiation, directly The Logical Structure of the World). Camap claims explicitly: "echte Wissenschaft ist stets Strukturwissenschaft" (ibid., p. 263)4 . However, all of this should not be overly surprising: a structuralistic program could hardly not intersect - at least on the wholly general level - an analytic program: the basic shared idea is to see complicated entities as certain 45 complexes of simpler parts, i.e. to carry out an analysis of their structure. Likewise, the doctrine of logical atomism, developed by Russell, Camap and the early Wittgenstein46 and representing, in effect, the core of classical analytic philosophy, can be thought of as a certain sophisticated elaboration of an analytico-structuralistic program. 47 But despite these possibilities, the overall approach to language by the early analytic philosophers was, generally speaking, closer to the nomenclaturistic view than to the structuralistic one. Changes were first instigated by members of the next generation of (post)analytic philosophers, especially Quine and Sellars: they realized that to see language as a nomenclature is mistaken, and thus they rediscovered much of what had already been indicated, sometimes in a way not quite intelligible for the 'analytic mind', by de Saussure. (Or at least, so I am going to argue). However, before we can tum our attention to this meeting points. The principal difference is in that whereas Husser! sought the foundation in the analysis of the way the world is grasped by a subject, Frege came to the conclusion that what is most fundamental for philosophy is language. See Dummett (1988) and Haaparanta (1994). 44 An illuminating discussion of Camap's 'structuralistic' inclinations is given by Kambartel (1968, Chapter 4). 45

Cf. von Wright (1993, §31). The parallels between structuralism and the philosophy of the later Wittgenstein are, I believe, even much deeper, but their systematic discussion will have to be left for another book. 47 See Peregrin (1995a, §5.6).

46

What is Structuralism?

55

'structuralism of postanalytic philosophers', we must analyze more carefully the concept of structure and some of the issues connected to it, and show how these themes can be dealt with using the language of analytic philosophy. The reader should notice that this language is far closer to the language of de Saussure's Course than, e.g., the language of the writings ofDerrida.

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Chapter Four

Parts, Wholes and Structures: Prolegomena to Formal Theory 4.1 Abstraction

An important source of human knowledge is clearly classification: dividing the vast spectrum of things with which we are confronted into groups of similar, or similarly useful, things. This is a caw (and hence it can be milked), whereas that is a tiger (and thence it is advisable to avoid it). Already Aristotle saw such classifying as the very principle of our reason: his view was, as Cassirer (1910, p. 4) puts it, that "nothing is presupposed save the existence of things in their inexhaustible multiplicity, and the power of the mind to select from this wealth of particular existences those features that are common to several of them." If we have a set of objects, we can collect the properties which are shared by all the objects; and similarly if we have a single object, we can 'abstract away' some of its properties and thus reach a collection of properties which can be shared with the object by other objects. And as we often understand such a subtraction of properties as passing from the original object to a new, 'abstract' object, it is precisely abstraction in this sense which is the basis of the passage from concrete to abstract objects. This is how we get from concrete, tangible trains going from Geneva to Paris to the abstract 'Geneva-Paris train' (see Section 3.3), or from concrete lines to their 'directions' (viz. Section 3.5).48 As long as we see the ranges of things with which we are confronted as mere sets of objects, the passage from one level of abstraction to another is quite straightforward- the set falls apart into 'equivalence classes' and they as if 'coalesce' into abstract objects. If we disregard specific differences, 48

The idea that 'the abstract' is in general a matter of this finding 'one within many' - of this making e pluribus unum - also lies at the foundation of the conviction of modem mathematicians (and the philosophers influenced by them) that the role of the general theory of abstract objects can be assumed by the theory of sets ( cf. Section 2.4). The point is that if any abstract object can be seen as engendered by a collection of some other ('more concrete') objects, then what we need to reconstruct it is precisely what set theory equips us with: namely the possibility to make any collection of objects into a new kind of entity, a set. This is then taken to imply that any abstract object is reconstructible as a set.

57

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Meaning and Structure

particular horses become equivalent for us, and we thus start to 'perceive' not the individual horses, but rather 'the horse' as a genus. Any such 'coalescence' can be seen as a matter of a certain equivalence; and from this viewpoint, equivalences and abstract objects are two sides of the same coin. (If we say "identity" instead of "equivalence", then what we have is de Saussure's "blending of the notion of identity with that ofvalue"). 49 However, the situation is far less simple when we take into account the fact that what surrounds us is not merely a vast set of particulars, but rather a vast set of particulars some of which are parts of others. This means that the coalescence of some particulars may force the coalescence of some other particulars: for if parts coalesce, the wholes which are composed of them necessarily coalesce too. Imagine a lego: if we stop distinguishing between pieces of the same shape and size, differing only in color (if we start to say "this is the same piece"), we thereby necessarily also stop distinguishing between complex constructions differing from each other only by their color (we could hardly say "this is not the same construction" without changing the sense in which we use the words "the same"). The point is that 'sameness' or equivalence gets necessarily projected from parts to wholes. This suggests that whereas in the case of a set of objects any division into 'equivalence classes', i.e. any equivalence, represents a reasonable classification of the objects, in the case of a part-whole system this is no longer so: in this case a reasonable classification is represented only by an equivalence of a specific kind. Let us call such an equivalence a congruence: thus, an equivalence is a congruence only if it has the property that it renders equivalent any two wholes the parts of which are pairwise equivalent (which, of course, presupposes that the wholes are analogous in the sense that there is a one-one correspondence between their parts). Let us imagine an equivalence which does not satisfy this condition, i.e. which is not a congruence. According to the definition just spelled out this means that there exist two wholes which are not equivalent, but whose corresponding parts are equivalent. Let us assume that they are the whole x consisting of the parts x~, ... ,Xn and the whole y consisting, analogously, of y~, ... Jln· We thus assume that

49

This constitutive role of equivalences is also reflected by Quine's often quoted aphorism "no entity without identity" (see, e.g., Quine, 1992a, p. 61), reflecting the fact that an establishment of a kind of abstract objects is impossible without making an equivalence of some underlying objects into the identity of the ones of the new kind; e.g. the schedule-induced equivalence between the tangible trains into the identity of the abstract schedule-trains. See also note 37.

Parts, Wholes and Structures

59

x 1 is equivalent withy 1, x 2 is equivalent with y2, Xn

is equivalent with Yn,

but xis not equivalent withy. Let us now imagine that all equivalent objects were to coalesce- thus x 1 were to coalesce withy], x 2 withy2, ••. , Xn withyn etc. This clearly means that also some non-equivalent objects would have to coalesce- namely x withy (for the coalescence of x and y is simply nothing else than the coalescence of x 1 withy 1, ••• ,and Xn withyn). If an equivalence is not a congruence, there is no possibility for all and only equivalent objects to coalesce - the coalescence of all the equivalent ones would necessarily bring about also the coalescence of some non-equivalent ones (like x andy in our example). If, on the other hand, no two non-equivalent objects were to coalesce, it would not be possible that all the equivalent would - in our example at least one of the pairs x 1 and Yh x 2 and y 2 , ••. , Xn and Yn would have not to coalesce. This means that the 'diagram' of coalescence of objects of a part-whole system - and hence of the process ofabstraction over the system -is always necessarily a congruence. Let us illustrate this fact by a trivial example. On the following picture we can see the lines AB, BC and CA, which constitute the triangle ABC.

c

Figure3

A

B

We conceive of four objects, the fourth of which consists of the first three. Let us now imagine that we draw an identical triangle A'B'C' on a transparency and we put it over the triangle ABC as in Figure 4. Now we have eight objects: the lines AB, BC, CA, A'B', B'C' and C'A' plus the triangles ABC and A'B'C'. If we move the transparency with the triangle

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Meaning and Structure

A'B'C' so that the line AB coincides with the line A'B', BC with B'C' and CA with C'A', also the triangles ABC and A'B'C' will inevitably coincide. Thus, if we postulated that AB is equivalent with A'B', BC with B'C' and CA with C'A', but not ABC with A'B'C', the resulting equivalence could not be taken as a record of a possible coalescence; i.e. it would not be a congruence.

c

c

B

B

Figure 4

A'

B

Congruences can therefore be said to picture how objects coalesce if we look at them with decreasing 'visual acuity'. If we lower the acuity, pairs of objects which are close enough to each other change into single objects. However, if all parts of some two wholes coalesce, there is no way for the two wholes not to coalesce - such a coalescence is, by its very nature, a congruence. And the model of looking at objects with (deliberately) decreasing 'visual acuity' clearly corresponds to the most basic mechanism of abstraction which is so important for our grasping the world around us. If we imagine, e.g., zoology, then we can say that with the highest level of acuity we perceive individual animals, on the next level we disregard some of the specific properties and have kinds such as cow, horse, dog, carp; and on a subsequent level these further coalesce into more abstract kinds such as mammal, fish etc. In this particular case it is, of course, more appropriate to speak about the level of abstraction than about acuity. Congruences thus can be seen as representing the part-whole system in question on various levels of abstraction. An abstraction over a range of objects some of which are parts of others is obviously a more complicated matter than an abstraction over a simple, non-structured set. The gist of our thesis now is that many collections of objects which are targets of our knowledge simply cannot be looked at otherwise than as part-whole systems - and that a prominent example of such a system is the system of expressions of our language. And as we are going to argue, the Saussurean structuralism appears, from this viewpoint, de facto as a doctrine

Parts, Wholes and Structures

61

about how what we perceive as "linguistic reality" can be explained as a kind of a 'by-product' of our abstractive grasping of this very part-whole system.

4.2 Part-Whole Systems and Compositionality Let us now elaborate upon these last thoughts. First, we should characterize the concepts of part and whole more rigorously. As indicated before, these concepts, similarly to the concept of set or indeed the very concept structure, are so general and so fundamental that we can hardly expect something like an explicit definition. Thus, the only thing which seems to be worth attempting is the characterization via assembling a list of principles which would capture their 'behavior' - i.e. some basic principles which are characteristic for any parts and wholes. Such principles could then possibly be used as axioms of a formal theory (since this very method has proved so fruitful in explicating of the concept set, the prospects of such a project might augur well). In fact, a formal theory of parts and wholes, mereology, was already put forward in the first half of the twentieth century by the Polish logician Stanislaw Lesniewski. 5° Similarly as set theory is actually the theory of the binary relation to be an element of, E (it is this symbol which is the sole non-logical term of set theory; the concept of set is then defined in its terms), mereology is the theory of the binary relation to be a (proper) part of, which is usually abbreviated to «. (The concepts of part and whole are then again defined in terms of this concept: a part is simply what is a part of something, a whole is what has parts). And just as the relation E is characterized by a system of axioms (some of which are accepted by all set-theoreticians, whereas others are subject to controversies), there is also a system of axioms characterizing «. Leaving the more technical details for Appendix I (Section 4.7), we can say that the basic axioms of mereology state that nothing is a proper part of its own proper part; that a part of a part of a whole is a part of the whole; and that if x is a proper part of y, then y has a proper part which does not overlap with x. Simons' (1987) basic system of mereology, "Minimal Extensional Mereology", consists of these three axioms plus the axiom guaranteeing that there will always be an object constituting the common part of two overlapping objects, which implies, together with the former axioms, that there can be no two different wholes consisting of the same parts. Should we accept the principle that no two different wholes consist of the same parts as a general principle characteristic of parts and wholes? It seems 50

See Lesniewski (1927-31).

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Meaning and Structure

that the question is to be answered in the negative: it appears that not every part-whole system is necessarily extensional. It is perfectly conceivable that within some systems the same parts may constitute different wholes - if we compose them in different ways. (Thus four legs and a board constitute a table because they are put together in a certain way, whereas when put together differently they might constitute, e.g., a stretcher). It thus seems that we can conceive of such systems of parts and wholes in which there are different objects sharing all their parts. Such part-whole systems will then inevitably lead to the question of what makes the difference between such wholes: and the straightfmward answer to the question is their different ways of composition, or their different structures. Hence it is in this context where we encounter the inevitable need of something as structure: within a context of a part-whole system in which the same parts may yield different wholes, the structure is what explains the difference. If we want to account for structures using mereology, we must extend it to a richer theory. Technically there is more than one option how to accomplish this (see Section 4.7 for details); we choose the one based on the idea of switching from considering objects with merely the relation of being a proper part to considering a collection of ways of forming more complex objects out of simpler ones. A part-whole system, conceived in this way, then consists of a universe of objects plus a collection of functions each of which takes, for some n, an n-tuple of objects ('parts') to an object ('the whole consisting of the parts'). 51 Let us call an object of a part-whole system (hereafter pws) simple if it has no parts; and let us call the set of all simple objects of a pws the basis of the pws. We will call a pws finitely generated iff its basis is finite and each object of its universe is ultimately composed of the elements of the basis- i.e. if each element of the universe is either an element of the basis, or is composed of the elements of the basis, or is composed of simple elements plus elements composed of simple elements etc. 52 This means that ifwe define a property for the elements of the basis and if we specify how to extend the definition to any whole from its parts, we define the corresponding property for all elements of the pws in question. Such a definition will be called, as might be expected, inductive. The properties which can be defined inductively, then, are those which are somehow 'projectible' from parts to wholes, i.e. for which their possession/nonpossession by a whole is always uniquely determined by their possession/nonpossession by the parts. (In the simplest case a whole possesses such a property just when its parts do - thus a whole is, for 51

52

Viz. Section 4.8, Definition 1. Ibid., Definition 2.

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instance, wooden if all its parts are wooden. However, the situation may be less simple: we can imagine, e.g., a property which is possessed by a whole when it is possessed by at least one of its parts - this is the case of the property to contain wood). 53 An example of a property which is not so projectible is to be heavy (or the less vague to weigh more than 10 kg): to decide whether a whole is heavy is surely not always possible on the basis merely of the knowledge of whether its parts are heavy (if at least one of the parts is heavy, then the whole is surely heavy too; but if none of them is, the whole may be heavy, but need not be). Let us now consider what we will call evaluations: assignments of values to the elements of a pws. Clearly an evaluation is inductively definable iff the value it assigns to a whole is always 'composable' from the values of its parts. (An example of such an evaluation is weight - the weight of a whole can be computed by adding up the weights of its parts. An example of an evaluation which is not of this kind is density - the density of a whole clearly cannot be computed from the densities of its parts, for to do this we would need also either the volumes, or the weights of the parts). Evaluations fulfilling this will be called compositional. And as compositionality is a concept which is crucial from the viewpoint of our structuralistic analysis of language, we will now discuss it in greater detail. To say that an evaluation V is compositional is to say that the values it assigns to the objects of the pws can be seen as 'built' in a way parallel to the one in which the objects themselves are build. If an object y is built from the objects x~. ... ,Xn in the way 0, i.e. y = O(x~. ... ,xn), then there must be a way, o·, to 'build' V(y) from V(x 1), .•• ,V(xn); hence V(y) = V(O(x~. ... ,xn)) = o*(V(xJ), ... ,V(xn)). This means that Vis compositional if and only if for every way of composition 0 there is a function 0 • such that for every n-tuple of objects x~. ... ,xn composable in the way 0 it holds that V(O(xJ, ... ,.xn)) = o*(V(x 1), ••• ,V(xn)). 54 Let us now imagine a complex object in which we replace one of its parts by a different object. The result is an object which is, in a way related to the original one - it is composed in the same way and also has almost the same parts - with the single exception. The object which arises from an object z via the replacement of its part x by an object y or vice versa will be called an [x[y]-variant of z. Defined thus, an [x[y]-variant of an object is an object which is composed of the same parts and in the same way as the original one, with the only possible difference that it has some occurrences of 53

Needless to say that this holds only as long as we restrict ourselves to considering

macroscopic parts. 54

Ibid., Definition 3.

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Meaning and Structure

x replaced by y, and/or some occurrences of y replaced by x. Clearly, if neither x, nor y is a part of z, there is only one [x[y]-variant of z, namely z itself; otherwise z has more than one [x[y]-variant. It can, of course, also happen that no [x[y]-variant of z exists: x can be so different from y that it is simply not possible to substitute the one for the other. 55 Let us imagine that we have two wholes Oi(x 1, ••• ,xn) and Oi(yl.···.Yn) (composed in the same way), and let us assume that their corresponding parts are evaluated in the same way, i.e. that V(xi) = V(y 1), ••• , V(xn) = V(yn). Then, if Vis compositional, it must necessarily hold that V(Oi(xl.···,xn)) = V(Oi(yl.···.Yn)). This means that in the case of compositional evaluation, sameness of values of parts implies sameness of values of wholes. Since the converse can also be shown to hold (if an evaluation has the property of identically evaluating two wholes whenever it identically evaluates their parts, then it is compositional), it follows that an evaluation is compositional if and only if it assigns the same value to two wholes (composed in the same way) whenever it assigns the same values to their corresponding parts. 56 Let V be a valuation. We will call two objects V-interchangeable iff their interchange within a whole cannot cause the change of the value of the whole. This means that x and y are interchangeable just in case any object has the same value as any its [x[y]-variants, i.e. just in case V(u) = V(v) for any two [x[y]-variants u and v. If we now call two objects x andy V-equivalent just when V assigns the same value to both of them, i.e. when V(x) = V(y), 57 it is easy to prove that if V is compositional, then every two V-equivalent objects are V -interchangeable. However, it can be proved that also the converse is the case: if every two V-equivalent objects are V-interchangeable, then V is compositional. This means that an evaluation Vis compositional if and only if every two objects that are V-equivalent are also V-interchangeable. 58 The concept of compositionality, which we have defined for evaluations in this way, can be straightforwardly extended to properties and equivalence relations - since both properties and equivalences can be seen as kinds of evaluations. A property can be seen as evaluating objects by the two truth values (thus, e.g., the property to be wooden can be seen as assigning truth to wooden objects and falsity to non-wooden ones), and we can consider it as compositional just when this evaluation is compositional. It is easy to see that this definition respects the compositionality-related intuitions for properties mentioned above (i.e. that properties such as to be wooden or to contain wood will come out as compositional, whereas the property to be heavy does not). 55

Ibid., Ibid., 57 Ibid., 58 Ibid.,

56

Definition 4. Theorem I. Definition 5. Theorem 2.

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65

Equivalences can be seen as functions mapping an object on the corresponding equivalence class. 59 Thus, an equivalence is compositional if and only if the equivalence class of a whole is uniquely determined by those of its parts. 60 Then it is easy to show that an evaluation Vis compositional if and only if the relation ofV-equivalence is a compositional equivalence. 61 Now it can easily be seen that what we called congruence in Section 4.1 is nothing else than a compositional equivalence. The point is that an equivalence, is, by our definition, a congruence if it can be projected from parts to wholes, i.e. if equivalence of all parts of two wholes always brings about the equivalence of the wholes. 62 Hence the concept of compositional equivalence is the same as that ofcongruence. 4.3 Actual and Potential Infinity

Before we proceed to the mathematical account of the Saussurean vision, let us pause and consider one more aspect of compositionality. What we concluded in the first section of this chapter can now be reformulated into the thesis that any diagram of a coalescence (and hence any capturing of an abstraction process) on a pws is bound to be an equivalence which is compositional. This means that on a pws, some relations and functions must be compositional. Now we further suggest that on a pws of the kind which will interest us most, compositionality is even more pervasive. The kind of pws I have in mind is the one the wholes of which are perceived as extending to infinity. Consider English - we usually think of its expressions as infinite in number. How is this claim to be understood? Surely not so that somebody has counted the expressions and that infinity is the result of his counting. The claim is rather the consequence of our finding out that the expressions cannot be counted; that however long we count, we never exhaust all of them. We know that the number of expressions is not expressible by means of any 'normal' number; however, we express this essentially negative finding by means of a claim of the same form as the claim which would result from successful counting. Thus, when we say that the expressions of language are infinite, we are not stating how many there are, but rather how

59

Ibid., Ibid., 61 Ibid., 62 Ibid., 60

Definition 6. Theorem 3. Theorem 4. Theorem 5.

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Meaning and Structure

many there are not. We say that we can form new expressions beyond any fixed limit. How do we know this? We know that our language has grammatical rules which allow us to use any expressions, however long, to form still longer expressions. The infinity of language thus consists in the fact that the grammatical rules can be applied recursively without any limit. The infinite set of expressions of our language is specified only 'potentially', it is somehow implicit in our grammatical rules (more precisely in their unlimited recursive applicability). And this entails substantial consequences for the nature of any property or any evaluation of expressions. We can never assign values to all expressions by simply making their complete list and writing the corresponding values alongside; the only thing we can really do is to assign the values to some basic expressions and to state how values spread from parts to wholes. And similarly we could never understood an existing property if it were not graspable otherwise than by going through the list of all the expressions. Hence it seems that the only evaluations which are definable or graspable for us are those which can somehow be projected from simpler expressions to more complex ones, i.e. which are compositional in the sense of the preceding section. Hence it seems that the only 'humanly manageable' relations and functions of expressions of a language are the compositional ones. This indicates that for a pws which allows for an unrestricted forming of ever more complex wholes, compositionality is an imperative. Now it is interesting to notice that there is a sense in which any kind of an infinite range of entities has the nature of a pws Imagine, for instance, the infinite domain like that of natural numbers. How do we know it is infinite? We have surely never been confronted with more than a finite amount of numbers - so how do we know that there is not only a finite number of them? Well, the situation appears to be analogous to the case of language: we know that each number necessarily has a successor, that given any number, there necessarily is a greater one. There is no limit to increasing numbers. Or take space: we also believe that it is infinite. Why so? For wherever we get travelling through it, there must be, we believe, a principal possibility to go on. This is not to say that we would have to be able to go on - there may be hindrances unsurpassable for us, due to the limitations of our actual abilities. But we believe that something must still be there further on - for the possibility of there being nothing does not really make sense to us. Hence there is no limit to the extension of space. This indicates that the concept of infinity is somehow secondary to the concept of unlimitedness: to the fact that some things can be continued or

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repeated without a limit, hence 'to infinity'. 63 Any number can be increased; any sentence can be prolonged; wherever we get through space, we can go further. Wherever we get in the corresponding process, we can always (assuming we can overstep possible hindrances) make a next step. Hence the primary context in which the term "infinity" comes to be employed is that of expressing the possibility of the unlimited going on: to go on 'to infinity', 'ad infinitum '. 64 Now a prototypical case of a step of this kind is the composition of parts into a whole (this is most obvious in the case of language, for the syntactic rules are typically rules of some kind of concatenation). A finitely generated pws is something essentially finite; it is a finite number of simple parts plus a finite number of rules of composition. However, it may nevertheless be capable of 'engendering' infinity: the infinity of its potential constructs producible by means of the infinite applications of its rules. And if we understand the concepts of part and whole abstractly enough, we can, conversely, see almost any infinite range as a part-whole system- the point is that any rule capable of 'leading us to infinity' can be seen as a kind of composition, as an addition of further part( s). Hence elements of a potentially infinite range - of a range, that is, engendered by a finite generating system - are given to us purely through the system; 65 and if we want to say anything about all of them, we are left with 63

See also Peregrin (1995a, §9.2). Thus, the infinity which is nothing more than such a metaphoric expression of unlimitedness, the potential infinity, is not usually considered as really existing, but rather merely as an imaginary limit of an idealized extrapolation of an unlimitedly repeatable action. However, modem mathematics has attempted to embrace also a more substantial concept of infinity, actual infinity: an actually infinite set is considered to be a thing real in the same sense as a finite set is. The infinity (or, more precisely, any infinity, for modem mathematics proposes to count with many levels of the infinite) is merely one more number. This is the upshot of the set-theoretical approach to mathematics due, in effect, to Georg Cantor (details of the genesis of this approach are nicely summarized in Chapters 3-5 of Lavine, 1994). It is an undeniable fact that mathematics based on this construal of infinity has proved fruitful and hardly dispensable in praxis (which does not mean that the concept of absolute infinity has not been vigorously criticized by many mathematicians); however, if what we are after is not mathematics, but the nature of the world surrounding us (and especially the nature of language), we cannot overlook how infinity is engendered by unlimitedness. 65 Wittgenstein (1953, §208) says: "We should distinguish between the 'and so on' which is, and the 'and so on' which is not, an abbreviated notation. 'And so on ad inf.' is not such an abbreviation." Given a finite set, we can list its members; and if we list only some of them and add "etc.", we can understand the "etc." simply as a shortcut which could be expanded into the list of names of the remaining elements. However, if the set in question is infinite, then we cannot make do without an "etc." - we can never list all its elements, and 64

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the mediation of the system. Thus if we have a property and want to specify which of the elements have it and which do not, we clearly cannot list them, we must do it so that we say which of the basic elements have the property and how the property is projected from parts to wholes. In other words, our characterization of the property cannot but be inductive; and the property thus cannot but be compositional. We have already seen how it is in the case of language - so let us take, as another example, the natural numbers. When we want to say which of them are even and which odd, we cannot make the list of all of them and mark the odd ones by "o" and the even ones by "e". We must do it in such a way that we say that the number one (the basic element of the corresponding generating system) is odd, that the successor of an odd number is even and that of an even number is odd. 66 The situation is similar when the elements of an infinite range are to be assigned values. We again cannot but specify which values are assigned to the basic, simple elements and how the values get projected from parts to wholesi.e. to form, for every rule of composition 0, a rule o* such that the value of any whole O(x~, ... ,xn) is yielded by the application of 0 * to the values of its parts Xt, ... ,Xn; i.e. that V(O(x~, ... ,xn)) = o*(V(x,), ... ,V(xn)). The assignment of values to all elements of an infinite range is thus essentially compositional. 67 In the previous chapter we stressed that the concept of structure is inseparably connected with that of composition of parts into wholes- that a structure is nothing else than the way in which a whole is composed out of its parts. In addition, we have now seen that if the ways of composition (e.g. the grammatical rules of a language) can be applied recursively, without a limit, this gives the collection of the constructs of the system the specific character which crucially differentiates it from systems with only a finite number of constructs. In the case of an infinite system it holds, we saw, that the elements of the system cannot be given otherwise than through some rules of composition, and that these rules are then also bound to mediate any ascription of a property, or of values, to the elements. In this way the rules, and the behavior of the elements with respect to them, become something essential and characteristic.

the "etc." here is not a dispensable shortcut. In this case, the "etc." has to refer to an unlimitedly repeatable procedure which can potentially yield us the elements of the set. 66 The more natural way to specify the even numbers is, of course, to say that they are those numbers which are divisible by two. In this way we reduce the concept of evenness to that of division, and then it will be the latter concept which will have to be defined inductively. 67 See also Peregrin (1995a, Chapter 9).

