Inference, Consequence, and Meaning: Perspectives on Inferentialism [Unabridged] 1443837784, 9781443837781

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Inference, Consequence, and Meaning

Inference, Consequence, and Meaning: Perspectives on Inferentialism

Edited by

Lilia Gurova

Inference, Consequence, and Meaning: Perspectives on Inferentialism, Edited by Lilia Gurova This book first published 2012 Cambridge Scholars Publishing 12 Back Chapman Street, Newcastle upon Tyne, NE6 2XX, UK British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Copyright © 2012 by Lilia Gurova and contributors All rights for this book reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. ISBN (10): 1-4438-3778-4, ISBN (13): 978-1-4438-3778-1

TABLE OF CONTENTS

List of Tables............................................................................................. vii Preface ........................................................................................................ ix Part I: Semantic Inferentialism and Its Discontents Chapter One................................................................................................. 3 What Is Inferentialism? Jaroslav Peregrin Chapter Two .............................................................................................. 19 Peregrin on the Logic of Inference: Situating the Inferentialist Account of Meaning Rosen Lutskanov Chapter Three ............................................................................................ 31 The Pursuit of Prescriptive Meaning Vladimír Svoboda Chapter Four .............................................................................................. 47 Pejoratives and Conceptual Truth Nenad Mišþeviü Chapter Five .............................................................................................. 69 Homogenous Semantics Boris Grozdanoff Part II: Implications of Inferentialism Chapter Six ................................................................................................ 85 Bolzano’s Semantic Relation of Grounding: A Case Study Anita Kasabova

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Table of Contents

Chapter Seven.......................................................................................... 105 Incommensurability and Inference Anguel Stefanov Chapter Eight........................................................................................... 115 Individuality and Inferences OndĜej Beran Chapter Nine............................................................................................ 131 Inferentialism and the Laws of Nature Controversy Lilia Gurova Contributors............................................................................................. 143 Index........................................................................................................ 145

LIST OF TABLES

2-1 Inferentially native operators .............................................................. 21 2-2 The native operators in logical and algebraic rendering ..................... 22 2-3 Inferentialism vs. Situation semantics ................................................ 28

PREFACE

The papers in this volume present the results of a three-year research project “Representation and Inference” which was conducted from the beginning of 2008 to the end 20101. The aim of the project was to assess the research program of inferentialism as it has been pursued during the last years by Robert Brandom, Mark Lance, Jaroslav Peregrin and others2. One of the central tenets of inferentialism as a theory of meaning is that what a linguistic expression means depends exclusively on the inferential rules that govern its use. Defined in this way, philosophical inferentialism is opposed to, and has the ambition to overcome the shortcomings of, the traditional representationalist theories of meaning built on the assumption that the meaning of a linguistic expression depends exclusively on what this expression refers to rather than on the inferences that this expression could be a part of. Using different strategies and building on different case studies, the authors of this volume elucidate the questions under what kind of conditions and to what extent the central tenets of inferentialism are tenable. Earlier versions of these papers were presented at the conference “Inference, Consequence, and Meaning” held in Sofia on the 3rd and 4th of December, 20083. Depending on their general stance to the inferentialist paradigm, the papers in this volume are divided into two parts. The papers included in Part I are focused on what is distinctive for the inferentialist approach to theory of meaning and on the advantages and disadvantages of this approach compared to its rivals. Some of these papers end with suggestions for modifications of the inferentialist research program. The papers that belong to Part II take a different stance to inferentialism. They do not discuss the inferentialist paradigm itself but try instead to trace the

 1

Two groups worked on this project. The first group was resident in Prague and affiliated to the Institute of Philosophy of the Academy of Sciences of the Czech Republic. The second group was resident in Sofia and its members worked at that time at the Institute of Philosophical Research of the Bulgarian Academy of Sciences and the New Bulgarian University. 2 See (Brandom 1994; Brandom 2000; Lance 2000; Peregrin 2008). 3 Information about the conference was published in The Reasoner, vol.3, No1 (January 2009), pp.7-8. (Available at: www.thereasoner.org).

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implications of this paradigm for problems which have not been yet considered part of the inferentialist research program. What follows is a brief description of the content of each of the contributed papers. Jaroslav Peregrin has long been known for his efforts to propagate and defend the version of semantic inferentialism that keeps to the tradition laid down by Wilfried Sellars and Robert Brandom4. In his paper “What is Inferentialism?” he summarizes the central tenets of the inferentialist theory of meaning and draws attention to the differences between inferentialist and representationalist theories of meaning on the one hand and between the Sellars-Brandom version of inferentialism and seemingly similar inferentialist conceptions, e.g. the inferential role semantics of Fodor, Lepore and their followers. Peregrin points out that although the term inferentialisim was originally coined by Brandom for his theory of natural language, it is applicable to similar views in philosophy of logic and that there has been increasing interest in the last years in logical inferentialist ideas connected to the studies in proof theory and substructural logics. The paper ends with a defense of semantic inferentialism against some of its most challenging critiques. In his paper “Peregrin on the Logic of Inference: Situating the Inferentialist Account of Meaning” Rosen Lutskanov questions one of the implicit assumptions of the inferentialist program: that the implicit logic of inference coincides with its explication. Lutskanov reveals that this assumption is in conflict with one of the central tenets of inferentialism, namely that the process of explication contributes to the improvement of our conceptual system. According to him, one cannot support both the claim that the explication fosters the development of our conceptual system and the claim that it changes nothing in respect to the implicit content which it reveals. His suggestion for getting out of this dilemma is to save the improvement through explication thesis and to abandon the implicit-explicit identity thesis. Lutskanov demonstrates how his suggestion could be realized by using the machinery of situation semantics to explicate the inferentialist concept of explication itself. The paper ends with suggestions on how the exchange of ideas and techniques between inferentialist and situation semantics could be fruitful for both sides. The paper by Vladimir Svoboda “The Pursuit of Prescriptive Meaning” does not challenge any of the central tenets of inferentialism. Its author insists instead that the concept of inference employed by Brandom and his followers is too narrow. This concept, Svoboda demonstrates, is applicable

 4

See (Peregrin 2000; Peregrin 2006; Peregrin 2008).

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to an assertoric discourse but is not suitable for the explication of inferential relations in any different discourse which does not contain exclusively affirmative sentences. In particular, he shows, the classical inferentialist notion of logical inference is not applicable to a prescriptive discourse. His proposal is to assume that along with rules governing our competence to draw inferences from particular true or false statements, we have rules that allow us to connect (and thus to make conclusions from) imperative sentences. At the end, Svododa makes the important claim that the inferentialist project for theoretical reconstruction of all kinds of language games is still in its infancy and much work should be done in order to prove its success. He also warns that in the course of submitting new language games to theoretical reconstruction it might appear that a more serious “rectification of the whole inferentialist paradigm” is to be made. In his paper “Pejoratives and Conceptual truth” Nenad Miscevic criticises Robert Brandom’s view of pejorative concepts as a paradigm case for inferentialism. According to Brandom, pejorative concepts have the same referents as their neutral counterparts which means, he says, that the negative connotations of pejoratives are entirely inferential in origin. Nenad Miscevic argues against this line of argumentation, starting with the assertion that some pejorative concepts do not have neutral counterparts at all and thus at least for them the argument of Brandom does not hold. Miscevic argues for the thesis that a representational theory of concepts which views them as based on theories about concepts’ intended referents, better account for the meaning of pejorative concepts than its inferentialist rivals. The paper „Homogenous Semantics” by Boris Grozdanoff does not directly address the issues of semantic inferentialism but it does address an issue which seems to be a problem for any referential semantics and thus it provides a case which might be of interest for the inferentialists looking for further promoting of their research program. The problem discussed is Benacerraf’s famous dilemma which in one of its versions states that one cannot embrace both a common (referential) semantics for mathematical and natural language propositions and a common epistemological account of the truth conditions for both mathematical knowledge and knowledge about the physical world. Grozdanoff’s main claim is that the dilemma rests on assumptions (about the metaphysics of mathematical and physical objects and about the way the non-homogenous metaphysics implies nonhomogenous semantics) which Benacerraf takes for granted but which are in fact questionable.

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Anita Kasabova’s central claim defended in her paper „Bolzano’s Semantic Relation of Grounding: A Case Study” is that semantic sequential relations rather than empirical causal relations are what episodic memory rests on. In order to elucidate her central notion of grounding relation, however, Kasabova does not rely on any modern version of semantic inferentialsim but turns instead to Bolzano, who according to her, is an early precursor of modern inferentialism. Anita Kasabova’s notion of grounding relation is a reconstruction of Bolzano’s notion of grounding relation (Abfolge). The grounding relation, she says, is the semantic base of episodic memory. Anita Kasabova demonstrates how her account of episodic memory can be used to explain the process of recollection. In his paper „Incommensurability and Inference” Anguel Stefanov addresses the question whether, in embracing an inferentialist approach to semantics of scientific knowledge, one should also agree with the notorious Thesis of Incommensurability (TI), according to which successive scientific theories which seem to refer to the same range of phenomena are semantically incommensurable. Stefanov explores two strategies that relate the central tenets of inferentialism to the Thesis of Incommensurability and demonstrates that they both point to a negative answer of the question about the alleged commitment of inferentialism to TI. An exception is the so-called hyper-inferentialism. Ondrej Beran’s paper „Individuality and Inferences” is an attempt to elucidate the much discussed problem of individuality in philosophy of language from a broadly construed standpoint of inferentialism. Beran tries to show to what extent inferentialism is suitable for understanding a special case of private language games which he calls “creative language games”. His conclusion is that the inferentialist strategy is not successfully applicable to such cases insofar as the implicit rules that allegedly govern these games cannot be easily identified and explicated. In the paper „Inferentialism and the Laws of Nature Controversy”, Lilia Gurova traces the implications of semantic inferentialism for the laws of nature controversy in philosophy of science. The traditional representationalist approach to scientific laws leads to the following dilemma: the law expressions either have real referents or they play an auxiliary role in science. Both horns of this dilemma lead to unsurmountable difficulties, that’s why an inferentialist construal of laws of nature that allows to avoid the dilemma looks very promising. The paper discusses the tenability of Toulmin’s inferentialist account of laws of nature as material rules of inference and the objections raised against it.

Inference, Consequence, and Meaning: Perspectives on Inferentialism

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It ends with conclusions about the epistemological merits of the inferentialist construal of law statements. There are few recently published book-length texts exploring the perspectives of the inferentialist research program5. We hope our volume will contribute to filling this gap. We expect that the essays included in this book will be of interest to all scholars of inferentialism, to philosophers and students of philosophy focused on philosophy of language, philosophy of logic, and philosophy of science, as well as to those who are interested in the possible applications of inferentialism in areas such as cognitive science, science education, moral reasoning and others.

Acknowledgments Many people contributed in one or another way to this project to achieve the outcomes as they are presented in this book but to some of them I am especially indebted. These are Juraj Hvorecký, who coordinated the Prague group working on the project “Representation and Inference”; Jaroslav Peregrin whose work on inferentialism inspired the conference “Inference, Cosequence and Meaning” held in 2008 in Sofia; and Anita Kasabova and Rosen Lutskanov who helped with the editorial work on this volume. Last but not least I acknowledge the invitation of Cambridge Scholars Publishing to publish the present volume with them as well as their kind assistance throughout the process of preparation of the manuscript for publication.

References Brandom, Robert. 1994. Making It Explicit. Cambridge, MA: Harvard University Press. —. 2000. Articulating Reasons. Cambridge, MA: Harvard University Press. Lance, Mark. 2000. “The Word Made Flesh: Toward a neo-Sellarsian View of Concepts, Analysis, and Understanding.” Acta Analytica 15: 117-135. Peregrin, Jaroslav. 2000. “Reference & Inference.” In Reference and Anaphoric Relations, edited by Klaus von Heusinger and Urs Egli, 269-286. Dordrecht: Kluwer. —. 2006. „Meaning as an Inferential Role.“ Erkenntnis 64: 1-36.

 5

A collection of essays that deserves to be mentioned is (Weiss & Wonderer 2010).

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—. 2008. “Inferentialist Approach to Semantics.” Philosophy Compass 3: 1208-1223. Weiss, Bernhard, and Jeremy Wonderer, eds. 2010. Reading Brandom: On Making It Explicit. London: Routledge.



PART I: SEMANTIC INFERENTIALISM AND ITS DISCONTENTS





CHAPTER ONE WHAT IS INFERENTIALISM? JAROSLAV PEREGRIN

Inferentialism and Representationalism Inferentialism is the conviction that to be meaningful in the distinctively human way, or to have a “conceptual content”, is to be governed by a certain kind of inferential rules. The term was coined by Robert Brandom as a label for his theory of language; however, it is also naturally applicable (and is growing increasingly common) within the philosophy of logic1. The rationale for articulating inferentialism as a fully-fledged standpoint is to emphasize its distinctness from the more traditional representationalism. The tradition of basing semantics on (such or another variant of) the concept of representation is long and rich. (Note that what is in question is representationalist semantics, viz. the idea that linguistic meaning is essentially a matter of representation; not a general thesis about the role of representations within the realm of the mental.) The basic representationalist picture is: we are confronted with things (or other entities) and somehow make our words stand for them (individual philosophers vary, of course, about what is to be understood by stand for). Within this paradigm, the “essential” words of our language are meaningful in so far as they represent, or stand for, something, and if there are other kinds of words, then their function is auxiliary: they may help compose complex representations etc. Many philosophers of the twentieth century took some form of representationalism for granted, seeing no

 1

Thus, Tennant (2007) states: "An inferentialist theory of meaning holds that the meaning of a logical operator can be captured by suitably formulated rules of inference (in, say, a system of natural deduction)."



4

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viable alternative basis for semantics; others had more specific reasons for entertaining one or another form of it2. An alternative to representationalism was put forward by the later Wittgenstein (whose earlier Tractatus3 may be read as an exposition of a kind of representationalism): he claimed that the alternative either an expression represents something or it is meaningless was wrongly conceived and that there was a third possibility, namely that “the signs can be used as in a game”4. Hence Wittgenstein’s proposal was that we should see the relation between an expression and its meaning on the model of that between a wooden piece we use to play chess and its role in chess (pawn, bishop …)5. This was, of course, not a novel proposal (the comparison of language with chess had already been invoked certainly by Frege, de Saussure or Husserl). But Wittgenstein’s influence was able to bring the relationship between meaning and the rules of our language games into the limelight of discussion. Another person to propagate the centrality of the rules of our linguistic practices for semantics was Wilfrid Sellars. He tied meaning more tightly to a specific kind of rules, namely inferential ones6. His follower, Robert Brandom, has since made the link between meaning and inference explicit: language, he says, is principally a means of playing "the game of giving and asking for reasons", hence it is necessarily inferentially articulated, and hence meaning is the role which an expression acquires vis-à-vis inferential rules7.

Inferentialism and logic In fact, roots of inferentialism can be traced back before Sellars and the later Wittgenstein. Even if we ignore its rudimentary forms which may be discernible in the writings of the early modern rationalist philosophers, such as Leibniz or Spinoza, as Brandom argues in (Brandom 1985) and (Brandom 2002), a very explicit formulation of an inferentialist construal of conceptual content is presented by Frege (Frege 1879, v). This

 2

As samples, see Etchemendy (1990), who urges for a representational semantics; Fodor’s (1981; 1987; 1998) notion of semantics as an annex to his representational theory of mind, or various approaches to semantics based on the concept of reference, such as that of Devitt (1981; 1994). 3 See (Wittgenstein 1922). 4 See (Waisman 1984, 105); cf. also (Wittgenstein 1958, 4). 5 See (Peregrin, forthcoming) for an elaboration of the model. 6 See especially (Sellars 1953). 7 See (Brandom 1994), (Brandom 2000). Cf. also (Peregrin 2008).



What Is Inferentialism?

5

anticipates an important thread within modern logic, maintaining that the meaning or significance of logical constants is a matter of the inferential rules, or the rules of proof, which govern them. It would seem that inferentialism as a doctrine about the content of logical particles is plausible. For take conjunction: it seems that to pinpoint its meaning, it is enough to stipulate A B A∧B

A∧B A

A∧B B

(The impression that these three rules do institute the usual meaning of ∧ is reinforced by the fact that they may be read as describing the usual truth table: the first two saying that A∧B is true only if A and B are, whereas the last one that it is true if A and B are.) This led Gentzen (1934) and his followers to the description of the inferential rules that are constitutive of the functioning (and hence the meaning) of each logical constant. (For each constant, there was always an introductory rule or rules (in our case of ∧, above, the first one), and an elimination rule or rules (above, the last two.)8 Gentzen’s efforts were integrated into the stream of what is now called proof theory, which was initiated by David Hilbert – originally as a project to establish secure foundations for logic9 – and which has subsequently developed, in effect, into the investigation of the inferential structures of logical systems10. The most popular objection to inferentialism in logic was presented by A. Prior (1960/61, 1964). Prior argues that if we let inferential patterns constitute (the meaning of) logical constants, then nothing prohibits the constitution of a constant tonk in terms of the following pattern A A tonk B

A tonk B B

As the very presence of such a constant within a language obviously makes the language contradictory, Prior concluded that inferential patterns do not confer real meaning.

 8

This works straightforwardly for intuitionist logic, thus making it more intimately related to inference than classical logic, for which this kind of symmetry is not really achievable. 9 See (Kreisel 1968). 10 One of the early weakly inferentialist approaches to the very concept of logic was due to Hacking (1979).



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Defenders of inferentialism, prominently (Belnap 1962) argue that Prior only showed that not every inferential pattern is able to confer meaning worth its name11. This makes the inferentialist face the problem of distinguishing, in inferentialist terms, between those patterns which do, and those which do not, confer meaning (from Prior’s text it may seem that to draw the boundary we need some essentially representationalist or model-theoretic equipment, such as truth tables); but this is not fatal for inferentialism. Belnap did propose an inferentialist construal of the boundary – according to him it can be construed as the boundary between those patterns that are conservative over the base language and those that are not (i.e those that do not, and those that do, institute new links among the sentences of the base language). Prior’s tonk is obviously not; it institutes the inference of A |-- B for every A and B. Inferentialism in logic (which, at the time of Belnap’s discussion with Prior, was not a widespread view) has recently also flourished in connection with the acceleration of proof-theoretical studies and the widening of their scope to the newly created field of substructural logics12.

From proof theory to semantics The controversies over whether it is possible to base logic on (and especially to furnish logical constants with meanings by means of) proof theory, or whether it must be model theory, concern, to a great extent, the technical aspect of logic. But some logicians and philosophers have started to associate this explanatory order with certain philosophical doctrines. In his early papers, Michael Dummett (1977) argued that basing logic on proof theory goes hand in hand with its intuitionist construal and, more generally, with founding epistemology on the concept of justification rather than on the concept of truth. This, according to him, further invites the "anti-realist" rather than "realist" attitude to ontology: the conviction that principally unknowable facts are no facts at all and hence we should not assume that every statement expressing a quantification over an infinite domain is true or false. Thus Dummett (1991) came to the conclusion that metaphysical debates are best settled by being reduced to debates about the logical backbone of our language. The Priorian challenge has led many logicians to seek a 'clean' way of introducing logical constants proof-theoretically. Apart from Belnap’s response, this has opened the door to considerations concerning the

 11 12



But cf. (Cook 2005) and (Wansing 2006). See (Došen & Schroeder-Heister 1993; Restall 2000).

What Is Inferentialism?

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normalizability of proofs (Prawitz 1965) and the so called requirement of harmony between their introduction and elimination rules (Tennant 1997). These notions amount to the requirement that an introductory rule and an elimination rule 'cancel out' in the sense that if you introduce a constant and then eliminate it, there is no gain. Thus, if you use the introduction rule for conjunction and then use the elimination rule, you are no better off than in the beginning, for what you have proved is nothing more than what you already had. A B A∧B A The reason tonk comes to be disqualified by these considerations is that its elimination rule does not 'fit' its introductory rule in the required way: there is not the required harmony between them and proofs containing them would violate normalizability. If you introduce it and eliminate it, there may be a nontrivial gain: A A tonk B B Prawitz, who has elaborated on the Gentzenian theory of natural deduction, was led to consider the relation between proof theory and semantics, by his examination of the ways of making rules constitutive of logical constants as 'well-behaved' as possible,. He and his followers then developed their ideas, introducing the overarching heading of prooftheoretical semantics13. It is clear that the inferentialist construal of the meanings of logical constants presents their semantics more as a matter of a certain know-how than of a knowledge of something represented by them. This may help not only to explain how logical constants (and hence logic) may have emerged14, but also to align logic with the Wittgensteinian trend to see

 13

See (Wansing 2000; Prawitz 2006) or (Schroeder-Heister 2006). See also (Francez and Dyckhof 2010) and (Francez, Dyckhof and Ben-Avi 2010) for an attempt at an explicit articulation of the proof-theoretic 'meaning' of an expression. 14 See (Tennant 1994).



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language as more of a practical activity than an abstract system of signs. This was stressed especially by Dummett (1993)15.

Brandom’s normative inferentialism Unlike Dummett, Brandom (1994, 2000) does not concentrate on logical constants; his inferentialism covers more uniformly the whole of language. As a pragmatist, Brandom sees language as a way of carrying out an activity, the activity of playing certain language games; but unlike many postmodern followers of Wittgenstein he is convinced that one of the games is 'principal', namely the game of giving and asking for reasons. It is this game, according to him, that is the hallmark of what we are – thinking, concept-possessing, rational beings abiding to the force of better reason16. It is this conviction that makes Brandom not only a pragmatist, but also an inferentialist (and, as we already stated, the initiator of inferentialism as a philosophical doctrine). For if our language is to let us play the game of giving and asking for reasons, it must be inferentially articulated: To be able to give reasons we must be able to make claims that can serve as reasons for other claims; hence our language must provide for sentences that entail other sentences. To be able to ask for reasons, we must be able to make claims that count as a challenge to other claims; hence our language must provide for sentences that are incompatible with other sentences. Hence our language must be structured by these entailment and incompatibility relations. In fact, for Brandom the level of inference and incompatibility is merely a deconstructible superstructure, underwritten by certain normative statuses, which communicating people acquire and maintain via using language. These statuses comprise various kinds of commitments and entitlements. Thus, for example, when I make an assertion, I commit myself to giving reasons for it when it is challenged (that is what makes it an assertion rather than just babble); and I entitle everybody else to

 15

A different approach to logic based on the 'practical' view of language is the game-theoretical semantics of Hintikka (1996). However, unlike the approach discussed here, this approach leads to the accentuation of the model-theoretic, rather than proof-theoretic foundations of logic. 16 Therefore, Brandom rejects the view of philosophers such as Derrida (1976) or Lyotard (1979) that all kinds of language games we play are, as it were, 'on the same level', or are even incommensurable. According to him, it is only in terms of the game of giving and asking for reasons that expressions can acquire real content.



What Is Inferentialism?

9

reassert my assertion reflecting any possible challenges to me. I may commit myself to a claim without being entitled to it, i.e. without being able to give any reasons for it, and I can be committed to all kinds of claims, but there are certain claims commitment to which blocks my entitlement to certain other claims. Brandom's idea is that living in a human society is steering within a rich network of normative social relationships and enjoying many kinds of normative statuses, which reach into many dimensions. Linguistic communication institutes an important stratum of such statuses (commitments and entitlements) and to understand language means to be able to keep track of the statuses of one's fellow speakers – to keep score of them, as Brandom puts it17. And the social distribution is essential because it provides for the multiplicity of perspectives that makes the objectivity of linguistic content possible. This interplay of commitments and entitlements is also the underlying source of the relation of incompatibility - commitment to one claim excluding the entitlement to others. Additionally, there is the relation of inheriting commitments and entitlements (by committing myself to This is a dog I commit myself also to This is an animal, and being entitled to It is raining I am entitled also to The streets are wet); and also the relation of co-inheritance of incompatibilities (A is in this relation to B iff whatever is incompatible with B is incompatible with A). This provides for the inference relation (more precisely, it provides for its several layers). Brandom's inferentialism is a species of pragmatism and of the usetheory of meaning - he sees our expressions as tools which we employ to do various useful things (though they should not be seen as self-standing tools like a hammer, but rather as tools, like, say, a toothwheel, that can do useful work only in cooperation with its fellow-tools). He gives pride of place to the practical over the theoretical and sees language as a tool of social interaction rather than an abstract system. Thus, any explication of the concepts such as language or meaning must be rooted in an account of what one does when one communicates - hence semantics, as he puts it, "must be answerable to pragmatics". What distinguishes him from most other pragmatists and exponents of various use-theories, however, is the essentially normative twist he gives to his theory. In a nutshell, we can say that what his inferentialism is about are not inferences (as actions of speakers or thinkers), but rather inferential rules. This is extremely important to keep in mind, for it is this that

 17

The concept of scorekeeping was introduced, in a slightly different setting, by Lewis (1979).



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Chapter One

distinguishes his inferentialism from other prima facie similar approaches to meaning, which try to derive meaning from the episodes of inferring rather than from rules (see the next section). This brings us back to the question of the way rules of language exist. Wittgenstein realized that the rules cannot all be explicit (in pain of a vicious circle), and hence we must make sense of the idea of rule implicit to a praxis. Brandom's response to this is that rules are carried by the speakers' normative attitude, by their treatings of the utterances of others (and indeed of their own) as correct and incorrect. But although the rules exist only as underpinned by attitudes, which is a matter of the causal order, the rules themselves do not exist within the causal order. In other words, though we may be able to describe, in a descriptive idiom, how a community can come to employ a normative idiom, the latter is not translatable into the former.

Other Varieties of Inferentialism An approach to meaning superficially similar to Brandom's inferentialism is constituted by what has been called inferential role semantics (Fodor and LePore 1992; Boghossian 1993), being a subspecies of conceptual role semantics (Harman 1987; Peacocke 1992), which claims, in the words of Block (2005), that "meaning of a representation is the role of that representation in the cognitive life of the agent, e.g. in perception, thought and decision-making". It is essential not to confuse this causal kind of inferentialism with Brandom's normative kind18. The drawing of inferences is something that happens within the causal world (in the mind, and hence in the brain); whereas rules, though underlain by normative attitudes, which are events within the causal world, are not themselves states or events within the causal order. Unlike normative inferentialism, causal inferentialism says that meaning consists in, or is caused by, certain events, namely individual drawings of inferences by individual speakers. (Note that inferential rules, which, according to the normative inferentialist, are the source of meaning, though underlain by certain causal attitudes of speakers, are not themselves part of the causal order.) Hence mistaking this view for the Brandomian inferentialism is pernicious. Moreover, though there certainly are causal functionalists, whether there are any serious proponents of causal inferentialism is less certain; and, not infrequently, the critique of

 18

See (Zangwill 2005) for a discussion of the difference between normative and causal functionalism.



What Is Inferentialism?

11

causal inferentialism ("inferential role semantics") is (mis)aimed at normative inferentialists19. Brandomian inferentialism should also not be confused with doctrines to the effect that we learn something ‘inferentially’ rather than ‘directly’, e.g. theories of linguistic communication that maintain the relevant message conveyed by a speech act is always, or often, or sometimes, inferred from the literal meaning or the expression employed to accomplish the speech act, rather than simply coinciding with this meaning. In this sense the term is employed, e.g., by Recanati (2002). Now, given that it is clear that inferentialism amounts to a normative (rather than causal) enterprise concentrating on the very nature of meaning (rather than characterizing individual communicative acts), we may distinguish theories according to what they take to be the scope of inferentialism. We can speak about narrow inferentialism if the scope is restricted to (plus minus) the logical vocabulary, and about wide inferentialism if it extends over the whole language. We have already discussed the former one above; the latter is, more or less, restricted to the school of Sellars and Brandom. Brandom (2007) further distinguishes between weak inferentialism, strong inferentialism and hyperinferentialism. Weak inferentialism is the conviction that an expression cannot be meaningful without playing a role in some inferences; i.e. that each meaningful expression must be part of some sentences that are inferable from other sentences and/or from which some other sentences are inferable. Weak inferentialism is clearly not incompatible with representationalism: believing that to mean something is to represent something is not incompatible with believing that sentences are inferable from other sentences. (Therefore, Brandom himself conjectures that in fact everybody would be a weak inferentialist, but I think that some representationalists would claim that an expression may be meaningful without being part of any sentence, or at least any sentence having inferential links to other sentences.) Strong inferentialism, according to Brandom, claims that this kind of ‘inferential articulation’ (i.e. being part of sentences that enter into inferential relationships) is not only a necessary, but also a sufficient condition of meaningfulness – though it construes the concept of inferential rule more broadly than we have done so far, so that it encompasses ‘inferences’, as it were, from situations to claims and from claims to actions. (Hence it accepts such ‘inferential rules’ as It is correct

 19

This kind of misunderstanding may also obscure the discussion between Brandom, on one side, and Fodor and LePore, on the other–see (Fodor and LePore 2001; Fodor and LePore 2007; Brandom 2007).



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Chapter One

to claim ‘This is a dog’ when pointing at a dog.) Hyperintensionalism, then, is the claim that ‘inferential articulation’ is a necessary and sufficient condition of meaningfulness on the narrow construal of inferential rules. This version of inferentialism is clearly untenable for a language containing empirical vocabulary.