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4.4 The Principle of Compositionality of Meaning To summarize: if meanings are, as de Saussure claims, abstracted from functional equivalences and if language is a pws, meaning assignment must be compositional. Moreover, if there is no fixed limit to the length of expressions of a language, the language cannot but be grasped as a pws; and, moreover, as an evaluation of elements of such an 'infinite' system must be compositional, we have a reason for requiring that meaning assignment be compositional independent of the acceptance of the Saussurean account. These considerations yield the well known principle of compositionality of meaning: The meaning of a complex expression is uniquely determined by the meanings of its parts and the mode of their composition. However, as this principle is often construed in a way which may appear to render it incompatible with our 'structuralistic' way of viewing language, let us discuss it in greater detail. According to our explanation, an evaluation V of the elements of a pws is compositional iff there exists, for every way of composition 0 of the pws, an 'algorithm' o* so that for every x~, ... ,Xn composable in the way 0 it is the case that V(O(x~, ... ,xn)) = o*(V(x 1), ... ,V(xn)). The assignment of meanings to the expressions of a given language is thus compositional iff for every grammatical rule we have a way of 'computing' the meaning of any complex expressions formed according to the rule from the meanings of its parts. As we have further shown, an evaluation V fulfils this requirement (and is thus compositional) iff any two V-equivalent objects are V-interchangeable (i.e. if for every two elements x andy such that V(x) = V(y) and for every element z and every of its [x[y]-variant z' it holds that V(z) = V(z')). The assignment of meanings is thus, according to this definition, compositional iff every two expressions which have the same meaning are interchangeable without changing the meaning of the whole in which they are interchanged. Thus, if we call the claim that synonyms are interchangeable without affecting meaning the principle of intersubstitutivity, we can say - understanding the term "compositionality" in the way we do - that the principle of compositionality states nothing else than the principle of intersubstitutivity. However, it is often taken for granted that the principle of compositionality does say something more - namely that it states that the meanings of parts are somehow more primary than the meanings of wholes; that the meaning of a whole is derived from the meanings of its parts. This reading might even seem to follow from what we said in the previous section, when we explained why

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any reasonable evaluation must be compositional: namely that the infinity of expressions can be given only through a finite number of primitive expressions (words) plus a finite number of recursively applicable grammatical rules; and that the assignment of such values as meanings can be grasped only through the assignment of meanings to words and the ability to 'compute' the meaning of wholes from those of their parts. An illustrious expression of this view can be found in a text of Gottlob Frege (1969, p. 243), with whose name the principle of compositionality is usually associated - although he himself never articulated it, at least not in the form presented above: It is remarkable what language can achieve. With a few sounds and combinations of sounds it is capable of expressing a huge number of thoughts, and, in particular, thoughts which have not hitherto been grasped or expres sed by any man. How can it achieve so much? By virtue of the fact that thoughts have parts out of which they are built up. And these parts, these building blocks, correspond to groups of sounds, out of which the sentence expressing the thought is built up, so that the construction of the sentence out of parts of a sentence corresponds to the construction of a thought out of parts of a thought. And we take a thought to be the sense of a sentence, so we may call a part of a thought the sense of that part of the sentence which corresponds to it.

Does it not therefore follow that the meanings of all expressions of language derive from the meanings of words - and hence that the meaning of a word must be independent of the 'horizontal' relations, its relationships to other words, rather than being constituted by them? Is the principle of compositionality a Trojan horse contaminating our structuralistic theory of language with precisely what we have so painstakingly tried to expel- i.e. the understanding oflanguage as a set of labels? 0 want to argue that this is not the case. Before we start to see Frege as an adherent of the nomenclaturistic theory of language, it is necessary to consider his views more systematically. And doing so, we cannot fail to notice that he often expresses views which are scarcely compatible with that suggested by the above quotation. Thus, in the Foundations of Arithmetic (1884, p. 73) he famously urges that It is only in the context of a proposition that words have any meaning.

This is often dubbed the principle of contextuality- and it appears to imply, contrary to the nomenclaturistic view, that the meanings of wholes are not derived from those of their parts, but rather that wholes somehow confer meanings on their parts. Was it, then, coherent for Frege to subscribe both to the principle of compositionality and to the principle of contextuality? And how is it possible to subscribe to the principle of contextuality in view of the

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fact that one cannot but grasp the infinity of expressions through grasping something finite? I am convinced that the answer to the first of these questions is that Frege construed compositionality in our 'neutral' way, and not as the statement of the derivedness of meanings of wholes from those of their parts. 68 If this is correct, then the principles of compositionality and contextuality do not contradict each other- on the contrary, they are complementary. Following the principle of contextuality and relinquishing the idea that the meaning of a word is a purely extralinguistic entity whose connection to the word could be accounted for, e.g., in causal terms, leaves us with the need for some substitute: we need something to let us individuate meanings of words. And this is precisely the work the principle of compositionality does: it specifies that the meaning of a word is simply the contribution which the word brings to the meaning of the sentences in which it occurs. This becomes particularly evident when we reformulate the principle of compositionality as the principle of intersubstitutivity. In this form it can be read as specifying what the meaning of a part is: it is that which the part shares with all other parts which can be interchanged with it without thereby changing the meaning of the corresponding wholes. (The details of this theoretical gripping of meaning will be considered later- in Chapter 8). What, then, about the problem that our knowledge of the meanings of each of the potential infinity of expressions must be mediated by a finite knowledge? It seems indubitable that if we understand a sentence which we have never heard before, the reason is that we know the meanings of the words of which the sentence is composed. How is it possible to reconcile this fact with the 'contextualism' which claims that the understanding of an expression is, the other way around, a matter of the extraction of the contribution of the expression from the meanings of the statements in which it occurs? The answer is that although our everyday understanding of many sentences may stem from our understanding of the words of which they consist, this does not entail that the understanding of words necessarily derives from the direct association of words with things. Our grasping of the meanings of words may derive from our understanding some basic, finite stock of sentences which constituted our entering wedge to the language in question. As Quine (1960, p. 68

Hence I disagree with the explanation given by Janssen (1997) that Frege subscribed both to the principle of compositionality, and the principle of contextuality, but in different phases of his development, and not simultaneously; instead I support Stekeler-Weithofer (1986, §8.13) in his view that Frege's pronouncements which appear to contradict the principle of compositionality (such as our above quotation) are to be understood merely as certain vivid metaphors, by means of which Frege did not subscribe to the 'nomenclaturistic' view of language.

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9) describes the situation, we come to understand some sentences as wholes, and then we realize how their parts function and we learn to use the parts in a way analogous to the way they functioned in the basic cases. And as Blackburn (1984, p. 227) puts it, the fact that we grasp the meanings of some sentences because we grasp the meanings of corresponding words, while our grasping the meanings of the words is derived from our grasping some sentences in which the words occur, is no more mysterious than the fact that a chess player can assess a new position on the chessboard because he knows the power of individual pieces, while the power of the pieces is a matter of exclusively their role in the game. 69

4.5 The Birth of Values out of Identities and Oppositions Let us now return to the principal project of this chapter, to the 'mathematization' of de Saussure. Our thesis is that what de Saussure calls "identity" corresponds to what we call (in accordance with the jargon of modem mathematics) equivalence. De Saussure's "opposition" is then, in our interpretation, the complement of such an equivalence - namely the relation which holds between two objects just in the case when they are not in the equivalence relation in question. (It seems that what de Saussure usually had in mind were "identities" and "oppositions" corresponding to equivalences which we could call binary - namely those which yield merely two equivalence classes. It is this kind of equivalence which corresponds to a property or a concept: thus, e.g., the property to be wooden classifies objects into wooden and non-wooden. The corresponding "identity" then holds between any two objects such that either both are wooden, or both are non-wooden; and the corresponding "opposition" holds between any two objects one of which is wooden and the other is not). When we talked about abstraction, we said that the passage to a higher level of abstraction (e.g. from individual animals to their kinds) is one side of the coin the other side of which is the establishment of an equivalence between objects of the original level (e.g. between animals of the same kind). Such an abstraction can thus always be seen as an establishment of an equivalence; and conversely the establishment of any equivalence can likewise be seen, as suggested by the term "equivalence", as an establishment of the corresponding values, shared by the equivalent objects. Hence any equivalence can be seen as 69

What is, however, nontrivial, is that one is able to extract the meaning, i.e. gain the ability to employ a word in an unlimited ('infinite') number of contexts, from a finite number of cases in which one has observed its usage. This is a case of what Stekeler-Weithofer (1994) calls Entfinitizierung, i.e. 'de-finitization'; but this is no more mysterious than that one can learn, e.g., to swim on the basis of a restricted amount of learning.

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literally an equi-valence, as a specific, 'abstractive' evaluation; namely as a function which maps each object on 'that which it shares with all its equivalents'. (The fact that we see all wooden objects as in a sense equivalent can be accounted for by means of saying that they share a 'value', namely 'woodenness'). This evaluation will be called the canonical projection of the corresponding equivalence: the canonical projection of an equivalence, we can therefore say, will be the evaluation which arises when we look at the equivalence as at an equi-valence. 70 However, when we work with a range of objects which is not a mere set, but rather a pws, we face the problem of compositionality. For reasons discussed earlier in this chapter we will not see an equivalence as 'acceptable' unless it is a congruence, and likewise we will not see an evaluation as 'acceptable' unless it is compositional. What if we encounter an evaluation which does not appear to be compositional? If what we have said so far is correct, it cannot be but that such an evaluation is somehow 'parasitic' upon a compositional one. How can this arise? The mechanism which allows a compositional evaluation to give rise to a non-compositional one is quite simple: our well known decrease of 'visual acuity' (or increase of level ofabstraction). Imagine there is a (compositional) evaluation V and imagine that we move from the values constituting the range of V to their equivalence classes. Then there is no guarantee that the resulting evaluation will still be compositionaC 1 - but this is not possible without the evaluation's resting upon a compositional one. This means that a compositional evaluation can engender, via increasing the level of abstraction in respect to its values, a non-compositional one. Thus we must correct our previous claim that the only acceptable evaluations of the elements of a pws are compositional ones: the acceptable evaluations, as we now see, include both the compositional ones and the non-compositional ones engendered by the compositional ones. This means that if we encounter what looks like a non-compositional evaluation, to find out whether it is 'acceptable' is to find out whether it is underlain, in the above sense, by a compositional evaluation. How is it possible to find out this? Let us imagine a non-compositional equivalence and try to find a compositional equivalence which might be seen as engendering it. We have stated that the only way such an engendering may proceed is the 'coarsening' of the system of values of the original evaluation; hence to move from the engendered evaluation to the compositional one which underlies it requires a 'de-coarsening', i.e. a refinement. What may such a 70

Section 4.8, Definition 7.

71

Ibid., Theorem 6. (See also the example discussed by Peregrin, 1997).

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refinement amount to? Seen from the viewpoint of the corresponding equivalence classes, it amounts to adding new boundaries while leaving the old ones intact. (Imagine we move from an outline of the USA showing state borders only to an outline containing also district borders within individual states). The question therefore is: which equivalences constitute such refinements of a given equivalence E? And the answer is straightforward: any of those which are contained within E. 72 (The point is that the 'borders' separate elements which are not equivalent, and so by making more elements non-equivalent we clearly add borders). The search for a compositional equivalence underlying E thus seems to be reasonably conceivable as a search for a compositional equivalence which is a part of E - and as we want to find the equivalence closest to E, it seems to be reasonable to conceive it as the search for such a compositional 'subequivalence' ofE which is the closest one to E. Thus, we define the compositionalization of E as a compositional equivalence which is a part of E and which is a proper part of no other compositional equivalence which is a part of E. 73 It turns out that every relation has a uniquely determined compositionalization; and if a relation is compositional, it equals its own compositionalization. 74 Let us now imagine that we want to compositionalize an evaluation (e.g. a canonical projection of a non-compositional equivalence). As we know that an evaluation V is compositional just in case the corresponding V-equivalence is compositional, to compositionalize V is the same as to compositionalize the V-equivalence. However, to compositionalize the V-equivalence is, as we have just concluded, to make some hitherto V-equivalent objects non-V-equivalent (and hence to refine the corresponding equivalence classes). From the viewpoint of V this clearly means to refine the range of values assigned by V to the elements of the pws in question. This brings us to an important moral, namely that compositionalization may necessitate a refinement of existing values. 75 An equivalence can lead, as we saw above, quite trivially to a system of values- it is enough to look at it from an 'objectivizing' angle (formally this means passing from the equivalence itself to the corresponding canonical projection). However, if we have the additional requirement of compositionality, the resulting system of values may cease to be trivial. Let us call the canonical projection of the compositionalization of a given equivalence the compositional projection of the equivalence. 72

Let us stress that it is every equivalence contained in E, not every relation. Ibid., Definition 8. 74 Ibid., Theorem 7. 75 Ibid., Theorem 8.

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The compositional projection of an equivalence may therefore involve values not required by its canonical projection. (It may, e.g., happen that while the canonical projection makes do with a finite number of values, the compositional projection necessitates an infinite number). What I claim is that it is just such a compositional projection which represents the mechanism of the arousal of 'the structural'. We can say that whereas the canonical projection reveals the values implicit to a given equivalence (in the sense that it allows us to see the equivalence explicitly as equi-valence), the compositional projection reveals those implicit to the 'real' equivalence behind what we see as a self-standing equivalence only for the lack of visual acuity or for a too high level of abstraction. 4.6 Examples

1. Let us imagine a lego, i.e. a set of bricks of various kinds, which can be used to construct various buildings. The set of all buildings which can be constructed from the bricks can be seen as a universe of a part-whole system - let us call the elements of the set, for brevity, constructs (thus every brick will itself be a construct, and everything which results from any kind of combination of bricks will again be a construct). The simple constructs of the system will be the individual bricks. Let us now consider relations on the universe of the pws. Consider the relation to be of the same color- and imagine, for the sake of simplicity, that also constructs consisting of parts of different colors can be assigned a unique color, such as black-blue, white-yellow-red etc. 76 In addition to this, consider the relation to have the same number of elementary colors (where elementary colors are such as blue, green etc., but not such as blue-green). Let us use the symbol C for the first of the relations and the symbol NC for the second. Let us now imagine that two constructs x andy share the same color, i.e. that x C y. Then it clearly holds that whenever x is a part of a more complex construct and it is possible to replace it by y there, it can be replaced by y without changing the color of the complex; thus for every construct z and each of its [x[y]-variants z' it holds that z has the same color as z', i.e. it holds that z C z'. This means that the relation Cis compositional. Let us further imagine an evaluation C which maps constructs on their colors. It is evident that we know the color of a complex construct once we 76

Let us stress that we use, e.g., "black-blue" for an object which is partly black and partly blue, not for one whose color is somewhere in between black and blue.

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know the colors of its parts (if we, e.g., know that it consists of a part which is blue and a part which is blue-green, then we know that it is blue-green). Hence we can say that for every way of combination 0 of constructs there exists a function o* SO that for all COnstructS XJ, ...Xn, COmposable in the way 0, the color of O(xJ. ...xn) can be determined with the help of 0 • on the basis of the colors of XJ, ...xn; i.e. that C(O(xj, ...Xn)) = o*(C(xJ), ... ,C(xn)). And this means nothing else than that the evaluation C is compositional. If we realize that the relation Cis what we called the C-equivalence (i.e. that x C y just in case C(x) = C(y)), we can see that the compositionality of C follows directly from the compositionality of C- above we have shown that an evaluation V is compositional if and only if the corresponding V -equivalence is. Conversely, the evaluation C can clearly be seen as the canonical projection of the equivalence C - i.e. as that which C becomes when we consider it as an 'equi-valence'. The point is that colors can clearly be seen simply as the products of the corresponding abstraction. Let us now consider the relation NC. It is evident that if x NC y, i.e. if x and y have the same number of elementary colors, it does not follow that we could always replace x by y without thereby changing the number of elementary colors of the complex in which we make the replacement. Let us, for instance, suppose that the construct consists of two parts, x and v (i.e. that for a way of combination 0 it holds that z = O(x,v)), such that x is green and vis blue. Let us consider a construct y, which is blue. As both x andy have one color, it holds that x NC y. However, if we replace x by y in z, we gain the [x[y]-variant z' of z consisting of two blue parts and thus having one color; so in view of the fact that z has two colors, it is not the case that z NC z'. The relation NC is thus not compositional. This means that neither is the evaluation NC, mapping every construct on the number of its elementary colors, compositional; for it is evident that NC is the NC-equivalence (and NC is a canonical projection of NC). This reflects the obvious fact that the number of elementary colors of a complex construct cannot be uniquely determined simply on the basis of the numbers of colors of its parts. What could guarantee that two constructs are freely intersubstitutive without thereby changing the number of colors of the complexes in which the substitution takes place? Intuitively, the sufficient condition is that the two constructs have not only the same number of elementary colors, but rather the same elementary colors, i.e. the same color in our extended sense. That this is really the case follows from the fact that given two constructs x and y such that x C y, for all [x[y]-variants z and z' clearly z NC z'. However, for systems of constructs rich enough, the condition turns out to be also a necessary one: this follows from the fact that if x and y do not have the same color, i.e. if it is not the case that x C y, then it is

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always possible to find a construct z such that its number of colors changes if we replace its part x by /• i.e. that for some z and its [x[y ]-variant z' it is not the case that z NC z'. 7 However, as we have just shown, two objects stand in the relation C just in case they are NC-interchangeable, so it follows that C is the compositionalization of NC, and hence also that the compositional projection of NC is C. In other words: if we consider objects from the viewpoint of the number of their elementary colors, and if we consider them 'compositionally', abstraction leads us not to numbers, but rather to colors. 2. Let us now imagine that our task is to design a lego of the kind in our previous example. We have an idea which kinds of buildings should be buildable from it (this means that in our mind there exists a certain set of complex constructs of the prospective pws), and we try to devise a set of bricks from which these buildings would be composable. Clearly, there will be a number of such potential sets - and we will try to specify a minimal one, one which will consist of only the bricks really needed for the prospective buildings. Now the situation differs radically from the previous example. There we were given a basic set of bricks and we thought about their composing; our consideration thus proceeded from parts to wholes. Now we are given a set of objects which we try to see as complex constructs of a hitherto non-existent pws, we try to decompose these 'prominent' constructs and to reach the basic bricks. We thus proceed, conversely, from (certain) wholes to parts. Whereas the perspective of the previous example can be called compositional, the one we assume now can be dubbed decompositional. Let us now imagine that we consider some of the differences among the buildings which we used as the point of departure of the considerations of the lego design insubstantial; hence that we see buildings differing only in this way as equivalent. This clearly gets projected to the parts into which we decompose the buildings: no two bricks such that their interchange within any building leads to a building equivalent to the original one can be reasonably considered as substantially different - unless we change the If not x C y, then there must exist either an elementary color possessed by x, but not by y, or an elementary color possessed by y, but not x. In the first case we must identify z with a construct with the following properties: (i) it contains x, (ii) all elementary colors possessed by y are possessed also by a part of z different from x, (iii) none of its part different from x possesses the color possessed by x, but not by y. In the second case it is enough to identify z with a construct such that: (i) it contains x, (ii) all the elementary colors possessed by x are possessed also by other parts of z, (iii) it does not possess the elementary color possessed by y, but not by x. 77

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meaning of the words "substantially different". The equivalence among the 'prominent' constructs thus engenders a certain equivalence among all constructs (especially among the simple constructs, bricks). Let us imagine that what we are interested in is merely the color of the buildings - that we take any two buildings of the same color as equivalent. (This is admittedly rather unlikely, but let us accept it for the sake of illustration). From this viewpoint we are clearly not going to distinguish any two parts with the property that their interchange always leads to a building sharing color with the original one - and two constructs (especially two bricks) are clearly in this relationship when, and only when, they have the same color. In this case, the engendered equivalence is a straightforward extension of the original one to the whole pws. However, let us further imagine that what we are interested in is the number of elementary colors - i.e. that we take not only buildings of the same color, but those which have the same number of elementary colors, as equivalent. (This means that, e.g., two buildings one ofwhich is blue-green and the other is black-white will be taken as equivalent). Then we will clearly not distinguish between two bricks such that their interchange does not lead to a change of the number of colors of any complex construct. When does a pair of bricks have this property? Within the previous example we saw that this is the case if and only if the bricks share the same color. In this case, then, the engendered equivalence is not a straightforward extension of the original one, it is its refinement. Not everything in the original relationship (i.e. having the same number of colors) is automatically also in the derived one (i.e. has the same color). In sum: An equivalence among some 'prominent' constructs can engender an equivalence among all constructs; and the engendered equivalence can in some cases be a straightforward extension of the original one, in other cases it must be, however, its refinement. At the same time it is easy to see that the engendered equivalence is precisely what we have called the compositionalization of the original one. If the original equivalence is C, the engendered one is C again (for Cis compositional and hence is its own compositionalization); while if it is NC, the engendered equivalence is C (for it is C which is, as we saw, the compositionalization of NC). And if what we are after are values, then the system of values into which the relation NC thus gets projected is the system of colors - for it is, as we saw, just this system which results from the compositional projection of the equivalence. 3. Let us now imagine that we want to theoretically reconstruct an unknown language. This task is in a certain important sense similar to the previous task of designing a lego: what we are primarily given are some

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utterances of native speakers, which we want to reconstruct as complex constructs of a pws (the simple elements of which will be the words of the native language and the ways of composition of which will be the grammatical rules of the language). Some utterances of the speakers will sound immediately so alike to us that we will take them as equivalent - as instances of the same sentences. What we therefore want to reconstruct, what corresponds to the imaginary buildings of our previous example, will not be individual utterances, but rather types of the utterances according to this equivalence. These types of concrete utterances, which can be called sentences, we will then, in analogy to the previous example, try to decompose into a finite collection of basic building blocks. (And just as in the case of designing a lego we will try to find - and recognize as words - the maximal units which would enable us to carry out the desired reconstruction). Thus we describe the syntax of the native language: we assemble the inventory of its basic units and of the ways these units can legitimately be threaded together into complexes. In the next phase we start to pay attention not only to which sentences the natives employ, but rather also to when and how they employ them. Then we may arrive at the conclusion that also some prima facie dissimilar sentences are equivalent in the sense of having the same linguistic function, of being capable of serving precisely the same communication purposes. More generally, from this viewpoint we consider equivalent any two expressions such that their interchange within any sentence also leads us to a sentence functioning in the same way as the original one - such expressions will be said to have the same meaning. (Two expressions thus will be ascribed the same meaning if they share the contribution they bring to the functioning of the sentences in which they are embedded). Let us denote the relation of 'the same functioning' among sentences as SF and the relation of 'the same meaning' as SM. It follows from what we have just stated that two expressions x and y have the same meaning (x SM y) just in case for every sentence Sit holds that it functions in the same way as any of its [x[y]-variants S - i.e. that S SF S. This clearly means that SF and SM are in the relation of such basic and engendered equivalence which we considered within example 2; hence that the relation SM should be the compositionalization of SF. This further implies that the assignment of meanings to individual expressions should be the compositional projection of the relation SF- the assignment of such values which two expressions share just in case they are intersubstitutive 'salva functione '. Let us now restrict ourselves to sentences. Their role within language is twofold: their 'primary' function is to be tools of speech acts, their

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'secondary' function is that they can enter more complex sentences. (Dummett, 1973, calls the two 'components' of the meaning of a sentence the "freestanding sense" and the "ingredient sense"). 78 The relation SF has been introduced in respect merely to their primary function; however, two sentences really function in entirely the same way only if they coincide also in their secondary function. And to ask whether the sameness of their primary function implies the sameness of the secondary one is to ask whether the relation SF is compositional (if so, then the relation SM for sentences coincides with the relation SF). Now imagine that the equivalence SF were reducible to a binary equivalence E (and hence to an opposition) - in the sense that £-interchangeability would coincide with SF-interchangeability. This mean that the compositionalization of E would coincide with that of SF, i.e. with SM. Imagine that E is the binary equivalence of sameness of truth value. In such a case, the relation SM would be that of the intersubstitutivity salva veritate. And in this case the question whether the ingredient sense coincides with the freestanding sense would boil down to the question whether the relation of sameness of truth values, hence the truth value assignment, is compositional. These examples illustrate what we stated at the beginning of this chapter: that abstraction on a pws might be of far greater complexity than an abstraction on an unstructured set. If, for example, we find some objects equivalent with respect to the number of their elementary colors, it would by itself lead simply to abstracting numbers; however, as we saw in the example 2, if we deal with a pws, it could lead to 'more fine-grained' abstract objects - colors. Similarly, in example 3 we saw how the recognition of 'sameness of functioning' of statements can lead not only to 'ways of functioning', but rather to the more fine-grained 'meanings'. The last example is important because it concerns a problem emblematic of the philosophical stance of those philosophers whose doctrines will be discussed in the second part of this book, namely the problem of deciphering an unknown language by a "radical translator".