Problems of Inferentialistic Semantics The notion of meaning that stems from the inferentialist view is that of an inferential role20. Just like being a (chess) king is nothing over and above being governed by such and such rules (of chess), so the inferentialist sees meaning thus and so as nothing over and above being governed by such and such (inferential) rules. Insofar as we take the rules to be a matter of pragmatics (but then we should stress that what we have in mind is normative pragmatics), we take semantics as being, in this sense, underpinned by pragmatics. Hence inferentialism falls into the stream of recent semantic theories which constitute what has been called the pragmatic turn21. The general idea that meaning might be a matter of inferences is a frequent target of criticism. We have already discussed the objection of Prior; the more general version amounts to the dual claim that (1) inference is a matter of syntax; and (2) syntax can never yield semantics. This also underlies the often cited objection to the Turingian idea that computers might be able to think: a computer, as Searle (1984) articulates the objection, can only have syntax (inferential rules), but never a true semantics. The inferentialist rejoinder turns on the equivocation of the word “syntax” as used in this objection: in one sense, syntax can never yield semantics (but syntax in this sense stops short before inferences22); in another sense syntax involves inference (but in this sense it can yield semantics23). The case of conjunction is instructive – as the inferential pattern appears to carry the same information as the truth table that is usually considered as being represented by the operator, there seems no reason to say that the inferential pattern cannot also confer meaning in so far as the table can.

 20

See (Sellars 1949; Peregrin 2006). See (Egginton and Sandbothe 2004). 22 It concerns merely the well-formedness of expressions. 23 In this sense, syntax amounts to what Carnap (1934) called logical syntax. 21



What Is Inferentialism?

13

A deeper objection concentrates on empirical vocabulary. This vocabulary, it would seem, cannot become meaningful without representing something (and it is a question whether we can have a language, worth its name, without this kind of vocabulary). We have seen that Brandom himself admits that to understand meanings of empirical words as their inferential roles, we have to stretch the notion of inference beyond its usual limits. Hence, is the inferentialist finally obliged to say the same as some representationalists, namely that empirical words acquire their significance through being tools of responding to objects of the extralinguistic world? Though it is clear that the position of the inferentialist is less secure here than with logical words, the assimilation of her position to a representationalist one would be an oversimplification. First, inferentialism commits her to a sentence holism, and so the point of contact of language and the world cannot be on the word-object level, but rather on the level sentence-situation or action. Second, she is a normativist, hence she is not interested in which responses in fact occur, but rather in which responses are correct. And third, she is convinced that no expression can become meaningful merely in force of such contacts–it must also be situated within the network of inferences proper. Some descendants of Brandomian inferentialism, notably Lance (1998; 2000), argue that the empirical aspect of natural language must be accounted for in terms of the embodiment of language24. Language, Lance argues, is more appropriately seen as a sport like a football than as a game like chess though the “space of meaningfulness” is partially delimited by mere rules, which can be violated, rather than inviolable natural laws, some of the rules are rules for coping with reality and hence the space is co-delimited also by laws. Another general issue of inferentialist semantics is the relationship between inferentialism and various formal theories of semantics which have flourished since the seminal works of Montague (1970a; 1970b) and Lewis (1972). From what was said above, it might seem that the inferentialist is bound to accept a proof-theoretical rather than modeltheoretical foundation of logic and automatically reject this kind of modeltheoretical semantics (which, moreover, is often seen as an embodiment of the representationalist notion of language25). However, if what is in question is natural language, then the situation is less straightforward: the representationalism/inferentialism distinction cannot be too closely aligned

 24 25



Cf. also (Haugeland 1998). See, e.g. Abbott (1997).

14

Chapter One

with the model-theoretic/proof-theoretic distinction – from the inferentialist viewpoint, model theory may be a tool for explicating the inferential roles of natural language expressions no less useful than proof theory26.

Acknowledgements Work on this paper was supported by research grant No. P401/10/0146 of the Czech Science Foundation.

References Abbott, Barbara. 1997. “Models, Truth and Semantics.” Linguistic and Philosophy 20: 117-138. Belnap, Nuel. 1962. “Tonk, Plonk and Plink.” Analysis 22: 130-134. Block, Ned. 2005. “Conceptual Role Semantics.” In The Shorter Routledge Encyclopedia of Philosophy, edited by Edward Craig. London: Routledge. Boghossian, Paul A. 1993. “Does an Inferential Role Semantics Rest Upon a Mistake?” Philosophical Issues 3: 73-88. Brandom, Robert. 1985. “Varieties of Understanding.” In Reason and Rationality in Natural Science, edited by Nicholas Rescher, 27-51. Lanham: University Presses of America. —. 1994. Making It Explicit. Cambridge, MA: Harvard University Press. —. 2000. Articulating Reasons. Cambridge, MA: Harvard University Press. —. 2002. Tales of the Mighty Dead. Cambridge, MA: Harvard University Press. —. 2007. “Inferentialism and Some of Its Challenges.” Philosophy and Phenomenological Research 74: 651-676. Carnap, Rudolf. 1934. Logische Syntax der Sprache. Vienna: Springer. Cook, Roy T. 2005. “What's wrong with tonk(?)” Journal of Philosophical Logic 34: 217–226. Derrida, Jacques. 1976. Of Grammatology. Translated by Cayatri Chakravorty Spivak. Baltimore: Johns Hopkins University Press. Devitt, Michael. 1981. Designation. New York: Columbia University Press. —. 1994. “The Methodology of Naturalistic Semantics.” Journal of Philosophy 91: 545-572.

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See Peregrin (2001) for a more detailed discussion of some of these issues.

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Došen, Kosta, and Peter J. Schroeder-Heister, eds. 1993. Substructural Logics. Oxford: Clarendon Press. Dummett, Michael. 1977. Elements of Intuitionism. Oxford: Clarendon Press. —. 1991. The Logical Basis of Metaphysics. London: Duckworth. —. 1993. “What do I know when I know a language?” in Dummett, Michael. The Seas of Language, 94-106. Oxford: Oxford University Press. Egginton, William, and Mike Sandbothe, eds. 2004. The Pragmatic Turn in Philosophy. New York: SUNY Press. Etchemendy, John. 1990. The Concept of Logical Consequence. Cambridge, MA: Harvard University Press. Fodor, Jerry. 1981. Representations. Cambridge, MA: The MIT Press. —. 1987. Psychosemantics: The Problem of Meaning in the Philosophy of Mind. Cambridge, MA: The MIT Press. —. 1998. Concepts: Where Cognitive Science Went Wrong. Oxford: Clarendon Press. Fodor, Jerry, and Ernest Lepore. 1992. Holism: A Shoppers' Guide. Oxford: Blackwell. Fodor, Jerry, and Ernest Lepore. 2001. “Brandom's Burdens.” Philosophy and Phenomenological Research 63: 465-482. Fodor, Jerry, and Ernest Lepore. 2007. “Brandom Beleaguered.” Philosophy and Phenomenological Research 74: 677-691. Francez, Nissim, and Roy Dyckhoff. 2010. “Proof-Theoretic Semantics for a Natural Language Fragment.” Linguistics and Philosophy 33: 447-477. Francez, Nissim, Roy Dyckhoff, and Gilad Ben-Avi. 2010. “ProofTheoretic Semantics for Subsentential Phrases.” Studia Logica 94: 381-401. Frege, Gottlob. 1879. Begriffsschrift. Halle: Nebert. Gentzen, Gerhard. 1934. „Untersuchungen über das logische Schliessen III.“ Mathematische Zeitschrift 39: 176-210. Hacking, Ian. 1979. “What is logic?” Journal of Philosophy 76: 285319. Harman, Gilbert. 1987. “(Non-solipsistic) Conceptual Role Semantics.” In New Directions in Semantics, edited by Ernest Lepore. London: Academic Press. Haugeland, John. 1998. Having Thought: Essays on the Metaphysics of Mind. Cambridge, MA: Harvard University Press. Hintikka, Jaakko. 1996. “Game-Theoretical Semantics as a Challenge to Proof Theory.” Nordic Journal of Philosophical Logic 1: 169-183.



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Kreisel, Georg. 1968. “A Survey of Proof Theory.” Journal of Symbolic Logic 33: 321-388. Lance, Mark. 2000. “The Word Made Flesh: Toward a neo-Sellarsian View of Concepts, Analysis, and Understanding.” Acta Analytica 15: 117-135. Lance, Mark. 1998. “Some Reflections on the Sport of Language.” Philosophical Perspectives 12: 219-240. Lewis, David. 1972. “General Semantics.” In Semantics of Natural Language, edited by Donald Davidson and Gilbert Harman, 169-218. Dordrecht: Reidel. —. 1979. “Scorekeeping in a Language-Game.” Journal of Philosophical Logic 8: 339-59. Lyotard, Jean-François. 1979. La Condition Postmoderne. Paris: Minuit. Montague, Richard. 1970. “English as a Formal Language.” In Linguaggi nella Societa e nella Tecnica, edited by Bruno Visentini et al., 189-224. Milan: Edizioni di Comunità. Montague, Richard. 1970. “Universal Grammar.” Theoria 36: 373-398. Montague, Richard. 1974. Formal Philosophy: Selected Papers of Richard Montague. New Haven: Yale University Press. Peacocke, Christopher. 1992. A Theory of Concepts. Cambridge, MA: The MIT Press. Peregrin, Jaroslav. 2001. Meaning and Structure. Aldershot: Ashgate. —. 2006. “Developing Sellars' Semantic Legacy: Meaning as a Role.” In The Self-Correcting Enterprise: Essays on Wilfrid Sellars, edited by Mark Lance and Michael Wolf. Amsterdam: Rodopi. —. 2008. “Inferentialist Approach to Semantics.” Philosophy Compass 3: 1208-1223. —. Forthcoming. “The Normative Dimension of Discourse.” In Cambridge Handbook of Pragmatics, edited by Keith Allan and Kasia Jasczolt. Cambridge: Cambridge University Press. Prawitz, Dag. 1971. "Ideas and Results in Proof Theory," In Proceedings of the Second Scandinavian Logic Symposium, edited by J. Fenstad, 237-309. Amsterdam: North-Holland. —. 1965. Natural Deduction. Stockholm: Almqvist & Wiksell. —. 2006. “Meaning Approached via Proofs.” Synthèse 148: 507-524. Prior, Arthur N. 1964. “Conjunction and Contonktion Revisited.” Analysis 24: 191-195. —. 1960/61. “Runabout Inference Ticket.” Analysis 21: 38-39. Recanati, François. 2002. “Does Linguistic Communication Rest on Inference?” Mind & Language 17: 105-126.



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Restall, Greg. 2000. Introduction to Substructural Logics. London: Routledge. Russell, Bertrand. 1912. The Problems of Philosophy. London: Williams and Norgate. Schroeder-Heister, Peter. 2006. “Validity Concepts in Proof-Theoretic Semantics.” Synthèse 148: 525-571. Searle, John. 1984. Minds, Brains and Science. Cambridge, MA: Harvard University Press. Sellars, Wilfrid. 1949. “Language, Rules and Behavior.” In John Dewey: Philosopher of Science and Freedom, edited by Sidney Hook, 289-315. New York: Dial Press. —. 1953. “Inference and Meaning.” Mind 62: 313-338. Tennant, Neil. 1994. “Logic and its place in nature.” In Kant and Contemporary Epistemology, edited by Paolo Parrini, 101-113. Dordrecht: Kluwer. —. 1997. The Taming of the True. Oxford: Oxford University Press. —. 2007. “Existence and Identity in Free Logic: A Problem for Inferentialism?” Mind 116: 1055-1078. van Heijenoort, Jean, ed. 1971. From Frege to Gödel: A Source Book from Mathematical Logic. Cambridge, MA: Harvard University Press. Waisman, Friedrich. 1984. Wittgenstein und der Wiener Kreis: Gespräche. Frankfurt: Suhrkamp. Wansing, Heinrich. 2000. “The Idea of a Proof-theoretic Semantics and the Meaning of Logical Operators.” Studia Logica 64: 3-20. —. 2006. “Connectives Stronger Than Tonk.” Journal of Philosophical Logic 35: 653-660. Wittgenstein, Ludwig. (1922) 1961. Tractatus Logico-Philosophicus. Translated by C. K. Ogden. Reprint, London: Routledge. —. 1958. The Blue and Brown Books. Oxford: Blackwell. Zangwill, Nick. 2005. “The Normativity of the Mental.” Philosophical Explorations 8: 1-19.



CHAPTER TWO PEREGRIN ON THE LOGIC OF INFERENCE: SITUATING THE INFERENTIALIST ACCOUNT OF MEANING ROSEN LUTSKANOV

The present paper exposes an alleged flaw of Brandom’s inferentialist semantics and its formal reconstruction, developed in a recent paper by Jaroslav Peregrin. The argument is structured as follows: Initially, I pose a question about the relation between implicit conceptual contents and their explicit counterparts, developed through the process of “making it explicit” (I); then I analyze the answer of this question proposed by Brandom and Peregrin (II). Subsequently, I endeavour to cast doubt on this particular answer through considerations stemming from Hegel’s dialectical logic (III). In the next two paragraphs, I sketch a simplified version of situation semantics (IV) and apply it in an interpretative strategy which substantiates an alternative answer (V). In the concluding section, I propose some arguments in favor of a modified or “situated” version of inferentialism (VI).

I Robert Brandom’s inferentialism is one of the most impressive and intricately articulated foundational projects in the theoretical field of philosophical semantics. It boils down to the suggestion to view logical vocabulary as a normatively specifiable machinery that “endows practitioners with the expressive power to make explicit as the contents of the claims just those implicit features of linguistic practice that confer semantic contents on their utterances” (Brandom 1994, xix). Recently, the conceptual stance of inferentialism was employed by Jaroslav Peregrin, whose logic of inference was designed to mirror formally the essential philosophical insights of inferentialism. Both of them, however, are

20

Chapter Two

founded on an unquestioned presupposition that this survey aims to reveal. In order to expose it, I shall ask an apparently trivial question: What is the relation between the implicit logic of inference and its explicit counterpart? As far as I can see, two readily conceivable but mutually alternative answers suggest themselves: (a) They are one and the same; (b) They are not one and the same. The first answer seems as cogent as possible because it is utterly strange to view A as an “explicitation” of B if A is not essentially identical with B. For example, if the X-ray image of my skeleton is not structurally identical with it, then it would be highly inappropriate to view the image as “making explicit” the status of my bones. Moreover, the image would be otiose (for this very reason). Probably, the manifest felicity of this answer was the reason why Brandom and Peregrin never asked the question in the first place. Their thesis is that the process of explicitation does not affect the conceptual contents of what is being made explicit , it is just the act of putting it in the daylight of reason. Not so according to the second (patently strange but still conceivable) answer. As we shall see, this is just the kind of answer a self-professed Hegelian (as Brandom) might like to put forward.

II There is no need to dig deep in order to find textual evidence that Brandom and Peregrin have rashly stuck to the first option. On many occasions provided by the mammoth volume of his major opus “Making it Explicit” (1994), Brandom was sufficiently clear on this point: “Semantic vocabulary is used merely as a convenient way of making explicit what is already implicit in the force or significance that attaches to the content of a speech act or attitude” (Brandom 1994, 82) “Logical vocabulary has the expressive role of making explicit – in the form of logically compound, assertible sentential contents – the implicit material commitments in virtue of which logically atomic sentences have the contents that they do … providing the expressive tools permitting us to endorse in what we say what before we could endorse only in what we did” (Brandom 1994, 402) “Logical vocabulary has been distinguished in this work by its expressive role in making explicit, as something that can be said, some constitutive feature of discursive practice that, before the introduction of that vocabulary, remained implicit in what is done” (Brandom 1994, 530)

Peregrin on the Logic of Inference

21

Plainly, the quoted passages show the consistent attitude to view explicitation as a process which lays bare something that was already there, or was present before the analytical intrusion of semantic vocabulary. Furthermore, in “What is the logic of inference?” (2008) Peregrin rigidly adopts the same (apparently natural) strategy: “… logical vocabulary appears as a means of ‘internalizing the meta’. It allows us to say within a language what can otherwise be said only about the language - i.e. within a metalanguage ... The logic of inference is the logic of operators the principal purpose of which is making inference explicit” (Peregrin 2008, 269-271) “… an inferential structure is standard [i.e. defines a structural relation of inferrability] iff it is embeddable into a Boolean algebra. This indicates that there is a sense in which elements of a standard inferential structure do implicitly have their conjunctions, disjunctions etc. although they do not have them explicitly” (Peregrin 2008, 290-291)

In order to appreciate these claims in their full extent, it seems appropriate to examine Peregrin’s “inferentially native” operators, by means of which the procedure of “internalizing the meta” (i.e. of making it explicit) is accomplished. To this end, let us consider the following table (Table 2-1) which shows the inferential roles of these operators: Operator deductor amalgamator explosion-detector

Introduction rule

Elimination rule

A՗Bҧ

AէBҧ

X, A, B, Y ՗ C ҧ

X, AՌB, Y ՗ C ҧ

X, B ՗՚ ҧ

X ՗ ӅB ҧ

AէB

X, AՌB, Y ՗ C X ՗ ӅB

A՗B

X, A, B, Y ՗ C X, B ՗՚

Table 2-1: Inferentially native operators The functions of these operators are obvious: (a) The deductor captures on the object-language level the meta-theoretical fact that one formula (B) is derivable from another formula (A); (b) The amalgamator expresses the metalinguistic operation of composition which produces a new formula (AՌB) for any given formulas (A and B) such that in any context the inferential role of AՌB is the same as the composition of the inferential

Chapter Two

22

roles of its constituents; (c) The explosion-detector displays the metarelation of incompatibility that holds between any two formulas which are not simultaneously satisfiable. These operations have natural counterparts in many logical systems. The next table (Table 2-2) displays their impersonations in the context of classical and intuitionist logic and the corresponding algebraic structures: Operator

deductor amalgamator explosiondetector

Logical rendering: a. Classical Logic (CL) b. Intuitionistic Logic (IL) a. CL-implication b. IL-implication a. CL-conjunction b. IL-conjunction a. CL-negation b. IL-negation

Algebraic rendering: a. Boolean Algebra (BA) b. Heyting Algebra (HA) a. Relative complement of BA b. Relative pseudocomplement of HA a. Meet of BA b. Meet of HA a. Complement of BA b. Pseudo-complement of HA

Table 2-2: The native operators in logical and algebraic rendering Thus everything that was said so far receives a straightforward verification: the logical operations (implication, conjunction, negation, etc.) are “over there”, in the algebraic semantics which is intended as the standard model of the formal language. So, in some sense they already “exist” before the corresponding logical constants are introduced in the regimented languages of classical and intuitionistic logic. But is this really the case? As we shall see in a moment, the voice of one of the “mighty dead” says loudly and clearly: No, it isn’t.

III Brandom has built the genealogy of his inferentialist approach around the names of several mythological figures, which he calls “the mighty dead”. As the following passage shows, one of them is the venerable Georg Wilhelm Friedrich Hegel: “… rationalist expressivism understands the explicit – the thinkable, the sayable, the form something must be in to count as having been expressed in terms of its role in inference. I take Hegel to have introduced this idea ...

Peregrin on the Logic of Inference

23

this rationalist expressivist pragmatism forges a link between logic and self-consciousness, in the sense of making explicit the implicit background against which alone anything can be made explicit, that is recognizably Hegelian” (Brandom 2000, 35)

Some commentators find that this self-professed Hegelianism is not conclusively verified by Brandom’s writings. Especially peremptory are Tom Rockmore’s critical remarks, according to which “Brandom always, or almost always, reads Hegel through the positions of leading analytic philosophers, in practice Quine and Sellars, and never, or almost never, reads Hegel directly … Brandom’s Hegelian inferentialism is not basically similar but rather basically dissimilar to, and incompatible with, Hegel's view” (Rockmore 2002, 434, 445). By the way, our initial question provides an apt occasion to observe the divergence between Hegel’s and Brandom’s views. In fact, Hegel suggests forcefully that the right answer is not (a) but (b). Wallace’s commentary to his translation of Hegel’s Logic leaves no place for reasonable doubt on this point: “That is an sich (implicit; natural; in, at, or by self) which is given in germ, but undeveloped ...That is für sich (explicit; actual; for self) which is actual ... the result of an sich when developed” (Wallace 1873, clxxvi) “Determinate being or somewhat is an sich somewhat else; and the process of determinate being is to lay it down or express it as such. When this explicitly-stated ‘other’ or limit is included in the Being, and reduced into a unity with somewhat in each (Being-for-self), it is said to be ‘aufgehoben’ ” (Wallace 1873, clx) “the seed is ‘aufgehoben’ in the plant which grows from it: it has perished and disappeared as a seed; but it is transfigured and retained in the existence of the plant” (Wallace 1873, clxxviii)

It is plain, that for Hegel the paradigm case of “making it explicit” is the germination of the seed: in this way what is implicit (the possibilities for development nested in the seed) becomes explicit (in the fully-grown plant). It is evident that in this case what we have in the beginning differs in content from what is produced in the end. Indeed, the text adduced above indicates that according to Hegel the process of explicitation can be rendered as a case of sublation (“Aufhebung”), as a procedure by means of which the implicit (“an sich”) is “aufgehoben” in the explicit (“für sich”). But, as far as in Hegel’s dialectical logic sublation is a paradigmatic content-infusing operation, it becomes evident that the implicit and the explicit stages in the development of logical form are not contentually

24

Chapter Two

identical. Then, if we stick to the reading according to which Hegel’s “rationalist expressivist pragmatism” is a prototype of Brandom’s inferentialism, it becomes unavoidable to admit that the purpose of the act of “making it explicit” is not just to make visible on the surface of language what was hidden in the depths of thought. As a matter of fact, it seems that some vestiges of this idea can be found in Brandom’s own writings: “Logic is the linguistic organ of semantic self-consciousness and selfcontrol. The expressive resources provided by logical vocabulary make it possible to criticize, control, and improve our concepts” (Brandom 1994, 384) “By providing the expressive tools permitting us to endorse in what we say what before we could endorse only in what we did, logic makes it possible for the development of the concepts by which we conceive our world” (Brandom 1994, 402)

It is clear that if the process of explicitation paves the way for improvement and development of our concepts, then the content which was made explicit cannot coincide with its implicit counterpart. To make explicit does not mean “to disclose what was hidden”. Something more is accomplished by the process of explicitation of logical form. “What?” and “How?” are the next natural questions to ask.

IV My principal proposal is to recruit the conceptual resources of situation semantics in order to clear away the mist, surrounding the process of explicitation. Initially, this may seem utterly inappropriate, insofar as situation semantics and inferentialist semantics are manifestly divergent approaches. While situation semantics stays within the limits of the objectivist paradigm by claiming that “meaning’s natural home is the world, for meaning arises out of the regular relations that hold among situations - bits of reality” (Barwise and Perry 1983, 16), inferentialism rests on the assumption that “the representational dimension of propositional content is conferred on thought and talk by the social dimension of the practice of giving and asking for reasons” (Brandom 1994, 496). But, as far as the design of situation semantics is to explain “situated inference”, or “the ability [of natural languages] to leave [inferentially relevant] parameters implicit in some circumstances, yet make them explicit in others” (Barwise 1989, 152), it seems possible to

Peregrin on the Logic of Inference

25

implement the mathematical tools developed by situation semantics in the exploration of inferential structures. Especially useful in this setting turn out to be CIAs (constraint infon algebras) introduced by Barwise and Etchemendy in “Information, infons, and inference" (1990) or, equivalently, the “perspectives" studied by Seligman in “Perspectives on situation theory" (1990). In the last part of this paper we shall deal with a toy-version of situated semantics, coached in the following list of definitions (following the model of Barwise and Etchemendy): Definition 1. By a situation we shall mean any part of the way the world happens to be.

After we have delimited some set of situations Sit (if the situation s belongs to the set Sit, we shall write s ∈ S) we can define a partial order թ on Sit (for any s1, s2 ∈ Sit, “s1 թ s2” shall mean “s1 is a part of s2”). Therefore, the members of the class of թ-maximal elements shall be called “worlds”. In other words, worlds are just a special type of situations, those who end the line of containment. Definition 2. By an infon we shall mean a piece of information about a particular situation.

To any s ∈ Sit we can juxtapose a set Σ of infons (just as above, if the infon σ belongs to the set Σ, we shall write σ ∈ Σ). Obviously, there shall be a transitive relation ҧ on Σ (for any σ1, σ2 ∈Σ, “σ1 ҧ σ2” means “the information carried by σ1 involves the information carried by σ2”). For example, the information “This apple is green” (i.e. the infon σ1) involves the information “This apple is not red” (i.e. the infon σ2), therefore we have σ1 ҧ σ2. Moreover, the above semantics forces the existence of a minimal element 0 (such that 0 ҧ σ, for any σ ∈ Σ) and a maximal element 1 (such that σ ҧ 1, for any σ ∈ Σ) for any sufficiently rich set of infons Σ. Furthermore, the following operations, defined by means of the relation “involves”, characterize the set of infons as Heyting algebra: • • • •

meet (“∨”): σ1 ҧ σ1 ∨ σ2 and σ2 ҧ σ1 ∨ σ2 join (“∧”): σ1 ∧ σ2 ҧ σ1 and σ1 ∧ σ2 ҧ σ2 relative pseudo-complement (“ →”): σ1 ∧ [σ1 → σ2] ҧ σ2 pseudo-complement (“ ¬”): ¬σ = σ → 0

Chapter Two

26

After we have determined the algebraic structures of Sit and Σ, we shall introduce the crucial notion of “support relation”: Definition 3. By a support relation we shall mean any relation ՝ ⊆ Sit × Σ such that:

• • • •

if s ՝ σ1 and σ1 ҧ σ2, then s ՝ σ2 for all s, s ՝ 1 and s բ 0 if s ՝ σ1 ∧ σ2, then s ՝ σ1 and s ՝ σ2 if s ՝ σ1 or s ՝ σ2, then s ՝ σ1 ∨ σ2

If s supports σ, then we can also say that σ is “true” of s, or that the situation “realizes” the particular piece of information. By means of ՝ we can single out a subset Sσ ⊆ Sit (the “support of σ”) for every infon σ: Sσ = {s ⏐ s ՝ σ}. On the other hand, support relations induce a natural ordering Ն on Sit: s1 Ն s2 (“s1 is contained in s2”) if and only if for every σ, if s1 ՝ σ then s2 ՝ σ. Finally, support relations give rise to another important entity: propositions. Definition 4. By a proposition p = (s : σ) we shall mean a set of support relations such that s ՝ σ; accordingly, the set of propositions Prop is a set of sets of support relations.

Propositions are systematically related to each other just as situations and infons are and the science of logic is built upon the realization of this simple fact. But, although the set of infons, conceived algebraically, gives rise to a Heyting algebra, the set of propositions carries a different algebraic structure – it turns out to be a Boolean algebra. The notion introduced by the following definition shows us why: Definition 5. By a constraint we shall mean the fact that a situation can carry information about other situations.

One important variety of constraints are “positive constraints”: we shall say that (s1 : σ1) “involves” or “constrains positively” (s2 : σ2), in symbols “(s1 : σ1) ՗ (s2 : σ2)”, if the fact that s1 supports σ1 entails the fact that s2 supports σ2. Obviously, the newly introduced relation “՗” is an order on the set Prop. Therefore, the properties of Prop can be extracted by means of the algebraic structure, definable through “՗”:

Peregrin on the Logic of Inference

27

• We can single minimal (0)and maximal (1) ՗-elements as before. • We can introduce a meet (“∨”):The proposition (s1 : σ1) is a meet of (s2 : σ2) and (s3 : σ3) if and only if they both involve it and any proposition (s4 : σ4) with the same property is involved by (s1 : σ1). • We can introduce a join (“∧”): The proposition (s1 : σ1) is a join of (s2 : σ2) and (s3 : σ3) if and only if they are both involved by it and any proposition (s4 : σ4) with the same property involves (s1 : σ1). • We can introduce a complement (“¬”): The proposition (s1 : σ1) is a complement of (s2 : σ2) if (s1 : σ1) ∨ (s2 : σ2) = 1 and (s1 : σ1) ∧ (s2 : σ2) = 0. Now it should be clear that although the set of infons has the structure of Heyting algebra, the set of propositions that is build over it can be extended to a (complete) Boolean algebra. Barwise and Etchemendy readily acknowledge this fact: “General considerations having to do with inference led us to a wellknown class of algebraic structures: distributive lattices ... all our models of infons turn out to be distributive lattices ... they turn out to be something more: complete distributive lattices (and hence Heyting algebras) ... However they are definitely not Boolean algebras ... We recall, however, that in situation theory there is a big difference between a piece of information [infon] and a proposition ... each infon algebra gives rise to a natural collection of propositions [constraint algebra] with a Boolean structure ... The basic idea is that given any situation s and an infon σ there should be two basic propositions: the proposition that s supports [realizes] σ, and its denial, the proposition that s does not support σ ... One of these should be true, the other false. That is, these two propositions should be propositional complements of one another in the classical sense" (Barwise and Etchemendy 1990, 36)

V I now come to the substantial part of the paper: the juxtaposition of inferentialism and situation semantics. Our analysis above came to the notion of constraint which captures the fact that propositions are linked together by the fact that some situations can carry information about other situations: if, for example, the present situation realizes the claim “Today is Monday”, then there is a future situation which realizes the claim “Yesterday was Monday”. Thus the proposition “Today is Monday” implies the proposition “Tomorrow it will be true that “Yesterday was Monday”” (in virtue of the informational bonds, linking present and future

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situations). This very fact is captured by one of the fundamental notions of inferentialism: the notion of “material inference”. “Material” are precisely the inferences whose correctness is not guaranteed by logical form, but by the respective (informational) contents of the premises (Brandom 1994, 97-98). Therefore, what Brandom calls “the implicit logic of material inferences” is precisely what Barwise construes as “constraint algebra”. Furthermore, there is a natural way to render the process of “making it explicit” in the setting of situation semantics: this is precisely the switching from constraint algebra to infon algebra. In order to effect such a transition, we have to analyze the structure of propositions and determine their constituents (the situation s, the infon σ, and the support relation ՝). Thus we lay bare the internal structure which is responsible for the validity of the material inference, we “make explicit” its logical form. What we gained thus far can be presented in the following table (Table 2-3): Inferentialism Material inferences

Situation semantics Constraint algebra

Ҩ making it explicit Formal inferences

Ҩ analysis Infon algebra

Table 2-3: Inferentialism vs. Situation semantics As we already noted, constraint algebra is essentially different from infon algebra. Therefore, the constraint-driven implicit logic of material inference does not coincide with the infon-driven explicit logic of formal inference. Indeed, in this case the first one is classical, while the second one is intuitionist which makes manifest that, at least according to the present reconstruction, the process of “making it explicit” does affect the conceptual contents of the inferential practices, which is completely congenial with Hegel’s answer of our initial question. We could even speculate over the reasons why this is the case. It may be argued that when we reason in our everyday life, we unwittingly presuppose that every claim is true or false. This simplifies the practically employed inferential patterns and forces us to accept the classically valid law of excluded middle. But when we try to build a formalized model of our everyday reasoning procedures, we replace truth with provability. Then, because of the inherent incompleteness of our formal systems, the claim that every proposition is provable or disprovable fails and we get intuitionist logic, where the law of excluded middle is not valid. Therefore, by means of

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29

“explicitation” we transform classical logic (Boolean algebra) into intuitionist logic (Heyting algebra).