78 The importance of what we call the 'decompositional' perspective, from which the "ingredient senses" (which are de facto meanings in the ordinary sense of the word) get extracted from the "freestanding senses" ('functionings' of statements) was pointed out by Brandom (1994, p. 345).

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4. 7 Appendix 1: Mereology and 'Structurology' Let « be a binary predicate with the intended interpretation of the relation of being a proper part. Further concepts of mereology, such as the property of being simple (S), the binary relations of being a part( Somebody was a logician. Types of inferences, such as X was P :::::> Somebody was P,

will be called inferential rules. That part of an inference or of an inferential rule which is before the symbol :::::> will be called, as usual, its antecedent; the part after :::::> its consequent. A statements which follows from anything (i.e. which constitutes the consequent of a valid inference with the empty antecedent) is necessarily (i.e. 'unconditionally') true. A necessary truth of a statement may thus be understood as a special case of inference, i.e. as an inference with an empty antecedent. Conversely, any valid inference can be expressed in the form of a necessarily true statement: If Mickey is a mouse, Every mouse likes cheese :::::> Mickey likes cheese is a valid inference, then If Mickey is a mouse and every mouse likes cheese, then Mickey likes cheese is a necessarily true sentence and vice versa. 161 It follows, as we stated in the previous section, that consequence and necessary truth are two sides of the same coin. This also means that accepting a statement as an axiom (i.e. 159

This is how consequence is often defined; we, however, prefer taking it as a primitive concept, informally explicable in terms of the practice of' giving and asking for reasons'. 160 Note that inference construed in this way is not relative to an arbitrarily chosen system of rules. 161 Within elementary logic, this fact is reflected by the so called deduction theorem. Of course that for formal languages, such a theorem is not universally valid - some such languages may, e.g., lack a connective corresponding to "if ... then".

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as an undoubted truth) and endorsing an inference are two things which are largely interchangeable. To avoid misunderstanding, let me make the following remark. Within formal logic a distinction is generally drawn between the concept of consequence, which is classified as semantic, and the concepts of proof and inference, which are classified as syntactic. The former is defined in terms of the concept of truth or other semantic concepts (S is the consequence of s~. ... , Sn iff S cannot be false unless at least one of s~. ... , Sn is false, or iff S holds under any semantic interpretation under which S,, ... , Sn hold), whereas the latter is defined in terms of a collection of 'rewriting' rules (S is inferable from s~. ... , Sn if it can be reached as the result of transforming s~. ... , Sn according to the rules of the collection). Now it is necessary to point out a certain ambiguity of the term "syntax". If we understand inferability or provability as transformability according to truly any set of rules, we gain a concept which is interesting only from a purely formal viewpoint, and call it "inferability" is in fact misleading. (Let us realize that we can have such rewriting rules as rewriting backwards or deletion of a character - and the corresponding concept of 'inferability' then has nothing at all to do with logic or with the inferential structure of language). Inferability becomes genuinely logically relevant only when we restrict ourselves to certain 'reasonable' classes of rewriting rules, in particular to these which preserve truth. However, if we define inferability as transformability by a set of truth-preserving rules, the concept clearly ceases to be 'syntactic' in the sense mentioped above. To see the difference between consequence and inference as that between semantics and syntax can thus be misleading: if we understand inferability as trans formability according to any set of rules, then it is, without doubt, a 'syntactic' concept, but a trivial and an uninteresting one; whereas if we understand it, more interestingly, as transformability according to truth-preserving rules, then it is not 'syntactic'. Does this mean that the concepts of consequence and (absolute) inferability simply coincide? No - for although every inference, in our sense of the word, is an instance of consequence, it seems to be reasonable to admit also instances of consequence which are not inferences. It is, for example possible to conceive of a statement's being a consequence of an infinite '1umber of statements. 162 Moreover in more complicated logical systems we might even conceive of instances of consequence based on the

162

This was famously urged by Tarski (1936).

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fact, demonstrated by Godel, that some statements are true in force of other statements being true without the former being inferable from the latter. 163 So why do we not dispense with the concept of inference altogehter and base our considerations solely on the concept of consequence? There is again a reason for not doing so. First, all the instances of consequence which are not inferences are in a sense parasitic upon inferences. We can never directly articulate an instance of consequence which is not an inference (we surely could not put down an inference with an infinite antecedent!); so any such instances are bound to be somehow engendered by inferences. If we assume a mathematical viewpoint, it seems natural to regard inference as a relation between finite sets of statements and statements. 164 The most basic properties of the relation then appear to be the following: 165 Any statement is inferable from itself (i.e. of the corresponding one-element set); i.e. for any statementS it holds that S:::::.S.

(:::::. 1)

Moreover, if a statement Sis inferable from a set of statements, it is also inferable from any enlargement of the set, i.e. inferable from any enlargement of S:::::.S.

(:::::.2)

And it also seems clear that if S is inferable from a set of statements and if every element of the set is inferable from another set of statements, then S follows also from this last set, i.e.

163

Giidel (1931) proved that the standardly accepted formalization of arithmetic is incomplete in the sense that however we fix the axioms, there will always exist a statement S such that neither S, nor ---,Swill be provable, i.e. inferable from the axioms. Moreover, he showed that given the axioms, this statement is bound to be true, for it is equivalent to a statement claiming this very statement's unprovability, which is the case. Hence if we take the axioms of arithmetic to be true, and also accept the underlying inferential machinery of predicate logic, we simply cannot reject S - it is true in force of the axioms being true, although it is not inferable from them. 164

Of course there are other possibilities. Gentzen (1935), for example, rendered inference as a relation between sets of statements, writing {S" ... ,Sn} => {S1', ••• ,Sm'} for "whenever all of S" ... ,Sn are true, at least one of S 1', •.• ,Sm' is true". 165 There exist logical systems for which some of these so called structural rules do not hold (see Dosen, K. and Schraeder-Heister, P., 1993, for an overview). However, such systems then clearly loose the character of direct accounts for consequence (which is, of course, not to say that they are not useful for other purposes).

Meaning and lriferential Role

if S~, ... ,Sn ~Sand for every i from 1 ton it holds that S1', ..• ,Sm' ~ S;, then S 1', ••• ,Sm' ~ S.

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(~3)

These 'metarules' (i.e. rules for infering not statements from statements, but rather inferences from inferences) allow inferences engender other inferences. (If we, for instance, stipulate that S 1 ~ S2 and that S2 ~ S3, we can use (~3) to conclude that thereby S 1 ~ S3 . And we could imagine that some of the instances of consequence which are not inferences result from the rule (~2) being applied 'infinitely many times'. However, thanks to Godel we know that some instances of consequence are engendered by inferences also in much more intricate ways). Taking inference as the basic concept of logic requires explaining other logical concepts, such as negation or conjunction, in its terms. (This is contrary to the usual way of defining these concepts in terms of truth-functions and then defining consequence as truth-preservation). These concepts can indeed be defined in terms of specific inferential patterns governing specific linguistic items (as it is done within systems of natural deduction); 166 but they can be defined in terms of inference also on a more abstract level, in the way envisaged by Koslow (1992). We can understand the conjunction of the statements S 1 and S2 as such a statement from which both S 1 and S2 are inferable, and which has, moreover, the property that it is inferable from any other statement from which S 1 and S2 are inferable. 167 (In algebraic terms, conjunction is the infimum of the two conjuncts with respect to the relation of inference). 168 Similarly the negation of S can be understood as an expression which is incompatible with S (in the sense that anything whatsoever is inferable from it and S), and which is inferable from any other statement incompatible with S. (In algebraic terms it is the complement of S). Other logical operators can be seen analogously. The 'logical' expressions of natural language can then be seen as tools making these implicit structural characteristics of the inferential structure explicit. (This also justifies seeing these expressions as means of explicitation of the implicit inferential articulation in the sense of Brandom, 1994).

166 167

See, e.g., Prawitz (1965).

Of course that if conjunction is defined in this way, there is no guarantee that a conjunction of every two statements always exists and that it is unique (although if it exists, it is bound to be unique up to logical equivalence). 168 See Rieger (1967, §7.1).

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8.3 Meaning as 'Encapsulating' Inferential Role In Quine's eyes, the holistic nature of language discredits the very idea of "separate and distinct meanings" (Quine, 1992a, p. 56). Thus Quine repudiates the nomenclaturistic picture of language by simply letting meaning go by the board. And he does not see this as a shortcoming - on the contrary, he hails the dissolution of meaning as a "stumbling block cleared away" (ibid.). So he replaces the Wittgensteinian slogan "meaning is use" with simply "there is no meaning". My opinion is, however, that Quine's banishing of the concept of meaning is preposterous. I think that even if we abandon the nomenclaturistic picture of language in favor of the Wittgensteino-Quinian toolbox-picture, there remains room for meanings conceived of as objects. Thus I do not think that the picture drawn by Quine is utterly incompatible with that drawn by 'formal semanticists' following Camap (such as Montague, 1974). It becomes incompatible if we see the objects associated with expressions as designated by the expressions in the semiotic sense; however, we need not do this - we can see the objects as our way of idealized objectualizations of the ways we use the corresponding expressions. In particular, if we accept the conclusion reached in the second part of this book, namely that the relevant usage of an expression consists in its inferential behavior, we can see the objects as encapsulations of their inferential roles. What does the inferential structure of language look like, and how it can give birth to something as a meaning or a denotation? How is it possible to grasp the inferential role of an expression as an object associated with the expression? Let us start with a trivial example, which we have touched several times before. Let us take the connective "and". To master the most basic function of the connective, to know its meaning, is to know that a complex sentence constituted by a pair of sentences connected by means of "and" is correctly assertible if and only if both the component sentences are. This means that if sl and s2 are statements and if sl and s2 is the statement which arises out of connecting them by means of "and", then we can infer both S 1 and S2 from S1 and S2, and we can infer S1 and S2 from S1 together with S2. Thus, if we replace "and" by the symbol ";.:' (to signal that we work with an idealized variant of "and"), we can write s~,

s2 => s1

1\

s]I\S2=> s1 s11\

s2 => s2

s2

(Al') (Al') (Al')

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It is clearly these three inference rules which exhaustively characterize the basic function of"and", and thus the meaning of"A". In view of the fact that we may want to see inference as a matter of truth-preservation, we can transform (!d), (A2) and (A3) into the following form: if sl and s2 are true, then sl /\ s2 is true if sl /\ s2 is true, then sl is true if sl /\ s2 is true, then s2 is true

(Al') (A2') (/\3')

(A2') and (A3') can then be further reformulated as if sl is false, then sl /\ s2 is false if S2 is false, then S1 /\ S2 is false

(A2") (A3")

(Al'), (A2") and (A3") can now be seen as determining the dependence of the truth value of S1 /\ Sz on those of S1 and Sz. (Al') says that if S1 and S2 are both true (they have the value truth, or T), then S1 /\ S2 is also true (has the value T). (A2") and (A3") then state that if at least one of S 1 and S2 is false (has the value falsity, F), then also S1 /\ S2 is false (has the value F). Hence the well-known table:

s1 s2 s1 /\ s2 T T F F

T F T F

T F F F

Now this table can obviously be seen as the definition of a function (in the mathematical sense) associated with the symbol "A": a function which assigns a truth value to every pair of truth values. And if we are to find an object which would 'materialize' the inferential role of"/\", then it is obviously just this function which comes naturally. The point is that a function, thanks to the proceedings of modem mathematics, is naturally conceived of as a set, namely a set of ordered pairs ({, , , } in our case); and sets are, as we noted earlier, modem successors to abstract objects. Thus this move appears to deliver us a real explication of the meaning of"A" and thereby of that of"and". In this way, the functioning of an expression can be characterized by inferential rules and the way it is governed by the rules then can be 'encapsulated' into a (set-theoretical) object, which can be seen as the meaning

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of the corresponding expression. The example provided here is, of course, very simple and one might doubt whether anything analogous could be done in cases of expressions of different kinds than "and". Let us consider, e.g., the word "rabbit". What is its inferential role and how could we 'encapsulate' it into an object? We have said that knowing the meaning of "rabbit" involves the ability of using statements such as "This is a rabbit" appropriately, i.e. knowing that the statement is true just in case one points at a rabbit, and not when one points at, say, an elephant. However, these are the practical transitions of the type world-language which, as we stressed in the preceding chapter, no theory can aspire to capture explicitly (see Section 7.6). The knowledge of the meaning of "rabbit" nevertheless also involves the knowledge of certain inferences featuring statements containing the word, e.g., X is a rabbit ~ X is a mammal X is a rabbit ~X is not an elephant It might seem that here, in contrast to the case of "and", no object offers itself as a natural capturing of the inferential role. However, we will try to indicate that we can find candidates for such capturing if we think about inferential articulation more systematically. But before doing this, we must discuss some of the objections which such an approach to the explication of the concept of meaning has to face.

8.4 Ontologico-semiotic View of Meaning Strikes Back? It might seem that we are heeding a kind of reconciliation of our

'structuralistic' approach to semantics with the approach which we dubbed ontologico-semiotic in Chapter 2, i.e. with the approach according to which meanings are abstract objects. It seems that we too have now come to see meanings as such objects. Has, then, the ontologico-semiotic understanding of meaning, once thrown out the door, now returned via the window? Has our earlier rejection of the approach thus proved itself unwarranted? It is important to realize that between our current approach and the ontologico-semiotic view of language there still exists a substantial difference: we do not claim that meanings are abstract objects; what we claim is that they can be accounted for- or, as I would prefer saying, modeled- as abstract objects. From our viewpoint, what is presented by the theories taking meanings to be abstract (usually set-theoretic) objects are only idealized models of language. If there arises the question whether the meaning of an expression really is the object which is assigned to it by such a theory, the way to the answer, from our viewpoint, would not lead via searching out a

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'christening' or a 'semiosis' by which the connection between the object and the expression was established, but rather via investigating the inferential role of the expression and assessing whether the role may be usefully modeled by the object. 169 We can illustrate this difference by means of an example from a wholly different field, namely physics. Take Bohr's atomic model, which envisages the atom as a core surrounded by electrons orbiting it similarly to how the planets circle the Sun. The model was accepted for a while by part of the physicists as a possible true depiction of the inside of the atom (for in some respects atoms did behave as the model predicted); however, it has soon become clear that the situation is more involved and that this construction does not accord with how atoms behave in certain other respects. Bohr's model, nevertheless, has not vanished from physics - however, instead of as a direct account of the inside of atom it is now taken as a simplified and idealized version of something which is really far more complex. In one word, it is taken as a model. And the reason why such a model maintains its place within physics is that it provides for a certain kind of insight into those aspects of the atom's functioning which are in accordance with it. "The ubiquitous practice of using models," writes Dennett (1991, p. 36), "is ... a matter of trading off reliability and accuracy of prediction against computational tractability." What we add is that gaining an insight is a motif no less important that "computational tractability". And the kind of modeling which has to do with gaining insight is closely connected with explication in the specific sense introduced by Carnap (1947, §2) and Quine (1960, p. 258-9). 170 Applied to the concept of meaning it leads to the approach which David Lewis (1972, p. 173) aptly characterized as follows: "In order to say what a meaning is, we may first ask what a meaning does and then find something which does that." Thus, our structuralist approach to language and our view of meanings as abstract objects is analogous to the post-Bohrean approach to Bohr's model: though we take it as a very useful thing which may help us understand semantics, it is nevertheless only a model. Viewing the inside of the atom through the prism of Bohr's model is surely helpful- up to a certain limit. If we take this model too literally, it will corrupt our view of the nature of the atom. And similarly we would be led to a corrupted view of the nature of meaning if we took semantic models of the kind we will build too literally. This is to say that when Sellars (1992, p. 109n.) claims that "[Carnap's formalization of semantic theory in terms of a primitive relation of designation 169

See Peregrin (1998).

170

See footnote 38.

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which holds between words and extralinguistic entities] commits one to the idea that if a language is meaningful, there exists a domain of entities (the designata of its names and predicates) which exist independently of any human concept formation", we must disagree. What Sellars obviously disregards here is the possibility of understanding the Camapian "formalization of semantic theory" not as a straightforward description of data, but rather as the result of a peculiar kind of 'data processing', which is carried out with the aim of reaching a certain kind of helpful 'visualization'. Needless to say that viewed from this angle, Camapian meanings become more tools of semantic theory than its direct subject matter. Perhaps, though, our quarrel with the ontologico-semiotic view is merely terminological? Let us imagine somebody telling us: "There is really no Eiffel tower, it is only iron (and other things) arranged in a certain way - the Eiffel tower is only a posited hypostasis which we use to capture or to model this arrangement." - We would probably object: "But the Eiffel tower simply is just this arrangement- it is no abstract entity existing over and above it." And thus if we say: "In reality there are no objects we could call meanings; what exists are merely certain linguistic practices of the speakers, and the objectually captured semantics represents only a model of certain aspects of these practices", could not somebody object analogously: "But the meanings simply are the aspects of the practices"? I think an answer to this objection lies in stressing two points. First, when somebody says that 'to have such and such meaning' means 'so and so function within the framework of the practices of the users of language', then he does not present the conception which we called ontologico-semiotic. Remember that what was crucial about the approaches to meaning which we dubbed semiotic was that the existence of meanings (whatever they might be) precedes the existence of language and makes it possible in the first place (via a 'semiosis', or in Sellars's words quoted above, via a "primitive relation of designation" quoted above). On the other hand, if meanings are 'functionings', then their existence is not a precondition of language, but is bound to be co-developed together with language. Second, the modeling of meaning which we are talking about always involves the element of idealization, discussed in Section 8.1, which turns semantic models into genuine models, in just the sense ofBohr's model of atom. Let me elucidate this returning once more to the approach of Horwich (1998), which we briefly discussed in Section 7.9. According to Horwich, words literally have meanings (i.e. are related to specific kinds of entities); it is a fact that, e.g., the word "dog" is related to a certain entity which Horwich calls a concept. However, such "meaning-facts" are "constituted" by something "underlying", namely by the way the words in question are used.

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Thus, according to Horwich, meaning talk can be seen as consisting of two levels: on the 'lower' level we have the ways expressions are used by the speakers, on the 'higher' one we have concepts as entities linked to expressions. Now I think such a picture is puzzling unless we explain why there should be such two levels; and this question is answered by our approach. The answer is that the 'higher' level is the product of a process of idealization and abstraction, which helps us orient ourselves within language and which is simply an instance of a mechanism which underlies our orientation in the world in general (as we will discuss it in the next chapter). So for us, in contrast to Horwich, the step from describing the usage of expressions (especially, not to forget, of the norms governing their usage) to talking about their meanings conceived of as objects has more substance than a simple switch of vocabularies: it essentially involves idealization. Language, in our opinion, is not literally a nomenclature, or a code; 171 nevertheless, it remains useful, at times, to see it as a code, just as it is often useful to see atoms as cores orbited by electrons. We must, however, keep, in mind the substantial feature of our approach which makes it basically different from the ontologico-semantic view and the code conception of language: in our perspective, there is no one correct semantics - just as there is no one correct atomic model (or nc one correct plan of an unknown city). There are, to be sure, better and worse models, and there are also models which are plainly unacceptable - nothing, however, excludes the possibility that there may be two or more substantially different models offering parity of usefulness. 8.5 Why Meaning Can be Inferential Role

Let us now consider two objections which have been raised against the inferential construal of meaning. Probably the most serious discrediting of inferential semantics is often ascribed to Prior (1960; 1964), who pointed out that if we allowed for an unrestricted establishing of meanings via inferential rules, we would open the door for a 'pernicious' operator- an operator, that is, which would make any language to which it were added contradictory by its mere presence. For imagine the operator tonk governed by the following inferential rules:

s, => s, tonk s2

S, tonk S2 => S2.

171

Cf. my reply (Peregrin, 1993) to TichY's (1992) defense of the code conception oflanguage.

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It is easy to see that in any language containing the operator any statement is inferable from any other; especially any statement is inferentially equivalent to its own negation. (The obvious reason is that for any two statements S1 and S2 it holds that S1 => (S 1 tonk S2) => S2). Hence any language containing tonk is eo ipso contradictory; and it would seem that we should block the very possibility of introducing such an operator. Prior's example is, of course, relevant and important. However, its upshot seems to be only that not every set of inferential rules can be meaningfully seen as establishing a meaning of a word - not that such establishment would not be possible. (E.g. the fact that the rules (td)- (/\3) uniquely determine the meaning of"/\" seems hard to deny). What is clear is that we cannot allow for unrestricted defining of operators via sets of inferential rules - that we have to somehow distinguish between 'good' sets of inferential rules (governing 'well-behaved' words) and 'bad' ones (making words into pernicious mutants). And ways to do this have been proposed, e.g., by Belnap (1962) or Koslow (1992, §1.4). Another argument against inferential understanding of semantics is due to Jerry Fodor and Ernest LePore (1993). Their paper seems to contain two arguments; and we will try to show that while the first of them is simply wrong, the second one is principally right but does not exclude inferential semantics understood in the way we understand it. The first argument goes as follows (ibid., p. 23): - Meanings are compositional. - But inferential roles are not compositional. - So, meanings can't be inferential roles.

It is obvious that as we have committed ourselves to the first premise, to be

able to reject the conclusion we have to reject the second premise. How do Fodor and LePore argue in favor of it? They say (ibid.): Consider the meaning of the phrase 'brown cow'; it depends on the meanings of 'brown' and 'cow' together with its syntax, just as compositionality requires .... But now, prima facie, the inferential role of 'brown cow' depends not only on the inferential role of 'brown' and the inferential role of 'cow', but also what you happen to believe about brown cows. So unlike meaning, inferential role is, in the general case, not compositional. Suppose, for example, you happen to think that brown cows are dangerous; then it's part of the inferential role of 'brown cow' in your dialect that it does (or can) figure in inferences like 'brown cow - f dangerous'. But, first blush anyhow, this fact about the inferential role of 'brown cow' does not seem to derive from corresponding facts about the inferential roles of its constituents. You can see this by contrasting the present case with, for example, the validity of inferences like 'brown cow - f brown animal' or 'brown cow - f non-green

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cow'. 'Brown cow' entails 'non-green cow' because 'brown' entails

'non-green'. But it does not look like either 'brown' or 'cow' entails 'dangerous', so, to this extent, it does not look like the inference from 'brown cow' to 'dangerous' is compositional.

Now this argument is simply wrong. To see why, we must realize what exactly an inferential role is. Whereas the inferential structure of language as a whole is determined by which of its statements entail which other, it is not the case that the inferential role of a particular statement would be determined by which other statements entail it and which are entailed by it. (Moreover, such a definition of an inferential role would not be applicable to subsentential expressions, the inferential roles of which are what Fodor and LePore talk about, at all). The inferential role of an expression in general consists in what all the statements which contain the expression entail and what entails them. This means that even in case of a statement we must consider not only inferences involving the very statement, but also inferences involving statements containing it. Now if Fodor and LePore claim that '"brown cow' entails 'non-green cow"', the only way to interpret this I can see is that any sentence of the shape X is a brown cow

entails Xis a non-green cow.

So let us say that a predicate P predicatively entails a predicate Q if XisP

always entails Xis Q.

What Fodor and LePore urge is that a composite predicate PQ may predicatively entail R, without R being predicatively entailed by either P or Q. For a predicate P, let us call the predicative inferential role everything that all the statements XisP

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entail and what entails them. Then it is true that the predicative inferential role of a composite predicate PQ need not be derivable from the predicative inferential roles ofP and Q. The mistake, however, is to identify the inferential role of a predicate with its predicative inferential role- in fact, Fodor's and LePore's argument merely provides a reductio ad absurdum of the possibility. If XisR is entailed by Xis PQ without being entailed by either Xis P or Xis Q, then it eo ipso belongs to the inferential role ofP that in combination with Q it predicatively entails R, and it belongs to that of Q that in combination with P it predicatively entails R. The reason is that what the concept of inference is primarily applicable to are statements - there is no other way to introduce the inferential role of a word save as the inferential role of the sentences in which it appears. Now as a matter of contingent fact, it might be the case that sameness of inferential roles of certain kinds of statements in which two given words occur guarantees the sameness of roles of some other kinds of statements in which they occur. Take a first-order language interpreted so that there are no nameless individuals in the universe: then two unary predicates, P and Q, have the same inferential role (i.e. every formula F is equivalent with its variant containing P instead of Q or vice versa) as soon as P(I) is equivalent with Q(I) for every available term T. Now suppose we go second-order, i.e. extend the language with predicates predicable of the original first-order predicates. Then there is no a priori necessity to exclude the possibility that for some second-order predicate S, S(P) is not equivalent with S(Q). However, we may want to exclude this possibility by an axiom schema, as indeed usually is the case:

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Vx(P(x)BQ(x)) ~ (S(P)BS(Q)) 172 Now it is an empirical question whether something like this axiom ts appropriate for natural language (and it seems obvious that it is not). 173 Fodor and LePore then further claim that the situation might in principle be saved by assuming that meaning consists only in analytic inferences where what they call analytic inferences are in fact those inferences which are compositional in their sense. This renders the compositionality of inferential roles trivial, for the inferential role is now 'the role in such inferences which do not violate compositionality'. Thus, "analyticity, meaning (and compositionality)," as Fodor and LePore (ibid., p. 26) put it, "scrape out a living by doing one another's wash". However, Fodor and LePore claim, this move is possible only if we accept, pace Quine, the analytic/synthetic boundary - and this is what they do not consider reasonable. Now what appears to be clear is that meaning cannot be any more determinate than analyticity is. Rejecting the boundary, as Quine repeatedly stresses, involves rejecting the concept of "individual meanings". This is a fact independent of whether we want to subscribe to inferential role semantics or not. However, we insist that although there is really no sharp analytic/synthetic boundary, it is sometimes useful to represent language as if there were one, to idealize it - and consequently that although there is really no sharply delineated meaning, it is sometimes useful to work with models in which there is one. 8.6 The Extensional Model of Meaning

Similarly as the study of the inferential behavior of "and" led us to the introduction of its idealized version "/\" and to the assignment of the usual truth function to "A", the study of the inferential roles of further basic components of our language leads us to the usual logical constants such as the usual disjunction "v", negation "--,", or implication "~". As the inferential behaviour of these operator is a bit more complicated than that 172 If we allow for second-order quantification, we can, of course, tum this schema into an axiom proper: 'v'x(P(x)~Q(x))---+ 'v'j{f{P)~j(Q)). (See Henkin, 1950, p. 53, axiom 10, for a generalization to the (1)-order predicate calculus). 173 Fodor's and LePore's mistake appears to be connected to the 'non-Sellarsian reading of Quine' (see Section 7.9), according to which predicates (or at least some of them) get their meanings from observation sentences, i.e. from the sentences of the shape 'This is P', and the way they function within other sentences must be derived from it.

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of "A", and as its turning into the respective truth-tables is therefore less straingtforward, let us consider the case of at least one of them in some detail. Consider negation. It is characterized, first, by the fact that a negation of a statement is incompatible with the very statement; inferentially 174 statement statement

(Al')

Second, there is a characteristic of negation which cannot be formulated as an inferential rule, namely that -.S1 is the 'maximal' statement satisfying (-.1). This means that S3 ::::::> -.S1 for every S3 such that S 1, S3 ::::::> S2 for every S2• Now it can be shown that if our language is 'well-behaved' enough to make the inferential role of"-," representable as a truth-function at all, the representation is bound to be the well known function taking T to F and vice versa (see Koslow, ibid., §19). On an informal level, it is not difficult to show this. Given not all statements of our language are necessarily true, it follows from (-.1) that -.S1 cannot be true always when S1 is true; hence the truth value of the function for T cannot be T, and hence if there is to be such value, it is bound to be F. Now suppose that the function maps F on F. Then, as -.S1 is to be inferable from any statement incompatible with S~, there cannot exist a statement incompatible with another statement and at the same time true. Given our language contains a contradictory statement C (i.e. that C ::::::> S 1 for every S 1), as C is clearly incompatible with every statement (C, S 1 ::::::> S 2, for every S 1 and S2), every statement is bound to be necessarily false. Hence on certain assumptions, which appear to be a matter of course for any natural language (namely that not all the statements of the language are necessarily true and that at least one of them, altnough not all of them, is necessarily false), the inferential role of negation envisaged above yields us the well known truth function: S T

-.S F

F

T

Going on in this way, we may gain, through the analysis of the characteristic inferential rules something like meaning of the linguistic expressions "and", "not" etc.; more precisely of their idealized 'models' 174

An alternative to the reduction of the concept of incompatibility to the concept of inference is the converse reduction of the concept of inference to the concept of incompatibility (see the proposal of Brandom, 2000, Chapter 6), which would thus become the ultimately primitive concept of inferential semantics.

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"/\", "---.,", .... Now we can think about completing these 'models' of the operators into a very primitive model of the whole language; thus reaching what is usually called the (classical) propositional calculus. The vocabulary of such a model would consist of logical operators ("/\", "---.,", "v", "~") plus a set of symbols representing statements; and its grammar would be determined by the possibility of constructing complex statements with the help of the operators: for every pair of statements S1 and S2 we can form the statements --.S~> S1 1\ S2, S1 v S2, and S1 ~ S2. How would it be with the 'meanings' of the expressions of this primitive model of language - i.e. with the set-theoretical objects which would be assigned to the expressions as their denotations? (Let us, from now on, use the term denotation as the model-internal counterpart of the intuitive concept of meaning: hence the denotation of an expression of a formal language will be taken as an explication of the meaning of the corresponding natural language expression). The denotations of"/\", "v", "---.,", and "~" will clearly be the corresponding truth functions; what, however, should be seen as denoted by statements? We can see that the role of statements within the inferential rules of the propositional calculus is a trivial one - they merely help specify the roles of the operators and from the viewpoint of their role they are indistinguishable. All the inferential rules concern all statements without exception (the symbols S~> S2, ••• can be substituted for by any statements - in contrast to inferential rules of the kind of "X is a rabbit"=> "X is not an elephant", which do not hold for any statements, but only for statements with the specified predicates), so that the corresponding inferential roles of all of them are in fact indistinguishable, identical. Should we thus assign one and the same denotation to all statements? In preceding chapters meaning has been characterized not merely in terms of its groundedness in inferences: we have also pointed out that meaning is characterized by the principle of compositionality, stating that the meaning of a complex expression is always determined by the meanings of its parts. How does this work for the expressions we are considering now, i.e. expressions of the kind of S1 1\ S2? The principle of compositionality says that the meaning of a complex expression must be 'computable' from the meanings of the parts- i.e. that, e.g. the denotation of sl 1\ S2, I sl 1\ S211, should be 'computable' from the denotations of the parts of the statement, i.e. from I S1 II, I 1\ I and I S2ll- If we identify the denotation of 1\ with the usual truth function, then the principle of compositionality would surely hold even if all statements had one and the same denotation (if we denoted this common denotation of all statements by the symbol ®, the 'computation' of the denotation of a complex

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statement from the denotations of its parts would amount to the trivial algorithm yielding ® independently of the input values). However, there readily occurs also the usual, much more elegant model, which would result from the identification of the denotation of a statement with its truth value: the denotation of St 1\ S2 (its truth value) would then be computed as the result of the application of the denotation 1\ to the denotations (truth values) of Stand Sz, i.e. as II 1\ II (II Stll, II Szll ). The conclusion that we should not identify the denotations of true and false statements is also urged by a principle which appears to characterize meaning similarly generally as the principle of compositionality and which I have called, elsewhere, the principle ofverifoundation:t?s two expressions which have different truth values cannot have the same meaning. Statements with different truth values thus should not be, as it seems, assigned identical denotations if we want to respect at least the most elementary semantic intuitions - for it would be obviously absurd to say of two statements, one of which is true and the other false, that they mean the same thing. Let us thus identify the meaning of statement with its truth value. (Even in this way we will obviously not reach a model which could be taken seriously from the viewpoint of explication of meanings of statements, for we would hardly want to claim that all true statements have the same meaning; however, this model at least will not be in direct contradiction with the most general semantic principles which we have just formulated, and it could be helpful from the viewpoint of the clarification of the functioning of the operators, the inferential roles of which we have just discussed). The identification of the denotation of statement with its truth value leads to a model which is very 'handy' in that the denotation of each complex statement is computable simply by applying the denotation of its operator to the denotations of its component statements: 11-.sll = 11-.IICIISII) liSt 1\ Szll = 11/\II(IISdi,IISzll) liSt vSzll = llviiCIIStii,IISzll) liSt~ Szll = llviiCIIStii,IISzll) Within the framework of this model we can thus compute the denotation of every complex statement from the denotations of its parts - and, moreover, we can do it quite simply, by applying the denotation of one of the parts to

175

See Peregrin ( 1994 ).

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those of the other parts. 176 The semantics reached in this way is tantamount to the one usually associated with the classical propositional calculus. This language can be further extended in the direction of the predicate calculus: we replace the primitive propositional symbols by symbols for names plus those for predicates and add a grammatical rule forming a statement out of a predicate and an appropriate number of names. What should we now proclaim as the denotations of these new kinds of words? Since they inherit, from the propositional symbols which they replace, the indifference to the inferential rules introduced so far, we need only respect the principle of compositionality - to secure, that is, that the denotation of the combination of a predicate with the appropriate number of names (which is to be a truth value) is the result of a combination of the denotation of the predicate with those of the names. This can, of course, be done in many ways, but the most natural appears to be to follow Frege (see Section 2.4) in taking the denotation of the predicate as a function applicable to the denotations of names and having truth values as its values. 177 Hence it will hold that that Hence it will hold it will hold that Hence and we retain the 'applicativity' of the language. In this way we build a model of semantics which can be called extensional (in Camap 's, 194 7, sense of "extension"). Although this model may be further developed in various directions, it is still clearly inadequate if taken as a model of meaning of natural language. The only types of expressions whose meanings it actually captures are the logical operators (which are, not to forget, merely simplified versions of the corresponding expressions of natural language). Expressions of the other types act, within the model, merely as a necessary background for envisaging the roles of the operators; their own meanings are surely not explicated adequately. 178 If we extend this language in the well-known way by means of the quantifiers ::3 and V, we reach the (classical) (first-order) predicate calculus, i.e. what we called elementary logic earlier in this book (see Section 5.8). However, quantifiers are expressions which have no direct 176

Therefore, such semantic interpretation could be called applicative; see Peregrin (2000d). 177 If we had only unary predicates, we could also do it the other way around, namely to make the denotations of names into functions applicable to the denotations of predicates; something like this is done, in effect, within Montague Grammar. 178 It can be - and in fact was developed with this intention- taken as a model of reference.

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counterparts within natural language and their introduction, moreover, necessitates the introduction of a wholly new kind of expressions, variables, which are also alien to natural language. This move makes the structure of the resulting formal language significantly different from that of the natural one, and therefore the resulting formal language cannot be considered as such a straightforward model of natural language as the propositional calculus. 179 Of course, the founders of modem formal logic who developed the predicate calculus, were not aiming at such a direct model of natural language we have in mind. Their aim was to set up a minimal formal language capable - in some, possibly rather complicated ways - of rigorously reconstructing the core of natural language underlying all our argumentation (and seen in action most clearly within mathematical arguments). Frege, Russell and others subsequently developed the art of what came to be called the logical analysis of language - namely seeking such logical formulas which can be understood as representations of various kinds of natural language statements. And that this need not be a simple matter was soon documented by Russell's analysis of 'definite descriptions' (expressions of the kind of "the king of France") - according to Russell (1905), the 'true' logical form of the sentence "The king of France is bald" is worlds apart from its surface, and it must be spelled out by the rather complicated formula 3x (KF(x)

1\

Vy

(KF(y)~(x=y)) 1\

B(x)).

This means that what this sentence, in Russell's view, 'really' says is that there is an entity x which is a king of France and which has the property that it is identical with any other entity which is a king of France (i.e. that it is the only king of France), and the entity xis, moreover, bald. 180

179

For details see Peregrin (2000d). If our aim is the modeling of meanings of expressions of natural language, we can circumvent this historical path of modem logic and form slightly different formal languages, with their syntax more straightforwardly parallel to the syntax of natural language. Instead of the usual quantifiers :3 and V we can introduce quantifiers more straightforwardly reflecting the way quantification looks in natural language: we can introduce logical constants which would behave like the expressions 'every', 'some' etc. Such quantifiers have been studied by the so called theory of generalized quantifiers (see Barwise and Cooper, 1981 ); within it they are, however, usually considered not as an alternative, but rather as a 'superstructure', to the machinery of the standard, Fregean quantification. 180

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8. 7 Meanings as Products of the Truth/Falsity Opposition

Note that the model of semantics the development of which we have just sketched resulted from the interaction of general intuitions about the nature of meaning (the principle of compositionality, the principle of verifoundation) with the conviction that meaning (or its theoretically tractable part) is a matter of inferential roles. The principle of compositionality reminds us that a statement cannot be seen merely as a self-standing unit, but also as a building block entering into other, more complex statements (that it has, in Dummett's terms, not only a "freestanding sense", but also an "ingredient sense"). 181 Besides this, the principle is what allows us to individuate meanings of subsentential expressions at all - it indicates that the meaning of such an expression should be seen as the 'contribution' which the expression brings to the functioning of the statements in which it occurs. Note further that the meanings of the expressions of our model can be seen as representing the intersection of the Saussurean 'syntagmatic' and 'paradigmatic' relations (see Section 3.4). Take the denotation of "/\": syntagmatically it is constituted in opposition to the denotations of those expressions together with which it is capable of constituting grammatical wholes, in our case with statements - not only that it differs from the denotations of statements with respect to its category, but its category is also such that denotations of statements 'fit' into it (i.e. it is applicable - as a function - to them). The 'syntagmatic' character of an expression is thus projected into this 'syntagmatic' aspect of its denotation. The denotation of "/\" is, moreover, constituted by the fact that "/\" differs inferentially from other expressions of the category of 'sentential connectives' (i.e. from those expressions which can be substituted for it salva grammaticitate - i.e. "v" or "~"). The denotation of "/\" must therefore be in 'paradigmatic' opposition to the denotations of these expressions - this opposition is not, however, manifested by an intercategorial difference, but rather by a difference which is intracategorial: denotations of sentential connectives are of the same category (all of them are functions assigning truth values to pairs of truth values), but they are different objects. It is also possible to take a more explicitly Saussurean perspective on the whole situation, as follows. We have a certain basic semantically relevant opposition - the opposition between truth and falsity. It is manifested by what we have called the principle of verifoundation: statements which differ in truth value necessarily differ semantically (i.e. by their meanings). This opposition then interferes with the part-whole 181

See Section 4.6, part 3.

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system of statements: the conditions for statements' having the same semantic value is not only that they are not directly in this opposition, that they are equivalent in respect to the opposition (i.e. that they have the same truth value), but rather also that they are intersubstitutive in respect to the opposition. Seen from this angle, two statements have the same semantic value - i.e. the same meaning - if and only if they are intersubstitutive in respect to the opposition between truth and falsity, i.e. if and only if one of them can be replaced, within any statement, by the other without thereby causing the statement to change its truth value. In short, they have the same value iff they are intersubstitutive salva veritate. Within our extensional model, the assignment of truth values is compositional, which means that two statements are intersubstitutive salva veritate just in case they have the same truth value. Using the terminology of Chapter 4 we can say that the compositional projection of the opposition truth/falsity in this model simply coincides with the canonical projection, i.e. with the assignment of truth values. This is what makes it possible to identify the denotation of a statement with its truth value - and it is in fact also what the extensionality of the model amounts to. However, the addition of further, more complicated inferential rules can bring about a violation of extensionality, i.e. of the compositionality of the assignment of truth values - it can lead to a model in which not every pair of statements sharing a truth value is intersubstitutive salva veritate. This is what we will see in the following section. 8.8 The Intensional Model of Meaning So let us move to further, more complicated inferential patterns which are characteristic of natural language. Let us take the adverb "necessarily", which we will, as it is usual in logical literature, schematize as "0". It seems to be clear that if something is necessarily the case, then it is the case, so we can write DS=>S

(0 1)

However, the inverse inference does not hold - surely it is not the case that if something is the case, then it is bound to be necessarily the case: S'X> OS

(02)

What nevertheless seems to be in place is to infer the necessity from inferability from the empty antecedent - if something follows from anything,

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then it is necessary; and, moreover, its necessity is not a contingent matter, hence it also follows from anything. This means that if ::::>S, then => 0 S

(03)

Let us now try to add 0 to our extensional model and to find the truth function which should be assigned to it. It obviously follows from (0 1) that if Sis false, OS is bound to be false too: S

OS

F

? F

T

But what should replace the question mark? If it were T, OS could be inferred from S- which contradicts (02); hence it cannot beT. Could it be F? Could II OSII be F, whenever IISII is T? This, in turn, clearly contradicts (03) - for (03) states that there are statements (namely those inferable from anything), which have the value T and yield statements with the value T if prefixed by 0; i.e. for such an S, IISII is T and II OSII is T, too. The trouble appears to be that the truth value of OS is not uniquely determined by that of S- some true statements are true necessarily, others not. This means that were we to continue identifying meanings of statements with their truth values, our theory would come to contradict the principle of compositionality. Using the terminology of Chapter 4, we can say that as soon as we engage the operator governed by the inferential patterns (0 1)-(03), 182 it no longer holds that two sentences which are equivalent in respect to truth (i.e. share the same truth value) are also intersubstitutive in this respect (i.e. are intersubstitutive salva veritate). In this situation the system of values into which the opposition between truth and falsity gets projected ceases to be trivial: the compositional projection of the opposition ceases to be identical with the canonical projection. To preserve the intersubstitutivity of synonyms salva veritate, synonymy must be radically reduced (it can no longer hold that every two statements sharing the same truth value are synonymous), i.e. the denotations of statements must be radically multiplied. This also helps make our model more realistic. It might seem that the situation would be solved by letting statements denote, instead of T and F, the four values NT ('necessary truth'), CT 182

Neither (02), nor (03) are inference rules in the sense of our definition. (02) amounts to a denial of an inference rule, whereas (03) is a 'metarule'.

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('contingent truth'), CF ('contingent falsity') and NF ('necessary falsity'). The point is that then we could define I 0 I as the function which assigns NT to NT and NF to the other three values. However, we must realize that then we also would have to redefine the denotations of all the 'extensional' logical operators accordingly; and this brings about further problems. For which function should we assign, e.g., to "A"? The results which this function should yield for some pairs of the new values seem to be clear (thus it should obviously assign NT to two NT's, or CT to NT plus CT); what, however, should it assign, e.g., to CT and CF? The conjunction of a contingent truth and a contingent falsity is surely a falsity, but it may be either a contingent or a necessary falsity. (The former case is illustrated by "Russell was a logician and Russell was a cowboy", the latter one by "Russell was a logician and Russell was not a logician"). This indicates that we cannot make do with four values: at least contingent truths and contingent falsities would have to be further differentiated according to how they behave from the viewpoint of conjunction. It can be shown that if we make such further differentiation, we get an infinite system of denotations, constituting a Boolean algebra. (The set of the two truth values is also a Boolean algebra, but a trivial one). Thanks to Stone's representation theorem this system can be identified with a system of subsets of a set, 183 and the elements of the underlying set can be seen, as it turns out, as 'possible worlds' . 184 The ensuing semantics can thus be seen as making a statement denote the set of all those possible worlds in which it is true. "0" is then taken to denote a function assigning classes of possible worlds to classes of possible worlds -namely that function which maps the set of all possible worlds on itself and any other set on the empty set. Writing W for the set of all possible worlds, we can write 185

I OSII = w iff IISII = w = 0 otherwise

183

See, e.g., Landman (1991, p. 280). This, 'intensional' explication of meaning stems from the logico-philosophical considerations of Carnap ( 1947) and from the logical results of Kanger (1957) and Kripke (1963) concerning modal logics. 184

185

This is, of course, an oversimplification, as are many of the things said in this chapter. If we say that something is necessarily the case, it need not mean that it is the case in every possible world - it may mean only that it is the case in all such possible worlds which are somehow thinkable as alternatives or possible future stages of the present world. To capture this would require the introduction of an 'accessibility relation' between possible worlds (see, e.g., Hughes and Cresswell, 1968).

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Now it is also not difficult to redefine the meanings of the extensional logical operators: conjunction will come to denote the intersection of sets of possible worlds, disjunction the union etc. It is important to realize that "D" is by far not the only operator which we need in connection with natural language and which is not graspable in extensional terms - the inferential patterns of the kind of those governing "D" do not govern only adverbs like "necessary" (which themselves, from the viewpoint of natural language, could possibly be deemed as somewhat peripheral). A more substantial case is constituted by various kinds of counterfactual conditionals. It is clear that the truth value of the conditional If it were the case that S 1, then it would be the case that S2 is not uniquely determined by the truth values of S1 and S2 • With a certain amount of oversimplification we can say that such a sentence is true (in eve~possible world) if S2 is true in all such possible worlds in which St is true 8 - if we schematize the counterfactual conditional by means of the symbol "::t", we can write can write

= W iff {w I wE I Szll or w ~ II Szll }=W (i.e. iff every world belongmg to II Stll belongs to II Szll) = 0 otherwise

Hence to determine the truth value of such a sentence we again need to know more than whether St and Sz are true. Tenses constitute another important case. It seems natural to understand a sentence like "Mickey will eat cheese" as the result of applying a 'future-tense operator' (which, like negation, is really a matter of a grammatical construction) to the sentence "Mickey eats cheese". And again, such an operator will scarcely be accommodable within the framework of extensional semantics- if we denote it as F, then the truth value ofFSwill clearly not be computable out of that of S. This means that if we took II F S I and II S I to be truth values, there would exist no truth function which could be seen as denoted by F. In contrast to the previous example, the analysis of tenses calls for relativizing truth not to possible worlds, but rather to time moments (which differs from the set of possible worlds in that it has a certain structure, namely it is linearly ordered). If we identify the meaning of a statement with a set of time moments (namely of those moments in which it is true), the denotation for F is forthcoming: it will be that function which maps a 186

The situation is again really more complicated. The counterfactual conditional seems to claim, more precisely, something like: S2 holds in all those possible worlds in which S 1 holds and which otherwise do not differ from the current one in any substantial respect.