VI We saw that “situated inferentialism” gives a completely different rendering of the process of explicitation which is much closer to Hegelian dialectics than Brandom’s original approach1. Therefore, the future collaboration between inferentialism and situation semantics seems bound to be fruitful. On the one hand, as far as inference is a paradigmatic case of information-processing technique, inferentialist semantics can be naturally implemented in the formal framework developed in Barwise and Seligman's “Information flow: the logic of distributed systems" (1997). In this setting, we can easily simulate the complex behaviour arising from the interplay of intersubjectively acknowledged commitments and entitlements, studied in Brandom’s “Making it explicit” (1994). Moreover, it would be utterly interesting to compare the formal system developed in this way, with Peregrin’s reconstruction, presented in “What is the logic of inference?”. On the other hand, as far as in situation-theoretic semantics the concept of object is not primitive, we have to show how objects emerge through the flow of information across situations. Brandom’s inferentialism is particularly apt for such task, because it strives to show that representational (object-related) features of linguistic discourse stem from its inferential (information-processing) features.

 1

As is well known, in the Hegelian rendering of the process of explicitation is boosted by contradiction: conceptual articulation is nothing more but deployment of inherent inconsistencies. Therefore, the question of the status of true contradictions in the context of Hegelian dialectics and their possible relevance for the inferentialist program seems to be crucial, although it remains completely neglected both in the present article and in mainstream inferentialism as far as both Brandom and Peregrin seem to accept the law of non-contradiction as unconditionally valid. In my opinion, relevant logic may prove its relevance in the present context, because its models include the so-called “impossible worlds” whose characteristic property is that they can render as true propositions of the form „p ∧¬p” (see Angelova 2010). This paves the way for a completely different approach to explicitation which does not presuppose the incompatibility relation as basic (Brandom) or the explosivity of the classically conceived relation of consequence (Peregrin).

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References Angelova, Doroteya. 2010. “Logical and Epistemological Significance of Inconsistent and Incomplete Worlds and Their Applications.” In: Logica Yearbook’09, edited by Michal Peliš, 3-15. London: College Publications. Barwise, Jon. 1993. “Constraints, Channels and the Flow of Information.” In Situation Theory and Its Applications, vol. III, edited by Peter Aczel, David Israel, Yasuhiro Katagiri, and Stanley Peters, 3-28. Stanford: CSLI Publications. Barwise, Jon. 1989. The situation in logic. Stanford: CSLI Publications. Barwise, Jon, and John Etchemendy. 1990. “Information, Infons, and Inference.” In Situation Theory and Its Applications, vol. I, edited by Robin Cooper, Kuniaki Mukai, and John Perry, 33-78. Stanford: CSLI Publications. Barwise, Jon and John Perry. 1983. Situations and Attitudes. Cambridge, MA: MIT Press. Brandom, Robert. 2000. Articulating Reason. Cambridge, MA: Harvard University Press. —. 1994. Making it Explicit. Cambridge, MA: Harvard University Press. Peregrin, Jaroslav. 2008. “What is the Logic of Inference?” Studia Logica 88: 263-294. Rockmore, Tom. 2002. “Brandom, Hegel and Inferentialism.” International Journal of Philosophical Studies 10: 429-447. Seligman, Jerry. 1990. “Perspectives on Situation Theory.” In Situation Theory and Its Applications, vol. I, edited by Peter Aczel, David Israel, Yasuhiro Katagiri, and Stanley Peters, 147-192. Stanford: CSLI Publications. Wallace, William. 1873. The Logic of Hegel. Oxford: Clarendon Press.

CHAPTER THREE THE PURSUIT OF PRESCRIPTIVE MEANING VLADIMÍR SVOBODA

Over the last 100 years of the development of analytic philosophy we have learned much about the nature of (linguistic) meaning. A large part of what we have learned is negative - we have come to know what meaning is not. But we have also gained a loose idea of what the nature of meaning (if we allow this somewhat controversial term) could be. The philosophical views that have substantially influenced the shape of the present debates concerning this issue include those of Wittgenstein, Quine, Sellars, Dummett and Davidson. Currently the conception developed by Brandom under the label inferentialism (and advanced in some respects by Peregrin, Lance and others) seems to offer the most promising way to further elucidate the notoriously tricky concept of meaning. In this paper I would like to present some ideas that aim at the emendation of the inferentialist paradigm. I don’t want to challenge the central tenets of inferentialism, I only want to suggest that the notion of inference adopted by Brandom and his followers is somewhat too narrow to allow for a comprehensive and fully adequate exposition of linguistic meaning. In the first part of the paper, I will turn my attention to the substantial role that prescriptive language plays within the totality of our linguistic practices. I will argue that the traditional inferentialist picture of our apprehension of meaning is not fully adequate, as it puts too much weight on assertoric discourse. Subsequently, I will outline some problems concerning the elucidation of meaning of some expressions employed within prescriptive discourse and point out some problems concerning scorekeeping in prescriptive language games. I believe that the inferentialist conviction that understanding language is closely connected with our ability to keep track of the statuses of one's fellow speakers provides the best starting point for the elucidation of meaning within prescriptive discourse. Most of the work in this area is, however, yet to be done.

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I The means of prescriptive language plays a crucial role in our linguistic practices. This claim may seem bold and difficult to substantiate. Its proper substantiation would require complex empirical research, and even then, such research might not be able to conclusively prove the claim. As I am incapable of offering a suitable empirical substantiation, I will instead be depending on some fundamental intuitions and memories of the reader. But first, as an auxiliary means of convincing her/him, I will use an argument from authority: I will refer those who have a tendency to neglect prescriptive language to the philosopher who introduced the crucial notion of a language game into philosophical debates – Ludwig Wittgenstein. When we read his Philosophical Investigations we can hardly overlook the fact that the very concept of a language game is introduced by examples that employ prescriptive rather than descriptive language (recall the Slab! language game).1 To illustrate the import of the prescriptive component in the rudimentary ontogenetically important language games, I will describe a game I used to play with my son Tonda when he was about eighteen months old. Me: “Tonda! Come here!” Tonda comes. Me: “Where is your bib? Bring it please!” Tonda finds his bib, brings it and gives it to me saying: “BIB.” Me: “THANKS. Sit down on the chair! ” Tonda, with my assistance, sits down. Me: “Look at the yummy yummy pudding I have for you! Open your mouth!” Tonda opens his mouth and I give him a spoon of pudding. He eats. Me: “Well, is it good? Do you want more?” Tonda: “MO.” I continue feeding him with the spoon. Tonda tries to catch the spoon himself. Me: “Leave the spoon! YOU MAY PLAY WITH THIS.” I give him a plastic ring. Tonda is not interested and tries to spin his pudding bowl. Me: “Don’t play with the bowl!” Tonda: “MO.”

The games generally lasted much longer and this particular one is a better example in that he liked the food. The type in the above text looks

 1

Wittgenstein (1953), §. 2.

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somewhat odd because the sentences from different compartments of our language are distinguished by different fonts: prescriptions are written in italics,2 questions in Arial and, finally, Courier is used for expressions whose status is not clear–they may be assertions (the "Mo" can stand for “I want more” or “I am ready to eat more”), prescriptions (“Give me more!”) or something in between (such as “You may give me more”). I reserved bold letters for assertions, but you can see that the record does not contain any sentences in bold–we did not assert much during these 'feeding' games. I present the above “record” or scenario in order to illustrate two observations: The first is that communication with small children is often dominated by prescriptions and questions. The second is that we often need not (or even cannot) classify moves in language games as belonging to one or another category (neither to descriptive nor to prescriptive discourse). This especially concerns the utterances of small children, but the status of some of the commonly used expressions of “adult” language can be unclear as well: the sentence “You may play with this” is grammatically indicative and can be used to state a (normative) fact, but it is also naturally taken as expressing permission and so belonging to prescriptive discourse. (Later, in fact, I will be treating permissions as prescriptions.) The question I want to raise is: Was the communication with Tonda during his feeding a productive component of the process of his learning language? Or, more specifically: Could the communication help Tonda to grasp some propositional contents? If we take the traditional inferentialist framework extremely strictly, we could conclude that it must have been idle or nearly idle from this perspective. The communication does not include any assertions which are the central items of the game of giving and asking for reasons. Prescriptions do not enter the game (at least, not as it is traditionally conceived). They are not bound by inferential relations– inference, as it is classically conceived, is a relation that is supposed to preserve truth, and neither prescriptions nor questions can be reasonably equipped with truth values. But this negative answer to the question–namely, the claim that the game could not substantially contribute to Tonda’s progress in understanding contents conveyed through language games – is, in my view, clearly inadequate. I am quite certain that Tonda could acquire a partial understanding of language (naturally only a very small one) from

 2

In games like this, it is probably not adequate to distinguish commands, requests, pieces of advice, etc.

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the communication and that the small step into the realm of meanings he made during our exchange was not less important than the steps he used to make during assertoric language games. If I am right, this suggests that either we should give up the thesis that meaning is closely bound with inferential roles or we should conceive the term “inference” more broadly than as a name of a relation between expressions that (typically) have the pragmatic significance of assertions. I am opting for the second option. I would like to stress that I don’t believe that we should view different discourses within our everyday linguistic practices as separated or separable (and I don’t want to suggest that Brandom and other inferentialists necessarily view them in this way). The discourses are naturally intertwined and attempts to distinguish them often have rather limited theoretical rationalization. Generally, we can say that a comprehensive theory of language must give an account of the totality of the communicative practices. In theorizing, however, it may be useful to distinguish the particular kinds of discourse. If we adopt the distinguishing approach (which, as it seems, Brandom implicitly adopts by reserving the crucial role for assertions) we may raise a general question: Q1: Could a person get the full grasp on meaning of natural language expressions just by taking part in assertive (descriptive) language games?

The question is far from clear and, if it can be answered at all, it would have to be backed by some rather complex (and probably somewhat dubious) empirical research. Without such research at our disposal, we may only formulate a conjecture: CON1: A full grasp of natural language cannot be acquired just by taking part in assertive language games. The meanings characteristic of prescriptive language expressions (prescriptive contents) are an important component of the realm of meanings and thus any knowledge of language acquired solely within the assertoric discourse would be incomplete.

This conjecture may seem to be rather obviously true, but it might still be the case that only assertive language games open the realm of propositional contents for us – meanings in a narrow sense. So we should perhaps ask different questions: Q2: Could a person grasp meanings (taken as propositional contents) just by taking part in assertive language games?

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and Q3: Could a person grasp meanings just by taking part in non-assertive language games?

Similarly to before, any answer we can formulate straight away will necessarily be only speculative. Such speculations, however, seem to suggest that there is no significant reason to give a positive answer to Q2 rather than to Q3.3 Consider another record of a communication between me and Tonda: Me: “Tonda! Pass me the ball!” Tonda passes me a plastic egg. Me: “Don’t give me the egg, give me the ball!” Tonda passes me the ball. Me: “THANKS!” Tonda points to a pile of toys and says: “BOX!” Me: “Do you want me to pass you a box?” Tonda: “BOX!” Me, pointing to two boxes: “The big box or the small one?” Tonda: “BIG BOX!” I pass him the box, he takes it and puts the box on top of another box.

I am rather sure that Tonda had a chance to learn something concerning language use–for example, how to use (and not to use) the word “ball” (and “egg”) and how to use the phrase “big box.” So I would claim that he had a chance to learn (or at least to take a small step towards learning) something that deserves to be called “propositional content.” One could probably argue that all this possible import of the nondescriptive language is just illusory and that the game could have its “learning effects” just because the communication, in fact, contained a significant portion of hidden assertive communication. But such a claim is strange. It suggests that the communication in reality was only a covert

 3

Brandom would probably disagree: “Interpreting the members of a community as engaging in specifically discursive practices, according to the view put forward here, is interpreting them as engaging in social practices that include treating some performances as having the pragmatic significance of assertions. ..... Since all other varieties of propositional contentfulness derive (substitutionally) from the propositional, this is to say that the application of concepts is a linguistic affair [...] in the sense that one must be a player of the essentially linguistic game of giving and asking for reasons in order to be able to do it.” (Brandom 1994, xxi). Brandom's position is not entirely clear, but what he says suggests that concepts are wedded with assertions (but not with other kinds of speech acts).

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version of a 'proper' linguistic exchange whose import could be brought to light by a suitable paraphrase like: Me: “Tonda, there is a ball over there. Pass me the ball!” Tonda passes me a plastic egg. Me: “This is an egg, this is not the ball. Give me the ball!” Tonda passes me the ball. Me: “Yes, this is the ball. THANKS.” Tonda points to a box and says: “Over there is a box. Give it to me!” Me: “There are two boxes here, a big one and a small one. Do you want me to pass you the big box or the small one?” Tonda: “I want the big one.”

In this paraphrase, most of the sentences are assertions and this might explain how the original language game could be (parasitically) a productive event in the process of Tonda’s acquisition of meanings. For me, such a way of looking at language is hard to swallow. I do not want to deny that the paraphrase is a more or less adequate transcription of what happened during the communication and that it manifestly spells out some assumptions that were implicit in the original version. I do not think, however, that games like the original language game should be seen, in some sense, as being secondary with respect to the latter kind of games. If they were, it would mean that while, for children, assertive games open the gateway to linguistic contents, the games of prescribing and asking perform, at most, a subsidiary role. But this is rather obviously not the case. We can learn the same lesson about the correct use of the words “box” and “ball” (for example, that they are not synonymous but incompatible) from “Don’t pass me the box, pass me the ball!” as from “This is not a ball, this is a box.” Thus, I think that if we see the inference (or inference rule): J1

This is a ball This is a round thing

as an explicit manifestation of a piece of content of the word “ball,” we should similarly see the inference (or inference rule): J2

Do not pass me a round thing! Do not pass me a ball!

as a manifestation of the same (or similar) piece of content. This, in my view, holds true in spite of the fact that, in the second case, we obviously

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cannot speak about inference in the sense of a truth-preserving relation. If I am right, then we should conclude that the concept of inference is not bound so much to the concept of truth but instead to the concept of (in)compatibility which, however, needs to be conceived more broadly than usual. This conclusion is certainly not at odds with the inferentialist picture (we should remember that Brandom allows for speaking about such unaccustomed things as material inferences), but it is still controversial. The concept of incompatibility calls for a further explication, but to rely on it seems quite natural. The claims: “This is a ball” and “This is not a round thing” (fixed in the same context, i.e. pronounced together pointing to the same objects) generate incompatible commitments. And the same holds true about the pair of prescriptions “Pass me a ball!” and “Don’t pass me anything round!” Though the person issuing commands (prescriptions) is not directly susceptible to the “traditional” game of giving and asking for reasons, she/he is susceptible to the rules of a similar game. To be considered as a competent speaker, one has to respect the inferential relations of issued prescriptions including their material adequacy (for example, one should not command “Pass me the red ball!” in a situation when no red ball is around.) To summarize–the use of words and phrases (and to some extent grammatical constructions) is governed by implicit rules that should not be associated with just one particular discourse (namely the assertoric one). They should be seen as transcending discourses and contexts. If we wished to formulate a slogan that could epitomize the importance of prescriptive discourse we could say: SLOG Language is not primarily a tool by which we make others believe something but a tool by which we make others do something.

Perhaps this slogan should not be taken too seriously as it oversimplifies things. But I believe that it contains a significant point. It is, nevertheless, important to keep in mind that stressing the import of nonassertive language is not at odds with admitting that concentrating on assertoric discourse and traditionally conceived inference rules can, normally, be more convenient for theoretical purposes. We, however, should not overlook the fact that non-assertoric discourse is more practical in the sense that mutual understanding is immediately and practically tested–the language-entry and language-exit moves are typically manifestly observable. Put briefly: if I say to my son “There is a red ball on the table,” it may or may not be true and he may or may not grasp what I mean, feedback being typically unstraightforward.

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But if I say to him “Pass me the red ball from the table!”, he is forced to confirm whether what I say makes sense and I can immediately see whether he grasped what I meant. And we should bear in mind that: „Understanding can be understood, not as the turning on of a Cartesian light, but as practical mastery of a certain kind of inferentially articulated doing, responding differentially according to the circumstances of proper application of a concept, and distinguishing the proper inferential consequences of such application.” (Brandom 1994, 120)

If my previous considerations are not misconceived then the inferentialist doctrine should, in addition to inferential rules of the shape IR1

A B

where A and B are indicative sentences, accept also rules of the shape IR2

A! B!

where A! and B! are imperative sentences. But this is perhaps not enough. It seems that our understanding of a language is often based on (or at least can be reconstructed with the help of) rules of the shape IR3

A B!

Rules of this kind perhaps govern use (and meaning) of the basic value words like “good” or “correct.” It seems quite natural that inference rules like JF1 The action X is good. Do X! or JF2 It is correct to proceed in this way. Proceed in this way!

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capture a substantial part of what it means to appraise something as good or correct.4 If I am right, then the concept of an inferential rule commonly adopted in inferentialist treatises is in need of a rectification.

II Extending the concept of inferential rule in the way that I have suggested opens space for a proper inclusion of the linguistic means of prescribing into the inferentialist meaning theory. Of course, many principles applied within prescriptive discourse are closely bound with those applied within assertoric (or descriptive) discourse, but there are also some specific problems connected with the prescriptive use of language. Before turning our attention to them, we should perhaps begin with the basics. The general question to start with is: What kind of act are we performing when we issue a prescription? In my view, the answer could be roughly formulated in the following way: by making a prescriptive move in a language game we typically generate (or modify) a specific relation between us (the speaker or the authority) and the addressee of the prescription. We could call the relation, for example, the demandatory relation.5 Constitutive of the relation is the responsibility connected with the position of the authority of a demandatory relation. The authority issuing orders or permissions assumes a kind of responsibility for the addressee’s actions that are (to be) affected by the prescriptions. The addressee assumes a different kind of responsibility - responsibility for the consequences of his conforming and especially for his not conforming to the prescriptions.6 Thus, though prescriptive moves in language games are

 4

We might think that inferences like this subvert Hume’s well-known (or the isought) thesis, at least conceived in a certain sense (Cf., e.g., Hudson 1969). The thesis, however, will be subverted only if the gap between is and ought is viewed as a gap between sentences having indicative grammatical form and sentences having imperative form. If we conceive the distinction in another way, then the above rules do not bridge any gap. Evaluative sentences are often placed on the ought side of the gap. Cf. Hare (1952), Svoboda (1993). 5 The same kind of relationship can arise also in other ways, even without any speech acts. Agents, for example, often consciously or unconsciously use simple methods employing combinations of rewards and punishments. 6 If we approach the process of prescribing extremely schematically, we can distinguish successful language games and unsuccessful language games and for simplicity assume that the players basically cooperate while playing a game. For more about such assumptions and the concept of a successful prescriptive language game, see Svoboda (2003).

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not governed by the rules of the traditional version of the Sellarsian game of giving and asking for reasons, their role in communication is obviously governed by rules that concern the interface language–the world as well as rules concerning relations of linguistic items (events) to other linguistic items (events). My ambition here is not to examine the rules in any detail (though I believe that such an ambitious project is worth launching). I only want to indicate what kind of specific problems we have to face when considering prescriptive inferences. First, I will show some problems that concern inferential rules in a more-or-less traditional sense. Then I will try to suggest that, if we want to achieve a satisfactory account of meaning of items of the prescriptive language, we have to take into account the dynamics of prescriptive discourse. Let us start with two inferences: J3

Bring me the bib and sit down! Bring me the bib!

J4

Bring the box! Bring the box or the ball!

If we look at the inferences intuitively there is hardly any doubt that the first one is correct. We can even be bold and say that it is logically correct. If, however, we try to formulate the inferential rule that is exemplified in the inference, we might soon face difficulties. Two patterns seem available: JF3a A! ∧ B! A! and JF3b (A ∧ B)! A! At first glance, both patterns may look appropriate but, on closer inspection, we will see that the first pattern is problematic. If we take the symbol "∧" as representing propositional conjunction, then it is clear that the formula A! ∧ B! can be taken as meaningful only if we assume that expressions like A! are equipped with truth values. Though there are philosophers who are ready to speak about true or false imperatives or

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commands7 from an intuitive viewpoint, claiming that sentences (or utterances) like "Bring me the bib!" are true or false is quite bizarre. We could perhaps stick with the inferential rule and avoid the problem by substituting the symbol "∧" with a different kind of conjunction capable of connecting imperatives, or we can adopt the view that even in prescriptive discourse the only conjunction we really need is a conjunction connecting truth-bearers. The second approach leads to adopting JF3b as the adequate formalization of J3. More serious questions are connected with the inferential pattern J4. Is it intuitively valid? Or, more generally, should the following inferential pattern be adopted as a pattern that co-characterizes the behaviour of "or" in prescriptive discourse? JF4a A! (A ∨ B)! This issue is surprisingly controversial. On the one hand, most people8 consider this pattern intuitively valid. On the other hand, most native speakers feel uneasy about accepting that inferences like J5

Burn this letter! Burn this letter or send it to the police!

are correct.9 The problem is that, on the one hand, we tend to see the prescription (A ∨ B)! as a prescription that weakens the more specific prescription A! (or B!). But, on the other hand, it seems that this cannot be the case as the command "Burn this letter or send it to the police!" seems to offer the addressee a choice. Sending the letter to the police is legitimized by this choice offering command, while we certainly cannot say that any such action is legitimized by the command "Burn this letter!". Once again, we could suppose that the dilemma could be solved by saying that the inferential pattern JF4a is invalid while the inferential pattern JF4b A! A! ∨ B!

 7

Among those who don't mind attaching truth values to imperatives are, for example, Lewis (1979) or Walter (1996), though their reasons are quite different. 8 Or, more precisely, most of those who have are affected by logic to the extent that they can read the formulas. 9 In fact, inferences of this form have given rise to a persistent controversy in deontic logic known as the Ross paradox.

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is valid, as its conclusion represents the proper version of the weakening of the command in the premise. But this solution faces the problems of the interpretation of the connective "∨" that affected the interpretation of "∧" in JF3a. These simple examples show that though prescriptive discourse seems incorporable into the inferentialist theory of meaning, a number of potentially tricky problems arise within this discourse. I think that taking the problems seriously may result in a rectification of the whole inferentialist paradigm.

III In the last part of my paper, I would like to suggest that if we want to provide a comprehensive explication of meaning in the inferentialist manner, we need to take into account the dynamics of our language. The problems related to the dynamics of language are, in fact, closely connected with problems of scorekeeping in prescriptive language games. As a framework for addressing the scorekeeping problems we can employ a framework introduced by David Lewis. Lewis focused on the problems of linguistic games of this type in several papers. Here I adopt the version presented in his paper A problem about permission (Lewis 1979b). The game has three players: the Master, the Slave and the Kibitzer. Though the Kibitzer is an interesting figure, I will omit him in the examples of the game presented here. The denominations of the players as “the Master” and “the Slave” are surely vivid, but they may be somewhat misleading. They evoke a particular and extreme association in which one subject is under the complete control of the other. As I want to take into account not only cases when prescriptions are enjoined but also cases when their issuing and respecting is based solely on respect or a kind of common purpose shared by the players, I will switch from the loaded terms “The Master” and “The Slave” to a more neutral denomination of the players and use the terms “the Prescriber” and “the Doer” instead. The Prescriber’s moves in the game consist in issuing commands and permissions (to the Doer). The Doer’s moves consist in making what the Prescriber requires to be the case (or not). We can see the Prescriber’s moves–issued prescriptions–as shaping the space of freedom for the Doer. If we translate this to the possible world talk, we can say that those worlds in which the Doer’s actions conform to the Prescriber’s prescriptions (commands and permissions) form the sphere of permissibility (SP). The sphere can thus be identified with a set of possible worlds.

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Lewis suggests that the effect of a move consisting in issuing a command is not difficult to determine. Commanding shrinks the Doer’s sphere of permissibility. In the case of a series of commands, the SP evolves as the intersection of the set of worlds constituting the actual SP with the set of worlds that are permissible with respect to the newly issued command. EXAMPLE 1 1. Sit down on the chair! 2. Don’t play with the spoon! 3. Don’t play with the bowl! “S” stands for the Doer’s sitting. “P” stands for the Doer’s playing with the spoon. “B” stands for the Doer’s playing with the bowl. Now the following matrix depicts schematically how the SP evolves during the short game. S 1 1 1 1 0 0 0 0

P 1 1 0 0 1 1 0 0

B 1 0 1 0 1 0 1 0

0L 9 9 9 9 9 9 9 9

1 9 9 9 9 x x x x

2 x x 9 9 x x x x

3 x x x 9 x x x x

The first row of the matrix represents the set of worlds (situations) in which the Doer is sitting in the chair, playing with the spoon and with the bowl and similarly for the other rows. “x” marks the situations that are, by the Prescriber’s moves, placed outside of the sphere of permissibility, ”9” marks the situations that are left inside (or put inside by the prescriber’s moves). Assuming that the matrix depicts the development of the sphere of permissibility correctly, we can see that after the third move only the worlds that are characterized by the Doer’s sitting and not playing with either the spoon or the bowl are permissible (are within the SP). This is

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straightforward. In simple, common games like this, we normally have no problem keeping track of the score. Let us now briefly consider another example that includes another kind of Prescriber’s move–a permission. EXAMPLE 2 1. Sit down on the chair! 2. Don’t play with the bowl! 3. If you finish eating the pudding, you may play with the bowl! “F” stands for the Doer’s having finished eating the pudding. If we conceive this game intuitively, we have no problem determining how the SP should develop throughout the game. The development is depicted by the following matrix: S 1 1 1 1 0 0 0 0

B 1 1 0 0 1 1 0 0

F 1 0 1 0 1 0 1 0

0L 9 9 9 9 9 9 9 9

1 9 9 9 9 x x x x

2 x x 9 9 x x x x

3 9 x 9 9 x x x x

It is, nevertheless, surprisingly difficult to explicitly state rules that would yield the intuitive outcome and that would, moreover, be applicable (with an intuitively acceptable outcome) in other games in which permissions are used as the means of amending the normative situation (SP). This observation forms the core of the problem of permission pointed out by Lewis. But we should notice that even the language games consisting solely of commands evoke problems. Let us take one more very simple example of a game consisting of two commands: EXAMPLE 3 1. If you do not sit down, stay in the bedroom! 2. If you do not sit down, stay in the kitchen!

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How should we deal with this situation? What is the outcome of the acts of the speaker (authority)? It seems that we can adopt at least three different positions: a) The Prescriber that issued the two commands made an illegal move in the language game when issuing the second command, because the second is incompatible with the first. Thus, perhaps, the game should be conceived of as 'crippled' in some sense (as a game that leads to a blind alley). If this approach is adopted, it should be made clear how we can discern legal moves from illegal ones. It should also be made clear how the problematic second move affects the normative situation, namely commitments of the participants of the game. b) When issuing the second command the Prescriber implicitly abolished the first. So the game is all right and the resulting normative situation is the same as would have resulted from just issuing the second command alone. If this approach is adopted it should be made clear what the rules are of implicit derogation of previous moves. c) By issuing the second of the two commands in the sequence, the Prescriber neither “crippled” the game nor affected the validity of the first prescription – the moves simply result in the same situation as if he had issued the simple command “Sit down!”, as sitting down is for the Doer the only strategy that can keep him inside of the sphere of permissibility shaped by the two commands. As mentioned above, this paper is not intended as an attempt to deal with possible treatments of the problems concerning the kinematics of prescriptive language.10 I only want to point out some of the problems and show that they represent a challenge for the inferentialist account of language. We can hardly say that we have achieved a proper insight into the nature of meaning if we don't have a good theoretical grasp on what is going on in language games like those just outlined. The project of a theoretical reconstruction of the language games of all kinds (combining different kinds of moves – descriptive, prescriptive, interrogative and others) is, however, quite complex and is only in its infancy. Investigations aimed at the rules that govern the use of particular terms (within different kinds of contexts), as well as investigations focused on the structural and dynamic rules that are constitutive of specific discourses, constitute a rather substantial part of the vast philosophical enterprise aimed at understanding what meaning is. The purpose of this article was to suggest that the direction of these investigations should be

 10

An attempt to provide a solution to the problem can be found in ChildersSvoboda (1999 and 2002) and Svoboda (2003). A different solution is presented in Belzer (1985).

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rectified so that they devote more attention to non-assertoric discourses, in particular to prescriptive discourse. Though the inquiries are in many respects troublesome and call for adjustment of some well established starting points, I am convinced that a shift to a more open panorama of linguistic practices can substantially enrich the inferentialist paradigm.

Acknowledgments I am grateful to the Czech Science Foundation for support in preparing this paper with project n. P401/10/1279 and to Jaroslav Peregrin for helpful comments concerning previous versions of this paper.

References Belzer, Marvin. 1985. “Normative Kinematics (I): A Solution to a Problem about Permission.” Law and Philosophy 4: 257-287. Brandom, Robert. 1994. Making It Explicit. Cambridge, MA: Harvard University Press. —. 2008. Between Saying and Doing. Cambridge, MA: Harvard University Press. Childers, Timothy and Vladimir Svoboda. 2002. “On the Dynamics of Prescriptions.” In Meaning: The Dynamic Turn, edited by Jaroslav Peregrin, 185-199. Amsterdam: Elsevier. Hudson, William Donald. 1969. The Is-Ought Question. London: Macmillan. Hume, David. 1978. A Treatise of Human Nature. Oxford: Clarendon Press. Lewis, David. 1979a. “Scorekeeping in a Language Game.” Journal of Philosophical Logic 8: 339-359. —. 1979b. “A Problem about Permission.” In Essays in Honour of Jaakko Hintikka, edited by Esa Saarinen, Risto Hilpinen, Ilkka Niiniluoto and Merrill Provence Hintikka, 163-175. Dordrecht: Reidel. Svoboda, Vladimir. 1993. “Hume's Thesis and Modern Logic.” In Logica Yearbook’92, edited by Vladimir Svoboda, 95-109. Praha: FÚ ýSAV. Svoboda, Vladimir. 2003. “Modeling Prescriptive Discourse.” The Journal of Models and Modeling 1(1): 23-46. Walter, Robert. 1996. “Jörgensen's Dilemma and How to Face It.” Ratio Juris 9(2): 168-171. Wittgenstein, Ludwig. 1953. Philosophical Investigations. Oxford: Blackwell.



CHAPTER FOUR PEJORATIVES AND CONCEPTUAL TRUTH NENAD MIŠýEVIû

The paper discusses Brandom’s view of pejoratives from the wider perspective of theory of concepts and conceptual knowledge. It derives and explores the consequences of Brandom’s theses, in particular the thesis that there are pejorative concepts and that they refer to the same items as their neutral counterparts Such concepts involve materially false (incorrect) components (inference rules or propositions). The largest part of the paper derives and defends the consequence that propositions and inferences analyzing these concepts are neither necessarily true, nor correct, not a priori knowable. This finely dovetails with similar explanations of false concepts of natural kinds, along the lines of Putnam and Burge. Conceptual norms are analogously liable to being (externally) incorrect, although concept-constitutive. The last part of the paper, in contrast, criticizes the third, inferentialist thesis according to which pejorative concepts, like all other concepts, are grounded in inferences. It attempts to show that all the phenomena discussed in the first part can be better accounted for by a representationalist view of concepts.

Introduction Making It Explicit is a wonderfully rich book. In this paper I am trying to resist this temptation, and to focus upon one very narrow topic, hoping to derive from it some general philosophical morals.1 Namely, Brandom

 1

A brief pre-history of the paper. My acquaintance with Brandom’s monumental work started four years ago, on a fine day in Evanston at the bookstore, when my host, Professor M. Williams gave me as a present a copy of Making It Explicit, urging me to read it and write a comment. The copy that was sitting in my bag, almost got stolen on a train, but luckily for both the thief and for me, it survived,



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introduces his highly original account of both method of philosophy and of basics for a semantics using the example of derogatory predicates or pejoratives, more particular, unjustified pejoratives, like for instance “Boche” or “nigger”, used for slurs (and in the sequel by “pejoratives” shall be meant only unjustified ones). His decision is wise, since such pejoratives seem to be a semantical gold-mine. He digs along the lines proposed by M. Dummett in a very brief but quite inspiring paragraph in his book on Frege (1993, 454-5), and comes back with some genuine gold, at least to my lights. This paper attempts a further dig, focusing upon the links connecting Brandom’s proposal about pejoratives with a wider view on concepts. Initially the dig follows Brandom’s line, but at some it point veers in a slightly different direction, representationalist instead of inferentialist. Let me explain. The paper naturally starts from a point of agreement. The second section details Brandom’s diagnosis. According to Dummett and Brandom, the serious use of a pejorative, for instance of “Boche” for a German licenses the inference from “Hans is a Boche” to “Hans is cruel”. Brandom’s diagnosis is that (unjustified) pejoratives involve “materially false inference rules”, like the ones that take the thinker from one’s being German to one’s being Boche to one’s being cruel. These rules and materially (and not only politically) incorrect inferences are part of the sense of the pejorative expression. The importance of Brandom’s diagnosis lies in the fact that pejoratives can be used as a testing ground for theories of predicate senses, i.e. of concepts. So the next (third) section of the paper sympathetically discusses his view that pejoratives stand for concepts full of materially false conceptual garbage (it is not true that all Germans are cruel and compares it favorably to its rivals. The next section, fourth, then points out that the view rightly subverts the traditional picture according to which concept-analyzing (“analytical”) propositions or rules are necessarily true. Brandom’s idea is further generalized to incorrect non-empty concepts of natural kinds (FISH-WHALE). An important epistemological consequence follows: being concept-constitutive does not

 and ended up being all underlined and covered with my remarks. Later, Professor Boros generously invited me to his Brandom conference, and I had the luck to present my queries and worries to Professor Brandom, who had the patience and kindness to reply to them in detail. I thank them all, as well as Professor T. Williamson, who discussed with me the sketch of the first version of the paper, and Professor James Cargile who discussed with me his view of pejoratives and conceptual truth. Finally, I presented a version of the paper at Sofia conference, thanks to Lilia Gurova. The remarks on illocutionary and perlocutionary force owe their origin to conversations with A. Smokrovic.



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entail being a priori knowable (or even a priori justified). Another important and welcome byproduct of the analysis is that some conceptual norms can turn out to be de facto incorrect about their target concept, although in a sense constitutive of it. The fifth section is dedicated to a disagreement with Brandom. He takes inferential rules to be basic for and constitutive of the concept. I argue for the opposite, more representationalist and theory-based view: the owner of the pejorative concept accepts a definition and thereby a mini-theory about the intended referent, and conceptual norms follow from requirements on such theories. At each step questions are raised for Brandom.

Materially false inferences Let me briefly present Brandom’s basic idea on pejoratives. It is contained in the sub-section of Making It Explicit, with the longish title, “Non logical concepts can incorporate materially bad inferences”, to which the reference will be made throughout the present paper.2 Three decades ago, Dummett has introduced the example of the pejorative “Boche” and described its use in the following terms: “The condition for applying the term to someone is that he is of German nationality; the consequences of its application are that he is barbarous and more prone to cruelty than other Europeans. We should envisage the connections in both directions as sufficiently tight as to be involved in the very meaning of the word: neither could be severed without altering its meaning.” (Dummett 1973, 456). Brandom distances himself from the view about the inappropriateness of the use of some pejoratives quite plausibly attributed to Dummett, in accordance to which the culprit is simply the presence of a material inference: each such inference is accused of derogation of conservativeness. But including material inference “is no bad thing”, Brandom says (1994, 127), so the mistake lies in the inappropriateness of this particular material inference where, what is meant by material inferences are “inferences whose propriety essentially involves the nonlogical conceptual content of the premises and conclusions” (Brandom 1994, 102). Let me illustrate. The pejorative P is linked with a constitutive tie to some negative, devaluing concept D, most often with a handful of such (NIGGER with STUPID, VIOLENT, BOCHE with CRUEL). The constitutive tie licenses inferences of the form “Every P is D”. For instance, the racist use of “nigger” licenses the racist inference from “X is a nigger” to “X is

 2



It is Ch 2, section IV, subsection 5 of the book.

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stupid and brutish”. If we represent the ties as inferential rules we could think of following sort of rules (with “N” for neutral characterization, “P” for pejorative, and “D” for a devaluing characteristic): P-introduction: x is an N x is a P P-elimination: x is a P x has D And here is the application to the Boche example. The P-introduction rule allows the Germans-hater the following inference: Hans is a German. Hans is a Boche. And the P-elimination gives him what he ultimately wants Hans is a Boche. Hans is cruel and barbarous. Now, this sort of rules is standardly used to explicate the meaning (sense) of logical constants. Dummett and Brandom extend the use to nonlogical concepts. So their explanation of pejoratives involves the claim that pejorative expressions have corresponding semantic i.e. conceptual content. “Boche” does not just mean “German” with some disapproval added (call this option “mere disapproval view”, but builds properties of cruelty and barbarous character into the concept of being German. Here is my own argument against the disapproval view as presented by Cargile (1997) and Hornsby (2001), to mention two well known names. A lot of pejoratives are of figurative origin. “Nigger” and “Boche” are not, and this has obscured things in the discussion. “Bitch” is a metaphor (from dogs to humans), “cunt” a synecdoche (from part to the whole person), and in my native Croatian and Serbian the main fashionable political chauvinistic pejoratives are synecdoches as well: Serbian use of “ustasa” for all Croats (generalizing from Croatian Nazis to the whole nation) and the Croatian use of “cetnik” for all Serbs. Now, a figurative use involves a lot of work. The sexist takes the vehicle “bitch-dog” and projects some descriptive features (real or imagined) upon the person. Then he transmits the negative evaluation: same supervenience basis in dogs and persons, same value properties in



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both. The Croatian chauvinist takes the negative features of Serbian “cetniks” from the Second World War or from paramilitary criminals from the nineties, and projects them upon all Serbs. With negative features goes negative evaluation. The mere disapproval view has no means to account for the conceptual complexity that goes with the genesis of figurative pejoratives. Back to Brandom. By building the new content in (into, say the content of GERMAN), one gets a new conceptual content, and the new concept BOCHE. Since none of us believes that national belonging involves having bad character traits, we, who are not xenophobic, know that the inference summarized and reglemented above is cognitively incorrect. While Dummett blames the incorrectness on disharmony between the introduction and the elimination rules, Brandom introduces the idea of a “materially bad” inference. “The problem with ‘Boche’ or ‘nigger’ is not that once we explicitly confront the material inferential commitment that gives them their content, it turns out to be novel but that it can then be seen to be indefensible and inappropriate”(Brandom 1994, 127). He summarizes his view in the title of the sub-section: non logical concepts can incorporate materially bad inferences. I very much agree, and in this section will be deriving philosophical consequences from this claim. But first some elucidations. Since I find the claim both congenial and quite revolutionary, I shall make it also graphically explicit by giving it and its parts names. (PC) There are pejorative concepts involving materially false constituents.

The thesis is conjunctive. Its first part is (PC1) There are pejorative concepts (meanings). Pejorativeness is not just part of the tone, or pragmatic implicature, but part of the cognitive sense.

The second is (PC2) Some typical pejorative concepts involve materially false constituents.

I speak of “constituents” to have a more general thesis at hand. The specifically inferential version of it will be discussed in the third section. Now, (PC) rests on an important, albeit natural assumption. We assume that “Boche” refers to Germans, “nigger” to Blacks and the like. Let us make it explicit. As a co-referentiality assumption



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Chapter Four (CA): A pejorative concept P refers to the same items r to which its neutral counterpart N refers.

The assumption (CA) is the simplest and most natural explanation of linguistic and inferential reference-determining practices involving pejoratives. As Brandom puts it, with the “Boche” example: “If one does not believe that the inference from German nationality to cruelty is a good one, one must eschew the concept Boche. For one cannot deny that there are any Boche—that is just denying that anyone is German, which is patently false” (Brandom 1994, 126). We feel we know what a racist or a homophobe are talking about when they use their respective pet pejoratives. We do not normally conclude from inappropriateness of the use that there are no niggers. Nor does the repentant ex-racist. On the contrary, he would typically think that, yes, those people he was talking about do indeed exist, he just had misconceptions about what they are like. This stands in marked contrast with expressions like “witch” where we are inclined to say simply that there are now witches. In this respect the racist is (in a purely cognitive, non-moral respect) more like someone who believes that whales are fish, not mammals. When corrected, such a person would admit that there is nothing that exactly fits her fishWhale notion, but will take her previous thoughts to have referred to whales. In the rest of this section I will briefly discuss (PC). First, some brief comments on (PC1), then on (PC2). Next comes a comparison with other views of concepts, and finally, and most importantly a review of philosophical consequences implicit in (PC). Let me first very briefly defend (PC), Brandom’s most general claim. An opponent could accept (CA) and use it to deny (PC). Same reference, same sense, one can argue. More than a decade ago J. Cargile (in his 1991) proposed along similar lines that concept BOCHE just is concept GERMAN, and that the derogatory aspects of the word “Boche” are not factual, but expressive. They are not sense-constituting but limited to the “tone” of the utterance. The problem with the view is that the sincere use of BOCHE carries implications that go way beyond mere expression of dislike, in being cognitive and factual: “Hans is a Boche” implies that he is prone to cruelty, which is not only more specific than “Hans is German, and I dislike them”, but specific in a cognitive, factual or descriptive direction. Tim Williamson has suggested that “Boche” and “nigger” carry a negative conventional implication, which is not part of their truthconditional meaning. In a sense this is trivial, given co-referentiality assumption (CA). If pejorative P and its neutral counterpart N have the same reference, then their referential contributions are the same, so that



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their contribution to truth conditions of the sentences they occur in is the same in all extensional contexts. But it leaves open the issue whether their contribution to proposition or sense is the same. I conclude that (PC1) is the most natural semantic assay of pejoratives: they indeed do have senses and stand for pejorative concepts. End of the brief defense. It is now time to follow Brandom to his decisive step and bring in our non-racist (and non-xenophobic, not-sexist , non-homophobic, and so on) convictions. Since we are decent people, we do not believe the stuff that racists believe about Blacks, and homophobes believe about gays. We think that these beliefs are false. This entails (PC2) Some typical pejorative concepts involve materially false constituents.

As mentioned already, a pejorative concept P is linked with a constitutive tie to a negative, devaluing concept, most often with a handful of such (NIGGER with STUPID, VIOLENT, BOSCH with CRUEL). The constitutive tie licenses inferences of the form “Every P is D”. Now, if concepts allow for material falsity, then inferences (or, alternatively propositions) that constitute them need not, and cannot be always materially true. Horwich has argued along similar lines, but in the propositional format, that truth is not needed for concept-analyzing proposition; it is sufficient that they be “taken as true”. (TT) To have the F-concept involving G- concept the thinker must take as true that Fs are Gs, i.e. taking Fs are Gs as true is necessary and sufficient for having the F- concept.

In our example, and translated into inferentialist format, to have the Pconcept involving a D-concept, the thinker must take the inference from Ps are Gs to be correct (materially true). However, even this seems to be too much, and an opponent, rejecting PC2, might take this to be a chink in our armor. She might formulate her worry in terms of the issue of having concepts one does not endorse. In the section we concentrated upon, Brandom recounts O. Wilde’s answer to the question, raised by a judge whether he thinks such and such a passage from his work constitutes a blasphemy: “Blasphemy is not one of my words”. He rightly suggests that a non-racist would have the same kind of attitude to a racist pejorative: “’Nigger’ is not one of my words” would be an appropriate answer by a non-racist to some analogous question. Now, Wilde presumably understood what “blasphemy” means, the same way our non-racist might understand what “nigger” means.



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This seems to put in jeopardy even the modest proposal TT (to the effect that taking some inferences (or propositions) as correct (or true) is necessary and sufficient for having the relevant concept). As Tim Williamson has pointed out in a discussion, TT’s being a necessary condition entails that, unless A believes that Fs are Gs (or infers x is G from x is F), she cannot grasp the F- concept. But we do grasp concepts the use of which we normally reject (e.g. pejoratives). The opponent might then argue that the whole PC2 analysis is faulty. She might claim that some variant of “Fs are Gs”-claim is true about F- concept. In particular, some version of “niggers are stupid” is true of concept NIGGER. Here is a difficulty for this line. Agreed that “nigger” refers to Blacks, it is hard to see on this analysis how to avoid the unwanted conclusion that Blacks are stupid. The opponent is thus driven to denying the coreferentiality of the pejorative and its neutral counterpart. The referent of the pejorative is empty (nobody is stupid because it is of such and such skin color, as implied by nigger-concept). But then the offending inferential rule (If one is a nigger, then one is stupid) is true, albeit vacuously. This is extremely counterintuitive. We already quoted Brandom saying that “one cannot deny that there are any Boche—that is just denying that anyone is German, which is patently false” (Brandom 1994, 126). The other extreme would be to revert to the earlier mentioned proposal made by Cargile, according to which there are no specifically pejorative senses, only a pejorative tone. But this is quite implausible. Here, then, is the middle road, distinguishing two mutually related senses of “possessing a concept” and rejecting necessity for the less demanding of them. On a stronger sense, taking inferential commitments (or believing the truth) in relation to “Fs are Gs” is both necessary and sufficient for possessing a concept. In this sense, a non-racist does not strongly possess the concept NIGGER, nor does an atheist strongly possess concept BLASPHEMY. These are not their concepts, as Wilde would put it. Most concepts are acquired by endorsing the corresponding inferential commitment (accepting the corresponding belief). Exceptionally, one acquires F-concept meta-conceptually, by learning that others accept “Fs are Gs”. Then, one has the F-concept in a weak sense. A non-racist, knowledgeable about racist discourse, possesses racist pejoratives in such a weak sense. (TT*) taking Fs are Gs as true is sufficient for having F- concept.

To put it in Brandom’s terminology, the non-racist does not endorse deontic commitment of racist pejoratives. What she does is then open for further analysis: she might simulate the commitments, or engage in



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pretended endorsement and the like. Such ersatz endorsement is sufficient for concept possession in the weak sense.

Placing the view on the map Let me now pass to a very brief compare–and-contrast exercise, placing the view just worked out (i.e. my reading of Brandom, based upon and developed from (CA) and (PC)) in the context of some main traditional and recent competitors, and deriving one more question for professor Brandom. The competitors are first, the Quinean view that there are no particular constitutive links for concepts, second, the analysis which contrasts concepts as the necessarily correct items with conceptions that admit mistakes, third, Jackson’s (and his Canberra school’s ) “network view”, and fourth, Devitt’s causal referentialism. Pejoratives are a fine testing-ground for all these various views. Let me start very very briefly with Quine and his “no constitutive links” stance. The present view differs by assuming that some links are indeed constitutive (or constitutive to a high degree), while others are not (or are such to a vanishingly small degree). On the other hand, the present view concurs with Quine in denying that links are necessarily correct, a priori, and immune to revision. The present view seems more intuitive. Its weak spot is the issue of principled criterion. So a sympathetic question for Brandom is in order at this point: how does one determine which inference is constitutive? Next competitor, the more traditional conception-analysis. Many authors of otherwise very different persuasions who cling to the special status of concept-analyzing propositions contrast concepts with conceptions. In their terminology, the former encompass only definitory, necessary and sufficient links, which are reference-determining and therefore never incorrect, while the latter might contain redundant, incorrect and revisable links; for instance, a whale-conception might contain the incorrect and revisable link to FISH, but the concept WHALE does not. Pejoratives do not fit well with the conception-analysis. There is no incorrect nigger-conception to be contrasted with the correct NIGGER concept. The later is itself incorrect. Moreover, some pejorative concepts might have developed from mere stereotypical conceptions (e.g. from racist stereotypical conception of Blacks to concept NIGGER). They are ex-conceptions that have turned into concepts. The contrast between the correct concept and incorrect conception is of no help in analyzing them. So the conception-analyst will have to retreat to some less palatable



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alternative, e.g. that there are no pejorative concepts, only derogatory tone or conventional implication indicated by the pejorative expression. Let me pass to the network view (Jackson 1998). A given concept C is represented by a network of links, and what is definitory is a weighted disjunction of them. Presumably, a link to FISH has been part of the WHALE network, but an optional one, and it was replaced by its competitor, a link to MAMMAL. So, ultimately incorrect disjuncts drop out and get replaced by correct ones, as the result of some empirical research and a lot of armchair reflection. The concept thus retains its original status, in spite of minor changes in some of its disjunctively constitutive links. Unfortunately, the strategy does not work well with pejoratives. The devaluing ties are not optional and disjunctive, but mandatory and conjunctively constitutive: it is constitutive for the BOCHE concept that if x is a Boche, then he is cruel. Shorn of such links, the pejorative concept P would collapse into its neutral counterpart N. The network view gives the wrong prediction, the present, Brandom-inspired view gives the correct one. Let me now pass to the last competitor, Devitt’s causal referentialism. Only those items that strictly determine reference belong to a meaning or concept, it claims. “The meaning of a word is its property of referring to something in a certain way, its mode of reference” (Devitt 2001, 461). So, there are no incorrect concepts, just empty ones. For natural kind words, referentialism appeals, correctly, to causal links. “…some modes of reference, including those for names and natural kind words, are causal and non-descriptive. If the historical-causal theory is right for such a mode, it is a property of referring by a certain sort of causal chain.” (Ibid.) But it radicalizes the appeal, and excludes everything else from the sense or concept. So the concept WHALE is just the causal link (doesn’t sound like a concept at all), and no ties to FISH ever come into consideration. It is not clear what a Devitt-style referentialist would say about pejoratives. They refer either to nothing which is very implausible, or, more plausibly, to the same items that their neutral counterparts do (“Boche” refers to Germans). The referentialist would then have to say that the meaning of a pejorative is the same as the meaning of its neutral counterpart. But then we are back to Cargile: there are no specifically pejorative senses. This implausible conclusion seems to speak in favor of the Brandom-style account, against the referentialist. The contrast with the referentialist finely illustrates a further point: on the present account: elements that don’t strictly and ultimately determine reference of “P” belong to the P-concept.



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This concludes our all-too-brief exercise in comparison. However, an additional bonus to be got out of it has to do with generality. Pejorative concepts are not an isolated phenomenon, but akin to other conceptual items, like most prominently, incorrect natural kind concepts. Concept BOCH is like FISHWALE (the concept of WHALE involving being a fish in the sense of being of the same wider kind as tuna and mackerel). It is only the insistence that concepts have to be correct that leads philosophers to deny that there are incorrect natural kind concepts. Brandom notes this in the section we are discussing. “Highly charged words like ‘nigger’, ‘whore’, ‘Republican’, and ‘Christian’ have seemed a special case to some because they couple “descriptive” circumstances of application to “evaluative” consequences. But this is not the only sort of expression embodying inferences that requires close scrutiny. The use of any concept or expression involves commitment to an inference from its grounds to its consequences of application. Critical thinkers, or merely fastidious ones, must examine their idioms to be sure that they are prepared to endorse and so defend the appropriateness of the material inferential transitions implicit in the concepts they employ.” (Brandom 1994, 126)

And he explicitly appeals to scientific low-level theoretical concepts, using TEMPERATURE as his example: “The concept temperature was introduced with certain criteria or circumstances of appropriate application and with certain consequences of application. As new ways of measuring temperature are introduced, and new consequences of temperature measurements adopted, the complex inferential commitment that determines the significance of using the concept of temperature evolves. (Brandom 1994, 127). Once we accept the existence of pejorative concepts, we shall be more free to endorse other incorrect concept-like items, and treat them as bona fide concepts. The present account thus nicely dovetails with the PutnamBurge general line on concepts. Here is a quote from Burge: Scientific practice indicates, however, that a definition that functions as the most basic explanation of a concept at one time can later be displaced and even seen to be false. This is possible because the thinker, or theory, has, besides the definition, other epistemic hooks on the entities that the concept applies to—for example, other theoretical characterizations that had seemed less fundamental; or experimental identifications that are not fully dependent on the definition (Burge 1993,314)



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In conclusion, to the extent that (PC) is the best accounts for pejoratives, it undermines to some extent conception-analysis, network view and representationalism. If (PC) can be generalized (e.g. to incorrect natural kind and theoretical concepts), it will undermine them more seriously. Let me add a few remarks about the pragmatics of pejoratives. Pejoratives are normally used to express negative attitudes, so that a typical illocutionary act of using one is expressive. On the perlocutionary side, there is an important thing to say: uses of pejoratives seem to have a canonical range of illocutionary acts associated with them. Most obviously, they are typically used to offend. But here is one problem: often racists use pejoratives between themselves, in the absence of the target individuals, sexist men routinely use gender pejoratives in the exclusively male company, and the same with chauvinists and chauvinist pejoratives. One could argue that the associated perlocutionary act is offending in absentia (as my friend Dunja Jutronic proposed in a discussion in Rijeka). However, successfully offending someone presupposes uptake, and offending in absentia lacks the right one. We need something else. A line worth pursuing is the following: a typical perlocutionary act intended and often performed between like-minded users of a pejorative in the absence of the target is building solidarity against the target. (How far this appeal goes is an interesting issue on the border with socio-linguistics). I am inclined to think that this is the central canonical perlocutionary act-type associated with the use of pejoratives in absentia of the target. Be it as it may, the topic of the associated perlocutionary act has not been explored to my knowledge in the context of discussion of pejoratives, and it is, I think, worth exploring in detail.

Subverting conceptual truth Brandom’s thesis that we labeled (PC) claims that concepts can involve materially false (incorrect) constituents. Being constitutive of a concept does not guarantee being true or materially correct. So, rules (or propositions) defining pejoratives offer a nice example of false conceptanalyzing rules (or propositions). The revolutionary consequences of this claim have not been widely discussed in the literature. The most obvious and most important is the following: Analyticity of an item (rule or proposition), in the standard sense of item’s being concept-analyzing does not guarantee truth. An item (rule or proposition) that is analytic in P can be false about the intended referent (extension) of P



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If you need an example, the racist inference rule takes the racist thinker from “x is a nigger” to “x is stupid”, corresponding to proposition “Niggers are stupid”, both analyzing the concept “nigger”. On traditional reading they would be an analytic rule and an analytic proposition respectively. But we know they are false about the intended referent, namely Blacks. Brandom prefers not to talk about analyticity, but only of the property of material inferences being constitutive of concept. This is why I use the term “concept-analyzing” instead of simpler but charged “analytic”. And in the relevant section of his book Brandom is very clear about corrigibility of such rules constitutive of a given concept: “Grooming our concepts and material inferential commitments in the light of our assertional commitments (including those we find ourselves with noninferentially through observation) ant he latter in the light of the former is a messy, retail business” (Brandom 1994, 130).

In this sense material concept-analyzing rules (or propositions, if one prefers propositional, representational format) carry in the best case just plain material correctness or truth, they can be “groomed” i.e. revised under the impact of noninferentially/observationally acquired commitments. Concept-analyzing items are no better than any other: they are not immune but revisable, and indeed in the light of empirical evidence. The ground of non-immunity is that “concepts can be criticized on the basis of substantive beliefs” (Brandom 1994, 126). If a concept can be criticized, so can concept-analyzing and concept-constituting items. The conceptual items Brandom concentrates upon are, of course, conceptual material inferential norms. Traditionally, philosophers who accept that conceptual content is normative (i.e. for any given concept there are correct and incorrect ways of deploying it) have been willing to make steps of the following kind. First, possessing a concept entails conforming its deployment to these standards of correctness (to some degree), second, possessing a concept entails knowing norms of its use. Third, and most importantly, norms of use alone determine the truth-values of some judgments. Therefore, the truth-values of some judgments are knowable merely on the basis of possession that is a priori. Brandom would probably rejects the third step: the xenophobe’s norm of use for “Boche” does not determine the truth of “All Boches are cruel”, since it is an empirical question whether all Germans are cruel or not, and it has been answered in the negative. The fact that the inference in question is endorsed by the users of “Boche” is not enough:



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The proper question to ask in evaluating the introduction and evolution of a concept is not whether the inference embodied is one that is already endorsed (so that no new content is really involved) but whether that inference is one that ought to be endorsed. (Brandom 1994, 126)

The alternative proposed can be then summarized in the following short inference: We correct referentially incorrect norms for the use of empirically applicable concepts. We reject pejorative norms as referentially inadequate.

Therefore, Norms regulating the use of empirical terms, “F”, are and relevant for or even constitutive of empirically applicable concepts, follow the constraints of their referent, they are geared to external correctness. Conceptual norms are answerable to objective reality.

Brandom has written wonderful passages on objectivity, in particular the ones surrounding and presenting the short illustrative story about the Constable and the criminal (Brandom 1994, 594). I would like to stress that his main point, just summarized, is valid independently of the complicated mechanism of issues of substitutional quantification, with which it is entangled in the relevant chapters. Brandom’s view thus subverts an important equation that equates “being conceptual (concept-analyzing, analytic)” with “being necessarily true” and immune to revision. We have dramatized this in the title of the section, speaking of subverting conceptual truth. Given the way conceptual truth is usually understood, namely as truth guaranteed by being conceptual, or in virtue of being conceptual, and therefore immune to refutation, the title is justified. We have already noted the contrast with Quine and now we can reformulate it slightly: Quine accepts the equation, emphatically believes in non-immunity, and rejects conceptual items (links, propositions, rules) branded by him as “analytic”. Brandom likewise believes in non-immunity, but accepts conceptual items and rejects the equation. The traditionalist accepts the equation, and conceptual items (that she describes as analytic), but rejects non-immunity. The second consequence is epistemological. Given that the equation that links being conceptual to being necessarily true has been subverted, there is no reason to assume the availability of an a priori passage from being conceptual or concept-analyzing (“analytic”) to being a priori



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knowable or even a priori justifiable. Brandom is not quite explicit about this point. Although the bulk of the book is dedicated to conceptual content which is traditionally linked with topics of reason-based and a priori knowledge, he is quite silent about these epistemological issues, in contrast to those concerning perceptual knowledge (which have been quite prominent in the discussion with McDowell). However, the consequence is quite important and I find it most welcome. I surmise that it generalizes: having a concept that unfortunately turns out to be one of fish-whale does not a priori ultimately justify the naïve thinker in believing that whales are fish, although it might give her a good excuse for such a belief, a sort of prima facie and very week justification, akin to blamelessness. Now, if material inference is not a source of a priori knowledge and justification, one should start wondering about formal inference. Can at least logic be justified a priori? Or should one go Quinean about it?