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set of time points on the set of all such time points which are followed by at least one point from the original set. Schematically:

IIFSII =

{t l:lt' (t'>t !\ t'E IISII)}

With a certain oversimplification we can say that while an extensional model is adequate for a language which states only what actually is the case ('actuality'), natural language is characterized by various kinds of statements of what only could be the case (i.e. 'potentiality'). In a general intensional semantics we should then relativize both to possible worlds, and to time moments. Models of language of this kind were proposed in the early seventies by Montague (1970), Tichy ( 1971 ), Cresswell (1973) and others. 8.9 Intensionality as the 'Catalyst of Meaning' The intensional model of meaning makes it possible to clarify one important point concerning meaning. We have stated that meaning is the result of the projection of the truth/falsity opposition - that meaning is in this sense a matter of truth. On the other hand it seems to be clear that meaning must be something which can be known independently of knowing truth: we can surely know the meaning of "Aragorn is a warrior" without knowing whether the statement is true. In general we could surely know the meaning of every statement of a language (i.e. understand the language) without knowing the truth value of every statement. It is similar with reference: we can understand the meaning of "the only human who survived the pilgrimage of the Fellowship of the Ring" without knowing to whom it refers. Note that in the case of an extensional language this is, by definition, impossible: in this case the meaning of a statement is the same as its truth value, and hence to know meaning eo ipso means to know truth value. The situation is, however, different in the case of a language which is intensional: here to know meaning does not mean to know truth value, but rather to know in which worlds the statement is true, i.e. to know truth conditions. Thus if we insist that the meaning is the projection of the truth/falsity opposition and simultaneously that at least for some statements we can know their meaning without knowing their truth value, we must conclude that extensional languages do not allow for the genuine concept of meaning. (Insufficient reflection on this fact is the root cause, I am convinced, of much confusion concerning the relationship of natural language and logic). Intensionality appears therefore, from this viewpoint,

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to be a necessary condition for something being a language in the genuine sense of the word. It is precisely the inferential structure which represents those aspects of the truth/falsity opposition which are a matter of the knowledge of language (as opposed to the knowledge of extralinguistic facts). If we understand the sentence "Mickey is a mammal", it does not follow that we must know whether the sentence is true, it nevertheless does follow that we must know, under which conditions it is true (i.e. that it is true, e.g., in the situation when Mickey is a mouse), and especially which sentences entail it (i.e. that it is entailed, e.g., by the sentence "Mickey is a mouse"). However, as we now see, it is only an intensional language which enables the 'truth structure' to fall into a purely semantic part (the knowledge of which is the knowledge of language) and an 'ontological' part (the knowledge of which is the knowledge of the state of the world). Intensionality is thus that feature of language which makes the projection of the truth/falsity opposition into something which can be known without knowing extralinguistic facts. It is important to realize, however, that the boundary between such 'semantic part of the truth structure of language' and 'ontological part' of this structure is again a variant of the boundary between the analytic and the synthetic. To say that the fact that mice are mammals is a matter of the meaning of the word "mouse", and not of the state of the world, is to say that sentences like "If Mickey is a mouse, then he is a mammal", in the extensional sense of"if ... then", are analytic (and this is, in tum to say that sentences like "If Mickey were a mouse, then he would be a mammal", in the counterfactual sense of "if ... then", are true) - and there is hardly a criterion which would decide unambiguously whether this is so or not. Is he who does not know that mice are mammals ignorant of the meaning of "mouse" - or is he rather ignorant of something factual? Only very few words of natural language possess an explicit definition uniquely determining what belongs to their meanings and what does not. However, although the boundary in question is in this sense problematic, it does not seem to be a viable option to deny that there is a difference, albeit a fuzzy or context-dependent one, between the knowledge of language and knowledge offacts expressed by the language. 187 In addition, as we stated 187

One of the possible ways to make the concept of analyticity tenable even for natural language is indicated by Lance and O'Leary-Hawthorne (1997): they suggest explicating the concept analytic sentence as a sentence such that "failure to assent to it is (or would be) taken as excellent evidence that the person has failed to understand one word or other (and thus, relatedly, as good grounds for moving from the realm of substantive argument to that of stipulation, paraphrase, or pedagogy)" (p. 96). It is nevertheless obvious that if we

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above, a sharp boundary between the analytic and the synthetic may have its place in the context of formal models of language of the kind we have been discussing here. And, moreover, to see natural language via the prism of formal languages has become so commonplace (though often not reflected upon) that it largely influences and shapes the very way we . natura11anguage. 18'B' perceive 8.10

Semantic Models Reflecting Other Types of Inferences

We have seen that in the case of an extensional language, two statements are intersubstitutive salva veritate if and only if their truth value is identical - thus within the extensional model two statements share the same denotation if and only if they share the same truth value. (Hence the direct identification of the denotation with the truth value). In the case of an intensional logic two statements are intersubstitutive and thus obtain the same denotation if and only if they are true with respect to the same possible worlds. If we use the symbol B, as is usual in logic, to denote the sameness of truth values (so that SBS can be taken as shorthand for (SAS)v(-SA-S)), then we can say that within extensional semantics SandS' share the same denotation if and only if SBS, whereas within intensional semantics they share the same denotation iff D(SBS). This means that within intensional semantics the necessary and sufficient condition for S and S being intersubstitutive salva veritate is D(SBS). However, it turns out that in case of natural language, this is still not quite adequate. Consider the verb "to believe". Imagine that somebody X believes that S (let us write B(X,S) ); e.g. that X believes that one plus one equals two. Let us further imagine that S is true in the very same possible worlds as S, i.e. that D(SBS). Then it necessarily holds, within the intensional semantic model, that B(X,S), for B(X,S) is the result of substituting S for Sin B(X,S), where S and S are, thanks to the fact that 0 (SBS), understand the concept of analyticity in this way, the answer to the question "Is this or that sentence analytic?" will often be indeterminate, and may even vary depending on circumstances. 188 Quine's scruples then can be seen as a warning against the absolutization of this view. As Putnam puts it (1962, p. 135), "we have a model of natural language according to which a natural language has 'rules', and a model with some explanatory and predictive value, but what we badly need to know are the respects in which the model is exact, and the respects in which the model is misleading.... The dispositions of speakers of a natural language are not rules of a formal language, the latter are only used to represent them in a certain technique of representation; and the difficulty lies in being sure that other elements of the model, e.g. the sharp analytic-synthetic distinction, correspond to anything at all in reality." See Peregrin ( 1999a) for a further discussion.

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intersubstitutive without changing the denotation of the corresponding whole. However, let us imagine that Sis "1 plus 1 is 2" and S' is "the square root of 144 is 12". It seems obvious that the two statements hold in the same possible worlds, i.e. that D(S~S'): both are non-empirical, mathematical truths which are independent of the state of the world and thus hold in any world. However, it seems to make little sense to insist that if somebody believes that 1 plus 1 is 2, she is bound to believe that the square root of 144 is 12. This entails that the inferential behavior of the predicate B (and of the verb "to believe" which it captures) is such that it cannot be fully accommodated within the intensional model. It appears that the sufficient condition for intersubstitutivity within contexts of the 'propositional attitudes', such as that created by "to believe", is not only that the two statements to be interchanged are true in the very same worlds, but rather that, in addition, the subject to whom the attitude is ascribed could not fail to see that they are. This seems to imply that in general we can consider two statements as intersubstitutive only if they are not only equivalent from the viewpoint of intensional semantics (i.e. true in the same possible worlds), but if this equivalence is somehow 'unmistakable'. This appears to be the case when the two statements are syntactically so much alike that anybody who ·is sane and knows the meanings of all the words occurring in them cannot fail to notice it (especially when one of them is obtained from the other by nothing more than a replacement of synonyms by synonyms, like "1 + 1=2" from "one plus one equals two"). This indicates that if we take propositional attitudes seriously, we must conclude that expressions which differ too much syntactically cannot have the very same inferential role; and this leads to the conclusion that meaning - in contrast to the way we have viewed it up to now - somehow reflects syntactic structure. From this viewpoint, it may be feasible to capture the meaning of an expression as an object with a structure which is- to some extent - parallel to the syntactic structure of the corresponding expression. Since the seventies, when many people working on semantics of natural language began to focus on the problem of propositional attitudes, several theories of this kind have been proposed. Some of them seem as relatively ad hoc solutions (as, e.g., the theory of Lewis, 1972, further developed by Cresswell, 1985, and others), whereas others are integral parts of sophisticated theories of language or thought which, however, as they stand, may not be compatible with our structuralistic approach. This is the case of situation semantics of Barwise and Perry (1983), which appears to be what we would class (in terms of Chapter 2) as a psychologico-semiotic theory of meaning, or of the transparent intensional logic of Tichy (1988),

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where meanings are identified with "constructions" 189 and which we would class as an ontologico-semiotic theory. However, semantics such as Tichy's can be considered, from our viewpoint, as a reasonable response to the problem of 'propositional attitudes'- provided we understand it as a model of semantics of natural language (in the sense of Section 8.4), not as its direct depiction. Other interesting inferential patterns, which can lead us to a wholly different kind of sophistication of the semantic model of language, are encountered when one starts to analyze the inferential behavior of various anaphoric elements of language. The prototypical examples of such expressions, pronouns, obviously behave like certain 'context-dependent names': thus the sentence "Luthien loves him", behaves like an (inferential) equivalent of "Luthien loves Beren" when it follows "Beren is brave", whereas it behaves as an equivalent of "Luthien loves Glum" when it follows "Glum is ugly". Inferential roles of expressions of this kind thus differ substantially from those of the expressions we have considered until now, and they cannot be adequately captured by any of the models so far mentioned. 190 However, it has turned out that a promising route to an adequate acount of these phenomena leads via identifying meanings of statements with functions mapping a certain set on itself (a set of what we can see as something like 'contexts' or 'information states'). Thus a statement is now understood as something which leads from one context to another context, from one information state to another, usually 'informationally richer' state. Just as in the case of intensional semantics the meaning of a statement captured its truth conditions, now the meaning captures its 'context-change potential', i.e. it expresses which kind of change of information state the assertion of the statement brings about. Various notable 'dynamic' models of semantics and connected dynamic logics have been developed in the nineties - see e.g. Kamp and Reyle (1993) or Muskens et al (1997). And again, such models can be made compatible with the inferentialist approach to semantics (see Peregrin, to appear). 189 TichY's constructions can be envisaged in the following way. The meaning of a compound expression is, according to the principle of compositionality, the result of a combination of meanings of its parts (in the simplest case it is the result of the application of the meaning of one part to those of the others). Thus, within the intensional model the intension of a compound expression is the result of the combination of the intensions of its parts. And what Tichy now claims is that the genuine meaning of the compound is to be identified not with the intension resulting from the combination, but rather the combination itself, the construction, as it were, of the intension of the whole from the intensions of the parts. This, however, requires that the concept of construction is given a rigorous sense and this is what Tichy does. 190 See Peregrin (2000a).

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8.11 Syntax and Semantics Semantic models of the kind we have sketched briefly above constitute the subject of the discipline of model theory 191 (although the usual model theory restricts itself to what we called the extensional model and is not generally understood as a theory of semantics, but rather as a theory of 192 However, as we have expressibility of classes of model structures). stated, the semantic models are usually understood differently from the way suggested here: not as 'materializations' of inferential properties of expressions, but rather as representations of relationships which exist between expressions and that which they denote or express within the world. They are thus likely to be taken as accentuating the ontologico-semiotic (or sometimes even psychologico-semiotic) notion of language. Of course, it is understandable that if we are convinced that expressions are, by nature, labels to be stuck to things, we will require that a logical model of language involves (possibly in addition to capturing the inferential behavior of expressions) capturing that to which the expressions are stuck, i.e. meanings. After all- the story usually goes - until we specify which kind of object is stood for by an expression, the expression is no more than an 'empty shell', and this cannot be helped by specifying its behavior (even if the behavior includes its inferential role). It is only the assignment of meaning which makes something into an expression worth its name. Until we assign meanings, it is claimed, we are within the realm of syntax, but a real language must necessarily have a semantics. As Searle (1984, p. 34) once put it- in a slightly different context- "syntax alone is not sufficient for semantics". 193 It is important to realize that structuralism, as it is understood here, consists in just the opposite view - namely that syntax, in the form of inferential articulation, not only in some cases can alone be sufficient for semantics (the meaning of some expressions is directly a matter of their inferential roles), but in all cases it is essential for semantics (for something can have meaning only if it is inferentially articulated, i.e. if it is in inferential relations to other expressions). 191

Note the ambiguity of the word "model": whereas we use this word in its ordinary sense and see formal languages with their semantics as models of language in the sense in which a wooden imitation of a steamboat is a model of a real steamboat, the use of "model" in "model theory" is more idiomatic and has little to do with this sense. 192 Cf. Etchemendy (1990). 193 Searle uses this slogan in support of his view that a computer cannot think. He claims that a computer is merely able to manipulate noninterpreted symbols, i.e. that it has "by definition, syntax alone" (ibid.).

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To avoid misunderstanding, we must distinguish two senses of "syntax" which are often confused (and it is this confusion which causes misunderstandings of the kind which can result from the ambiguity of the term "inference" discussed in Section 8.2). In one sense the syntactic properties of a word are those which concern only its 'design', and are thus a matter of only the very expression, independently of any other linguistic or extralinguistic entities (such properties may be, e.g., to start with the character "a", to contain more vowels than consonants, or perhaps to have a subject-predicate structure). In the other, wider sense syntactic properties of an expressions are all those which do not concern the relationship of the expression to extralinguistic entities (but possibly do concern relationships to other expressions). What we can infer from a given statement is then a 194 matter of syntax in the second sense (although surely not in the first one). If we take the inferential articulation, i.e. the rules of inferring statements from other statements, as a matter of syntax, then syntax is essential for semantics. An expression becomes meaningful not by being used to christen some antecedently given object, but in that it starts to function within a certain kind of human interaction (an interaction for which some specific kind of objects may be crucial, but which nevertheless also necessitates the inferential articulation). An expression is thus meaningful, partly or wholly, thanks to assuming a place within the logical space of inferences. The word "and" becomes meaningful not due to the fact that we christen by it a truth function, but due to the fact that it starts to function within certain inferences; and the word "rabbit" does not become meaningful merely due to the fact that we somehow associate it with rabbits (and surely not due to the fact that we would literally christen by it an abstract rabbithood or an abstract concept of a rabbit), but necessarily also due to the fact that it becomes usable in certain inferences. Thus we must reject the idea that to be able to do semantics we must first identify and inventorize basic components and parts of the world (i.e. do metaphysics), and only then can we determine on which of the so identified parts of the world our expressions rest. However, we do not reject the idea that what we express by our sentences are, in a sense, components of our world. We can surely see our world as consisting of facts (following Wittgenstein, 1922, § 1). What we reject is that our world would be structured into facts independently of our language. The point is that if facts are "sentence-shaped items" (see Section 5.10), then we perceive our world as falling apart into them only when we see it through the prism of language. "Language," as Davidson puts it (1997, p. 22), "is 194 The wider notion of syntax is, I think, especially due to Camap (cf. Peregrin, 1999a). Camap also sometimes used the term logical syntax to characterize what belongs to syntax in the wider sense, but not in the narrower one.

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the organ of propositional perception." This means that (formal) semantics is not merely an appendage of (formal) metaphysics, but rather that we cannot do metaphysics, in this sense of the word, over and above doing semantics. 195 As Davidson (1984, p. 201) claims, it is plausible to assume that "if the truth conditions of sentences are placed in the context of a comprehensive theory, the linguistic structure that emerges will reflect large features of reality."

195

See Peregrin (1995a, Chapter 10).

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Chapter Nine

The 'Natural' and the 'Formal' 9.1 What does Having a Structure Mean? Up to now we have discussed the concept of structure and the nature of the structure of language that is constitutive of its semantics. However, what does it mean for an entity to have a structure in the first place? In particular, what does it mean for language to have the inferential structure which we claim condenses into the meanings of its expressions? In particular, is here 'having a structure' more like 'containing copper' (a matter of possessing something 'by itself), or rather more like 'being in perspective' (i.e. that of being seen, by us, in a certain way)? This question can be seen as part and parcel of a general question which has played a central role within modem philosophy. As Kant stressed, whereas philosophers before him had taken for granted that things are such as they appear to us by themselves, we cannot understand the nature of human knowledge unless we realize that how things appear to us may be more a matter of us than of them. However, by now it seems evident that the real challenge is not to solve the 'by themselves'/'for us' dilemma, but to make a clear sense of it. Take color. Is it something which a thing has by itself, or does it rather amount to a way how we see the thing? It seems that we can give either answer, depending on how we explain the sense of "by itself'. The point is that there surely is a sense in which things have colors by themselves - we can say that to have such and such color is to (be disposed to) reflect light in such and such way, and this is clearly something which things do by themselves. However, there is also another sense in which we can understand colors as resulting from the interaction of the reflected light with the receptors of our eyes (or maybe from the activation of the relevant neurons of our brain). 196 For many, Kant's very idea of a 'thing in itself, or of a way a thing might look 'in itself, i.e. to an 'innocent eye', is simply misguided. Thus Putnam (1995, p. 29) writes:

196

The situation is, of course, resolved by postulating a 'canonical viewer', like God, whose way to see things amounts, by definition, to how they really, 'in themselves', are. Then the question Do things have colors by themselves? would reduce to Does God see them as colored? However, this is clearly not a discovery, but rather a regimentation.

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[Kant's] confusion was to suppose that a description that is shaped by our conceptual choices is somehow, for that very reason, not a description of its object "as it really is". As soon as we make that mistake, we open the door to the question. "Well, if our descriptions are only our descriptions, descriptions shaped by our interests and nature, then what is the description of the things as they are in themselves?" But this "in themselves" is quite empty - to ask how things are "in themselves" is, in effect, to ask how the world is to be described in the world's own language, and there is no such thing as the world's own language, there are only the languages that we language users invent for our various purposes.

I think that independently of whether we agree with Putnam on the point of despising Kant or not, if the last century's analytic philosophy with its linguistic tum has taught us something important, then it is the distrust of unclear questions and of attempts at giving accounts of matters about which nothing clear can be said. "A nothing," says Wittgenstein (1953, §304), "would serve just as well as a something about which nothing could be said". Therefore, we will leave the general 'by themselves' /'for us' question to those who feel it does make a clear sense, and we will concentrate on a related, but a much more down-to-earth question, namely Is structure of a thing unique, or can the same thing be feasibly ascribed various nontrivially different structures in different circumstances or by different ascribers? (The relationship to the general question we have discarded is clearly that those structures for which the latter is the case, i.e. whose being possessed by things somehow depends on a visual angle, would seem to be more plausibly seen as not directly 'within' their respective things). And we will indicate that in cases of the structures which are relevant for us here, especially the structure of language, it is indeed more reasonable to see the structure as dependent upon 'visual angle' and on the context in which we ascribe it. 9.2 Radical Translation Revisited

Let us now once more slip into the skin of a radical translator/interpreter. Imagine you observe, accompanied by a group of, say, ten natives, a rabbit and you check for their willingness to assent to "gavagai?" in this situation. Suppose that all the natives react by what you have identified as the gesture of assent. And further suppose that you have established that this group is in this respect a representative one, i.e. that it is reasonable to assume that any other group would behave similarly. The conclusion you draw in this case will undoubtedly be that "gavagai" means rabbit. This is a straightforward expression of a certain regularity within what you observe: namely the regular willingness of the natives to utter "gavagai" (or to assent to "gavagai?") when there is a rabbit around.

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Hence what you do can be seen as the Sellarsian functional classification, as the classification of "gavagai" as •rabbit•, i.e. as an expression having the role akin to our "rabbit". It is an instance of recording a 'unity within multiplicity' (unity of function- or meaning- within the multiplicity of the natives' reactions) which generally underlies our theoretical coping with the world. You have found a regularity, and you have articulated it. (Disregard, for the time being, the perplexities of projecting such regularities into a meaning assignment, discussed in the previous chapter). Now imagine a slightly different (and perhaps more realistic) situation. Imagine that only nine out of the ten natives assent to "gavagai", whereas the tenth one dissents. (And let us again assume that we have found out that this group may be taken as representative, in this respect, of the whole native community). Even in this case it will probably be reasonable to conclude that "gavagai" means rabbit - and that the dissenting native is mistaken (perhaps mistaking the rabbit for a cat?). However, now your conclusion can no longer be seen as a straightforward report of a regularity. Your "gavagai" means rabbit

(1)

can no longer be taken as a mere shorthand for all natives are willing to assent to "gavagai?" in the presence of a rabbit, (2) for (2), we have assumed, is no longer true, such a regularity simply does not exist in the new situation. What, then, does your (1) in fact report? One possible answer would be that it reports something as a great majority of natives are willing to assent to "gavagai?" in the presence of a rabbit.

(3)

However, why, then, capture this 'statistical' or 'imperfect' regularity by means of an equally 'categorical' statement as in the case when the regularity itself is 'categorical'? Is it not a kind of cheating to insist on the 'categorical' statement when the factual regularity is not such? To avoid misunderstanding: our point now is not that any human statement which has the form of a 'categorical' or a general claim about the world is fallible, for it cannot be based on more than a finite number of observations or experiments, and can always come to be falsified later. Hence the problem is not that we are willing to conclude that "gavagai"

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means rabbit although we are not able to exclude the possibility of being proven false later. This is what empirical knowledge amounts to - the most we can do is to make sure that the data we have amassed can be considered as reasonably representative, and this is what we have assumed. The real point is that we make the 'categorical' conclusion, (1), despite the fact that what we have found out is merely a 'statistical' regularity, (3). We might be tempted to answer that (1) does not really report (3), but rather something as every native is willing to assent to "gavagai", when she believes that a rabbit is present.

(4)

According to this explanation, (3) spells out a categorical regularity after all, namely (4); although now not a regularity concerning the relationship between the word "gavagai" and rabbits, but rather one between the word and beliefs about rabbits. The trouble is that (4) is not what we can really observe. Why do we think that the nine assenting natives believe that a rabbit is present, while the dissenter does not? Obviously only because the nine say they see a rabbit, whereas the tenth says he does not. 197 However, to be able to infer what they believe from the words they utter we have to know, or to assume, what the words mean (which exemplifies the inseparability of the finding out about meanings and finding out about beliefs stressed by Davidson). This is to say that the source of our conviction that the assenting natives believe there is a rabbit around is our knowledge that they assent to "gavagai?", and our conviction that "gavagai" means rabbit. Hence "The nine natives believe there is a rabbit around" is inferred from "The nine natives assent to 'gavagai?"' and "'Gavagai' means rabbit". Similarly "The tenth native believes there is no rabbit present" is inferred from "The tenth native dissents from 'gavagai?'" and "'Gavagai' means rabbit". This means that our accepting (4) (i.e. our conclusion that the natives who assent to "gavagai?" are precisely those who believe there is a rabbit in their vicinity) is due to the fact that we use (1) to conclude that he who assents to "gavagai?" believes there is a rabbit around him. This means that (4) is notoriously incapable of explaining how we get from the 'statistic' regularity (3) to the 'categorical' claim (1). To claim that what (1) really reports is not (3), but rather the 'categorical' regularity (4) is futile: (1) is not derived from, but rather underlying (4). 197 There might possibly exist exceptional cases when a native's belief could be somehow read off her behavior (perhaps a belief that something dangerous is happening?). In general, however, there is obviously no such possibility.

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Of course it could be further objected that (4) need not be understood as merely the consequence of (1 ); that although we do not see beliefs, they are, 'tangibly', somewhere 'in the heads' of the speakers - we could, e.g., think that they are coded by some objectively discoverable states of the neurons of their brains. In this case, (4) would not be a mere consequence of (1 ), it would amount to a hypothesis like every native is willing to assent to "gavagai", if and only if his brain contains x.

(5)

However, it would hardly be possible to claim that what (1) says is (5): this could be feasible only if we accepted an additional premise, such as

x is (a belief) about the presence of a rabbit.

(6)

How could we find out this? Perhaps by somehow experimentally discovering that the state x obtains within the brain of a speaker of English if and only if the speaker tends to utter "(lo, a) rabbit" or tends to assent to such an utterance? Perhaps what (1) spells out, then, is every native is willing to assent to "gavagai", if and only if his brain contains something that is contained by a brain of an English speaker (7) assenting to "rabbit". However, is this really feasible? Suppose that neuroscience discovered that the brains of two people having the same belief need not have anything neurologically significant in common (a result which is predicted by Davidson's anomalous monism 198 and which would not seem to be too striking). Would we then say that there are no beliefs and hence that what the radical interpreter does is a misguided enterprise? As we stressed (see Section 7 .2), the nature of beliefs is functional, and to seek them in the brain is futile: believing something is, as Brandom would put it, a normative status, not a psychological state. The upshot is that we cannot avoid the conclusion that the translator somehow posits a categoricity where there really is none: the regularities articulated in his translation manual, like (1 ), are not straightforwardly reported, but rather also, to a certain extent, posited. Obviously he is not altogether free in writing his manual- but he can, legitimately, smooth the curves which emerge from his data. From this viewpoint, meaning is a 198

See footnote 124.

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means of positing exact structure of an inexact reality; and beliefs are means of accounting for the deviations of reality from this structure. Let us elucidate this seemingly peculiar way of dealing with reality by means of comparing interpretation (i.e. the effort to account for an unknown language by means of a theory of its meaning) with another human intellectual enterprise, namely with the effort to account for the spatial aspects of the world by means of geometry. As a preliminary to this comparison we will first overview some relevant features of geometry. 9.3 Geometry Mathematicians sometimes come to wonder how geometry manages to serve our purposes within our real, 'tangible' world, when it deals with things which in fact never occur in this world at all. The point is that within our world we can find nothing which is a 'real', perfect line or a 'real', perfect triangle. We always encounter only things whose shapes may be considered lines or triangles at most by courtesy. This problem became especially pressing during the nineteenth century, when mathematicians started to wonder whether traditional geometry, as canonized by Euclid and his followers, really is the true geometry. The alternative proposals due to Lobachevskii, Bolyai and others (being partly by-products of attempts to prove the independence of Euclid's fifth postulate) afspeared to make it plausible that there are other interesting candidates. 1 9 Moreover, it soon became clear that no experiment can perform is able to decide whether it is the Euclidean geometry, or rather a suitable non-Euclidean one, which is appropriate for our world? 00 (However, if we realize that the true objects of geometry, the true lines, triangles etc., are not to be found within the real world, the fact that no such measurement is possible should not be too surprising). The discussions provoked by the appearance of the non-Euclidean geometries were fierce and not free of misunderstandings. Take the dispute 199 The non-standard geometries differ from the Euclidean in that they take the sum of the angles of a triangle to be not 180°, but either more (in case of the so called elliptic geometries) or less (in the case of the hyperbolic ones). 200 Whereas it is clearly possible to make measurements excluding the possibility of the sum of the angles of a triangle being, e.g., 250° or 100°, it is not possible to exclude a small enough deviation. The most famous experiment in this direction was carried out by Gauss, who measured the angles of a huge triangle determined by the places of Brocken, Hohenhagen and Inselberg. The result was, of course, indecisive: it was not exactly 180°, but the deviation from 180° did not exceed the tolerance expectable in case of measurements of this kind.

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between Henri Poincare and Bertrand Russell. 201 Russell took it for granted that if a theory is to be taken as geometry, its terms must be in a direct relationship with specific aspects of our real space. Thus, he insisted that "if the quantities with which we end are capable of spatial interpretation, then, and only then, our result may be regarded as geometrical." (Russell, 1897, p. 45). In contrast to this, Poincare claimed that the existence of the non-Euclidean geometries together with the fact that we cannot tell which of the geometries is 'the right one' shows that this cannot be the case. He was convinced that we are free to decide whether we accept the Euclidean geometry or some of its alternatives, and that what we call lines, triangles etc. is a matter of our own decision. He thus concluded that "one geometry cannot be more true than another; it can only be more convenient" (Poincare, 1908, p. 235). A similar kind of dispute took place between Gottlob Frege and David Hilbert. Like Russell, Frege was convinced that geometry captures something which we are confronted with already before we build any geometric theory; and he criticized Hilbert for not having clearly delimited what the terms "point", "line" etc., occurring in his theory, were supposed to apply to. He states (Frege, 1976, p. 73): ... your axioms of order also contain the words "point" and "line" whose meanings are also unknown. Your system of definitions is like a system of equations with several unknowns, where there remains a doubt whether the equations are soluble and, especially, whether the unknown quantities are uniquely determined. If they were uniquely determined, it would be better to give the solution, i.e., to explain each of the expressions "point", "line", "between" individually through somethimng that was already known.

Hilbert, assuming a standpoint close to that of Poincare, but more formalistic, was, however, convinced that Frege had tried to smuggle into geometry something which did not belong there. For Hilbert, geometry was a closed system which neither needed to be, not indeed could be, supported by anything external to it. The sense of terms like "point" or "line" was, according to him, delimited 'implicitly', by the roles they play within geometric theory (ibid., p. 66): I do not want to assume anything as known in advance. I regard my explanation as the definition of the concepts point, line, plane .... If one is looking for other definitions of 'point' ... , then I must indeed oppose such attempts in the most decisive way; one is 201

A more detailed discussion of this dispute, as well as of the one between Frege and Hilbert discussed below, is given by Coffa (1991). See also Shapiro (1996).

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looking for something one can never find because there is nothing there; and everything gets lost and becomes vague and tangled and degenerates into a game of hide and seek.

This is what Frege simply rejected to understand- for him it made no sense to want to formulate axioms with the help of terms which would not be equipped with a clear sense prior to the formulation. From the viewpoint of what we are after here, these discussions are instructive. Where is the truth? What we claim is that to a certain extent it is on both sides; that the quarrels are partly misunderstandings rather than real disagreements. They are, we claim, misunderstandings stemming from an insufficient reflection upon the relation between the 'formal' geometry, a matter of an abstract structure, and the spatial aspect of the real world which we try to account for by using this structure. Frege and Russell considered it of essential importance to stress that geometry should be answerable to something pre-geometric, namely to our 'spatial intuitions', or our pre-theoretical notions of point, line etc. - for these pre-theoretical intuitions or concepts are what made us develop the theory, and consequently they are what the theory is about. Thus they stressed that the structure posited by the 'abstract' or 'formal' geometry has to be applicable to our real world, that it has to be considerable as a structure of the world. I think it would be hard to deny this; and I do not think it would make sense to interpret Poincare or Hilbert as denying it. I think that what they found important to stress was that if geometry was to be entertained with the formal rigor which the modem mathematics had begun to achieve (paradigmatically for arithmetic, via Peano's axiomatization), the pre-theoretical intuitions could not play a real role within the system as such. What was mathematically tractable, in the strict sense of the word, was the structure, not the way in which it applied to the real world. And again, this is hardly deniable; and it would be hardly adequate to interpret Frege and Russell as denying this. I do not think that it would be feasible to blame Frege, whose Begriffsschrift set the basic standards for the logical regimentation of our arguments, or Russell, whose Principia offered a magnificent systematization of the incipient formal mathematics, of underestimating rigor. I think it is more appropriate to read them as stressing that rigor is of real value only if it helps us capture something 'factual', something which already confronts us as a problem before it is posited by a theory. On the other hand, Poincare and Hilbert simply urged that if we want to do geometry 'formally', in the way Peano showed us how to do arithmetic, if we want to leave nothing unproved, then we have to treat geometry as an abstract, 'ideal' system, whose terms acquire their senses only via their position within the system. And this does not contradict the point of Russell and Frege, namely that something is reasonably called "geometry" only if it

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is capable of serving a certain purpose, namely of helping us cope with the spatial aspect of our experience. Neither Poincare, nor Hilbert can be interpreted as having thought that literally any system of axioms (say Peano arithmetic), can be called "geometry" in an equally reasonable sense in which the Euclidean system is so called.Z02 I think that most probably they held this not being the case for too self-evident to dwell on it. They rather stressed that such a notion as 'spatial interpretation' is vague and hence not too interesting, for many things can be 'spatially interpreted' in a variety of ways - and that interesting roles within the explication of our 'spatial intuitions' could be played not only by the Euclidean geometry, but also by its rivals. I think that the situation gains in perspicuity if we see geometry as a way of finding a unity in a multiplicity, as a way of accounting for a vast realm of certain phenomena (concrete things considered from the aspect of their shapes) by means of a certain structure (the forms of abstract geometry), i.e. as a matter of projecting a certain structure onto certain phenomena, and observing the phenomena by its prism. (Modem geometry is then specific in that it is concentrated, far more than any previous geometrical theory, upon the structure itself, with an utter negligence of that onto which it is to be projected). Then we can see that at least part of the dispute is more or less simply terminological. Frege and Russell wanted to stress that to call an (investigation of an) abstract structure "geometry" is not reasonable unless we can show how this structure can be helpfully related to our real space; whereas Poincare and Hilbert stressed that a truly mathematical treatment can be given only to the structure, not to its relationship to reality. However, a quarrel concerning the use of the term "geometry" - whether to reserve it for the abstract prism alone, or to use it for the prism together with its intended projection - does not amount to a deep problem. If we subscribe to the former terminological proposal, we must remember that a given 'structural' prism is reasonably called geometry only thanks to the existence of its interesting projection on the real world, whereas if we opt for the latter one, we must realize that it is only the prism, not the projection, which can be subjected to purely mathematical treatment. 202

Should we not say that they believed that any consistent system of axioms consisting of geometrical terms (in contrast to, e.g., arithmetical ones) is as good a geometry as the Euclidean one? Not really. For what makes a term "geometrical"? If we say that a link to an extralinguistic entity, then we concede to Frege and Russell; which Poincare and Hilbert surely were not willing to do. And if we say that it is its belonging to a geometrical theory, then the claim that a theory is geometrical if it is couched in geometrical terms clearly begs the question.

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9.4 Structure as a Formal Prism

What we now claim is that the relationship between our real space and geometric theory on the one hand, and that between our real language and its explicit semantic theory on the other, are of a similar kind. Both consist in seeing something in terms of a certain structure. Thus the status of meanings is similar to that of geometrical forms: we should not seek them within the phenomenon accounted for, they should be rather seen as elements of a prism which we employ to understand, in our human way, the phenomenon. The abstract shape triangle is, for instance, a prism which we use to perceive or understand some of the things which surround us. Let us look at Figure 6.

Figure 6

The first of the shapes clearly is a triangle (despite the fact that with the help of a microscope we would surely find some irregularities). Also the second one could be seen as a triangle - although as a deformed or a distorted one. However, we would probably not be willing to take the third one as a triangle, and we would surely reject the fourth (this one could perhaps be taken as a distorted circle). Some degree of deformation or discrepancy from an ideal form is accommodable - but increasing the degree causes the form to vanish. Consider Figure 7. We would probably be willing to call the first square white (with a blemish or a defect); and similarly we would be willing to call the second one black. However, we would be less ready to call the third one either white or black - too much blemish, we can say, ceases to be blemish (and provides for dappledness instead). In this way, we try to squeeze what we see- or, more generally, what we encounter- around us into certain simple forms, structures or categories, calling the deviations from them 'imperfections', 'blemishes', 'defects' etc.

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Figure 7 Now imagine that the drawings of Figure 4 represent variants of a 'map' of the speakers of the language which we are about to radically interpret: the cases in which a native is willing to react to an appearance of a rabbit with "gavagai" are marked in white, whereas those in which this is not the case in black. The translator again attempts to grasp the situation by means of an idealized 'form', which he now articulates using the concepts of truth and meaning; and for the deviations from the form he uses the concept of false belief. If we now return to Section 9.2, we can finally clarify the rationale behind passing from (3) to (1): The fact spelled out by (3), i.e. the fact that a great majority of the natives are willing to assent to "gavagai?" in the presence of a rabbit, is accounted for by saying that the natives are in such a situation willing to assent to "gavagai?" with the exception of those who are convinced that it is not a rabbit; and this is what underlies (1 ). The thesis that "gavagai" means rabbit does not require, as supporting empirical data, that every native assents to "gavagai?" in the presence of a rabbit; it requires that those who do not do so can be reasonably taken as exceptions, whose views we record as 'false beliefs' 203 (just like the thesis that something is a triangle does not require that it is in perfect accordance with the ideal geometrical form, but rather that its discrepancies from the form do not exceed a reasonable limit). What we are suggesting is that radical translation is nothing else than an instance of a general technique with which we, human subjects, struggle to comprehend certain pieces and aspects of reality by means of structures. We can 'discover' a structure either more or less immediately and involuntarily (as discussed by the psychologists of perception), or gradually, even as the result of our intentional effort. Radical translation is the last case: in this case we weigh and assess, both consciously and 203

As Davidson (1984, p. 170) puts it: "The concept of belief ... stands ready to take up the slack between objective truth and the held true, and we come to understand it just in this connection."

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unconsciously, empirical data and on this basis we ascribe meanings and beliefs. Our ascriptions, of course, cannot be deliberate, they are (to a large extent) guided by the data; however, they are not determined to such an extent that we could reasonably see meanings as something which is directly a part of the data. 204 The fact, however, is that at least in the cases when the structure which 'emerges' from the data (and which we then see as what results when the true data are stripped off the 'noise') is a matter of conscious theoretical reflection there is no reason to be convinced that the data determine the structure uniquely. As Dennett (1991, p. 49) puts it, "there could be two different, but equally real, patterns discernible in the noisy world." 205 What is crucial is that the structure covers the data 'substantially'; i.e. that the amount of the data which does not quite fit with it and which we thus have to see as 'deviations', 'imperfections', or perhaps 'false beliefs', does not exceed a certain tolerable limit. And if this criterion is fulfilled equally well by two different structures, both of them will be equally acceptable - and to claim that the reality in question 'has' one of them will be equally correct as to say that it 'has' the other. It is, in this sense, better to see the structure as a prism through which we perceive reality than as something which we would discover 'inside' the reality. Hence the discovery of the structure is thus not like X-raying an arm and seeing how the bones connect inside it; it is rather like drawing out a plan to help somebody to orient herself in an unknown city. Besides this, it is necessary to realize that the 'tolerable limit' of the amount of deviation can change with circumstances. In some cases, a simpler structure capturing only rough outlines may be better, in other cases we need to minimize the deviations even at the cost of further complicating the structure. Thus if you draw an outline of an engine for the purpose of explaining the principles of operation of engines of this type, you may - and should - drastically oversimplify and produce an outline very different from any real engine. It only has to illustrate how the engine functions, and therefore it can disregard details of a concrete design. On the other hand, if you draw an outline for somebody intending to construct an engine, you will need to capture many kinds of details (although now you might be able to make some other, from the viewpoint of the current purpose harmless - or even desirable - kinds of simplification). 204 What is relevant concerning radical translation is, we saw, not regularities of use, but rules, norms of use- however, these are again, as we tried to show in the preceding part of the book, accessible only through certain regularities, namely the regularities of normative attitudes. (And prompting for assent/dissent is in fact nothing else than checking for this kind of attitude). 205 See also Dennett (1978).

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9.5 The 'Realm of the Natural' and the 'Realm of the Formal'

In Section 4.1 we stated that our introduction of abstract objects typically proceeds through abstraction, via the extraction of 'the one from the many'. However, now we have outlined a picture where structures instead of being simply shared by different, 'co-structural' things, as if .float free and be hired by our reason to assist its comprehension of things (although we stressed we do not subscribe to this Kantian picture); and sometimes it is apparently even necessary to 'squeeze' things into them in a somewhat violent way. In this picture, structures do not appear to be simply abstractions of common features of things, they appear to be something into which things are often pressed in the Procrustean way, by being cut to size. Hence it seems that if we want to take structures as abstract objects (and how else should they be taken?), we cannot restrict 'the abstract' to what is collected from straightforward abstraction, from the 'extraction of the common'. Returning to the example of geometry: we cannot imagine that geometrical objects and forms are simply abstractible from concrete things. Stekeler-Weithofer (1994) thus claims that if we consider the nature of 'the abstract', we have to take into account also something different from the 'extraction of the common', something which he calls ideation. Ideation amounts to the employment of structures and forms which are not the results of simple abstraction (and hence have no umbilical cord tying them to the 'concrete') and which play a complex role within our grasping of 'the concrete'- they are, as we have suggested, best seen as prisms through which we view various aspects of the world. Stekeler-Weithofer points out that in fact any 'categorical' speech has an 'ideative aspect'. He writes (ibid., p. 797): Every categorical statement talks first and foremost about something typical, abstract, about an ideal world 'in itself, and in its formal claim to validity does not yet contain the 'application' to the real world of our experience. Any such application is always a projection, and as such it requires a judgement during the assessment of whether the difference between the state of affairs to which the talk concretely points within the world of our experience and the state of affairs in an ideal model expressed by the formal talk is neglectible or substantial from the viewpoint of the needs of communication.

To emphasize the crucial difference between 'experience' and 'ideal models', let us, taking inspiration from Plato's distinction between Becoming and Being, talk about 'the realm of the natural' and the 'realm of the formal'. The former is to be imagined as the world in which we live our lives, the latter as that of the 'structures' which our reason employs when it

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wants to 'make sense' of the former. Within the realm of the natural, everything appears as fuzzy, fluctuating and contingent; how things are in the realm can be found out ('a posteriori') and described (in the most systematic way within natural science). And it is just this world which is directly relevant for our lives. In contrast to this, the realm of the formal consists of fixed and immutable forms; everything in it is sharply delimited and given 'a priori'. Within this realm we can define, stipulate and prove. The most systematic means of studying the realm is provided by mathematics (more precisely by that of its parts which is devoted to the study of abstract structures, i.e. universal algebra). As Russell (1976, p. 100) puts it, using the terms "world of existence" and "world of being" instead of our "realm of the natural" and "realm of the formal": The world of being is unchangeable, rigid, exact, delightful to the mathematician, the logician, the builder of metaphysical systems, and all who love perfection more than life. The world of existence is fleeting, vague, without sharp boundaries, without any clear plan or arrangement, but it contains all thoughts and feelings, all the data of sense, and all physical objects, everything that can do either good or harm, everything that makes any difference to the value of life and the world.

The study of a concrete thing, be it with or without the help of a structure, concerns the realm of the natural; whereas the study of a structure, be it or be it not the structure of a concrete thing, concerns the world of the formal. To avoid misunderstanding, let us stress from the beginning that this talk about two 'realms' is not to be taken as more than a vivid metaphor, accentuating the essential difference between entities which we encounter and those which we fabricate as aids for coping with the former. We do not claim that the boundary between the two realms is clear-cut and unequivocal; and hence we do not want the metaphor to be taken literally. In fact, we will be claiming (Section 9.7) that if we do take it literally, it is likely to lead us astray. Nevertheless, as long as we are aware of the limitations of the applicability of the metaphor, it is, I believe, quite helpful. 206 Anyway, dealing with something by means of a prism of a structure and dealing with the structure itself are two essentially separate issues, and it is necessary to keep them properly apart. This was exemplified by the Poincare-Russell and Hilbert-Frege quarrels: the conclusion which we have reached can now be formulated in such a way that these quarrels were at least partly the result of the fact that one side took geometry to be the study 206

Elsewhere (Peregrin, 2000b ), I use it to elucidate concrete foundational problems of logic.

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of the spatial aspect of the real world by means of a structure, whereas the other side took it to be simply the study of the structure itself. 9.6 Formalization

Understanding or analyzing an entity frequently engenders isolating and studying its structure. Thus, it is often the structure which preponderates and demands attention. And as structure is something stable and immutable, it is suited to being studied by mathematical means. Does this, then, mean that the investigations of some (or all) empirically given entities can be reduced to the study of the corresponding structures, i.e. to a certain pure mathematics? It is important to realize that this cannot be the case: in order to be able to understand the study of a structure as the study of an entity, it clearly has to be the structure of the very entity, and whether an empirical entity truly has a given structure is a notoriously empirical question. Moreover, the inquiry into whether an entity possesses a particular structure may be far more nontrivial than the inquiry into the structure itself. The replacement of an entity by its structure - e.g. the replacement of a natural language by a formal one or of a system of natural events by a mathematical model- can be called the formalization of the entity. It is, in a sense, the reduction of a part of a 'natural-scientific' problem to a mathematical problem: and this is something which has proved to be extremely useful in the course of the development of modem science. (And it is not too great an exaggeration to say that it is precisely this method to which modem science owes its stormy development). However, it is a dangerous illusion to think that empirical questions can be reduced to mathematical ones without a remainder - there will always be an 'empirical residuum' concerning the adequacy of the formalization of the empirical phenomenon in question. However, is mathematics not able to yield us answers to some empirical, 'natural-scientific' questions? Can we not, say, ascertain the safe standing of a house we are planning to build through solving a system of differential equations? Of course we can, however, only provided that the system of equations captures the potential house with the necessary level of adequacy. The original empirical problem ("will the house which we will build stand secure?") is thus not reduced, via formalization, to a mathematical problem, it is divided into two parts: the mathematical part ("what is the solution of the system of equations?") and the empirical part ("does the system capture the relevant reality adequately?"). Hence, if we

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say "the solution of such and such system proves that the house is not going to collapse", what we in fact have in mind (which goes without saying for us) is that it will stand secure on the assumption that the system of equations in questions captures the house adequately. Obviously, the house can collapse contrary to any mathematical result - and in such a case we would say that the system of equations with which we worked failed to capture it with the needed precision (or that we made a computational error). Mathematics therefore cannot really solve an empirical problem: it can, however, solve a corresponding formalization and concentrate the empirical part of the problem into the question of whether the formalization is adequate. Hence formalization does not mean a reduction of natural science to mathematics, but rather provides for a useful division of labor it separates the mathematical and the empirical aspect of a problem in such a way that each of them can be solved by the appropriate methods. Take modem physics: it studies the behavior of objects of the ('natural') world; but nevertheless, by way of formalization, approaches many of its problems in a mathematical way - e.g. through solving certain, mostly differential equations. The solution of a system of equations can, however, tell us something meaningful about a factual phenomenon only to the extent to which the equations do indeed capture the phenomenon in an adequate and relevant sense. I do not mean to deny that if a suitable formalization is achieved, the empirical remainder cannot be more or less trivial. In many cases we can capture, e.g., the parameters of a planned house with such precision that the corresponding computations yield us something reasonably close to certainty. What I urge is that the adequacy of the formalization with which we work and the minimality of the corresponding 'empirical residuum' has to be permanently attended to. (The prospects of a technician paying no attention to the factual parameters of a house and trusting that mathematics itself would prevent the house from collapsing would surely not be of the brightest). If we do not keep in mind that turning an empirical problem into a mathematical one - as a matter of principle - is never possible without a remainder, we are likely to succumb to pernicious illusions. Such illusions, i.e. instances of the conviction that some questions of natural science can be solved by mathematics alone, however, are not uncommon (presumably because of the undeniable boost to natural science given by formalization and mathematization). Let us, e.g., look at how J.D. Barrow (1991, p. 32) comments on the perspectives of physics: Thus Euclid's axioms- for example that parallel straight lines never meet, or that there is only one straight line joining any two points on a flat surface -are the self-evident fruits of one's experience drawing lines on a flat surface. Later

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mathematicians did not feel so encumbered and have required only consistency from their list of axioms .... It remains to be seen whether the initial conditions appropriate to the deepest physical problems ... will have initial conditions which are directly related to visualizable physical things, or whether they will be abstract mathematical or logical notions that enforce only self-consistency. The first part of the quotation involves the confusion discussed in Section 9.3: geometry as a theory of an aspect of reality is something different from geometry as a theory of certain formal structures; hence the difference between the two kinds of geometries mentioned by the author is - to a large extent - a matter of the fact that each of them addresses something else. It is thus not a case that something empirical is being reduced to pure mathematics. What, however, is even more striking is the confusion marking the second part of the quotation: the idea that a purely mathematical theory could be a theory of the initial conditions "corresponding to the deepest physical problems" thanks just to its consistency is equally absurd as the idea that a sentence could describe the content of my pocket merely thanks to the particular number of words it would consist of. Barrow's pronouncement apparently builds on the idea that if we take relevant terms, there may be only one way to compose them into a consistent theory; and hence this theory is bound to be right. However, the attempt at making clear sense of this founders on explicating the term "relevant". If we agree that a term cannot get meaning without being incorporated into a theory (i.e. without being inferentially articulated), there is no way of saying which terms are 'relevant' for the initial conditions of our universe without their being part of a relevant theory. (Just as we cannot say that "+" expresses the arithmetical concept of addition before knowing that it is governed by such axioms as (x + y) = (y + x)) Hence we cannot first delimit 'relevant' terms, and only then think about which possible theories can be built out of them.Z 07 9.7 Bridging the Epistemic Gap? Our considerations concerning the problem of what it takes to have a structure have led us to conclude that at least the structures of the kind we are most interested in (paradigmatically exemplified by the structure of language) are more reasonably seen not as something which resides 207

The point is obviously analogous to the one made above in note 202 concerning geometrical terms.