Rules or theories? Brandom is famously an inferentialist. He takes inferential rules to be basic and constitutive for concepts, and he takes norms, in particular inferential ones, to be in charge of our fundamental relatedness to the world around us. “The story told here is Kantian not only in that it is told in normative terms but also in the pride of place it gives to normative attitudes in explaining how we are both distinguished from and related to the non-us that surrounds us.” (Brandom 1994, 626).

To start with, the use of concepts involves normative commitments: “The use of any concept or expression involves commitment to an inference from its ground to its consequences of application”, Brandom writes (Brandom 1994, 126).

The capacity to engage in inference is essential for concept possession. Further, this capacity involves capacity and willingness to undertake normative inferential commitments. Brandom claims that appeal to such commitments solves various traditional problems, for instance the issue of indeterminacy of reference. What makes one’s use of “Gavagai” into a report of the presence of a rabbit? “The inferentialist response is that the difference is not to be found in the reliable differential responsive dispositions, not in the causal chain of covarying events that reliably culminates in the response ‘Gavagai’, to which not only the rabbit but the



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flies or the fluffy tail belong. It lies rather in the inferential role of the response ‘Gavagai’. For instance, does the commitment undertaken by that response include a commitment to the claim that what is reported can fly?” (Brandom 1994, 429). It is the commitments to various material inferences involving “Gavagai” that guarantees the determinacy of concept and of reference. Brandom lists Sellarsian alternatives concerning the relation of material rules and meaning/concept he opts for the most demanding one (Brandom 1994, 102).3 (1) Material rules are as essential to meaning (and hence to language and thought) as formal rules, contributing to the architectural detail of its structure within the flying buttresses of logical form.

In application to performatives, this yields the following thesis: (INF) Pejorative concepts are grounded in normative material inferences rules. I agree that the use of concept involves material inferential commitments. But what comes first, normative rules or factual beliefs? The most plausible explanatory account of pejorative concepts and the attendant propositions starts from negative stereotypes, concerning the

 3

For ease of reference, here is the whole list: We have been led to distinguish the following six conceptions of the status of material rules of inference: (1) Material rules are as essential to meaning (and hence to language and thought) as formal rules, contributing to the architectural detail of its structure within the flying buttresses of logical form. (2) While not essential to meaning, material rules of inference have an original authority not derived from formal rules, and play an indispensable role in our thinking on matters of fact. (3) Same as (2) save that the acknowledgment of material rules of inference is held to be a dispensable feature of thought, at best a matter of convenience. (4) Material rules of inference have a purely derivative authority, though they are genuinely rules of inference. (5) The sentences which raise these puzzles about material rules of inference are merely abridged formulations of logically valid inferences. (Clearly the distinction between an inference and the formulation of an inference would have to be explored) (6) Trains of thought which are said to be governed by “material rules of inference” are actually not inferences at all, but rather activated associations which mimic inference, concealing their intellectual nudity with stolen “therefores.” (Brandom 1994, 102)



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prospective targets-victims of the use of pejoratives. The negative racist stereotype of a Black involves being stupid and brutish, the negative homophobic stereotype of a homosexual involves not only being effeminate, but being psychologically “queer” and morally perverted (a “sodomite”). The semantic kernel of such a stereotype defines then what it is to be an alleged “nigger” or “bugger”, or “faggot”. (Apparently, the etymology of “bugger” goes back to French “bougre”, originally designating a follower of the Kathar, “Bulgarian” heresy; since all heretics were portrayed by the Church as sodomites, the word “bougre” came to mean “homosexual”, and was then transmitted into English; again a figurative origin of a bad word) The use of pejoratives certainly does not start with inferential rules, but rather with racist, homophobic, sexist or other negative views about the referent. At some point the view is encapsulated into an implicit definition, and the new concept is born (or, if you are a Platonist about the concept “NIGGER”, accessed in the platonic heaven of pejorative concepts). In short, most plausibly a pejorative concept is a conceptualized (negative) stereotype. In conceptualization, only the kernel negative features are built into the concept, so that only essential negative properties, denoted by features, are represented in the concept(-definition). Schematically, one can start with the neutral concept N, cull from the negative stereotype the devaluing features, D1, D2 and so on, add them to the neutral basis constituting N, and build the pejorative concept P. Then propositions like “P is D1”,” P is D2” and so on analyze the new pejorative concept P and have the status of concept-analyzing propositions. A similar and symmetrical process concerns the deconstruction of negative (racist and similar) views. A great deal of effort, from heroic to routine, has been invested in showing that the particular target group does not de facto typically have negative traits attributed to it, and, even more importantly, that such traits are generally not had in virtue of group membership. The Bell curve polemic is a typical case; it is a polemic about facts about what concerns the correlation of race-membership and intelligence. Non-racist and anti-racists scientists produce evidence that social failure of some members of disadvantaged group is not due to their lack of capability, that anti-social behavior is not in their genes and so on. The race nominalist line, prominent in recent discussion, goes even further in maintaining that so-called racial characteristics are ill defined, so that the alleged ‘race’ is not correlated with anything significant whatsoever. The hope is, of course, that people will change their inferential practices as a result of changed descriptive, theoretical views: if they learn that ‘race’ is not correlated with intelligence, they will stop inferring “x is



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stupid” from “x is Black”. Again, belief (or theory) is ahead of normative commitment in the case of deconstruction and criticism in the same way as it is in construction. Brandom himself stresses that “concepts can be criticized on the basis of substantive beliefs» (126, emphasis added). To reiterate, it seems the racist holds the mini-theory about Blacks, encapsulated in the definition of NIGGER, and she does it to some extent on cognitive grounds. Believing all the nasty things from mini-theory about Blacks makes her use her nigger-concept and infer various derogatory things about x from “x is a nigger”. These simple facts give support to representationalism. On the representationalist or mini-theory view, the reading of pejoratives is the following. There is a concept BOCHE distinct from the concept GERMAN (and concept NIGGER distinct from the concept of a black person). It carries, associated with it, a set of concept-analyzing propositions that do the licensing, for the racist or xenophobic inferences. On the civilized view of nationality and race, these and analogous conceptanalyzing propositions are plainly false. The incorrectness of the racist norm derives from the falsity of racist substantive beliefs. This supports the following much weaker alternative from Sellars’ list: (4) Material rules of inference have a purely derivative authority, though they are genuinely rules of inference.

To reiterate, in application to pejoratives, and to introduction and elimination rules proposed in the second section, what comes first are beliefs, and the representational conceptual content as captured in definition (or a definition-like mini-theory) and not inferential commitments. And pejoratives are a fine miniature testing tube in which both approaches can be observed as work. The question for professor Brandom is, then, the following: what is possibly the explanatory story on the opposite, inferentialist side? Why accept (INF), given the fundamental role of factual beliefs? One line of answer for the inferentialist would be to equate holding a mini-theory with having certain inferential dispositions. In our example, one’s holding of the racist mini-theory about Blacks, amounts to nothing else but one’s disposition to infer various bad things about x from “x is Black”. Some formulations of functional-role semantics indeed suggest such a view. Brandom would, however, have to add the normative component: the racist finds herself wedded to the racist inferential norm. But then the issue of explanation raises its head again: in virtue of what does she endorse the norm? And the natural answer is that she does it to a large extent in virtue of her factual beliefs, i.e. her racist mini-theory.



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Another possible move would be to accept the explanatory and temporal priority of the mini-theory but to deny it conceptual priority. Although the racist indeed infers “X is D” from “X is a P” because she holds the racist-mini theory, having the mini-theory as such does not amount to having the target pejorative concept. It is only with the establishment of a relevant kernel of material inferential norms that the pejorative concept is constituted and is there to be had, as (INF) implies. But, if believing the mini-theory about the target explains the endorsing of corresponding inferential norms, and if believing the mini-theory amounts to having the definition of the target, why is it not sufficient for having the concept of the target? There seems to be tension in Brandom’s view between his two equally important claims: first (INF), the claim about primacy of normative inferential rules, and second, the externalist claim about the primacy of objective facts about the referent. If correctness of rules ultimately depends on how reality is, as Brandom’s moderate externalism claims, then this correctness is itself ultimately geared to representing the referent as it is. The authority of material inferential rules is derivative from the authority of reality and its adequate representation. But then representationalism wins.

Conclusion Let me summarize the discussion and reiterate my main questions for Brandom. First, points of agreement. I agree with his view that pejoratives have pejorative senses, and that they typically license materially false inferences. The view seems to entail a quite revolutionary consequence which I like very much: items constitutive of a concept can be false. First question, then: even that truth or material correctness are not even necessary for being constitutive of a concept, is there a principled basis for distinguishing inferences that are constitutive from those which are not? The revolutionary consequence ramifies further into semantics, concept theory and epistemology. First, it speaks against the traditional view that the only non-empty concepts are the (metaphysically) correct ones, whereas the non-correct items are low grade items like “conceptions”. Second, it encourages an analogous analysis of incorrect non-empty concepts of natural kinds (FISH-WHALE), and generalizations derived from them. Third, it blocks inference from being conceptconstitutive to being a priori knowable to be true (or even a priori justified). Finally, following Brandom, I have surmised, without arguing in



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detail, that the view that there are pejorative senses strongly supports norm externalism. This is the idea that some conceptual norms (either derived from definition, as in the theory-view, or constitutive of concept as in Brandom’s) are ultimately answerable to what their referents turn out de facto to be like, independently of a thinker’s assumptions. A conceptual norm can turn out to be de facto incorrect although constitutive of its target concept. Next question: is Brandom inclined to endorse such further ramifications of (what seem to me to be) his views? While agreeing with the view that pejoratives have pejorative senses that imply false inferences or propositions, I have argued against the primacy of the deontological inferentialist format that Brandom uses to explicate the semantics of concepts. On the positive side, I have defended the opposite, non-deontic view: the concept owner accepts a concept definition or a mini-theory about the intended referent. In the case of pejoratives discussed, such a mini-theory is the gist of the negative stereotype of the referent and it is easy to reconstruct the usual genealogy of such stereotypes. In contrast, it is hard to see how the corresponding inference rules might have become established in the absence of propositional beliefs (stereotype). Last question: what is Brandom’s reason for preferring the rule-based picture in such cases, in the face of obvious difficulties?

References Brandom, Robert. 1994. Making It Explicit. Cambridge, MA: Harvard University Press. Burge, Tyler. 1986. “Intellectual norms and the foundations of mind.” The Journal of Philosophy 83: 697-720. —. 1993. “Concepts, Definitions and Meaning.” Metaphilosophy 24(4): 309-325. Cargile, James. 1991. “Real and Nominal Definitions.” In Definitions and definability, edited by James H. Fetzer, David Shatz, George N. Schlesinger, 21-50. Dordrecht: Kluwer. Devitt, Michael. 2001. “A Shocking Idea About Meaning.” Revue Internationale de Philosophie, 208: 449-72. Dummett, Michael. 1973. Frege, Philosophy of Language. London: Duckworth. Hom, Christopher. 2008. “The Semantics of Racial Epithets.” Journal of Philosophy 105(8): 416-440. —. 2010. “Pejoratives.” Philosophy Compass, 5(2): 164-185.



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Hornsby, Jennifer. 2001. “Meaning and Uselessness: How to Think about Derogatory Words.” Midwest Studies in Philosophy 25: 128-141. Jackson, Frank. 1998. From Metaphysics to Ethics. Oxford: Clarendon Press. Putnam, Hilary. 1975. Philosophical Papers, vol. 2: Mind, Language and Reality. Cambridge: Cambridge University Press.





CHAPTER FIVE HOMOGENOUS SEMANTICS BORIS GROZDANOFF

In one of the most influential papers from the second part of the 20th century Paul Benacerraf argues, among other things, that the semantics for mathematical propositions must parallel semantics for the rest of the language. He dismisses with the Fregean notion of “sense” and takes the Tarskian referential notion of truth1 to be the leading candidate for building a common semantics. The underlying consideration behind all this is the strive for what he calls “homogenous semantics”. Such a semantics is supposed to regulate the truth conditions for all types of linguistic cases. In what follows I will discuss the homogeneity requirement and I will try to explicate the intuitions behind it, be they in support of or against it. Given referential semantics of a Tarskian type the terms (like natural numbers, triangles, functions and others) that figure in purely mathematical propositions lead their alleged reference towards abstract entities, that is, towards entities which unlike physical objects are supposed not to be in space and time. This seems to be the biggest, categorical of a kind, difference between the semantic domains of pure mathematics, on the one hand, and the semantic domains of natural language, scientific natural language included, on the other hand. It seems natural to agree with Benacerraf that the domain of reference for natural language, with some exceptions, leads to non-abstract entities, like electrons, tables and planets, located in space and time. Having this in mind the apple of discord seems to be the metaphysical nature of the domains of reference. If it were the case that the metaphysical nature of the two reference domains were the same, the homogeneity of semantics would not have been a problem enough to back up Benacerraf’s dilemma in the first place. Such conterfactual reasoning reveals that in Benacerraf’s dilemma implicit metaphysical tendings seem to regulate questions of

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See (Tarski 1944).

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semantics. The philosophical context, described by Benacerraf, which actually allows the formulation of the dilemma, meets an immediate difficulty. It is more or less uncontroversial that (I) questions of truth and meaning regulate questions of epistemology; we cannot know that x (described in a proposition P, be it purely mathematical or, say, naturally scientific) if we do not have the (a) meaning of the terms, that figure in P, (b) the meaning of P itself, (c) P’s truth conditions specified beforehand and (d) the truth conditions of P satisfied. (d) here complements (I) with (II): not only questions of truth and meaning regulate questions of epistemology but metaphysical states of affairs which satisfy (or not, for that matter) truth conditions of P’s meaning and truth regulate questions of epistemology as well. For if the metaphysical states of affairs that would render P true (false) do not obtain, we could not know that P and, as a consequence, P would not be able to deliver knowledge. For epistemology we seem to need both (I) and (II); neither of them would suffice on its own. This is not far from the reasoning which underlies Tarski’s semantic theory of truth and thus not far from Benacerraf’s view which supports the formulation of the dilemma. Only metaphysics, however, could deliver (II): we indeed need all (and perhaps more) in (I) to arrive at knowing that P, but the categorical nature of what P is about, that is, the nature of the state of affairs (encoded in (II)) that would render P true in the first place, is metaphysical. A natural question emerges: How do we know that metaphysics is as it allegedly is without using epistemology? It seems that (III): questions of metaphysics supervene on questions of epistemology. We begin to find ourselves in something reminding of a vicious circle that ties semantics, epistemology and metaphysics in a sort of a Gordian knot. Perhaps the worst point in the knot is the relation between semantics and epistemology: semantics generates truth and truth is indispensible for knowledge as far as only true propositions could be known. Therefore, we need to have truth conditions prior the (formulation or the epistemic evaluation of) propositions in order to have knowledge at all. But knowledge turns to be necessary in order to deliver the metaphysics which would give us the truth conditions of semantics; that is, we need knowledge about the metaphysical nature of the states of affairs that would be referred to by epistemically adequate meaning and truth conditions. To use Benacerraf’s dilemma as an illustration: the metaphysical nature of a planet (or any other physical object) is to be in space and time and to have all the necessary properties of a physical object. It is most natural to expect that the way we would be at all able to learn about the properties of the planet, say, Jupiter, is to approach them in



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a way that is epistemically adequate: we observe by telescopes, we measure properties that are measurable (both of these within a certain theory, perhaps like Newtonian Theory of Gravitation or General Theory of Relativity) and so on. It is the nature of the entity to be examined epistemically which determines the type of routes to gather information and, eventually, knowledge about it. Yet in case of pure mathematics, to use Benacerraf’s counter-case, it seems that all routes adequate for delivering knowledge about physical objects fail when we try to learn something about, say, numbers and functions. The metaphysical nature of numbers does not allow us to learn about them by observation and measurement or empirically in a typical way. We epistemologists, knowing this, are left with nothing else but to adjust our epistemic routes for delivering knowledge: one type for physical objects and obviously a second, different type, for mathematical objects. If we do not do this we would remain sceptical and ignorant about factual sources of knowledge: whether we observe numbers or not we do know a big deal about them and their properties. It seems that ex post we need to do what we have had to have already done: to acknowledge the actual source of knowledge for typical candidates for abstract objects like the mathematical ones. But, ironically, not before beginning to collect this knowledge but after having it. A disclaimer is apt here: the above scenarios supervene on the acceptance of semantics of a Tarskian type (like the one Benacerraf uses for the formulation of his dilemma and for the conclusion that referents of singular terms in true mathematical propositions point to abstract entities outside space and time, when governed by Tarskian type semantics) and on mainstream notions of objecthood of alleged referents and the like. If we ditch this particular type of semantics (which Benacerraf does not seem to accept as an easy move to do and especially so in the case with the language of natural science) and opt instead for fictionalism in mathematics (of a Fieldian type)2, a version of structuralism (one of many offered in recent literature) or even a more unorthodox view of the kind offered recently by Maddy3 we need no find ourselves in such troubles. Yet in the case of language of natural science Benacerraf seems to hold what is actually an influential position within scientists themselves, whatever epistemologist think. And even worse, in the case with pure mathematics, Benacerraf seems to be statistically not far from the right track, for many of the pure mathematicians actually prefer to think that

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See (Field 1980). See (Maddy 1980).

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everything they work with, mathematical entities like numbers and functions, actually exist. And the kind of existence is very close to the manner prescribed by classical mathematical Platonism, held by logicians like Gödel,4 empiricists like Quine5 and, in recent times, full-blooded Platonists in physics like James Robert Brown.6 Thus, the choice of the Tarskian type semantics in Benacerraf’s famous paper is highly non-trivial and non-arbitrary at all. We would have next to impossible task to dismiss with it as the de facto working semantics in the natural sciences and a socially grave task to convince the great number of professional mathematicians that what they actually believe about what they do for a living is in fact wrong, despite the success of their science.7 It seems that there is no easy way out of this knot. What seems worth mentioning is that if it were not for regulating semantics, the knot would not have arisen in the first place since there would have been nothing for metaphysics to decide upon. If semantics were homogenous it indeed might have been the case that metaphysics have had established which exactly semantics is to be homogenous; this, however, is a general philosophical question and not a specific one. The above reasoning could be taken as a sort of a basis to strive for semantic homogeneity. Yet this is not what obviously stays behind Benacerraf’s point in Mathematical Truth. The way I read it, his tenet is different: if it were the case that semantics is not homogenous we would have needed an ad hoc account for why it is so. In this sense, the point is sort of explicative: it needs to explain why homogeneity is broken. On pains of such an account actually lacking (with the exception of few related attempts, Hilbert’s in On the Infinite being perhaps the most notable one),8 Benacerraf dismisses with the non-homogeneity option. An explicative account, however, does not necessarily need to reach homogeneity as an option. The scenario where an explication shows that semantics is or could be non-homogenous for mathematics and the rest of the language is certainly conceivable. If we follow Benacerraf’s own example:

 4

See (Gödel 1986). See (Quine 1948). 6 See (Brown 1992a; 1992b; 1993). 7 I had the chance to withness the de facto Platonist views of many a professional mathematicians in Pittsburgh, Oxford, Budapest, Sofia and other places. An oftenly met reaction was “Of course they exist” and “Certainly, they do exist in a different way than planets and electrons” when asked about the existence of mathematical entities. 8 See (Hilbert 1964). 5



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There are at least three large cities older than New York. There are at least three perfect numbers greater than 17. There are at least three FG’s that bear R to a.9

we would see that (1) and (2) seem a great deal to be of the form of (3). It is not clear how the referential semantics works in the case of (2) although it is clear how it is supposed to work: “17” must be on a par with “New York” in such a way as that the reference of the one to be semantically regulated in the same way as the reference of the other. This would mean that we would need a relation between the cognitive agent and what renders the singular terms meaningful and truth-successful (within their function as terms in a well formed proposition) that would be the same in the case of the reference of “17” and the case of the reference of “New York”. Yet, to be there a relation R in (1) and (2) does not ipso facto mean that the relation is exactly the same in both cases. And also, to be there a reference of “17” and “New York” it does not mean that it has to be of the same metaphysical nature in both cases. Suppose the following case: imagine that a certain version of the String theory in physics is true (within a scientific semantics) and strings (one-dimensional atomic physical objects, vibrating in 10+1 dimensions, whatever this might actually be) are indeed the ultimate building blocks of the universe. They are so small and peculiar that in fact might happen to participate in the formation of the space-time structure. Space and time (or, following Minkowski and Einstein, taken as a 4 dimensional continuum–Spacetime) are exemplary in their being used by philosophers to constitute criteria of abstractness. Everything which is in space and time is considered non-abstract and everything which is not is considered abstract. Characteristic of the second kind is the lack of causal connection with its instances: no matter what, we cannot reach it via any sort of causal connection for causal connection operates only in space and time. Benacerraf takes causality as fundamental when it comes to establishing abstractness: if there is no possible causal connection with an object chances are the object is abstract and not in space and time. Thus, if strings, being too small to be reached causally with our present technology, are causally isolated from us, although constituting the physical world, they would be as good as abstract objects. Taking counterfactually seriously such scenario, yet to be evaluated by science (and philosophy): if strings are physical entities even though causally isolated due to our best scientific theories why should we take causality as a principle for abstractness in the first place? Metaphysically

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See (Benacerraf 1964).

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strings would be on a par with the real full-blooded abstract entities as platonic ones, to take a radical example; they would be of the same metaphysical nature. As a result causality would not be capable to establish whether the references of (1) and references of (2) stay in a relation that is different for the cases of “17” and “New York”, even if their respective propositions have the same logical form as in (3). The true drama behind such counterfactual speculations is far from benign: as current debates in philosophy of space and time as well as in philosophy of physics demonstrate, there is no sufficiently good understanding of the metaphysical nature of space and time (besides their relatively unproblematic instrumental use in physics) and therefore, being in space and time or not being in space and time could not be understood sufficiently well in order to use it as a criterion let alone to draw an argument out of it. The philosophically sloppy use of physical objects as exemplary spatio-temporal entities is not sufficient: on fundamental scale (and even on large scale, but this is beyond the present scope of the text) physical objects are most certainly far from similar to the entities we are used to deal with in our everyday life on Earth. If the very origin of the significance of notions like “space” and “time” stems from our scale limited experience we should not be surprised that the very physics (on fundamental level) reveals metaphysical nature, quite different from the one we have directly observed through our history. Thus, what I would like to question here is: a. The very foundation of the formulation of the abstract – nonabstract property b. The (consequent) possibility to use such problematically formed criterion for important purposes, like the one in the dilemma, in an argument which rests on the distinction between abstract objects (like the purely mathematical ones) and non-abstract objects (physical ones) c. The notion of causality, central for Benacerraf’s epistemology in the dilemma. The notion is far from clear on non-classical scales (large scales are governed by relativistic rules of causality and micro scales are governed by quantum principles like the Uncertainty principles and God knows what else on sub-Planck scales). Thus even if Benacerraf turns to be correct for classical scale epistemology we know much less about nonclassical scales epistemologies based on causality and especially given the historical fact that causality as a notion has always been intimate with classical physical experience. Due to (a) and (b) we can conceive of a scenario where the so-called abstract objects are, strangely enough, of the same metaphysical nature as the non-abstract (physical) ones. If this is the case, the whole metaphysical



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drama as well as the epistemic one, allegedly revealed by the dilemma, simply dissolves due to the ill formulation of an essential (for the purposes of the dilemma) property of the referents of the singular terms in the propositions in question (1 and 2). What is worse, in order to stress this point we can reformulate it in such a way that in the places of “17” and ”New York” we put only physical objects like “Jupiter” and “up quarck”10 or even “string”, the hypothetically postulated elementary physical particle. The differences between classical physical objects like tables and chairs and fundamental particles like quarks are not merely of scale but of kind and, space and time taken in mind, of a metaphysical nature. Quarks, although confined within the particle they comprise (proton or neutron) move at immense speeds. As it is known from the Special and General theories of Relativity, the spatio-temporal properties of the physical region(s) (“observers” taken in mind) change radically at such speeds. Distances, time durations and simultaneities between events start to differ so much from the classical physical world that it makes sense to talk about spatio-temporal differences in kind and not merely in scale. And this does not even begin to involve questions of dimensionality, painful in cases with the postulated (but increasingly popular within the scientific community) strings. Given such considerations it becomes clear that space and time are anything but easy to use even as a seemingly simple criterion to negatively define abstractness. As far as elementary particles are concerned they, to make an insolent statement, are practically not in the space and time of the classical physics. In this sense they are not the worst of candidates for being ... abstract particles, for most (if not all) of the philosophical debates on nature of abstractness construct them with space and time of classical physics and not with space-time continuum of relativity let alone with space and time in the weird micro world which would have constituted a philosophically precise criteria for abstract as not being in space and time. To conclude with (c), we have serious problems with the very notion of causality. A superficial look at current debates in relativistic causality11 would show how shaky this notion is and how after Einstein classical meaning of causality is not universally valid in physics (and not adequate at all in relativistic physics) let alone in epistemology

 10

The up quark is a type of an elementary particle that constitutes matter. It participates in the formation of both protons and neutrons. It has a partial electric charge (+2⁄3) and it is the lightest of the all six types of quarks. It has been first postulated in 1964 by Gell-Mann and was experimentally detected for a first time at SLAC in 1968. 11 See (Malament 1977; Janis 1983; Norton 1986; Rynasiewicz 2001; Ben-Yami 2006).



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and metaphysics, which purport to have great precision on a level of generality where science is merely a specific domain. Illustrations like this could serve to demonstrate that the relationship between metaphysics, on the one hand, and semantics and epistemology, on the other hand, are more intimate than it might look at first glance and not as straightforward as used in the formulation of Benacerraf’s dilemma. Another conceivable scenario is the one where questions of semantics instruct questions of metaphysics. Let us see the respective situations in the case of the mathematical truth. If metaphysics does not dictate any properties to semantics such a semantic conception of truth would not depend on how the things really are. Thus the truth of the proposition (1) would be the same no matter what is the reality behind the referents of its terms. New York might be as big as it wants to be and this would not influence the truth of (1). Further, the truth of the proposition (2) would not depend on how the numbers are which are alleged referents of its terms. The numbers that are greater than 17, in case they are, need not be perfect at all for this would constitute a metaphysical dependence on semantics. There is another, miracle sub-option, however. And this is the option where the referents of the singular terms of the propositions are indeed as the proposition says them to be but this fact is completely by chance, that is, we still keep the truth-functional semantics metaphysically uninstructed. In summary, such a relation between metaphysics and semantics does not look very promising for semantics would manage to tell us something about the way the things are only via some miracle. And we do not want this. A further conceivable scenario looks more interesting. In this case semantics tells metaphysics how things really are. Thus 7 + 5 = 12 not because of some properties of the numbers involved but because of some properties of the terms involved and their respective meaning. The property discourse in case of natural numbers immediately reminds us of a famous trans-temporal debate between Mill and Frege. Mill argued that numbers were properties of objects (pebbles were his preferred example) 12 and Frege famously attacked him in The Foundations of Arithmetic.13 Frege’s own conception about numbers put aside, offered a transient account of numbers as properties of concepts. This account seems quite close to the scenario in question here. Without going into details14 I would like to stress that tendencies in such a direction have been influential throughout the history of philosophy; another natural suspect is the

 12

(Mill 1843). (Frege 1980). 14 I have discussed the Mill–Frege controversy elsewhere in greater detail, see (Grozdanoff 2010). 13



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Kantian metaphysical doctrine (ignoring epistemic trouble with knowledge of properties of things-in-themselves which would be natural candidates for the modern term “referents”). In such and similar in spirit cases it is still theoretically possible for the terms to have referents but the relations between them to be dominated by concepts and not by referents. The platonic type of relation is not really present for the truth here would not be due to properties of the platonic entities. Yet again it is logically possible there to be some sort of a synchrony between the truth of the terms on the conceptual level and the correct reference of the terms. This truth again would be a mere miracle because of the domination of the conceptual level. The Kantian option would be specific where the domain of the alleged reference is secluded (as a Ding an sich domain) and the conceptual truth is not due to a proper relation between the things in the domain and the terms on the conceptual level but for some other reason. In this scenario we still keep a sort of a primacy of the conceptual domain over the referential one of the secluded entities but again we are left with the miracle option as a conceivable one. The metaphysics in this way might be related to semantics by miracle options or by non miraculous ones. Obviously we would like to dispense with the former and to keep some well grounded explanatory power where the relation between the semantics and metaphysics is philosophically reasonable. What then might be the source of the pathos behind the desire the semantics of mathematics to be the same as the semantics of the rest of the (natural) language? One direction to look for is to argue that mathematics is in fact a language that is of the same kind as the natural language. This claim would hold much more than the claim that mathematics is reducible to logic; for logic is a formal language and the formal language, although in a very intimate relation with the natural language, is different in kind. It is not likely that Benacerraf has this option in mind. Formality of the formal language stems from the attempt to preserve the logical structure of the natural language and this is not the case with the actual role of formalism in mathematics. The mathematical language tries to encode not merely linguistic but mathematical, that is, numerical and geometrical facts about the universe, and mathematical facts are unsurprisingly different from the natural linguistic ones. It is true, nonetheless, that huge number of the mathematical facts have naturally linguistic expressions both in arithmetic and geometry. Spatial phenomena in geometry have natural linguistic expressions which are often used in physics. In Euclidean geometry the (historically original) definition of a line has it as “a length which has no width”. Both terms come from natural language but denote mathematical phenomena, that is, ideal phenomena with ideal properties (like



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dimensionality 1 in the case of the line) which are impossible to find in physical world or at least so far.15 One might even argue that natural linguistic terms are the ones mathematical phenomena could only be thought through. The formalisation of geometry, for example, has been concluded by David Hilbert as late as above hundred years ago. Yet formalisation neither aims nor manages to show that formal and natural languages are of the same kind. It only demonstrates that all propositions of geometry could be derived from a finite and small number of axioms. Another direction to look for is to argue that it would be strange if the terms in natural, formal and mathematical language do not receive their meaning in the same sort of a way. Imagine that the natural number 7 and the term from the natural language “seven” do not mean one and the same thing. If they did not mean the same thing and if there were other cases of the same kind it would have been quite strange to see the relation between pure mathematics and natural languages and especially the one we actually see in the natural sciences. For mathematics has a natural linguistic expression and some natural linguistic expressions have mathematical counterpart as well. This naturally leads us to think that there exist an intimate connection between the two and some are even ready to suppose that the mathematical expressions came from natural linguistic ones, that is, that mathematics came from natural language. Following the history of mathematics and especially geometry such a theory is not hard to see as a player on the table. To use the illustration again, the very word “geometry” in Ancient Greek still carries the origin of a whole mathematical system which began as a practical way of measuring the land around the frequently flooded areas in the Nile Valley in Ancient Egypt. Yet this is far from sufficient. For geometrical terms like “point” and “line” receive, besides their explicit definitions (which gives them very different meanings from the ones they have in the natural language; point in Euclidean geometry is “which has no part”), a meaning only in the whole of the geometrical system where every term functions in very precise propositions such as theorems, which can be proved only from certain axioms and other definitions, following logic. In this sense, it is very difficult to see a parallel between the way geometrical terms receive their meaning and the way terms in natural language do. The question of the Fregean sense and the Tarskian reference remains practically untouched. Because even if we accept that the mathematical term, the number 7, and the natural linguistic term “seven” figure in

 15

I hope the kindly disposed reader would overlook my above illustrations with one-dimensional strings as (alleged and nevertheless empirically unobserved) physical objects.



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propositions that have the same logical form, we still cannot be sure that both have the same meaning, that is, the same sense or the same reference or the same both. It is hard to see how the reference of the natural linguistic term “seven” would be different from the one of the formal mathematical term, the number 7. In spite of the abovementioned differences between the meaning of the mathematical and natural scientific terms the reference constitutes an entirely new semantic dimension which needs to be spelled out precisely enough for the purposes of metaphysics and epistemology. If the reference of 7 and “seven” is the same, and if we extrapolate this as a principles for all mathematical and natural linguistic references, and if the reference constitutes the truth conditions for propositions of mathematics and natural language, then, it is not immediately obvious how mathematics and natural language would be different. On pains that they are different we either need something else, besides reference, like the Fregean sense, or we should implant the difference inside the reference producing something like different references. Benacerraf does not discuss Fregean sense, he takes it that Tarskian type of semantics is the most influential one and therefore reference and properties of reference are what carries the load of the semantics. If the semantics is to be homogenous then the references of 7 and “seven” have to be the same for every other mathematical term and its natural linguistic counterpart. Again, it is not clear how the references are to be the same. On the one hand the reference of mathematical term is likely to be platonic entity, if we follow Benacerraf and the Tarskian semantics, and, on the other hand, the very reference of the natural linguistic term might turn out to be platonic entity as well, if the term leads to something outside space and time. The question about the causal accessibility seems to come after the metaphysical question about the nature of references. As it was mentioned above, however, the question about the metaphysical nature of references cannot pass without some epistemic guarantee that we can indeed know that the metaphysical nature is such and such. In this way it seems that we should first try to come up with such guarantee, then receive the metaphysical nature and, at the end, we should ask about the homogeneity of semantics over mathematical and natural linguistic propositions. The route to guarantee does not seem clear: what could certify that the metaphysical nature of mathematical terms is what it really is? Semantics might seem to be a way as far as it delivers the meaning of terms and their propositions. To come back to semantics might look to come back where we started. Still, it is one thing to postulate that certain semantics regulates certain metaphysical domain and a different thing to discover which semantics in fact regulates or better, should



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regulate the domain. The question of homogeneity might arise only after the metaphysical question has been resolved and the puzzle about homogeneity would be settled quite naturally after we in fact know which semantics regulates which domain. Vis-à-vis metaphysics, Benacerraf does not even attempt to show that the metaphysical nature of the domains of reference (abstract and non-abstract) could not be the same. Instead, he simply assumes that the domains do have a different nature. Yet for this we would need an argument and especially such which takes achievements of modern physics into account. For, again, if it were the case that the metaphysical nature of the two reference domains were the same the homogeneity of semantics would not have been a problem enough to back the Benacerraf’s dilemma in the first place. The nature of the relationship between metaphysics, semantics and epistemology is much more complex than the one presupposed in the oversimplified formulation of Benacerraf’s dilemma. Thus the Benacerraf’s dilemma might be taken as a bit premature given the fact that we have not settled the question about which semantics should regulate the mathematical and the natural linguistic terms and propositions.

References Benacerraf, Paul. 1964. “Mathematical Truth.” In Philosophy of Mathematics, edited by Paul Benacerraf and Hilary Putnam, 403-421. Cambridge: Cambridge University Press. Ben-Yami, Hanoch, 2006. “Causality and Temporal Order in Special Relativity,” British Journal for the Philosophy of Science, 57: 459– 479. Brown, James Robert. 1992a. “EPR as Apriori Science.” In The Return of the A priori, edited by Philip Hanson and Bruce Hunter, Canadian Journal of Philosophy, Supplementary volume 18. Calgary: University of Calgary Press. —. 1992b. “Why Empiricism Won't Work.” PSA: Proceedings of the Biennial Meeting of the PSA 1992, 2: 271-279. —. 1993. The Laboratory of the Mind: Thought Experiments in the Natural Sciences. New York: Routledge. Field, Hartry. 1980. Science without Numbers. Princeton: Princeton University Press. Frege, Gottlob. 1980. The Foundations of Arithmetic, translated by J. L. Austin, 2nd rev. edition, Illinois: Northwestern University Press. Gödel, Kurt. 1986. Collected Works, vol. I, edited by Solomon Feferman. New York: Oxford University Press.



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Grozdanoff, Boris. 2010. “Fregean One-to-one correspondence and numbers as object properties.” Principia 13(3): 327-338. Hilbert, David. 1964. “On the Infinite.” In Philosophy of Mathematics, edited by Paul Benacerraf and Hilary Putnam, 183-202. Cambridge: Cambridge University Press. Janis, Allen, 1983. “Simultaneity and Conventionality.” In Physics, Philosophy and Psychoanalysis, edited by Robert S. Cohen, 101-110. Dordrecht: Reidel. Mill, John Stuart. 1843. A system of Logic, London: Longmans. Maddy, Penelope. 1980. “Perception and Mathematical Intuition.” Philosophical Review 89(2): 163-196. Malament, David. 1977. “Causal Theories of Time and the Conventionality of Simultaniety.” Noûs 11: 293–300. Norton, John. 1986. “The Quest for the One Way Velocity of Light.” British Journal for the Philosophy of Science, 37: 118–120. Quine, Willard Van Orman. 1953. “On What There Is.” In From a Logical Point of View, 1-19. Cambridge, MA: Harvard University Press. Rynasiewicz, Robert. 2001. “Definition, Convention, and Simultaneity: Malament's Result and its Alleged Refutation by Sarkar and Stachel.” In Proceedings of the Philosophy of Science Association 2001 (3): S345-57.





PART II: IMPLICATIONS OF INFERENTIALISM





CHAPTER SIX BOLZANO’S SEMANTIC RELATION OF GROUNDING: A CASE STUDY ANITA KASABOVA

I reconstruct Bolzano’s account of the grounding relation (Abfolge) which, I argue, is a precursor of inferentialism as a basis for semantics and I apply the grounding relation to a particular case: episodic memory. I argue that the basis of episodic memory is not the empirical relation of causality but the semantic relation of grounding which explains why we remember some things rather than others.

The grounding relation Bernard Bolzano, the 19th Century mathematician and philosopher who taught at the University of Prague, worked out a semantic notion of grounding (Abfolge) for providing proofs with an objective ground (Begründung) or explanatory force. He claims that a true statement or truth is grounded or scientifically proved if and only if it is shown to be objectively dependent on other truths.1 Bolzano holds a foundationalist view on which there are basic true propositions or axioms and basic beliefs that support derivative propositions and derivative beliefs based on the more basic propositions and beliefs. He claims that a semantic dependence relation holds between basic propositions or basic beliefs and derivative propositions or derivative beliefs, a relation he calls Abfolge, translated as the grounding relation, where grounding a statement means giving a reason for that statement.

 1

Beyträge II, (1810), § 12. cf. also 1817, §1 where he says that scientific proofs should be groundings (Begründungen) and introduces the terms Grundwahrheiten and Folgewahrheiten.



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It is said (Mancosu 1999) that Bolzano’s notion of grounding provides insufficient evidence for distinguishing grounds from consequences in mathematical proofs. While the proof-theoretical aspects of Bolzano’s theory of inference are problematic, grounding, as Jan Sebestik (2007) points out is a “material” relation in the sense that it depends on the “particular character of ideas” that occur in it (WLIII, § 348). This sense, I think, is compatible with Brandom’s (2000) theory of inferentialism, according to which inference is used to provide a semantics for nonlogical language. I focus on grounding as a material relation which governs the sequential relation between true propositions by ordering them as antecedent and consequent and I present a case study of the grounding relation. I claim that despite its formal shortcomings, the grounding relation is a semantic principle which is applicable to linguistic statements as well as to mental events. Literally, Abfolge denotes a sequence: something follows (folgt) from (ab) something else, but not because it is derived or deduced from that thing. Rather, the grounding relation provides the semantic conditions for a deduction (Ableitung, Herleitung). These conditions are designated by the conjunct ‘because’ which denotes the grounding relation, by virtue of which some terms act as grounds to others (WLII, § 162).2 The explanatory force of the grounding relation lies in “drawing out the elements of an implicit deduction”, by means of which we “obtain the key to new truths which were not clear to common sense”.3 The grounding relation holds only between true sentences of the form: ‘p because q’ which are compatible as ground and consequence and its terms are either single sentences or collections of sentences, respectively expressed by p and q. Bolzano calls these terms ground (Grund) and consequence (Folge). I think Bolzano’s grounding relation is a predecessor of the idea that inferentialism is a basis for semantics: consider how an inferential structure provides a semantic base in consecutive clauses expressing a “because” relation. “Because” is a causal conjunct expressing a reason for (or a proof of) either the antecedent or the consequent expression: “I am sad because you left me” or “because you missed class, you will be punished”; “they asked me to sing and I sang because they insisted”. A

 2

“ein sehr merkwürdiges Verhältnis, vermöge dessen sich einige derselben zu andern als Gründe zu ihren Folgen verhalten.” WLII, § 162; § 221.note: “der Begriff einer solchen Anordnung unter den Wahrheiten, vermöge deren sich aus der geringsten Anzahl einfacher Vordersätze die möglich grösste Anzahl der übrigen Wahrheiten als blosser Schlusssätze ableiten lasse”. 3 1804, Preface, p.8; 1810; Beyträge II, § 2; WLIV, § 401.



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consequent grounds its antecedent (and an antecedent follows from its consequent) when both consequent and antecedent are true and the consequent is the reason why the antecedent is true. The grounding relation governs a sequential grammatical structure, for “because” is expressed by subordinate or consecutive clauses and the structure of sentences with a main clause and a consecutive clause is sequential: the consecutive clause explains the main clause. The sequential or chain-like nature of the grounding relation allows ascension from consequence to ground or descent from ground to consequence.

The grounding relation is distinct from deducibility The grounding relation is not to be confused with the notion of logical consequence which Bolzano called deducibility (Ableitbarkeit). The question whether a conclusion follows from, or is a consequence of, its premises, is distinct from the question of whether an antecedent clause is explained by its consequent clause. Deducibility is a formal relation using the if… then construction denoted by the verb ‘implies’ which can relate either sentence-schemas, as in “B is a bachelor, implies B is unmarried” or parts of a sentence, as in conditional clauses. The relation holds between contents of linguistic statements, which Bolzano calls propositions (Sätze an sich) and these are roughly equivalent to Fregean thoughts, since they are truth-bearers expressible by linguistic statements. Bolzano’s notion of deducibility, it is said (Corcoran 1973; 1993; Etchemendy 1999), is a (primitive) precursor of Tarski’s (1936) notion of logical consequence. But the analogy between Bolzano and Tarski is limited (Siebel 1996).4 Although both notions concern the structure of valid arguments, Bolzano’s notion of deducibility relates to the validity (Gültigkeit) of formal or logical implication as well as material or relative implication, that is, Bolzano examines the process of deduction leading from premises to conclusions and the validity of implicational statements or inferences. Thus Q is deducible from P in a step-by-step deduction showing that Q is true if P is true. Tarski’s notion of logical consequence, however, concerns a metalinguistic framework and an interpreted language and turns on truthconditions or satisfaction conditions of propositional functions. A

 4

However, Bolzano also has a notion of logical deducibility (formal deducibility) and this notion is close to Tarski’s logical implication, since Bolzano says that in cases of deducibility such as “A implies B or A implies not-B” all except the logical presentations have to be varied. See Corcoran (1973; 1993) and Etchemendy (1999).



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propositional function Fd is satisfied if and only if all properties of F are satisfied by a domain or set of individuals d which is defined by the properties of F. For Tarski, “[t]he sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X” (Tarski 1936, 417).5 The open sentence “Zebo has stripes” is true in a model if and only if it is satisfied by all objects in the domain of the model. Or: the conclusion X “Zebo is a zebra” follows logically from the premises of the class K “Zebo is a zebra” and “Holly is a horse” if the objects satisfying the premise-functions Zz & Hh also satisfy the conclusion-function Zz by substituting variables (linguistic expressions capable of adopting any of a range of values) for non-logical terms of X and K. For Bolzano, on the other hand, an argument is valid if and only if it contains a variable presentation (Vorstellung), in regard to which the premises and conclusions follow from each other: P implies Q relative to V if and only if every uniform substitution for occurrences of members of V in P and Q making P true also make Q true (WLII, § 155.2). P and Q are placeholders for singular terms denoting propositions or sentence-schemas and V is a placeholder for a variable component of a proposition, a presentation (Vorstellung) which can be either logical or non-logical. Bolzano’s so-called method of variation concerns the substitution of presentations (Vorstellungen) composing a proposition – by replacing them we obtain true or false variants of the original proposition. Let’s also note that Bolzano’s deducibility is a three-place relation, whereas Tarski’s logical consequence is a two-place relation. For Tarski, variables are substituted for non-logical terms of P (statements expressing the premises) and Q (statements expressing the conclusion) whereas according to Bolzano, the variable terms are presentations in a proposition or sentenceschema and the distinction between logical and non-logical presentations is unstable (schwankend) (WLII, § 148.2). Deducibility is a semantic notion characterized by a compatibility constraint (Verträglichkeit) as well as by a substitutional criterion (Veränderlichkeit): a given class of propositions Q is deducible from a class of propositions P with respect to certain variable components if and only if all substitutions for a variable component V which produces only true propositions in P, also produce only true propositions in Q and the

 5

Beall & Restall (2005) rephrase Tarski’s (1936) definition as follows: “an argument is valid if and only if there is no model according to which the premises are true and the conclusion is not true. Put in positive terms: in any model in which the premises are true (or in any interpretation of the premises according to which they are true), the conclusion is true too.”



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propositions are compatible relative to their variable components V if at least one substitution for V produces only true propositions in P. (WLII, §§ 154.note; 155.2). Bolzano would not agree with Tarski that all nonlogical terms of P and Q are to be varied because that would violate the compatibility constraint. “Zebo is a zebra” is compatible with and deducible from “Zebo is an animal” and “Zebo has stripes” relative to the variable presentation “Zebo” if and only if replacing “Zebo” by other presentations does not generate a true variant of the premise and a false variant of the conclusion. In addition, Bolzano holds that more than one conclusion follows from the premises. For example: “it is not the case that some monkeys are not mammals” is deducible from “all monkeys are mammals” and “some monkeys are mammals” relative to the variable presentations “monkeys” and “mammals”. Due to the compatibility constraint, contradictions are not valid deductions and in this sense, Bolzano’s notion comes close to relevant logics in which the antecedent and consequent of conditionals must bear on the same subject. For Bolzano, the conclusion follows from the premises relative to a variable presentation if and only if they are compatible relative to this variable presentation. Implication also holds for conditionals related by the “if…then” conjunct where “implies” relates parts of a sentence to make a more complex sentence. Bolzano considers such implications as conditionals “in the broad sense of deducibility” which require knowledge outside the domain of logic (WLIII, § 223). He gives the following example: Caius is a man implies Caius has an immortal soul, where “implies” is relative to Caius. To accept or understand (einsehen) this, “we must know that all human souls are immortal”. But in order to know that the implication is correct (richtig), it suffices to recognize it as an instance of the inference scheme “for every x, if x is a man, then x has an immortal soul”. Cases where “implies” denotes a material implication, that is, if the “A implies B” means that A is false or B is true – are problematic because of counterintuitive results such as “if tigers are green, then lions are red” because the whole conditional is true whenever the antecedent is false or “if tigers are green, then lions roar” where the consequent is true. But conditional statements also express enthymematic implications in which the variable component is non-logical and this may be a way of avoiding the so-called paradoxes of material implication. Conditional statements are of different types, such as decisional: “if the boat comes, I will go” or causal: “if you push the cylinder, it will roll”. These implications are material since we need to understand the content of the statements in order to infer a conclusion as following from its premises. The antecedent materially



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implies the consequent if it is not true that the antecedent is true and the consequent is false, that is, if it is not true that you push the cylinder but it does not roll. This result does not violate our intuitions about implication. Enthymemes are valid deductive arguments where the link between premises and conclusions holds “for the most part” and from whose ordinary-language expression one or more propositions have been suppressed.6 The kind of enthymeme discussed here is what Aristotle calls probative enthymeme which “makes an inference from what is accepted”.7 “If the gun has the defendant’s fingerprints on the trigger, then he is guilty”. Bolzano’s compatibility constraint holds for enthymemes, such as “if you push the cylinder, it will roll” since the premises and conclusions have a common variable component: the meaning of an unstated causal principle, which relates the premise “if I push this cylinder” and the conclusion “then it will roll”. The suppressed premise contains a condition “for any roll-able object” which holds for the antecedent and the consequent of the conditional and connects the conclusion to the premises as following from those premises. I think the enthymematic role of material implications is common to both deducibility and grounding because conditional “if-then” statements as well as explanatory “because” statements are ordinary language-expressions of inferences where either a premise or the conclusion is implicit. Consider the advertising slogan for L’Oréal cosmetics: “because I’m worth it”. Bolzano, however, clearly distinguishes deducibility from grounding. Grounding holds between true propositions or truths, whereas deducibility or logical implication can also hold between false propositions and Bolzano uses “consequence” in relation to grounding and not deducibility. His example of the grounding relation is: “Well-functioning thermometers stand higher in summer than in winter because it is warmer in summer than in winter” (WLIII, § 198). The truth “It is warmer in summer than in winter” partly grounds the truth “Well-functioning thermometers stand higher in summer than in winter”, which is a partial consequence of the former. Unlike deducibility, the grounding relation is asymmetric (grounds are simpler than their consequences) and intransitive with regard to the nearest grounds of a truth, so the converse proposition is false: “It is warmer in summer than in winter because well-functioning thermometers stand higher in summer than in winter” (WLIII, §§ 198, 204, 209).8 The statement “Well-functioning thermometers stand higher in summer than in

 6

Aristotle, Rhetoric I, 2, 1356b15-18. Cf. WLIV, § 683.7. On this see Kasabova (2006). 7 Aristotle, Rhetoric II, 22, 1396b-27. 8 Cf. on this Corcoran (1973; 1993) and Tatzel (2002).



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winter” does not partly ground the statement “it is warmer in summer than in winter”. I discuss Bolzano’s view on partial grounds and partial consequences below, in the section after the next.

The grounding relation is distinct from epistemic and causal reasons Bolzano uses the grounding relation as a kind of proof for explaining why something is the case or how it is grounded.9 The distinction between groundings and epistemic reasons or confirmations is derived from Aristotle’s distinction between ϵIJȚ and įȚȩIJȚ. (1) knowing that p on the grounds of q where q explains why p is the case and (2) knowing that p on the grounds of q where q does not explain why p is the case.10 We either understand something through its explanation or we become acquainted with something without a scientific demonstration. Bolzano explicates this distinction by inverting the order between the propositions in a grounding relation.11 Explanation shows why something is the case: p

 9

ML, § 13 (1833-1841) in BBGA, II, A, vol.7, Grössenlehre; WLII, § 162. For an account of Bolzano’s grounding relation and his notion of justification, see Kasabova (2002, 21-33) and Armin Tatzel, “Bolzano’s theory of ground and consequence” (2002, 1-25). 10 Aristotle, Posterior Analytics, A13, 78a-b, trsl. Jonathan Barnes (1975), Clarendon, Oxford. Cf. Barnes’ commentary, p.155. Cf. WLIII, § 198, cf. also ML, § 14, WLIV, § 525. In addition, Bolzano mentions Leibniz’s “liaison de vérités” as a predecessor of the grounding relation. There is a clear parallel between the two authors, since both Leibniz and Bolzano distinguish the grounding relation from the epistemological connection between truths as cognitions. Cf. WLIII, § 198, note. 11 Bolzano notes that it is important not to invert the order of antecedent and consequent in proofs, for then the grounding relation does not obtain. For example, the truth that an equilateral triangle is possible contains the objective ground of the truth that two circles cut each other, “but if one only pays attention to the mere knowing, then the converse relation might quite easily occur”. If the order of the propositions in the demonstration is inverted, we fail to state the correct ground of the truth to be demonstrated. We know that an equilateral triangle is possible by



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is true on the grounds of q and q justifies p. A confirmation, on the other hand, shows that something is the case: I know that q is true on the grounds of p and p confirms q. To use Bolzano’s example: I know that it is cold because the thermometer has sunk, but the reason why the thermometer has sunk is because it is cold today (ML, § 13; WLIII, § 198). From an epistemological point of view, whenever I cognize something, there must be a reason (Grund) why I cognize it.12 We understand a fact on grounds of its explanation: knowing that p on the grounds of q where q explains why p is the case. But on Bolzano’s view, knowing that p on the grounds of q or recognizing that q implies recognizing that p could be just what he calls a subjective grounding or epistemic reason (Erkenntnisgrund). My belief that p because q is subjectively grounded if it is based on testimony or an observation statement rather than a proof showing that p is a consequence of q or depends on q. Subjective grounds, as premises, are confirmations (Gewissmachungen) which produce a cognition or which follow from a cognition as consequences. Hence in a confirmation we obtain an epistemic reason (Erkenntnisgrund) or the certainty that p. Such a subjective ground is what we obtain in a recollection enabling recognition, when we construct saliences or attention-magnets that, is detectable reasons embedded in a past situation which we construct as reasons for actions. The question is, whether we also obtain an objective ground (Begründung) and a ‘because’ relation which holds independently of our cognition, as in: p is true on the grounds of q and q explains why p is the case, so q justifies p. Bolzano distinguishes the grounding relation from epistemic reasons on one hand and from causal relations on the other. Ground and consequence cannot be special kinds of cause and effect, because causes and effects are real objects, whereas grounds and consequences are

 confirming this on grounds of the truth that two circles cut each other, but that is only the subjective ground. The objective ground is this: two circles cut each other because for every two points a and b there must be a third, c, which has the same distance ab from both a and b, so that ca = cb = ab. Cf. WLIV, § 525; ML § 13. 12 ML, § 13. (cf. also WLIII, § 198, WLIII, § 314, Aetiologie, § 4) “Von allem, was ich erkenne, muss ein Grund vorhanden sein, warum ich es erkenne”. In addition, the grounding relation is distinct from deducibility (Ableitbarkeit) or logical consequence. Bolzano determines the concept of grounding (Abfolge) as a “concept of an ordering of truths which allows us to derive from the smallest number of simple premisses the largest possible number of the remaining truths as conclusions” WLIII, § 221note. Hence the grounding relation is asymmetric because grounds are simpler than their consequences, cf. WII, § 209.



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propositions denoting singular terms and a grounding relation holds between propositions independently of whether the objects of the proposition actually exist or not. To put it differently, ground and consequence are truth bearers but not truth makers. Bolzano writes: “Does a certain thing, X, have the property x because the proposition, X has the property x, is true; or, conversely, is this proposition true because the thing X has this property ? - The right answer, in my opinion, is: neither the one nor the other. The ground why a proposition is true lies, if the proposition's truth has a ground, in another truth, not in the thing with which it deals. And even less can one say that the ground why X has the property x lies in the truth that X has the property x. If indeed X is an actual thing then there can be no ground why it has the property x, but there can be a cause why it has the property x, this cause lies in another thing”.13

In addition, Bolzano explains causality in terms of the grounding relation. Causal propositions are determined by a grounding relation between other propositions, so that the causal proposition: “x causes y” actually expresses the grounding relation: “the truth that x exists is related to the truth that y exists as a (partial) ground (Theilgrund) is related to its (partial) consequence (Theilfolge)”.14

The grounding relation as a part-whole relation: partial grounds and partial consequences15 Bolzano refers to partial grounds and partial consequences for two reasons. First, the grounding relation can be immediate or mediate: in the former case, it is a one-to-one relation: the consequence p is completely grounded by q. Bolzano gives the following example of immediate grounding, derived from Aristotle: my statement “you are pale” (partly or completely) immediately grounds my statement “it is true that you are pale”.16

 13

BBGA, vol.II.A.12/2: 60, my italics. WLII, §§ 168; 201; see also Bolzanos Wissenschaftslehre in einer Selbstanzeige, p.82.: “[…] die Lehre von den objektiven Zusammenhängen zwischen den Wahrheiten (...) einem Verhältnisse, kraft dessen einige Wahrheiten der Grund von anderen, diese aber die Folge jener sind; woraus dann auch das wichtige Verhältnis zwischen Ursache und Wirkung hervorgehe und auf eine neue Art erklärt wird.” 15 Following Bolzano, I use the term ‘part’ in a non-mereological sense, in which intransitivity is acceptable. 16 Aristotle, Metaphysics, bk Θ 10: 1051 b 6-9. See on this Tatzel (2002, 7). 14



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In the latter case, the consequence is only partially grounded by p. Second, the grounding relation is intransitive with regard to the nearest grounds. If p is the nearest ground of q, then q cannot be the nearest ground of p and (ii) if p is the nearest ground of q and q is the nearest ground of r, then p is only a partial or auxiliary ground of r (WLIII, § 213). The death of a patient suffering from tuberculosis is a consequence of the illness, but it is not a consequence of the cold drink which may have brought about the illness.17 Intransitivity is important for the ordering of ante and post in a grounding relation: if a proposition p is the nearest ground of a second proposition q, then q cannot be the nearest ground of p. Intransitivity is a shield against introducing alien intermediate concepts or kind-crossing. In order to secure the foundations of the demonstrative sciences, the young Bolzano (1804, 1810) introduced the rule that a completely strict proof is satisfactory if and only if it neither begs the question nor uses alien intermediate concepts or kind-crossing.18 Intransitivity also applies to the part-whole relation insofar as it applies to collections (Inbegriffe) and is governed by an ordering relation such as grounding.19 For example, in a collection such as the administration formed by the persons Caius, Sempronius and Titus, the physical parts of those persons are not part of the administration (WLI, § 83.1-2). I suggest that the intransitive grounding relation is a variant of the partwhole relation which allows for changing levels in a containment hierarchy - from a particular level “up” to the general level or from a general level “down” to a particular level.20 A part is named for a whole or the whole is named by a part, if and only if it is a defining or emblematic part of that whole. Thus a species is named for a genus or a genus is named for a species. For example, the expression “point of steel” names a sword. The genus “steel” refers to the species “sword”. Or vice versa, “sail” names a ship, an elephant is recognized by its tusk and a lion by its

 17

WLIII, § 213, Bolzano’s example. Bolzano, 1804, Preface: 6-7. Cf. also 1810, II, § 2, 1817, §1; Anti-Euklid: 208. Other conditions for the grounding are asymmetricality (grounds must be simpler than their consequences) WLIII, § 209 and irreflexivity (no truth can be based upon itself) WLIII, § 204. 19 Bolzano distinguishes between transitive and intransitive parts: if the order of the parts is arbitrary, as in a pile of coins, the parts are parts of a whole (a sum) (WLI, § 84.2). 20 “If somebody asks for the ground of a certain truth M, and then, if he found it in the single truth L or the collection of truths I, K, L,.., goes on to ask for the single ground or collection of grounds that one or some of the these truths have […], then I call this the ascension from consequence to ground' (WL § 216). 18



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claw because these are defining parts of the whole. As Bolzano says, perceiving an eye of an elephant would hardly enable us to recognize an elephant, whereas perceiving his tusk will enable us to identify an elephant (WLIII, § 284.3.a-g). Likewise, a present memorial is a defining part of a past event (such as a war) enabling our recollection of that event by transposing the sense of that event.21 But the memorial is not a physical part of the war. Semantically speaking, the part-whole relation is important for explaining the transposition of meaning from one item (or collection of items) to another. This part-whole transposition belongs to the inferential structure of meaning and the grounding relation operates that transposition. I now present a case study in which the grounding relation operates the partwhole transposition of meaning: episodic memory.