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'within' the things to which we ascribe them, but rather as prisms we use to make the things 'intelligible' for us. So the picture we have drawn seems to be that of 'free-floating' structures employed by us, in answer to our needs or interests, as prisms to look at various things. Does it not follow that we have to subscribe, despite our explicit rejection, to the Kantian picture of human reason imposing its structures on an unstructured reality (or on a reality structured in a way unintelligible for us)? Does this not mean that the picture of the human world as the result of squeezing a neutral content into our conceptual schemes, which we have, together with Davidson, thrown out of the door (Section 6. 7), is suddenly back through the window? It does not; and to get the picture right, it is essential to see why not. To begin with, it is a plain and non-controversial fact that we use various kinds of things as means of comprehending other things. Especially we are able to make entities for that purpose; we are able to draw maps and plans, to assemble models. Moreover, we have developed the skill of making intangible models, to build publicly accessible, though not perceptible mathematical structures which we are able to consider as structures of various things. (The prototypical way of bringing such structures into the public fore is via the axiomatic method). The fact that these things are of our own making establishes a closer relationship between us and them than there is between us and the things we encounter: we do have them in the way we want to have them (for we have made them so). This is especially true of mathematical models, for they are almost completely under our control. 208 Moreover, we tend to gras~ some of the things we encounter 'in terms' of the models we have made. 09 Visiting an unknown city, we usually either use a ready-made plan, or assemble one in passing within our minds. Trying to understand the depths of matter, we tend to see atoms as tiny suns orbited by tiny planets. And trying to make sense of an unknown language we either use a ready-made grammar, or assemble one in passing. Note that all these cases are down-to-earth platitudes. Pointing out that we are able to draw maps or to define mathematical structures is not going to cut any philosophical ice - it is a far cry from putting forward high-spirited philosophical theses stating that any thing we know is the 208

Although some mathematicians appear to take describing those mathematical structures which are addressed by model theory as something not quite dissimilar to describing empirical reality. A classical articulation of this stance is due to Hardy (1941, pp. 63-4): "Mathematical reality lies outside us, and ... our function is to discover or observe it, and ... the theorems which we prove, and which we describe grandiloquently as our 'creations' are simply our notes of our observations". 209 And here, I think, is where semiotics, which we have rejected as a feasible basis for semantics (Chapter 2), finds a vast space for its studies.

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result of our applying a form (provided by our reason) to a formless content (provided by reality). To pass from the former to the latter presupposes the "God's eye view": it presupposes that we are able to transcend our skins and peer at us and at the 'naked' reality, by definition never really perceptible by us, from somewhere above. And this is what the Quino-Davidsonian naturalism, to which we have subscribed, refrains from. In fact, this is one more important point where the views of the postanalytic philosophers discussed in this book seem to complement those of the late Wittgenstein (whose teaching was not intended to be addressed systematically here, but unavoidably surfaces intermittently throughout the whole book). Wittgenstein's view on the present matter is aptly summarized by Baker and Hacker (1984, p. 133): We quite naturally adhere to a captivating picture that words, sentences and symbols constitute a separate realm of entities (parallel to the realm of mental phenomena) which stands over and against the realm of objects, events, facts, states of affairs, actions, etc. It seems as if language and the world are divided each from the other by a metaphysical gulf. And it seems that if it is possible (as it surely is) to represent reality in thought and language at all, then this gulf must be fixed.

The picture which Wittgenstein sets against this 'myth', is, according to Baker and Hacker (ibid., p. 134-5) the following: Symbols are not to be set over against the world as if sounds and signs were not elements of the world. ... [W]hat gives signs their life, what makes them symbols, is the role we give them, the use we make of them, in our daily linguistic transactions. We use (parts of) the world to represent the world .... If the gulf between language and reality is illusory, then of course no bridge can span it. The statement that there is no connection between language and reality is not the affirmation of an antithesis of the thesis that they are connected by some mysterious mental or metaphysical bridging apparatus. It is rather a denial that there is room for any connection, for there is no gulf to span.

Baker and Hacker's reconstruction of Wittgenstein's stance, in my view, is accurate and illuminating. Moreover, I think that it is the very same train of thought which led Quine to his conviction "that knowledge, mind and meaning are part of the same world that they have to do with and that they are to be studied in the same empirical spirit that animates natural sciences" and Davidson to the rejection of the possibility to "imagine a mind asking itself, 'is there really a world out there?'" (see Section 6.8). The same point is made, even more vividly, by Brandom (1994, pp. 332-3):

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Discourse practices incorporate actual things .... They must not be thought of as hollow, waiting to be filled up by things; they are not thin and abstract, but as concrete as the practice of driving nails with a hammer. ... According to such a construal of practices, it is wrong to contrast discursive practice with a world of facts and things outside it, modeled on the contrast between words and the things they refer to .... Thus a demolition of semantic categories of correspondence relative to those of expression does not involve 'loss of the world' in the sense that our discursive practice is then conceived as unconstrained by how things actually are .... What is lost is only the bifurcation that makes knowledge seem to require the bridging of a gap that opens up between sayable and thinkable contents - thought of as existing self-contained on their side of the epistemic crevasse - and the worldly facts, existing on their side.

Thus, our predicament, as pointed out both by Wittgenstein and contemporary naturalists, is our always being amidst things. The structure of the world in which we live is, without doubt, inseparable from the structure of our language and the whole of our 'epistemic apparatus', but as there is no other, 'uncontaminated' or 'more authentic' structure of the world with which to contrast it, it makes no sense to say that it is not the structure of the world itself It seems that 'things-in-themselves' and all their modem successors belong to the philosophical equipment of which we have never been really able to make sense of. Here is also where our metaphor of the 'realm of the natural' and the 'realm of the formal' ceases to be helpful and becomes potentially misleading. It is when we start to see 'the natural' and 'the formal' as not merely products of a metaphor hypostasing two opposite poles of our pursuit-for-truth-language-game ('describing phenomena' and 'proving theorems'), but rather as two utterly distinct realms, that the need of bridging the epistemic gap becomes urgent. It is only than that we feel urged to play gods seeing things not only how we, humans do, but, in addition also how they really, 'in-themselves' are.

Chapter Ten

The Structures of Expressions 10.1 The Semantic Structure of an Expression? It may seem puzzling that so far we have not touched concepts which might seem imperative for a structuralist approach to semantics, namely the concepts of semantic structure and logical form. Are not the theories which try to approach meanings through such concepts structuralist theories par excellence? If this were really the case, the majority of contemporary semantic theories would indeed have to be structuralistic: especially the concept of logical form appears to play a central role not only within the theories of logically-minded semanticists (see, e.g., Sainsbury, 1991), but also in those of many linguists, especially those following Chomsky (see, e.g., Chomsky, 1986). However, to conclude that a theory would be structuralistic in the sense entertained here only due to the fact that it operates with the term "form" or "structure" would be preposterous. In which sense, within the framework developed in this book, can we talk about a 'logical form' or a 'semantic structure'? Until now we have been talking more about the structure of language than about the structures of its expressions: we have stated that the structuralistic approach to language is characterized by the fact that language is seen (and consequently possibly reconstructed) as a (finitely generated) part-whole system providing for the projection of certain oppositions from wholes to parts. Clearly, seeing language as a part-whole system is tantamount to seeing some of its expressions as wholes having others as their parts, and hence to ascribe them certain structures. Nevertheless, in this context we have talked merely about one type of structure, a structure which can be called syntactic. We have not faced the need of any other kind of structure which would be reasonably conceivable as semantic or logical. The point is that semantics, from our viewpoint, is not a matter of an independent structure parallel to the syntactic structure, but rather a matter of the way the opposition between truth and falsity gets projected along the (syntactic) structure from wholes to parts. We could also say that from the Quino-Davidsonian viewpoint of the radical translator/interpreter we see the syntax as a matter of which sounds the speakers use, whereas we see semantics as a very different matter of how they use them? 10 210

See Peregrin (1999a).

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It is true that if we take syntax to be an arbitrary reconstruction of language as a finitely generated part-whole system, then we can have many different 'syntaxes', some of which may be more suitable for the subsequent semantic analysis (the capturing of relevant inferences) than others. Moreover, it may tum out that some features or some elements of the syntactic structure of an expression are partly or wholly irrelevant from the viewpoint of its semantics; and thus only a part of the syntactic structure might appear as semantically relevant. This can lead us to talking about a semantic structure or about a logical form as something different from syntactic structure after all. However, construed in this way, this structure will not be independent of syntax - it will be merely a suitably 'purified' version of syntactic structure (or of one of the possible syntactic structures). It will be what results if we, in the words of Frege (1879, p.IV), "forego expressing anything that is without significance for the inferential sequence". Hence, as Quine puts it (1980, p.21), "what we call logical form is what grammatical form becomes when grammar is revised so as to make for efficient general methods of exploring the interdependence of sentences in respect of their truth values." Therefore, if there is a concept of semantic structure (or logical form) which would fit into our hitherto account for language, it would have to be somewhat trivial. In contrast to this, the logical and linguistic theories mentioned above appear to assign the concept a much more substantial role. Does this imply that they have somehow excavated beneath our 'syntactic' structuralism and reached some kind of deeper, 'semantic' structuralism? I think not, and in this chapter I try to explain why. Let us start with Chomsky.

10.2 "Logical Form" of Chomsky A theory of language is structuralistic in our sense of the word only if it sees the meaning of an expression as first and foremost the result of the way certain oppositions (especially that between truth and falsity) get projected, via the structure of language, onto it. The way the concept of structure is handled by linguistic theories inspired by Chomsky is, on the contrary, based on the assumption that the structure in question is something real, something which can be really found somewhere and described. Whereas from the viewpoint advocated here to ascribe a structure to an expression is only a way of expressing the place of the expression within the (inferential) structure of language, from the Chomskyan viewpoint such an ascription is a direct report of a finding, a description of something which the expression in some literal sense somewhere 'has'.

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Hence the "logical form" as conceived by Chomsky is something utterly real: it is, together with the syntactic structure, a part of that component of the human mind which governs the usage of language, of the human "language faculty". However, Chomsky is not too explicit with respect to the nature of these logical forms: in his probably most extensive work devoted to the philosophical background of his approach to language he characterizes logical form merely by saying that it is one level of the "structure of language" which constitutes "an interface between language and other cognitive systems" and "yields the direct representation of meaning" (viz. Chomsky, 1986, p. 68). To be able to explain the role of "logical form" within Chomsky's conception, we must first outline some general features of his approach. Chomsky's views on language are based on the assumption (supported by vast empirical data) that he who employs a linguistic expression does not perceive it as a mere sequence of signs or sounds, but rather as something which is hierarchically organized. What kind of empirical data support this assumption can be shown using a simple example concerning the mechanism of question formation, which Chomsky takes to be one of the most basic syntactic mechanisms which must be mastered by an adept of language. (The example is partly borrowed from Pinker, 1994). Let us consider questions formed by means of the pronoun "who". Declarative sentences of the kind of "A unicorn is in the garden" lead us to the question "Who is in the garden?" This looks like an utterly simple transformation, necessitating no recognition of a structure: it seems that the only thing required is the ability to identify a name and replace it with the pronoun "who". However, take the sentence "A unicorn and a rhino are in the garden". Now it is clearly not possible to simply take a name, "a unicorn" or "a rhino", and replace it by ''who"- unless we want to have questions like "Who and a rhino are in the garden?" or "A unicorn and who are in the garden?" What has to be replaced by "who" is the whole phrase "a unicorn and a rhino". So here the speaker cannot apply the question-forming mechanism correctly unless she is able to perceive that "a unicorn" is part of a more complex name, i.e. unless she at least implicitly knows that there is something as noun phrase and is aware that such a phrase behaves, from the given viewpoint, as an indecomposable whole. A sentence thus, for her, dissociates into certain parts (which then may further divide at 'lower' levels); hence the sentence is a hierarchically organized complex. Such a whole can be depicted, by a theoretician, by means of a tree like the following:

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238

VP

NP NP det a

C N

unicorn

and

NP

are

are

det

N

a

rhzno

.I

are

are

are

in det

det

N det det

Figure 8 Similarly consider the sentence "A unicorn that is eating a flower is in the garden". Simply using "who" as the proxy for "a unicorn" would yield us "who that is eating a flower is in the garden?". This means that here "a unicorn" again cannot be understood, on the relevant level, as a self-standing element: from the point of view of the question-forming transformation, "a unicorn that is eating a flower" appears to be an indecomposable whole. Hence we again see that a sentence is not merely a sequence of words, but rather a hierarchically ordered structure. Hence according to Chomsky, a learner of language necessarily perceives expressions as structured, hierarchically organized entities. Let us admit that arguments of this kind can challenge the way we have looked at syntax up to now (our excuse being that syntax is not the principal subject matter of this book). We have generally followed Quine (1972) in seeing syntax as what results when we try to delimit the class of all well-formed expressions of the language in question (which, in view of the infinity of the class, must acquire the form of a finite 'generating system'). Thus, we have looked at it as a matter of a theoretical reflection upon language and we have seen no reason why it should be articulated in any particular one of the many possible ways. In contrast to this, Chomsky indicates that aside of such 'theoretical' syntaxes there may exist also a 'practical' syntax, which is somehow directly embodied in the way language is handled by its speakers- and hence that even the 'theoretical' syntax, i.e. the explicit syntactical theory articulated by a linguist, should

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perhaps be much less of a theoretical construct, and much more of a report or an expression of something real, than would follow from our exposition so far. 21 t However, Chomsky's understanding of language involves also the idea that somewhere 'behind' the syntactic structure there exists another structure (in fact more than one, but this is not our present concern), which 'is semantics' in a similar sense to which the structure we have just discussed 'is syntax'. It seems that Chomsky sees the whole situation in such a way that the levels rest 'atop each other' somewhere within the human mind and differ from each other only in that whereas the elements of the one are words or morphemes, those of the other are some 'ideas' or mentalistically understood concepts (a picture we have criticized and rejected in Chapter 2). Such an assimilation of semantics to syntax is, from our viewpoint, simply misguided: we have stated that whereas syntax deals with which expressions are employed by the speakers, semantics is a matter of how these expressions are employed. Saying that if syntax is explained by revealing syntactic structure, then semantics is to be explained by revealing a semantic structure, is, from this viewpoint, similarly preposterous as saying that the explanation of the nature ofboots consisting in the description of their cut and their material need to be supplemented by a description of 'the cut and material of their usage'. Which expressions are employed by the speakers can, indeed, be explained by assembling a dictionary and a grammar, i.e. by reconstructing the language as a finitely generated part-whole system (thereby revealing the structure of language and consequently the structures of its expressions); however how they are employed cannot be explained by postulating another kind of structure. (The idea that this might be so is related to the failure to appreciate the functional nature of meaning- see Section 7.2). What surely is needed and why a concept of structure is important for semantics is to link semantics to syntax, i.e. to study how functions of expressions get projected from syntactic complexes to their constituents and vice versa. However, this reflects the fact that semantics cannot exist without syntax in the sense in which military ranks cannot exist without a hierarchically organized army not the fact that it would be analogous to syntax. 212

211

See also Blackburn's (1984, Chapter 1.5) comparison of Chomsky and Quine. In this sense Chomsky is also criticized by Davidson (1997, p. 21): "What we are born with, or what emerges in the normal course of early childhood, are constraints on syntax, not semantics."

212

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Meaning and Structure

10.3 "Logical Form" of Logicians The upshot of the previous section is that the Chomskyan notion of logical form, in contrast to the Chomskyan notion of syntax, has no place whatsoever within that view of language we have put forward here. This notion not only really has nothing to do with logic, but it is, moreover, based on seeing semantics in a way unwarrantedly analogous to syntax. However, there is also a wholly different concept of logical form, a concept which plays a crucial role within a context much closer to our own position, namely within the context of logical analysis of language as carried out by analytic philosophers. So how does this concept fare from our viewpoint? The classical example of what is taken to be the discovery of a decisive evidence for the fact that we must count with logical forms which may be wildly different from the corresponding 'surface' forms is Russell's (1906) seminal analysis of statements involving 'definite descriptions' (already mentioned at the end of Section 8.6). Russell reached the conclusion that the 'logical form' of the sentence The king of France is bald

(8)

is nothing like B(KF),

but rather

3x (KF(x)"' Vy (KF(y)~(x=y))"' B(x)).

(8')

This means that the sentence (8), according to Russell, does not really ascribe a property to an individual, but rather states that there exists a unique individual which is the king of France and this individual is bald. Now is this not an example of a genuine discovery of a semantic structure wholly independent of the syntactic one? Before answering this question, let us make the following experiment. Let us enrich the logical language Russell used by the mechanism of lambda-abstraction (developed several decades later by Church, 1941) making it, thereby, more flexible. What lambda-abstraction allows us to do is to 'extract' any well-formed part of a well-formed expression in such a way that the remainder is again a well-formed (and hence semantically 'self-standing' in the sense of having its own denotation) expression, and it is, moreover, an expression combinable with the extracted part back into the original expression (hence the rule of lambda-abstraction institutes

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something as a 'universal decomposability'). If a is a well-formed expression containing a well-formed subexpression 13 as its part, then

A.x.a[x/13] (where a[x/13] is the expression differing from a in that it has some occurrences of 13 replaced by x) is a well-formed expression for which it holds that

A.x.a[x/13](13) =a and more generally for any expression y of the corresponding grammatical category

A.x.a[x/l3](y) = a[y/13]. 213 So assuming this apparatus, we can extract KF out of (8') creating the expressiOn A.p.(:Jx (p(x)

1\

Vy

(p(y)~(x=y)) 1\

B(x))),

such that applied back to KF it yields a formula equivalent to (8'). This means that (8') can be equivalently expressed in the form (A.p.(:Jx (p(x)

1\

Vy

(p(y)~(x=y)) 1\

B(x))))(KF).

In the next step, we extract B and we again apply the result back to B, so that we again gain a formula equivalent to (8'): (A.q.(A.p.(:Jx (p(x)

1\

Vy

(p(y)~(x=y)) 1\

q(x))))(KF))(B).

If we now introduce the symbol KF* as a shorter name of the object denoted by A.q.(A.p.(:Jx (p(x) 1\ Vy (p(y)~(x=y)) 1\ q(x))))(KF), we can rewrite the last formula as Now Now

(8")

Now (8") consists of two 'semantically self-standing' parts, KF* and B, which can be straightforwardly associated with the subject and the 213

See, e.g., Barendregt (1980) for details.

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Meaning and Structure

predicate of (8) - thus, its form is no longer so distant from the 'surface', syntactic structure of(8), as it was in case of Russell's (8')? 14 What we see is that it suffices to merely extend the repertoire of formal means we use when analyzing language in order for the discrepancy between the structure of the analyzed sentence and that of the formula associated with it, apparentlr implied by Russell's analysis, to diminish or even to vanish altogether. 21 And what vanishes with it is the conclusion that Russell discovered an autonomous semantic structure - for we see that the fact that Russell reached a formula so structurally different from the analyzed natural language sentence is nothing more than a necessary consequence of the fact that he used a certain sparse logical language. What appeared as a discovery, now appears almost as a kind of awkwardness- or at least as the result of a kind of logical asceticism.Z 16 However, would it not be possible - despite what we have just stated to find some arguments in support of the thesis that the 'true' logical form of (8) is really (8'), rather than (8")? We claim that this is not the case: the formulas (8') and (8") are logically equivalent, which means that they share the same inferential role; hence from the viewpoint of logic, which is constitutive of them, they share the same content, 'express the same proposition'. Thus, from the viewpoint of the explication of the inferential role, truth conditions, or meaning of (8) they do not differ from each other more than two formulas one of which is printed in black while the other in blue. This means that if one wants to argue for the claim that (8') and (8") are not equivalent analyses of (8), he must be necessarily taking (8') and (8") to be something more than the logical formulas, one must take them as somehow describing or expressing some kind of structure behind the reach of logic. However, what kind of structure? If the answer is that it is the syntactic structure, i.e. that the best of possible logical analysis is that which is the closest to the syntactic form of the analyzed sentence, we end up with simply identifying logical form with syntactic structure - for, as we saw, making the structure of the analyzing formula as close as we wish to 214

If someone is disturbed by the fact that (8") makes what appears to be the 'subject' of (8) applied to what appears as its 'predicate' (and not vice versa, as it is usual within elementa,;y lo~ic), it is enough to define B. as a shorthand for Ap.p(B), and we can rewrite (8") as B (KF ). 215 We can, e.g., further define IS as a shorthand for Ap.'Aq.p(q) and rewrite (8") as IS(KF.,B), and if we write IS in the 'infix' way, we have KF• IS B. In this way, we reach an almost perfect correspondence between the original sentence and its analysis (save for the fact that "king of France" is still analyzed as a simple predicate). 216 And to be fair to Russell we must point out that for him precisely this kind of asceticism was a maxim: he was always trying to make do with "the smallest store of materials with which a given logical or semantic edifice can be constructed" (Russell, 1914, p.51 ).

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that of the analyzed sentence is merely a matter of engaging a rich enough logical language. And if the answer is that it is a structure different from the syntactic one, a structure somehow hidden 'behind' or 'under' the surface, we are back to the Chomskyan notion of logical form which we hoped to overcome with the help of Russell: we have been discussing the Russellian analysis precisely because we hoped that it might have been able to justify the existence of logical forms, whereas now we would have to rather presuppose this existence to make sense of the analysis in the first place. Of course all of this does not mean that the Russellian concept of logical form is totally senseless - surely it does make sense, however only in a situation when we, doing logical analysis, purposefully restrict ourselves to a simple language. (Also we do not claim that such restrictions do not have their point; they surely do: sparseness fosters perspicuity and smooth tractability). The ensuing logical form then is nothing absolute, but rather only something as 'the simplest analysis of the given expression by means of the given formal language'. This means that the only nontrivial usage of the term "logical form", is the usage which is de facto technical and which tells us nothing about expressions as such, but rather only about the consequences of our choice of the means of the analysis. In Chapter 8 we built semantic models of language reflecting various systems of inferential rules. Employing such models, we 'translate' expressions into formulas of the languages of the relevant logical systems (the formulas being more or less canonical means of designating the set-theoretical objects - extensions, intensions etc. - which the models in question offer as the explications of meanings). What we have just concluded does not imply the denial that we can see the formula thus assigned to a natural language expression as its 'logical form'- what it implies is that in such a case we must keep in mind that such notion of logical form is a model-relative and hence predominantly a technical concept.

10.4 Logical Form as Expressing Inferential Role From our viewpoint then, semantic or logical structure of an expression is not a property of the expression in isolation, but rather the articulation of its role, i.e. of its logical relationships to other expressions - it is the articulation of what entails, and what is entailed by, the statements whose part it constitutes. As Davidson (1970a, p. 140) puts it, to give the logical form of a sentence is to give its logical location in the totality of sentences, to describe it in a way that explicitly determines what sentences it entails and what sentences it is entailed by. The location must be

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Meaning and Structure

given relative to a deductive theory; so logical form itself is relative to a deductive theory. The relativity does not stop here, either, since even given a theory of deduction, there may be more than one total scheme for interpreting the sentences we are interested in and that preserves the pattern of entailments. The logical form of a particular sentence is, then, relative both to a theory of deduction and to some prior determinations as to how to render sentences in the language of the theory.

Thus if we say, e.g., that the logical structure of a sentence Sis S1 1\ S2, although it is not a conjunction 'on the surface', we do not say that we have discovered, somewhere 'behind' the sentence or within the minds of the people employing it, some two conjunctively joined components; what we say is that sis entailed by sl together with s2, and that, conversely both sl and s2 are entailed by S. Similarly if we say that the logical structure of the sentence (8) is (8'), we do not say that we have discovered the existential quantifier hidden somewhere 'within' the sentence - we again only make the inferential role of (8) explicit. 217 This means that to assess the correctness or adequacy of a 'logical form' proposed for an expression does not amount to descending into some hidden depths of the expression (or into the depths of the minds of its users) nor to ascending into a Platonist heaven and confronting the form with what we find there, it means checking for the inferential relations of the expression to other expressions of the language and considering whether the proposed 'logical form' envisages them in a helpful way. This means that we must consider two issues: 218 (i) Is the proposed 'logical form' F adequate to the given sentenceS in the sense that its inferential role within its formal language reasonably approximates the inferential role of S within its language? Hence do the formulas entailed by F (resp. those which entail F) come out as logical forms of those sentences which are entailed by S (resp. which entail S) and vice versa? (ii) Is the inferential role of the proposed 'logical form', as an element of the formal language we employ for the analysis, in some sense more explicit or more perspicuous than that of the analyzed sentence within its natural language?219 217

Rorty (1980, p. 260) duly points out that hence "a theory of meaning, for Davidson, is not an assemblage of 'analyses' of the meanings of individual terms, but rather an understanding of the inferential relations between sentences." 218 See also Peregrin (1998). 219 In the ideal case, what is inferable from what, in the formal language, is calculable according to the rules of a formal calculus.