The grounding relation and episodic memory Episodic memory is the memory of intentional human actions and experiences. It involves explicit or conscious recollection of past episodes belonging to one’s personal experience. Bolzano examines episodic memory in §§ 283-4 of his epistemology, the third part of the Theory of Science (1837) and the Athanasia (1838). On his view, a theory of recollection has to explain how a representation of a present experience and a representation of a past experience are connected in order for the former to prime or prompt the other: that is, it has to explain memory retrieval. Recollections are representational because they are compositionally structured, that is its elements can be constituents of other experiential states, allowing us to infer, for example, that a certain experience a at t1 is similar to a second experience b at t2. My experience of a person giving me bad news at t1 is similar to a second experience of seeing that person at t2 which is why my seeing that person a second time prompts my recollection of the bad news. An account of episodic memory has to clarify what principle enables us to infer that there is a causal connection between representations in order to show how one representation can prompt or renew another. He resolves the question of how we can make a causal connection between a past event and a present recollection by means of a dispositional account of memory traces.

 21



I argue for this point in Kasabova (2008).

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Memory traces and the grounding relation as a part-whole relation Friends of the memory traces theory explain the semantic relation between a past experience and a present recollection as follows: a recollection is partially grounded by a trace or latent engram of a past experience (such as the one of having learnt a poem by heart at school) and this trace is reactivated by a configuration of the experience of a past event with a present experience containing a distinctive sign of the past experience. The trace is a sequel of an experience and the renewal or recollection of this experience is possible if the signal received at present is compatible with the past experience. The recollection of an event and the original experience of that event stand in a whole-part relation; first, because this relation holds between the trace which is a latent sediment of the original experience at a time t1 and the signal motivating the recollection of the original experience at a time t2. Second, the retrieval of an experience at t2 is possible without the circumstances which produced it at t1. This (emblematic-)part-whole relation relates what is retained to what is retrieved and is expressed by a rhetorical figure of transposition called synecdoche. In our case, synecdoche relates past to present experience by transposing the sense of the former to the latter. Neither that which is retained (the trace) nor that which is retrieved (the recollection) are completely identical with the original experience, but they are related by a common part (an attentive perception of the trace). The trace is not a copy of the past event but more like a compression or residue of the former. Nor is the distinctive sign reviving the trace a copy of the past event, but a characteristic feature which specifies that event. This distinctive feature is what the original experience and the recollection have in common. It could be a location: we enter a room where someone close to us has died from a long illness and we recall that person lying in on their deathbed. Or it could be an attribute: if we have once thought of someone as a miser, we will recall his stinginess whenever we think of him. (WLIII, 284.3.a-g). Similarly, the scent of a particular perfume prompts my recall of the woman wearing that scent. Thus in recollection, an entire event can be instantiated by one of its parts, more precisely by its emblematic part or defining feature, because when I see that part, I recollect the rest. Bolzano gives the following examples of the grounding relation in recollection: if someone recites the first verse of a poem we know by heart, his recital will prompt us to recall the subsequent verses. If I am prompted with the line: “Let me not to the marriage of true minds admit impediments”, this cue may enable me to



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recall the entire sonnet. He notes that what enables our recollection is the order of precedent and consequent in a sequence. Or, if we recall a gun on hearing the shot and vice-versa, we recall the gun and shot as cause and effect because they are grounded on the semantic relation that one occurs because of the other (WLIII, 284.3.a-g). If someone gives me some bad news, I will retain that bad news and if I see this person a second time, my new perception of him or her will prompt a recollection of the bad news associated with this person (A, V: 151-153). The recollection of an event is not identical with the experience of that event. First, recollection and experience (or perceptual experience), are different modes of apprehending an object (perceiving a present object is different from recollecting an absent object). Second, recollection and experience have different temporal structures: a recollection is a compilation of past experiences: the latter are not recalled in real time but “edited” in subjective time, as a film director cuts, selects and organizes the scenes of a film, in a sequential order of “before” and “after”. The experience of the event is thus constructed in recollection. Hence the experience of an event and the recollection of that event do not have the same mode of presentation or the same time. A recollection does not recall all the parts or components of a past experience. Otherwise it would be obstructed by numerous details: a memory incapable of forgetting lacks the plasticity necessary for consolidating a coherent sequence of past experiences by economizing or abstracting from, uncountable details which, because they are uncountable, are irrelevant to the construction of the sequence. Consider such cases as Luria’s patient Shereshevskii (1968) or Borges’ hero Ireneo Funes (1962) who suffer from their incapacity to select or abstract from their present experiences, as well as from the absence of a temporal gap between past experiences and present recollections – since their memories are incapable of forgetting, they have a continuous experience of past and present or a present and lack criteria for individuating and hence recalling, past experiences. They cannot recollect their past experiences because they cannot configure what they remember at present with their past experiences. A grounding relation is necessary for this configuration to work, for that which is explicitly recalled is only a part, but a relevant, significant and defining part of what is implicitly retained. The grounding relation is the semantic cornerstone of the part-whole relation which is the principle of the memory trace. Thus I can recall an entire poem if I am prompted with a single line or I can recollect a past seaside holiday by looking at pictures of a seaside resort. A (whole) recollection is re-instated via a trace which is activated by a present



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perception and the recollection is partly grounded by the trace (its auxiliary ground).22

The grounding relation in episodic memory I argue that Bolzano’s grounding relation is the semantic base of episodic memory. First, the grounding relation enables recollection by transposing the sense of a past experience to the present, as shown above. Second, this relation yields an epistemological account explaining an important aspect of episodic memory: why we remember some things rather than others. We remember some things rather than others because they act as attention magnets or detectable reasons embedded in a recollected situation. For instance, if on seeing someone who has given me bad news, I remember the bad news (s)he gave me the first time I saw him or her, the bad news act are a detectable reason my attention is drawn to and this is the motivating force of my recollection. I am sensitive to this person because of the bad news s(h)e brought me. On another view, put forward by Wittgenstein in the Philosophical Investigations, the explanatory force of the “because” relation is a prima facie justification: now I feel ashamed because of a cutting remark I made earlier. My shame is explained by my recollection of my past behaviour, that is, my recollection is constructed as a reason for my present feeling of shame. As Wittgenstein puts it, what justifies the shame is the whole history of the incident (PI, § 644).23 The history of the incident explains why a feeling of shame is the case, it discloses the motives for my conduct, constructing my recollection as a salience or grounding the reason for my present conduct or action. Roman Ingarden (1968) makes a similar point: according to him, past events that are recollected may “now” disclose motives for conduct or action that “then” were still hidden. As a consequence of their disclosure (Enthüllung), the action changes its essential character and appears in a different light. What we held to be a defense against a foreign attack is revealed as a masked attack or what then appeared to us as a victory is now seen as an escape from danger.24 If constructed, these saliences produce recognition—ĮȞĮȖȞȦȡȚıȘ, as Aristotle would say, or a transition from ignorance to knowledge which is a hallmark of tragedy.

 22

If the trace is a partial ground of the recollection, Bolzano’s irreflexivity condition is fulfilled. 23 Ludwig Wittgenstein, Philosophical Investigations, § 644. This is a case of prima facie justification. I discuss this in Kasabova (2007; 2009). 24 See Roman Ingarden (1968, 123, 126).



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Second, the grounding relation is the ordering relation between tensed expressions such as: “it is the case that” or “it was the case that”. Bolzano’s grounding relation obtains in enthymematic implications expressed by consecutive clauses (Consecutivsatz) (WLII, § 168). Consider the statement: “he is in prison because he committed a crime”: p “he is in prison” is grounded or explained by q “he committed a crime”. q explains why p is the case and p is true on the grounds of q, independently of epistemic reasons or causal relations. Or “the defendant is guilty because the gun has his fingerprints on the trigger.” This implication is the explanatory variant of the conditional statement: “if the gun has the defendant’s fingerprints on the trigger, then he is guilty”. Now consider a recollective statement: “I remember the flower-seller because she was at the station last week (where I saw her)” expresses the material grounding relation as follows: “I remember the flower-seller” is grounded by “because she was at the station last week”. The reason I remember the flower-seller is because she was there. My recollective statement is at least partly grounded by a statement expressing the existence of the flowerseller. My recollection is a consequence of my previous perception of the flower-seller and can be derived from the statement: “she was at the station” which explains the recollective statement. In other words, the consecutive clause expresses the consequences of the events related in the main clause and the link between them is not epistemological but semantic. This irreflexive semantic link is quite simply the order of antecedent and consequent and I argue that this link is what autobiographical memory is based on. The link is irreflexive in the sense that no ground (or consequence) can be the complete ground (or consequence) of itself (WLIII, § 204). Hence, for the grounding relation to hold, it is important not to invert the order of antecedent and consequent. On my reading of Bolzano’s grounding relation, particularly regarding its conditions of irreflexivity and intransitivity, its crucial function is the ordering principle of ante and post or ground and consequence and the semantic dependence of the latter on the former. This ordering principle also regulates positioning in time by means of tensed expression. The grammatical divisions of time expressed by verbal tenses such as “wrote” or “write” are grounded by a semantic dependence relation between “ante” and “post”, or the sequential order of “is” and “was” and this is an objective grounding relation which is necessary for expressing positions in time. The main divisions in time (at least in IndoEuropean languages) are based on the ante-post principle: positions in time are constructed from a theoretical zero-point “now” back to the post-



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preterit, preterit and ante-preterit tenses and forward to the ante-future, future and post-future. The relation between present results of past events and the past events themselves is expressed by a perfect which tends to become a preterit or aorist, as in “he (has) passed out because he (has) drunk too much” or “because he is after drinking”, as the Irish would say, becomes “he (has) passed out because he had drunk too much”. Provided it bears the same relation to a past period as the perfect does to the present, a retrospective past time is expressed as the ante-preterit: “I have seen him last week” becomes “I had seen him last week”. If we could not refer back to previous positions in time, there would be no episodic memory to speak of. Conscious recollection is a mental state which tells us about what is inactual or occurred in the past, just as perceptions tell us about what is actual or happening now and imagination tells us about what is possible or could occur. Recollection posits a past possibility, just as imagination posits a future possibility and both mental states represent events that are not presently occurring, whereas perception presents events that are presently occurring. More importantly, the zeropoint “now” is a consequence of “then”, it is grounded on the past tenses which explain why “now” is the case: “earlier” grounds “later” and “later” is grounded in “earlier” because “earlier” explains “later”. The former gives reasons for the latter (and the latter are positioned as having occurred before). In addition, verbal tense and aspect distinctions indicating the position of an action or event in the past, present or future are defined in relation to the position in time when the action or event is described. The relation in which respective positions in time are defined is the grounding relation: actions or events stand in a grounding relation and this relation sequentially orders their positions in time as ante and post where the former explains the latter, from the perspective of the theoretical zeropoint “now” or the time of the utterance. This perspective presupposes an agent and an ergative language system which identifies the agent. Verbal tenses and aspects indicate the action (and its continuity or completeness) in relation to the time of the utterance and the verb identifies the animate perceived instigator of the action, as in: “John broke the window” or “the window was broken by John”, since the agentive relation is governed by cases which are not matched by the grammatical surface-structure relation of subject and object.25 Consecutive clauses expressing the grounding relation, such as “she cried because he hit her” coordinate the agentive

 25

See on this Charles Fillmore’s famous paper The case for case (Fillmore 1967, 25).



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relation and the sequentially ordered positions in relation to the action. This is also how the “because” relation coordinates agents, actions and events in episodic memory. That is episodic memory has a semantic base. Recalling a lazy summer, I say: “It was a restful time because I slept a lot, watched movies and read several paperbacks a week”. Or, remembering that John broke the window, I posit my past perception of that event as antecedent to my present recollection which is its (partial) consequence. Since my recollection occurs because of my perception, my recollection is justified, for the grounding relation obtains.

References Aristotle. 1975. Posterior Analytics, translated by Jonathan Barnes. Oxford: Clarendon. Beall, J. C. and Greg Restall. 2005. “Logical Consequence.” In Stanford Encyclopaedia of Philosophy, edited by Edward N. Zalta. http://plato.stanford.edu/entries/logical consequence/ Bolzano, Bernard. 1969. Bernard Bolzano Gesamtausgabe [BBGA]. Stuttgart: Fromann-Holzboog. —. (1804) 1981. „Betrachtungen über einige Gegenstände der Elementargeometrie”. In Bernard Bolzano (1781-1848): Bicentenary. Early Mathematical Works, edited by Lubos Novy. Prague: CSAV. —. (1810) Beyträge zu einer begründeteren Darstellung der Mathematik. Prague: Caspar Widtmann. [English translation by Sten Russ in: Bolzano, Bernard. 2004. „Contributions to a better grounded presentation of mathematics.““ In From Kant to Hilbert. A sourcebook on the foundations of mathematics, vol. I, edited by William Ewald, 174-224. Oxford: Clarendon Press.] —. (1833-1841) 1981. „Von der mathematischen Lehrart.“ In BBGA, Nachlass II.A.7, edited by Jan Berg. Stuttgart: Frommann Holzboog. [ML] —. (1832-1848) 1978. „Vermischte philosophische und physikalische Schriften.“ In BBGA, Nachlass II.A, edited by Jan Berg and Jaromir Louzil. Stuttgart: Frommann-Holzboog. —. 1837. Wissenschaftslehre. Sulzbach: Seidel. [partial English translations: by Rolf George. 1972. Theory of Science. Berkeley: University of California Press; Burnham Terrell. 1973. Theory of Science. Dordrecht: Reidel.] —. 1838. Athanasia. Sulzbach: Seidel. [A] —. (1816-1840) 1967. “Anti-Euklid” (manuscript). Acta Historiae Rerum Naturalium nec non Technicarum 11: 204 –215.



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—. 1949. „Bolzano’s Wissenschaftslehre in einer Selbstanzeige.“ In Leben und geistige Entwicklung des Socialethikers und Mathematikers Bernard Bolzano (1781-1848), edited by Eduard Winter. Halle: Niemeyer. Brandom, Robert. 2000. Articulating Reasons: An Introduction to Inferentialism. Cambridge, MA: Harvard University Press. Corcoran, John. 1973. “Meanings of implication.” In A Philosophical Companion to First-Order Logic, edited by Richard I. G. Hughes, 85100. Indianapolis: Hackett Publishing Company. Fillmore, Charles. 1967. “The Case for case.” In Universals in Linguistic Theory, edited by Emmon Bach and Robert T. Harms, 1-88. New York: Holt, Rinehart, and Winston. George, Rolf. 1983. “Bolzano’s Consequence, Relevance and Enthymemes.” Journal of Philosophical Logic 12: 299-318. Ingarden, Roman. 1968. Vom Erkennen des literarischen Kunstwerks. Tübingen: Niemeyer. Kasabova, Anita. 2002. “Bolzano’s Account of Justification.” In The Vienna Circle and Logical Empiricism edited by Friedrich Stadler, 2133.Dordrecht: Kluwer. —. 2006. “Bolzano’s Semiotic Method of Explication.” History of Philosophy Quarterly 3(1): 21-39. Ͷ͘ 2007. On Autobiographical Memory. Sofia: NBU Publishing House. (in Bulgarian) —. 2008. “Memory, Memorials and Commemoration.” History and Theory 47(3): 331-350. —. 2009. On Autobiographical Memory. Newcastle-upon-Tyne: Cambridge Scholars Publishing. Mancosu, Paolo. 1999. “Bolzano and Cournot on mathematical explanation.” Revue d‘histoire des sciences 52(3-4): 429-455. Russ, Stephen. 2005. The mathematical works of Bernard Bolzano. Oxford: Oxford University Press. Sebestik, Jan. 2007. “Bolzano’s Logic.” In Stanford Encyclopaedia of Philosophy, edited by Edward N. Zalta. http://plato.stanford.edu/entries/bolzano-logic/ Siebel, Mark. 1996. Der Begriff der Ableitbarkeit bei Bolzano. Sankt Augustin: Academia Verlag. Tarski, Alfred. 1936. “On the Concept of Logical Consequence.” In Logic, Semantics, Metamathematics, 409-420. Oxford: Oxford University Press. Tatzel, Armin. 2002. “Bolzano’s Theory of Ground and Consequence.” Notre Dame Journal of Formal Logic 43(1): 1-25.



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Wittgenstein, Ludwig. 1953. Philosophical Investigations. Oxford: Blackwell. Winter, Eduard. 1949. Leben und geistige Entwicklung des Sozialethikers und Mathematikers Bernard Bolzano (1781-1848), Hallische Monographien vol.14. Halle: Niemeyer.





CHAPTER SEVEN INCOMMENSURABILITY AND INFERENCE ANGUEL STEFANOV

The aim of the paper is, firstly, to reach an answer to the question whether inferentialism stays in support of the thesis of incommensurability, and secondly, to ascertain in which way theoretical models are inferential and in which way they are representational. The notorious Thesis of Incommensurability (TI), launched by T. Kuhn (1962) and P. Feyerabend (1962) more than forty-five years ago, still continues to appear as a methodological reef for all (kinds of) realistically minded philosophers. It states that successive scientific theories, pretending to refer to one and the same domain of phenomena, are incommensurable. This is not an epistemologically “innocent” claim, since it leads to the following two corollaries: I For every pair of incommensurable theories T1 and T2, no statement from T1 can presuppose, entail, contradict, or stand in similar logical relations to any statement from T2. II Thus, the dynamics of scientific knowledge ought to be construed as a mere superseding of theories, instead of the assumed scientific progress. The latter, if it happens, is either a matter of chance, or of pursuing of technical goals by scientists.

What contentions comprising TI lead to the above mentioned corollaries? These are two main claims, here labeled (C1) and (C2). (C1) The meaning of each term, belonging to a theory, is determined by its theoretical context, i.e. by the set of its basic statements (its principles and laws). (C2) The transition from T1 to T2 is accompanied by a radical meaning change of their linguistically shared terms, because of the differences in their respective theoretical contexts.



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To illustrate the validity of (C1-2) let us turn to an example, the TI-proponents, and involving the term ‘mass’ within the contexts of classical and relativistic mechanics. In the former term, traditionally indicated by the letter ‘m’, stands for a property of material bodies that is independent of their state of other words,

favorite to respective theory the functional motion. In

m = mo, where m is the mass of a moving body, and mo–the mass of the same body in a state of rest. This classical equality is broken in special theory of relativity, and takes the form of the equation m = mo /¥ 1- v2/c2. In this equation “m” stands already for a relational concept of mass, since the latter is dependent on the velocity – v – of a moving body, in relation to a given frame of reference. The word “mass” has different meanings within classical and relativistic mechanics, since it represents two different concepts: the one functional (and even attributive in a traditionally classical dynamical context), the other relational. Thus expressions incorporating this word would conceal different messages, from the point of view of the two theories. Many similar examples of this kind could be attracted in support of (C1-2). And it is easily seen that the validity of these claims, together with the natural assumption that for the comparison of theories a shared semantics of their languages is needed, lead to the corollaries (I-II). Certainly, they are not at the heart of many philosophers. However, TI should not be rejected because of its methodological corollaries in the myopic manner of some of its opponents, assessing them to be unacceptable. Instead, one has to give an answer to the question: “Can the admitted meaning change be estimated, and theories, being dubbed ‘incommensurable’, then be evaluated?” I have tried to answer this question elsewhere1, by paying attention to the semantic theory that TI is entirely based on. As H. Sankey puts it: “Incommensurability stems from semantic dependence of the vocabulary employed by a theory upon the theoretical context in which it occurs. Such dependence leads to semantic variance between theories… Thus, to say

 1

I have suggested a theory of meaning change in my book The Challenge of Incommensurability (Stefanov 2000, 122-132).



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that a pair of theories is incommensurable is to say that the languages of such theories fail either in whole or in part to be intertranslatable.” (Sankey 1994, 1).

Indeed, (C1) is the backbone of the contextual theory of meaning. The latter is not a discovery of TI-proponents, but is exploited by them for their own purposes. Philosophers of science and of language, for instance N.R. Hanson and E. Hutten, had already insisted before TI had been raised and had become popular, that even quite observable things like the dawn are conceptualized in a different manner within the framework of different astronomical theories (e.g. by Johannes Kepler and by Tycho Brahe), or that the meaning of logical and theoretical terms is obtained by the specific way in which they are used. Notwithstanding historical considerations, the contextual theory of meaning in its pragmatic construal, concerning the usage of theoretical terms by scientists, can be brought under the inferential theory of meaning, elaborated recently by Robert Brandom and Jaroslav Peregrin. Broadly speaking, according to this theory meanings are neither “tangible things, elements of our physical world”, nor “mental entities”, but stem out of the way in which meaningful expressions are being used in the course of communication (Peregrin 2008). To put it more strictly, “the meaning of an expression is, principally, its inferential role” (Peregrin 2003, 193). And the latter is determined by an inferential pattern, structured by an exhaustive set of valid inferences among sentences, containing the expression, and thus introducing it. Meanings of logical terms are directly attainable through the construction of their inferential patterns. Let us take the case with the classical conjunction – and – between two logical propositions, symbolized by A and B. Based on the truth table of this logical connective, the inferential structure, needed to establish the logical meaning of and is the following (Peregrin 2008, 8): A and B Ō A A and B Ō B A, B Ō A and B. And how are the meanings of non-logical terms obtained? They also enter their characteristic inferential schemes whose inferences are usually not of a purely formal pattern. This means that their validity is secured not on account of their logical structure, but on account of some previously established meanings of key expressions. These inferences have been christened “material inferences”.



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The kind of inference whose correctness determines the conceptual contents of its premises and conclusions may be called, following Sellars, material inference. As examples, consider the inference from “Pittsburgh is to the west of Princeton” to “Princeton is to the east of Pittsburgh,” and that from “Lightning is seen now” to “Thunder will be heard soon.” It is the contents of the concepts west and east that make the first a good inference, and the contents of the concepts lightning and thunder, as well as the temporal concepts, that make the second appropriate. Endorsing these inferences is part of grasping or mastering those concepts, quite apart from any specifically logical competence (Brandom 2007). It is easily seen now that TI-proponents would readily subscribe to the presented inferentialism, since their semantic pretension is just the same. They also insist that the meanings of theoretical concepts depend on their usage which is directly determined by the set of the accepted theoretical principles and laws. Let us turn to the same example with the concept of mass in classical mechanics. Its meaning is exhaustively determined by the well known three Newtonian principles, as well as by his famous law of gravitation, leaning on the assumption about the identity of dynamical and gravitational mass. Every statement, containing the term “mass” should thus be correctly inferable, or entirely consistent with the mentioned basic statements of classical mechanics. And if we move into the context of another theory, say of special theory of relativity, the meaning of this same term would be altered, just because it becomes dependent on inferences with different premises. They must surely include Einstein’s fundamental equation connecting mass with energy, E = mc2, which underlies the already shown meaning change of this key concept. Does inferentialism then stay in support of TI? In order for a clear answer to this question to be provided, one must have a precise understanding of what is meant by “inferentialism”. Robert Brandom outlines three varieties of this semantic view: weak inferentialism, hyperinferentialism, and strong inferentialism (Brandom 2007). Weak inferentialism “claims only that the inferential connections among sentences are necessary for them to have the content that they do” (Brandom 2007, 656). Those connections are necessary to the effect that if some of them were different, then sentential contents would alter, as well. One can hardly insist that weak inferentialism guarantees the validity of TI. Hyperinferentialism involves the claim that formal inferential relations among sentences are sufficient to determine their contents. It is a theory about the meanings of terms that comprise the logical vocabulary, which are defined by sets of correct logical rules of inference (as in the example



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above with the meaning of the logical connective and). This variety of inferentialism, if extended to the non-logical vocabulary of scientific theories, would certainly stay in support of TI. Most interesting of all is what R. Brandom calls “strong” inferentialism, endorsed by him and his followers. What may be called “strong” inferentialism claims that the inferential articulation of concepts, broadly construed, is sufficient to determine their contents. By “broadly construed” in this formulation is meant three things. First, the inferences in question must be understood to extend beyond logically or formally good ones–those whose correctness is settled just by the logical form of the sentences involved. They must include also those that are materially correct–that is, those that intuitively articulate the contents of the nonlogical concepts involved… Second, besides material inferential relations among sentences in the sense of their proper role as premises and conclusions, material incompatibilities among sentences, which underwrite inferential relations in a narrower sense, are included. Thus the fact that the correct applicability of square precludes the correct applicability of triangular, so that the inference from square to nottriangular is a good one, is also to be considered. Third, and most important for understanding the difference between the hyperinferentialist and strong inferentialist theses in semantics, is that inferential relations between noninferential circumstances of appropriate application and noninferential appropriate consequences of application are also taken into account… Thus the visible presence of red things warrants the applicability of the concept red–not as the conclusion of an inference, but observationally. And the point is that the connection between those circumstances of application and whatever consequences of application the concept may have can be understood to be inferential in a broad sense, even when the items connected are not themselves sentential (Brandom 2007, 657-8). It was just this inferentialist doctrine I’ve tried to present so far, and this was the reason for the just adduced long quotation, taking it as an important complement to my previous considerations. It is readily seen that strong inferentialism is less strong than hyperinferentialism. Does, then, strong inferentialism, named hereafter merely inferentialism, since this is the central view endorsed by the proponents of this semantic approach, stay in support of TI? Two strategies might be followed in pursuing the negative answer to this question. The first one relies on the admittance of specific portions of noninferential knowledge. Within natural language they are expressed by giving meaning to observational situations, taken to be “noninferential



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circumstances of appropriate application” of a word – e.g. of the word “red” at the presence of red things, to come back to the quotation above. TI cannot be directly surmounted by relying on the presence of noninferential knowledge; because of the defended contention that observational terms are also theory laden (i.e. their meanings still depend on theoretical contexts). The strategy might be elaborated in such a way, that some referential components of the otherwise intensional contents of theoretical terms might be isolated and compared in case of two (or more) different theories, dealing with one and the same set of phenomena. This strategy, however, stays beyond the semantic basis of inferentialism, although the referential connotations, being exploited for the purpose, are not taken to be direct representations of objects from the shared domain of the incommensurable theories2. The second strategy that I’m going to develop here, may not abandon inferentialism as a semantic view. However, TI cannot be surmounted on its grounds, alone. It is my claim that a methodological notion of representation must be attracted for help. More precisely, the notion I have in mind has an epistemological status; its level is different from that of a purely semantic representation. If this methodological step were not undertaken, TI could hardly be surmounted, and inferentialism would be looked upon as rather staying in support of the doctrine of incommensurability, than vice versa. The word “representation” that I am here making use of, is often met in the claim that theoretical models, or theories as a whole3, represent some fragments of reality. The cognitive nature of theoretical models in science enjoys an increasing philosophical interest, which has recently crystallized in the inferential conception of scientific representation4. Representational construal of theories might be admitted by TI-proponents, however, as merely a conventional (or metaphorical) way of saying that a theoretical model constitutes its own subject, but is in no way a vehicle for presenting the subject’s “real” properties and behaviour, being independent of the model. Thus a necessity arises for a purely epistemological premise to be attracted. This is the rarely articulated belief about the existence of real natural and/or social systems, which are susceptible to scientific representation through the involvement of theoretical structures. So, the notion of representation is “globalized” and transferred from the semantic

 2

The strategy is developed in my theory of meaning change, see footnote 1. I’ll not make any difference here between theoretical models and theories, in so far as it is often contended that theories model the state of affairs in their respective domains. 4 See (Suárez 2004; Contessa 2007). 3



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sphere, where it is attached to the content formation of separate linguistic expressions, to the epistemological sphere of entire theoretical models. It is said that they represent their putatively real objects in the sense that they suggest theoretical structures through which they are known. Elucidated in this way, the notion of representation contributes to the overcoming of TI. In spite of the fact that two theories might prove to fail in their respective representations, they are not incommensurable, but could be ranked according to their epistemic merits, because both of them refer to one and the same fragment of reality. Representations of theoretical models secure the knowledge of their respective objects, although representations are not supposed to be isomorphic or homomorphic with those objects, metaphorically named “target systems” of the models. Unlike material models, theoretical ones fall short of this requirement. They represent by involving systems of abstract constructs, depicted by means of specialized languages. An author who otherwise seems to be sympathetic to the idea of isomorphism in scientific representation, takes it for granted that “we do not simply model a phenomenon, we model it as something. Thus, for example, we model a gas as a system of billiard balls” (French 2003, 1478). Gravitation is modeled by a mathematical expression of a force, mutually attracting material bodies to one another, in classical physics, and as an effect due to the local curvatures of space-time in the general theory of relativity. For similar reasons S. French readily supports the claim that “models denote and do not resemble” (French 2003, 1478). An argument that representations may be, but are often not isomorphic, is that models do not denote by summarizing the “denotations” of the separate expressions which comprise their non-logical vocabulary. Because concepts, even playing a key role in a model, may not denote anything. Let me take as an example a successful model in physics, traditionally used for educational purposes – Bohr’s model of the hydrogen atom. (I call it “successful”, because it stays, in the words of I. Lakatos, at the start of a progressive research programme in quantum physics.) It is traditionally named “the planetary model of the atom”, since the electron orbits the hydrogen nucleus, the proton, just like a planet revolves around the Sun. Thus the concept of the orbiting electron plays a central role in the model. It also explains why a photon of light, with a definite frequency, is emitted out of the atom whenever the electron “jumps” from an outer to an inner orbit. This central concept, however, has later proved to be inadequate, since the electron of a hydrogen atom, in a free state, is



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really situated around the nucleus, but does not follow the path of some definite circular orbit. Because of this argument the notion of denotation is poor of meaning, except to notify that a theoretical model stands for its target system; that it is directed to it with the pretension to represent it. After elucidating the notion of representation, it is now time to see what we have in mind when saying that models are inferential. We may differentiate two inferential aspects of theoretical models. The one refers to inferentialism as a semantic view, how terms from the vocabulary exploited by a theoretical model, obtain their meanings. The meaning of every term is determined by its inferential relations with other concepts from the model, and the consequences of its proper application, i.e. by its inferential role. Let us take an example from chemistry–the proton model of the group of chemical compounds known as “acids”, and ask for the meaning of the expression “HCl”. The inferentialist answer would be that the meaning of this expression is provided by the circumstance that it is a symbol of a chemical compound that renders protons (hydrogen nuclei) in chemical reactions, and to this effect it is an acid, as well as by the fact that those reactions lead to the formation of chlorides as a typical kind of salts. Thus the meaning of HCl becomes locked in the name “hydrochloric acid”. The second inferential aspect involves a central cognitive pretension of theoretical models: the opportunity to infer states of affairs (properties, relations, etc.), obtained as a result of operations within the model, from the model towards the target system. This inferential aspect has recently been referred to as surrogative reasoning in current methodological literature. “’Surrogative reasoning’ is the expression introduced by Chris Swoyer (…) to designate those cases in which someone uses one object, the vehicle of representation, to learn about some other object, the target of representation. A good example of a piece of surrogative reasoning is the case in which someone uses a map of the London Underground to find out how to get from one station on the London Underground network to another. The map and the network are clearly two distinct objects. One is a piece of glossy paper on which colored lines and names are printed; the other is an intricate system of, among other things, trains, tunnels, rails, and platforms” (Contessa 2007, 51).