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However, it is necessary to stress once again what we have already stated several times: namely that capturing natural language by means of a formal one always involves an idealization, it posits sharp boundaries where there are none and takes as absolute something which is really relative to a context. Thus if we require that "formulas which are entailed by F' be "logical forms of those sentences which are entailed by S', we must keep in mind that what is a consequence in a formal language can often legitimately capture something which really is merely a contextual inferability in a natural language; and what is an element with a definite inferential role within the formal language can legitimately represent to an element of a natural language whose inferential role is vague or fuzzy. The inferential roles of the explicating formal language therefore usually will not be identical with those of the explicated expressions of the natural language, but rather 'only' their 'reasonable idealizations'. (And it is hardly possible to give strict criteria for deciding when an idealization is still 'reasonable' and when it ceases to be- just like it is not possible to give fixed criteria for deciding when a plan of a city still fosters orientation in the city and when it is no longer useful). What, then, do we gain, according to this view, when we state that the logical form of (8) is (8')? Do we thereby state the truth conditions of (8)? If it were so, then it would be no significant achievement - for we know the truth conditions as soon as we understand (8); we know that (8) is true if and only if the king of France is bald. So do we thereby find out that (8) 'really' says something else than it appears to say (namely that there exists one and only one entity, which is the king of France, and it is bald)? We have already rejected this possibility - such "really" could not, as we concluded, mean anything else than "when we restrict ourselves to some sparse logical language". The only thing we do gain is that we transform (8) into a form in which it wears its inferential role (and so insofar as the inferential role is identifiable with meaning, also its meaning) on its sleeve. The point is that now we, e.g., directly see that (8) entails the existence of a unique king of France - and that it thus cannot be true unless there is such a unique king.

10.5 Logical Form as a Prism Replacing statements of natural language by formulas of a formal language (being considered their 'logical forms') with which we then 'calculate' according to the rules of a formal calculus, is, of course, nothing else than a formalization in the sense of the previous chapter, and hence it is subject to everything already said about formalizations and its quandaries. Modem,

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Meaning and Structure

symbolic logic has indeed provided for the formalization of a large part of the basic subject matter of logic, i.e. argumentation - it has succeeded in transforming it into the study of mathematical properties of certain formal structures. However, the study of such structures solves the problems of real argumentation only to such an extent to which they are conceivable as formalizations of the structures of the factual argumentation. We can treat something in a mathematical vein only when it belongs, as we put it in the previous chapter, to the 'realm of the formal', i.e. if it is a thing our reason has completely 'under control'. This is what L. E. J. Brouwer (1907, p.76) had in mind when he talked about people who commit the fallacy of "thinking that they could reason logically about other subjects than mathematical structures built by themselves." Proving, in the mathematical sense of the word, is a matter of the 'realm of the formal', principally unavailable within that of 'the natural'. To see the kind of blind alleys we can be led into if we neglect this feature of formalization, consider the following example. Imagine someone who is to answer the question whether a particular horse is female. Imagine that his reaction is "First you must tell me whether it is a mare - only then will I tell you whether it is female." This reply could be seen as an (inapt) attempt at a formalization: an attempt to reduce the given problem to the non-empirical question "Is a mare female?" (the positive answer to it is secured merely by the meaning of the word "mare") with the empirical residuum "Is the horse in question a mare?". Such a reply, however, would be surely considered ridiculous: the point is that the non-empirical part of the 'formalization' is entirely trivial, whereas the corresponding empirical residuum is no easier to answer than the original question. My point now is that logical forms are sometimes engaged for similarly futile enterprises. Let us consider a law of logic, say the principle of contradiction, claiming that no statement can be true together with its negation. Is it ever possible to correctly assent to both a statement (S) and its negation (---,S)? The logician's answer is, of course, no (underscored). Someone not schooled in logic may try to provide a counterexample: he might, for example, insist that he both does and does not like danger. However, in such a case he will undoubtedly be told that this very fact - namely that he is willing to assent both to "I like danger" and "I do not like danger" cannot mean anything else than that the latter statement is (for him) not the negation of the former; that the reality is, e.g., such that he likes some aspects of danger and dislikes other ones. What looks like a negation or conjunction within natural language need not be negation or conjunction in the logical sense. And it is facts of this kind which have enticed logicians and philosophers to the pursuit of 'true' logical forms.

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However, let us realize that an argument like this could be adapted to defend any kind of purported logical law, including exceedingly weird ones. Imagine somebody insisting that there is a law of logic which is in utter contradiction with common logical sense, say contradiction contradiction

(9)

If we produce a counterexample to this 'law', e.g. the obviously false statement "If Prague is in Czechia or in China, then it is in Czechia and in China", its proponent can say that this only proves that the counterexample does not have the logical form (9). In the extreme case he might claim that his 'law' holds even when it has no instance whatsoever in natural language. (Many logicians really appear to be of the opinion that it is entirely irrelevant if- and how - the laws of logic they study and express by means of formal languages are instantiated in a natural language. The laws of logic, they say, are a necessary, noncontingent matter, while the factual natural languages are empirical, contingent entities!) Of course that we can argue against (9) also in an alternative and more conclusive way - namely by pointing out that "v", "~" and "A", as they are understood by logic, are names of certain truth functions, and this makes it possible to prove (very easily) that (9) does not hold. (And it is this viewpoint that leads to the conviction that it is wholly irrelevant if or how the operators are expressed in a natural language). However, it is easy to see that this is again a case of trying to shift the problem from the 'realm of the natural', where we articulate our arguments which logic is to classify, into the 'realm of the formal' -which, as we saw in the previous chapter, cannot mean anything else than changing the problem into a different one. The point is that the problem of the relationships between the values of some exactly defined functions, into which the problem of validity of (9) thus mutates, is obviously a purely mathematical problem, whereas logic is concerned - ultimately - with the validity of our factual arguments couched in our real, usually natural language. It is again crucial to distinguish between a formal system as such and the way the system is 'projected' onto natural language. Let us realize that if we identify logic with the study of formal systems as such (which is presupp0sed by the view that the non-validity of (9) can be mathematically proved), then it is hard to justify any claim to the effect of the superiority of one logical system over another. There is no way to judge one formal structure as better than another formal structure (unless of course we were to understand better as, say, simpler- in which case the best logic would be the void one). There is even no justification that one structure (e.g. that of

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Meaning and Structure

the propositional calculus) amounts to logic, whereas another (say that of Hilbert space) does not. In such a case, our habits are the only lead: "logic" is simply the name commonly used for the investigation of not every kind of structure. The situation alters as soon as we bring into consideration the usefulness of this or another formal system for the sake of analysing factual argumentation in a factual language. Then a clear (although 'pragmatic' and surely not sharp) delimitation of the bounds of logic is forthcoming: a formal system is justly called "logic" if it can be usefully related to the argumentation so that we somehow envisage, canonize or materialize the part of its structure which is generally essential for argumentation in the language. According to this criterion, e.g., the formal propositional or predicate calculus is a logic (for how to use these to account for the factual argumentation has been shown numerous times). However, maybe even a system accepting (9) could count as a logic - subject of course to an interpretation which would usefully relate it to the study of language and argumentation (and obviously such an interpretation would not be the usual one, taking "v" as the counterpart of "or","/\" as that of "and", and"~" as that of "if ... then"). What exactly does it mean "to relate a formal system to natural language"? It clearly involves positing some rules (explicit or implicit) for seeing the formulas of the system as representations of the sentences of natural language. 220 In some cases such rules are obvious (some logical languages are made in such a way that they wear what they are to represent on their sleeves - as, say the statements Bald(Russell) 1\ Mammai(Pluto) ), in other cases they must be formulated (if the statement P1 (T 1) 1\ P2 (T2 ) is to be understood as representing a particular sentence of natural language, this must be stipulated; and similarly even in such cases as when we take the formula Vx (Dog(x)~Mammal(x)) as representing "Every dog is a mammal"). 221 Such a schematization, as stated in the previous chapter, is adequate if the inferential properties of the statements of the formal language to some substantial extent (modulo idealization) coincide with those of their intuitive counterparts within the natural language which they are supposed to represent. What is of course crucial is the qualification "to some substantial extent": the occurrence of, e.g., intuitively non-contradictory statements which come out as represented by contradictory formulas (viz. "I do and do not like danger") is tolerable- if 220

A paradigmatic example of such formulation are Montague's (1973) laws for translating a fragment of English into his intensional logic. 221 As what the formula \fx (Dog(x)~Mammal(x)) directly schematizes is something like "For every x it holds that if x is a dog, then x is a mammal", that it can be taken as the counterpart of"Every dog is a mammal" is not entirely trivial.

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they are true exceptions. The point is not that we can tolerate some exceptions from logical laws, but rather that we can tolerate exceptional failures of our analysis (and see them, e.g., as a matter of discrepancy between the 'surface structure' and the 'logical form') - but too many failures in particular cases equals the general failure of the analysis.

10.6 Logical Forms as 'Universal Compensators' The situation is the same as we considered in the previous chapter: within the prima facie overwhelming linguistic activity of people we can discover a certain unity which we can grasp in terms of a structure, which can be materialized with the help of a formal language - and this still works when there exist deviations and exceptions. However, they must be true deviations and exceptions - if their number exceeds a certain reasonable limit, the whole enterprise loses its point. In such a case, logical forms, which stand as intermediaries between the real language and logical laws, may easily become 'universal compensators' used to neutralize any kind of discrepancy between the posited laws and what is really going on when we talk and argue. One more anecdotic illustration: 222 Imagine a person, Mr. Seer, who decides to make money by predicting, for a small fee, the sex of an unborn child (of course without using ultrasound or similar means). He claims to be able to foresee the future birth of the child and hence to correctly predict its sex, save for the cases when there occur certain disturbances which alter the course of events-to-happen and spoil his predictions. Imagine, however, that in fact he simply guesses and blames the 'disturbances' for all his failures (and perhaps returns the money to those parents in whose cases he is not successful). He claims that what will ultimately happen can be seen as the result of the interplay of 'what is to happen' and the possible disturbances. Schematically, predicted event + disturbances = real event

(10)

However, what he is actually doing is explaining away all cases when his guess fails by invoking the disturbances, i.e. in view of the above equation he, in effect, simply defines the disturbances as neutralizing any disparity between the other two elements of(lO):

222

See also Peregrin (in print).

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disturbances = real event - predicted event

(11)

Needless to say that given (11), (10) reduces to the trivial real event = real event What could convince us to take a person making this kind of prediction seriously? Surely the fact, if it be a fact, that his predictions are successful to such an extent that this is not explainable by mere chance, in this particular case that his predictions are correct in a number of cases which 'statistically significantly' exceeds fifty percent. In such a case - and only in such a case - we would probably accept, at least tentatively, that he was doing something over and above mere guessing. However, in any other case we would conclude that he really makes the disturbances-factor of his claim into a 'universal compensator' capable of neutralizing any kind of discrepancy between his predictions and real happenings (thus violating the Popperian maxim of falsifiability of contentful claims). It is improbable that it would be of any help for Mr. Seer to insist that the reason why he should be taken seriously is that he possesses 'clairvoyance', the ability to see the things-to-happen. Perhaps some centuries ago this indeed might have been accepted as a reason (there may even have existed allegedly decisive ways to decide whether someone was clairvoyant or not); however, with the development of modem science this has become simply obsolete. Now it is generally accepted that clairvoyance is not an ability to be had (by a human being). Now compare the above with the predicament of a logician or philosopher carrying out logical analysis. What he claims is that logical forms are not reflected by the surface forms of the corresponding expressions directly, but instead usually only in a distorted or imperfect way. Hence, what he claims can be expressed as logical form + imperfection = real expression

(12)

This is structurally similar to (1 0): in both cases we see an observable entity (the sex of a child, resp. an expression) as the sum of two independently unobservable factors (the sex-to-be-had by the child plus 'disturbances', resp. the logical form of the expression plus 'imperfections'). Moreover, the character of one of the factors makes it tempting to make it into a 'universal compensator': like in the case of predicting it is easy to blame the 'disturbances' for any failure of prediction, it is easy to acquiesce in the feeling that doing logical analysis means inspecting 'abstract' logical forms and that any question concerning

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whether a factual expression happens to have a particular logical form is to be left to empirical linguistics. (And should the task of associating natural language expressions with the logical forms thus studied tum out to be problematic, then the worse for natural language!) Does this mean that logical analysis of language is an essentially misguided enterprise? Of course not - it is just a particular view of what logical analysis amounts to which is misguided, and which robs the analysis of its purported sense, namely to reveal the logical structure of the very language we are employing to make claims and to justify them. (Moreover, investigations of abstract forms alone are also not necessarily altogether senseless- they can yield interesting mathematical results).

10.7 The Dialectics of Structure In the previous chapter we stated that structures serve us the purpose of positing 'categorical' regularity where there really is none. What we stress now is that such an enterprise makes legitimate sense only when the discrepancies of the underlying reality from the posited structure are in a sense negligible. There exists what we could name a 'dialectics of structure': a structure easily lends itself to being seen as a Platonist entity, investigable by means of pure mathematics, independently of studying whether anything really possesses it; however, on the other hand, what makes such a study genuinely relevant for us is that there are things, within our real, non-Platonist world, which do possess it. This means that although the structure as such is something non-empirical, its being the structure of something is empirical. Thus although logic, in the clear sense, is the study of a non-empirical structure, the determination of which structure it should be is inevitably an empirical matter. Hence there is also a certain sense in which logical concepts are an empirical matter. This fact makes human language and human thinking appear somewhat Janus-faced. They can be seen as having an 'inside': the norms of our language, if seen from within the language, amount to plain necessities, whereas if seen from without, they appear as arbitrary 'conventions' or empirical facts. 223 And as logic, in my view, is a

223

See Peregrin (1995a, esp. §§ 10.6 a 11.6). Recently I have discovered that the very same point was made, in almost so many words, by Coffa (1991, p. 139): "In the range of meanings, what appears conventional from the outside is what appears necessary from the inside .... When regarded from outside a linguistic framework, [a sentence expressing an a priori claim] must be seen as part of the definition of one such framework, a definition in

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matter of the explication of some of these norms (namely the most general ofthem), 224 it is also marked by this Janus-facedness. Let us return to the Kantian distinction between the 'realm of law' and 225 From the current the 'realm of freedom' revived by Brandom. perspective we can say that norms are laws which can be disobeyed. Theoretically we can get outside of any norm (despite the fact that the grip 226 which some of the norms have on us may seem all-pervasive ); however, we also have the option - and it is taking up this very option which can be seen as tantamount of our being human - of staying 'inside' them, thus availing ourselves of values and meanings. When we return to the structure of language, we can say that from the viewpoint from 'inside' of a language the 'dialectics of structure' acquires a peculiar nature. The structure into which I am born delimits the space in which my utterances may operate if they be intelligible - hence the space of what I am able to say (cf. Section 7.8). However, as the structure is nothing transcendental to the linguistic activities of the speakers and exists solely through them, my utterances may influence it and, in the long run, possibly change it. Here we have a principal difference between the classical analytic philosophy and postanalytic philosophy of the variety discussed within the second part of this book: Carnap thought of language in terms of a qualitative break between its 'meaning-determining part' and its 'facts-stating part': there is, first, the establishment of meanings, and only then there can be communication. Quine, on the other hand, pointed out that this is not really the case: that there is really no sharp boundary between the enterprises of 'meaning-determining' and 'facts-stating'; and hence that meaning not only is what makes contentful utterances possible, but also is - in a kind of feedback - influenced by the utterances, for it is conferred on expressions by nothing else than the utterances and our normative attitudes towards them. Here is also where one could try to find a parallel between the philosophers discussed here and the French poststructuralists: for the cancelling of this boundary appears to be closely related to what distinguishes them from their structuralistic predecessors, namely to what Derrida and company envisage as cancelling of "the center of structure". disguise; when regarded from within the defined framework, that very sentence now expresses a claim, one true in virtue of the constituted meanings and therefore necessary." 224 See Peregrin (2000c). 225 See footnote 154. 226 As Wittgenstein (1969, p. 110) once puts it, we perceive the rules of our language as no more arbitrary than the fear of fire or of a furious man approaching us.

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Derrida ( 1967, p. 41 0) says: "The concept of a centered structure is in effect the concept of a founded game, constituted on the basis of an essential immobility and reassuring certainty, which themselves stand besides the game." If rules are established and agreed upon antecedently to the (linguistic) game (hence they are then 'transcendent' to the game), any kind of unclarity or clash can be resolved by a recourse to them; however, if they may be influenced and modified by the course of the game, we have nothing truly solid to lean upon.

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Chapter Eleven

Conclusion At the beginning of this book we confronted two views of language. First, there is the prima facie plausible, 'semiotic' picture based on the idea that the elements of the domain of signifieds and those of the domain of signifiers, which together compose the foundation of language, exist independently of each other and of the existence of language; and language then comes into being simply by their interlinking. In contrast to this, Ferdinand de Saussure outlined a picture of language in which the signifiers and the signifieds constitute themselves only via the constitution of their links, i.e. via the constitution of language. Language thus is no sum of independent links of the word-thing type; on the contrary, the words and things, the signifiers and the signifieds, are in an important sense parasitic upon language as a system. Language, according to this view, is no collection of words being assigned to things - language is the catalyst of forming words, things and their interrelations. Hence language is no 'nomenclature'. We have pointed out that the Saussurean outlook gains support from an unexpected source; namely from the American (post)analytic philosophers with their holistic notion of language: indeed Quinean holism and Saussurean structuralism have much in common. What Quine, Davidson, Sellars, Brandom and their companions criticize in the views held by their analytic predecessors and what they reject is basically just this conception of language as a nomenclature: they reject the picture in which language is simply a set of labels stuck to things by which we - within our minds equip things in the way exhibits in a museum are equipped with their tags. What, however, distinguishes these (post)analytic philosophers from de Saussure are the consequences they draw from rejecting this view - they have increasingly withdrawn themselves from the view that it is reasonable to see language primarily in terms of signifiers and signifieds (which, for de Saussure, still remained a matter of course, despite his new perspectives) and they have increasingly embraced the Deweyan and Wittgensteinian picture of language as a kind of toolbox containing various tools for interacting with other people and for coping with the world. Elements of language conceived in this way are then primarily characterizable not in terms of what they designate, but rather in terms of how they function within human practices or in terms of their usefulness from the viewpoint 255

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of these practices. Put in the Saussurean way, meaning is more of a value than of a thing. The holism of these philosophers results from their conviction that once we see language as a toolbox employed within the man-man and man-world interaction, we cannot fail to realize that linguistic expressions always function 'collectively'; even in cases where there seems only a single expression in play, its function can be fulfilled only with the aid of a hidden support from other expressions. Moreover, we see that expressions are tools peculiarly different from any other kinds of tools: any of them may be replaced by any other string of letters without undermining the functionality of language. (This is, we may say, the gist of what de Saussure calls the "arbitrariness of the linguistic sign"). Does it, then, follow that language has the magical property of being wholly indifferent to what it is like, that it can fulfil its function in any possible shape? Of course not: there is something which conditions its proper functioning, and this something can be seen as its structure. Thus within language we can freely and with impunity change the "substance" (individual words), but not the "form" (the relevant relationships between them). Davidson proposed that the structure of language which is relevant from this viewpoint is connected with the truth of its statements: that it is the structure which emerges if we do a systematic theory of how the truth of complex statements depends on the truth of their substatements and how that of the substatements depends on the meanings of their parts. Such a theory was effected in the thirties by Alfred Tarski; but Davidson pointed out that the Tarskian theory of truth is not to be read as spelling out how meanings yield truth, but rather, vice versa, how meanings come to be creatures of truth. Put in the Saussurean way, Davidson presented semantics as a projection of the truth/falsity opposition along the part-whole structure of language. In tum, Brandom can be seen as volunteering a further explanation of why this is so; why 'truth-dependence' is so crucial from the viewpoint of the nature of language. He claims that this stems from the fact that it is our inferential practices, our "game of giving and asking for reasons" that is constitutive of any language worth its name. What we primarily use language for is giving and asking for reasons; so we need some of our statements to be usable as reasons for other statements; hence we need the truth of some statements to guarantee the truth of other statements. It is not by chance that our language is inferentially articulated, that it possesses the meaning-bearing structure - it is a matter of the very nature of language. In this way, we accentuated the conclusion that meaning is not a thing, but rather a value. However, we have also suggested that this way of seeing the nature of language need not be utterly irreconcilable with the

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formally-logical view of semantics which results from construing meanings as objects and which has been elaborated by Carnap, Montague and others. The condition of the reconciliation is, however, seeing the reconstructions of language yielded by formal semantics as mere models - i.e. not as 'true pictures', but rather as (purposeful) idealizations that are not to capture all aspects of the modeled language. It is important to realize that although the structuralistic outlook largely challenges the view that meaning is an object, it does not entail that it could not be useful to model meaning as an object. To assume this vantage point means to forego what I am fond of calling the 'syndrome of romantic cartographer': the conviction that the only picture which is worth drawing is an unidealized, perfectly correspondent one. To see what I mean, imagine a cartographer who is to draw a map of a village, but who feels frustrated by the fact that he is to render a wonderful medieval chapel with just the regular symbol used to mark a chapel on a map. "How could I," he muses, "trade the amazing impressiveness and the awesome atmosphere of the edifice for such a plain geometrical figure? Would it not be an awful violation?" As a result, he refuses to draw the map. (And, as a consequence, nobody from outside is able to find the village and admire the glorious chapel). Now the common confusion about formal semantics can, I think, be pictured on the model of this situation: the conviction that unless a model is able to account for all details of language functioning, or to capture its 'spirit', it is a failure, is similarly pernicious as the paralysis of the Byronic cartographer. 227 We have also considered some contemporary theories of 'semantic structure', and we have concluded that the way in which they see 'semantic structure' analogously to syntactic structure is misleading. It is, to be sure, true that we can distinguish between two kinds of questions, namely questions concerning which expressions constitute language and how complex expressions are compounded of their parts (syntax), and those concerning how the expressions function within language, especially when 227 Voicing a motive recurrent in their circles, the prominent poststructuralists Deleuze and Guattari (1980, p. 14) claim: "there is no language in itself, no universality of language, but only the concurrence of dialects, jargons and specialized languages". Similar pronouncements have been made also by their postanalytic colleagues: "There is no such thing as a language," writes Davidson (1986, p. 446), "not if a language is anything like what many philosophers and linguists have supposed". Such claims are effective within the context of arguments against mistaking our idealizations or models of language for the factual phenomenon; but they should not be taken as robing idealized models of any point. If someone mistakes studying maps for travelling to the places which the maps represent, it is appropriate to point this out to him - but such cases hardly substantiate an overall depreciation of maps.

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they are true (semantics). However, semantic theory is not a matter of a specific structure (provided we are not interpreting "specific semantic structure" as "specifically 'purified' syntactic structure" or "the capturing of expressions in a specific formal language"), but of inquiring into the relationships between the functioning of wholes and that of their parts, especially of how individual expressions contribute to the truth values of statements in which they occur. Thus, semantics is a matter of how the truth/falsity opposition gets projected from parts to wholes and how the projections can then, conversely, be considered as 'adding up' to constitute the truth conditions of statements. Finally, we noted that any 'structuralist' analysis of language must count with a specific kind of 'dialectics' which governs the concept of structure: while structures themselves are non-empirical, mathematically tractable entities, the assessment of whether a structure is possessed by a given empirical entity (e.g. by a natural language or an expression of the language) is always inevitably an empirical matter, not directly susceptible to mathematical treatment. The exposition of languages and their semantics by means of formal models is a useful and fruitful enterprise; it is, however, crucial not to mistake the model for the thing modeled and to keep in mind that any kind of model necessarily involves, by its very nature, an amount of idealization.

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