The lines just quoted are “a good example”, indeed, of surrogative reasoning how someone could infer from the model (the map) for the correct moves in a real Underground trip. Theoretical models, which are



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my main subject of interested here, allow for the same inferential step– surrogative reasoning, providing valuable knowledge about the target system (represented by the model), often some fragment of the world. Thus, an astronomical model of the solar system, no matter whether it is based on the Ptolemaic or the Newtonian paradigm, is expected to predict when a solar eclipse would occur and of what kind, total or partial. So, the second inferential aspect of theoretical models is the possibility new knowledge to be inferred from the model about the target system. At that, it appears that the very possibility for surrogative reasoning is an inherent feature of theoretical models, since without it they fail to adequately represent their target systems. Thus the inferential and the representational function of theoretical models go hand in hand; something that seems to have incited the introduction and the elaboration of the already mentioned view, known as “inferential conception of scientific representation”. How different theoretical models represent their respective target systems, i.e. what are the methodological components of a representation and whether there are different types of representations, are issues of separate interest. I am not going to treat them here, because they stay outside of the theme of inferentialism as a coherent semantic view.

References Brandom, Robert. 2007. “Inferentialism and Some of Its Challenges.” Philosophy and Phenomenological Research 74(3): 656-657. Contessa, Gabriele. 2007. “Scientific Representation, Interpretation, and Surrogative Reasoning.” Philosophy of Science 74: 48-68. Feyerabend, Paul Karl. 1962. “Explanation, Reduction, and Empiricism.” In Minnesota Studies in the Philosophy of Science, vol. III, edited by Herbert Feigl and Grover Maxwell. Minneapolis: University of Minnesota Press. French, Steven. 2003. “A Model-Theoretic Account of Representation (Or, I Don’t Know Much about Art … but I Know It Involves Isomorphism).” Philosophy of Science 70: 1472-1483. Kuhn, Thomas Samuel. 1962. The Structure of Scientific Revolutions. Chicago: University of Chicago Pres. Peregrin, Jaroslav. 2003. “Meaning and Inference.” In Logica Yearbook ’02, edited by Timothy Childers and Ondrej Majer. Praha: Philsophia. —. 2008. “Inferentialist Approach to Semantics. Time for a New Kind of Structuralism?” Philosophy Compass 3(6): 1208-1223. Sankey, Howard 1994. The Incommensurability Thesis. Avebury: Ashgate.



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Stefanov, Anguel. 2000. The Challenge of Incommensurability. Sofia: Academic Publishing House “Prof. M. Drinov”. Suárez, Mauricio. 2004. “An Inferential Conception of Scientific Representation.” Philosophy of Science 71: 767-779.





CHAPTER EIGHT INDIVIDUALITY AND INFERENCES ONDěEJ BERAN

This paper is an attempt to look briefly at the problem of individuality, from the perspective of post-analytical philosophy. Individuality is a traditional philosophical topic and it also was, and is, much discussed within the non-analytical philosophical circles. But it has never been exposed as an important or salient question for the philosophy of language. The standpoint I adopt here is more or less that of inferentialism, though understood not in the strictly technical manner (as a strategy dealing with problems from the domains of logic and semantics), but rather more broadly and more philosophically. As I think the topic of individuality has been hitherto rather neglected by post-analytical philosophy, I consider the following discussion to be a kind of footnote to (what I understand as) inferentialism–a footnote that is not vitally important but may turn out to be interesting. The discussion should begin with repeating few central points of the post-analytical view on language. Most of these points were anticipated by Ludwig Wittgenstein in some form, but post-analytical philosophy including inferentialism doesn’t directly owe these insights to him. However, we should be aware of Wittgenstein’s presence in the debate; his contribution, though lacking width in technical elaboration, lies in his deep and acute insight into the philosophical level of the issue. I will also more or less follow Wittgenstein’s terminology which is not that formal and suits the topic better. First of all, the language we are talking about here is ordinary, natural language. It is therefore of an intersubjective nature: it is a matter of mutual communication among many people–the members of a linguistic community. According to this, language is never “private”. No segment of language (such that can be communicated) can be one person’s exclusive



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property, its meaning being genuinely inaccessible and incomprehensible to anyone else. Secondly, the intersubjective language space is framed by commonly shared rules of language. Rules govern the use of language in various games, of which the body of language consists. Following the rule decides whether someone plays the game or not, and whether she plays it well (correctly) or not. Rules codify which steps, moves, transitions–in the broadest sense, inferences–a speaker can do are correct, and which are not. The incorrect ones prove to be incompatible; “incompatibility” being understood here not as a contradiction in the strict logical sense, but just as incompatibility in terms of the respective game.1 Rules are usually present in the linguistic practice implicitly. But they mostly can be made explicit, at least in an approximation; though this is neither easy nor an equally easy enterprise in all cases. Thirdly, the meaning of the spoken does not depend on the speaker’s “intention”. Nor does the fact whether she plays (correctly, i.e. successfully) the respective game. It is always the linguistic community who “decides” about it, that is, other people than the speaker. Inferentialism calls this a “stance attitude”–the stance of the others is what is decisive. What one says means what the others take it to mean. In a very important sense, I am who I am taken to be by the others. We should keep these three points in mind, when thinking about individuality. Certainly, what is meant by “individuality” needs some clarification. The word has multiple meaning in the natural language. English vocabulary distinguishes among the following, at least: 1) the particular character or aggregate of qualities distinguishing a person or thing from others (its sole, personal “nature”), 2) a person herself or a thing itself, which is of an individual or distinctive character, 3)

the state (quality) of being individual, existence as an individual,

 1

E.g. when a cheater reveals to his victim during the action of the fraud, that he lies in order to cheat her, it turns out to be incompatible with the rules of the game of cheating (though he is telling the truth at the moment). By doing this, the cheater ceases to play the cheating game or at least, ceases to play it well and successfully. He may begin to play some other game–e.g. confession, or relieving his conscience.



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4) the interests of the individual as differing from the interests of the 2 community. As we saw, philosophy of language takes into account only what is intersubjective, only what is equally learnable among all speakers (via mastering rules), and only the stance of the others. All these conditions may lead to difficulties when confronted with the natural language intuitions about “individuality”, as reflected by the definitions above. How to treat individuality consisting in a person’s or a thing’s being such and such “in itself”, or her/its (internal?) “qualities” making her/it individual? In what sense can an individual’s interests (manifested in the linguistic expression of her individuality) make her individually distinct from the community; so that we can consider 1) her as a speaker and 2) the community representing the unified norm of the body of language as opposites? I think at least some of these problems can be disentangled when we try to distinguish among the meanings of “individuality” more acutely and from the point of view of philosophy. The meanings are multiple and, in addition, this multiplicity is expressed in ordinary language terms. Further difficulties may be caused by ordinary language’s notorious inattentiveness toward the rules of its “grammar”. Philosophy must not “solve” the problem so that it picks up only one meaning of “individuality” and claims the other options to be irrelevant. Such would be the functioning of the “craving for generality” characteristic for most of philosophy, as Wittgenstein puts it. On the other hand, philosophy cannot follow the whole variety of the ordinary language usage, either. Thus the limitation of the following analyses and distinctions means not to confine oneself to only what is relevant (philosophically or however else), but rather to what can be interesting. What can “individuality” mean from the philosophical point of view? The first possible answer is: everyone is an individual–due to her unique trace in space and time, as well as due to her unique personal history, “thrownness” or “facticity”, as Heidegger calls it. This is no doubt true. No one’s trace in space and time, no one’s personal history can cover fully with that of anybody else. That would be impossible, even if the person wanted to “unify” herself with somebody else this way. This “philosophical” impossibility, making the claim of such individuality an unbreakable principle, has much in common with the notions of “numerical identity” and “numerical distinctness”. The tradition of these

 2



These examples are taken from http://dictionary.reference.com.

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notions reaches perhaps to Leibniz, but it became popular within analytical philosophy thanks to Max Black’s discussion of the “identity of indiscernibles”. Just as the notion “numerical identity” should only express the fact that–despite qualities or properties–each entity is (identical with) itself and cannot be (identical with) another entity, the above sketched notion of individuality comprises that only I am myself and this is what my “individuality” consists in. The same is true in the case of all people, so that everyone is her- or himself and cannot be anyone else, nor can anyone else be her or him. Of course, we talk about “individual” people in this sense, too, but this is quite trivial philosophically. It is impossible not to be an individual this way. Moreover, this notion seems to be very close to much more informative concepts like “human being”, “rational agent” or “speaker”. In this sense, the notion of “individuality” would be superfluous. Such meaning of “individuality” also does not cover well the important nuances of the dictionary sketch of the ordinary language usage of the word, presented above. We are interested in such philosophical conception of individuality, that goes together well with the look into the dictionary, but is not trivial–so that we can say that the term “individual” says rather more in someone’s case that in someone else’s case. Here we verge to, but not quite unify with the dictionary meaning no. 2. (Benefits following from no. 4 will turn out later.) In the following text, I will try to display one possible direction of such a perspective. I think the assignment may be fulfilled by what we can call “critical” individuality. A person that is individual in this sense is someone who critically reflects the ordinary use of language and therefore opposes the corruptive life processes moved by Heideggerian “das Man”–the “one”, the “they” and the “public neuter”. That means a person who undertakes responsibly the task of shaping her own life-form, along with the choice and pattern of language games she plays and the way she plays them. Unlike the above sketched “numerical” individuality, this is neither something everybody does nor does everybody (who does it at all) do it the same way or to the same extent. Hereafter I will focus on various forms of critical individuality. When speaking about critical or other “individuality”, I will refer by this term both to the person supposed to be individual and to her being such a person. Of course, “individual” (a person) and “individuality” (the person’s being individual–what the fact that she is an individual consists of ) could be distinguished. But I think it is not necessary for the sake of the following discussion, nor can it cause, I think, any seriously harmful confusion in this context.



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I have said that critical individuality means to reflect critically the default mode of speaking, and so to undertake the task of shaping responsibly one’s own life-form, i.e. the way of speaking. How can such general and rather vague conception be understood? Particular philosophical projects proposed by various philosophers purport a couple of examples and may offer certain clue for understanding the notion. One example is represented by the later Wittgenstein’s claim of philosophy as therapy. According to Wittgenstein, philosophy is a purely descriptive enterprise. However, this proposal itself is rather proclamative than selfdescriptive. First of all, the analysis of philosophy as a descriptive discipline is not at all an exhausting description of the variety of activities bearing the label “philosophy”. It is much rather a demand than stating the matter of facts; and as such a demand it is far from being a matter of description itself. The proposed descriptive attention towards real language usage is also not a purpose in itself. Since ordinary language implications tempt speakers to endorse misleading views and attitudes which may cause the respective speaker’s intellectual “diseases”, philosophy becomes a struggle against the consequences of such implications. The description is designed to cure philosophical diseases in the first place; but philosophical diseases, as Wittgenstein pictures them (in a highly metaphorical manner), evoke a variety of psychical and physical inconveniences and troubles. The originally descriptive critical enterprise ends in a struggle for preserving one’s own intellectual and personal integrity and reaching the peace of mind. Such a project is of course far from being dis-interested, non-committing or non-personal. Nevertheless, it is not only analytical philosophy that provides pictures of philosophical projects exemplifying what I call critical individuality. There is also Martin Heidegger’s conception of “authenticity”. I have already briefly mentioned the topic of “das Man”. Authenticity consists in a person’s awareness of her own continuous living under the rule of “das Man”. This influence cannot be eliminated. Being authentic doesn’t mean living untouched by the way “one” lives, but rather an unremitting effort to oppose “the one”–trying to take the way I live into my own hands, to undertake the responsibility. Such effort is motivated by the “voice of conscience”, which is a linguistic phenomenon of a particular kind. In the pragmatic sense, conscience is contextualized “giving to understand” that should move the recipient of the message to do something about her own life. Authenticity is not a “full obedience of one’s own conscience”, it rather means “to want to have conscience”. It is a matter of good will, practical interest in one’s own life-form. And of course, since someone’s life-form and the language games she plays are two sides of one coin, the



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same is true about the person’s authentic existence and her authentic speech, which is the articulation of her conscious, understanding existence. Hints of this perspective can also be traced in the later Heidegger’s works. Heidegger speaks there about the relation between the ordinary, everyday, spoken language, and what he calls “poetry”. According to Heidegger, every piece of language is a piece of poetry. Speaking poetry (Dichten) means providing things with a “measure”, i.e. making them understandable for people, making them things they are for us. Poetic language in this sense is a transcendental medium within which we can make a meaningful experience with the world. This is not in disaccord with the view on language held by Wittgenstein as well as by postanalytical philosophers. Yet to make language, always poetic in the sketched sense, a piece of “poetry” also in the more usual, non-trivial sense, means to reconstruct language from its default form to the form realizing its “measuring” potential in a more “original”, more “pure” manner. Heidegger probably means something more striking and more imaginative by that. The procedure is quite analogous to that of constituting authentic speech: undertaking language in its available everyday, clumsy form, and then understanding and mastering it so that one can poetically “measure”–picture, show the world in a unique, impressive way, inimitable by anyone else. None of these three projects (of course, they are not the only projects admissible for the sake of critical individuality) tries to doubt or subvert language as it is mostly used in everyday practical life. Even the most “critical” speaker cannot emancipate herself from the way language is mostly spoken by most speakers. The pattern is always more or less the following: respecting given rules of language (moving within the space delimited by them), but not being content oneself with what is prefabricated, predigested within language–always trying to speak and be on one’s own. When we consider critical individuality more generally, apart from particular philosophical projects, we can see at least three modes–three ways how to endorse, to “be” a critical individuality reflecting upon one’s linguistic habitus. These are possible attitudes to the critical task set in front of us. The first can be called “creative” individuality. What I mean by that is an author, for instance a writer (most paradigmatically a novel writer) or also a philosopher, who creates a brand new language game, a new “world” of fiction or of thinking, in a sense. Such a world includes its own laws and rules, constituted by the creative act of the creator. The creative



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activity represents often the introduction of a new paradigm of some discipline. Here we can think of people like J.R.R. Tolkien in the domain of fiction, or of Wittgenstein or Heidegger in philosophy. A new creative world can be called “world” also thanks to the fact that innumerably many (in potentia) people can learn to know the rules and laws of the created space, and to orientate themselves within it. This is not just a passive, purely receptive enterprise: to understand the “world” constituted–say–by Heidegger is no minor task. And competent understanding of the created world (space of discourse) has its criteria–in the form of playing the appropriate language game correctly. Whether someone is a competent “expert” in the domain of Heidegger’s or, say, Kafka’s writings, can be decided on the basis of her competence to play the game of understanding or interpreting. As well as in whatever enterprise where any discrimination is possible, it is linguistic skill in playing the appropriate game what provides the most part of decisive criteria. But the game played by experts is not identical with the creative game. The former is so to speak a second-order game with respect to the latter. To play competently the two types of games requires also different talents or linguistic skills and this difference is sometimes quite big. Certainly, this doesn’t mean they are disjunctive. Each of the two types of games, both creative and expert, is genuinely non-trivial, hence individual. For it is not at all easy to master and play either game and, on the other hand, to prove oneself as a competent player of such a game is also tied to considerable social prestige. Since language is in many ways analogous to a living organism, its natural reaction to any requirement is an attempt to spare energy as much as possible, but reaching the same profit. This tendency finds expression in the third, quite special kind of critical individuality–constituting and playing a “parasitic” game. When it takes too big an effort to master a critical game, but the temptation of its status is too seductive, speakers may constitute simplified substitutions of creative or expert games, usually easier to play. An example is “café Heideggerese”, a pseudo-Heideggerian discourse performed by philosophy students in evening cafés; unlike genuine creative or expert games, it doesn’t require that much concentration or endeavour and doesn’t depends on the speaker’s being more or less sober. The non-trivial individual investment in such a parasitic game consists in the art of playing such a game so masterly that the speaker is very difficult to be discovered as a not really competent player of a real creative or expert game. This exposé of parasitic games is not a matter of “social” criticism–their existence is a natural consequence of the existence of certain situated contexts where sharp or explicit rules of creation or expert



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understanding are lacking or hard to discern. The fact that parasitic games are played mostly by those who cannot or don’t want to play a creative or an expert game (and in this sense they seem to be “easier”) doesn’t mean that to play them successfully is not an individual and inimitable enterprise as well. The latter two types of games–expert and parasitic–represent no serious problem for the language-game conception. They are liable to intersubjective criteria of being a language game–such that consists in practically identifiable, i.e. learnable rules and inferential patterns. There are some “outward” criteria of whether one plays such a game, and whether she plays it correctly (successfully). And it is the linguistic community (the others) which possesses the authority of deciding about it. However, a problem may lurk here in the case of the first type of critical individual games–creative games. I think that the problem lies here in the claim of the intersubjectivity of language games. In what sense can we speak of creative games as intersubjective, that is, as a matter of community? The intersubjective status of a game consists in the existence (presence) of rules, that can be learned and followed equally well by more than one speaker. In a broader sense, the normative situation of equalty is required here. But what sort of equalty is meant here? Is it equality in the access to appropriate rules of the game? The alleged rules turn out as extant mostly within the medium of reflection, where they become explicit. It is often those who want to grasp the core of the game in order to profit from it, who reflect on the rules and try to make them explicit. Reflection on rules, making them explicit–for one or another practical purpose–is not a matter of the creative game itself. It is quite usual that rules of a game are themselves implicit (the players of the game master them in practice, as a skill or technique), and they are made explicit within another game. In most such cases, the presence of explicitly expressed rules, though not necessary for the game, is neither incompatible with the game nor felt as obstacle, as something inconvenient or inappropriate. But this is not really the case of creative games. Their rules are usually being made explicit either for the sake of “human knowledge” or something similar (if the “explicitors” play an expert game), or for the sake of the explicitors’ personal profit (if they play a parasitic game) A creator makes no use of such rules–the explicitation barely helps her to do anything better, or at all. In fact, since the existence of explicit rules should facilitate the mastery of game (via following the “manual”) to anyone, it is a straight antithesis of the creative spirit. For whereas the existence of explicit rules of swimming facilitates



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teaching swimming more people more easily–which is also a matter of public interest, something socially useful and desirable – creative games reluct such a scenario. The existence of explicit rules for creativity in literature discovered either by an expert or by an astute “parasite” doesn’t help more people to become more easily competent writers. But even if it did (which it doesn’t, I think), and though it helps in fact to produce more people of certain kind (e.g. alumni of creative-writing courses), it is not a warranted way to creativity. And it is at least debatable, whether it is necessarily something socially useful and desirable. It is most likely quite indifferent with respect to any practical purpose including the “public interest”. At best, we can say that the rules governing the use of language in creative games (their inferential patterns, if there are any) can be pointed at only from within the form of their “expert” reflection or explanation, or used in the form of their parasitic exploitation. However, the fact can be expressed also in a less neutral way: once the game is or can be played intersubjectively, as a discourse (thanks to the existence of intersubjectively accessible rules), it cannot be a creative game. In this sense, creative games seem to fail to fulfill a requirement necessary for regular language games–the requirement of intersubjectivity.3 We face a question here: even if there are some rules for creative activity, aren’t they genuinely implicit, i.e. such that cannot be made explicit at all? Why, we must admit that the attempts to discover these rules are far from being satisfying. Such explicit rules are often either trivial (e.g. that a novel is a continuous text filling some number of pages),

 3

It is clear to me that this exposition perhaps narrows the situation. For I omit here the – undoubted – existence of team-written literature. This is, certainly, a minor phenomenon, but some of its examples are considered generally as pieces of great work (such as books by the Strugatskis, or the Goncourt brothers). I think that these examples draw our attention to the fact that reflexion on rules (on the designed procedure) can be important even in literature; and not necessarily only in the case of team-written works. Actually, it is right here where we see that even something of the very heart of the work creation can become a subject of intersubjective communication. In sum, the purpose of the preceding exposition was not really to deny the possible role of forethought, reflection or discussion in literature. (Certainly this role seems most likely to be wider than I have pictured a bit tendentiously.) However, there are still some pieces of literature where this role is negligible, if any–a good literature as well; which makes us to see that what constitutes literature lays somewhere else than in reflection. The question of the practical role and relevance of literary language games has not been answered, either.



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or they are not accepted in agreement (since there are so many contending views/theories on what literature consists in). The problem with creative language games has also another side. I will try to show that creative games stand close to “private language” in a couple of points. Wittgenstein presents various arguments why there is no private language, or better, why nothing what we would consider as “language” can be called “private”. The point concerns what I have mentioned in the beginning: language is necessarily intersubjective due to the fact that being a competent speaker depends on following appropriate rules, where the deciding authority is held by the community of speakers, that is, by the others. And thanks to this fact, language can be taught and learned. What about creative games? In order to teach someone else a game I master, I must provide either a theoretical explanation, or a practical demonstration. But as I have said, writing novels is not like swimming–the demonstration cannot proceed via doing something and making the other do the same as I do. Theoretical explanation is also problematic–it requires detecting the rules, in order to be able to explain them. But those who work with explicit rules are usually experts or exploiters. Many creators, including the most successful and most respected ones, may be quite unable to put forward the rules of writing, to tell how to do that. Actually, most of them are able to talk about their writing and/or about writing in general, and it is often very interesting. But I understand “putting forward the rules” here in the sense of telling something that makes the other equally good writer, something that helps to teach her how to write literature–just like telling the rules (requirements) of swimming can help to teach someone to swim. As we know, following rules distinguishes between playing the game correctly and the opposite. When the possessor of the skill is notoriously unable to demonstrate or explain her skill to someone else, the question arises: how can she be sure that she plays the game correctly herself? Consider a writer in action–can she distinguish between correct inferential steps or transitions (such that are not “incompatible” with the frame of the game she plays here) and incorrect ones? It is not at all clear. If the writer is uncertain about the correctness of her procedure, she cannot decide about it, as she usually has no rules available as discrimen. She would have to rely upon an ineffable intuition. And if she is convinced about the correctness of the writing direction, she may as well only think that the direction is correct. From her standpoint, the writer herself has no method of distinguishing between “writing correctly” and only believing to do that. And with respect to the peculiar character of creative games, she



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cannot expect the decisive, final word from the side of the others. They hold no real authority, and their opinion is at best secondary here. This is also one of the most important characteristics of Wittgenstein’s private language: there is no difference between following a rule and only seemingly following the rule–thinking that I am following the rule. But there is also another feature making creative games converge to private language: creative games are not continuous (identical) through time. The reasons are following: the moment of establishing the game is the completion of the work.4 Once the game is established (once the work is finished), it is also over–how could the author or anyone else continue to “play” the game of writing a novel that has been finished? Such a game seems to be a single-shot. There is also another, related problem: we can neither state easily the unity of the game through the time of the creation process, nor the game-identity between two pieces of work, even by the same author. That is to say: we can neither point easily at the rules governing the game over all the time of its existence, nor at the rules governing equally the steps (inferential transitions) in both works. The question would be: did Homer do the same (did he follow the same rules) in the beginning of Iliad (e.g. in the ships catalogue) as in its end (e.g. in the night dialogue between Priamos and Achilleus)? Or: did Homer follow the same rules during composing Iliad as during composing Odyssey?5 Such questions are absurd. Not only because they sound ridiculous, but mainly because there is no plausible way how to answer them. And this is also a feature of private language: there is no way how to decide whether a speaker of a private language “calling” her “inner experience” A yesterday as well as today plays the same game (follows the same rule, says the same thing) in both cases. There is also another related problem making the discussion about literary writing as a language game so vague and disappointing. We are not even able to put forward a plausible decision, whether novel writing is a single language game, or it is a cluster of several language games (comprising each some “type” (?) of novels), or each novel represents a game on its own (if it is a single game at all). This is why it is so difficult

 4

No one could have been hundred-percent sure about the rules of quidditch, until Joanne K. Rowling had finished her book series about Harry Potter. The game was so to speak her property–the ultimate (the only) authority of constituting or changing the items of the game belonged to her. Now she has withdrawn the authority and the rules of quidditch are finally sure (since she claims that no other books about Harry’s adventures will appear), but this does not mean that the linguistic community gained the right to change them in the moment. 5 Let’s leave aside the question about the identity of the authors of both eposes.



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to start listing the rules ohne weiteres. But that is not only an explanation why the precedent analysis must look vague and dissatisfactory. I think it is, first of all, an argument concerning the very nature of literature–the fact that it is not a regular language game at all. And the defective character of literary language games is, vice versa, the reason why this discussion is that much dissatisfactory. The character of creative language games as something private brings them close also to other, more usual linguistic phenomena. The situation of a writer is following: she usually cannot play the game she constituted with anyone else (once the game has got a more determinate shape, it is finished), and being recluse in such a private sphere, she loses herself any certainty as to the correctness of the steps made and the very nature and identity of the game. Now consider a similar person: a neurotic, anxious man, suffering from any contact with other people and necessity to negotiate anything. Such a man faces huge difficulties, whenever he tries to pass through any situation requiring communication (communication functioning well in practice) with others. For such a man, everyday linguistic practice is a series of misunderstandings and failures in the attempts to make himself comprehensible in the manner he wants to be understood. And in such a linguistic isolation, he loses the practical certainty about the correctness of his speech steps (steps within the domain where only he can be sure the words mean what they mean and are understood without problems). The “meant” meaning of his utterances, being discontinuous with their “outward” public meaning, hovers in the air. Just like literature, this is another situation where inferential rules, if any, are melting and finally become untraceable. Certainly, I speak here of a kind of psycho-pathological symptom. But my aim was not to link literature essentially to psychic difficulties or diseases. I think rather that the two are rather dissimilar examples of a more general linguistic phenomenon. In fact, any notorious communication failure–the inability or impossibility to make the receivers understand the very message one wants to communicate–also bears the signs of this status. Despite the fact that the speaker’s intention (how she “means” her utterance) is an irrelevant notion for the (post-)Wittgensteinian analytical philosophy, the situation I refer to here can be described just in terms of a discrepancy between the speaker’s intention and the understanding made of it by the others (i.e. what they take it to be or mean). “Intention” is not to refer here straightforwardly to anything inner or mental, it is rather an abbreviation for a complex of the speaker’s (not just linguistic) behavior; a complex of “imponderable evidence” which constitutes and is a sign of the speaker’s discontent with the interpretation of the utterance. It is true that



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the situation of literature is a bit different–especially in the case of the respected literary works we usually assume that the author’s intention has been understood well. However, this understanding doesn’t introduce the reader into a communication with the author, but constitutes another game, discontinuous with the creative one. Notorious failure in communication is tied closely to another interesting phenomenon–the “ineffable mystery” of everyone’s unique existence or life. Just due to the unique “thrownness”, nobody can be understood (seen) by the others exactly the same way as she understands (sees) herself. For such an understanding would mean to occupy the perspective or standpoint from which the person makes her utterances. Roughly said, to understand what someone says is not the same as to understand what is it like to be this person. Though the latter notion may not make much sense (since it is impossible to execute such transpersonal introspection–this is why we speak of “ineffable mystery”) and is definitely not very important in practice, it is still present in whatever communication and bears meaning of something exclusive for the respective person. It may even enter communication explicitly. At least, it is present there as a part of our everyday interpretations of the other’s speech acts. But this is a part of everybody’s “numerical individuality”, something trivial. Does it mean that the analysis of the creative variant of critical individuality goes back to this philosophically uninteresting notion? In a sense, it is true. Yet there is a difference. Unlike “numerical individuality”, the creative one opens a new space of discourse for the others. It enables them to found their own “expert” or “parasitic” language games (hence, life-forms) on its basis. Which is not at all the case of everyone’s being “numerically” individual. The consequences for the relation between creative and expert games may not be obvious. Expert games are indebted for their existence to creative ones, in a sense. Thus for their own sake, they cannot and must not try to reduce the latter into a form of as genuinely intersubjective language games as they are themselves. This would destruct or transform them into something else. An expert game is intersubjective, its result – interpretation of a piece of creation – as well, but the piece of creation is not and presumably could not have been such. To insist that any creative activity must be performable as an intersubjective language games would mean to miss the point. Much of it will never fulfill this condition. This laissez-faire attitude that expert games should adopt towards creative games is a kind of ethical stance, in Lévinas’ sense. Such a stance means to admit the Other’s creative life-form to be irreducible – to admit



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that its core doesn’t lie in “what it is taken to be” by the linguistic community, but rather in the Other’s situated point of interest and happiness. That is, according to Lévinas, to doubt my own interpretative freedom and sovereignty with respect to the understanding of who the Other is. Of course, this is nothing that is necessary for the procedure of linguistic communication within a community–hence, as an ethical claim rather than a semantic one, it is nothing that must, but rather should be fulfilled. Only this stance enables speakers to constitute an expert game and not just a parasitic one; and so, to get as close to the “ineffable mystery” of the other’s existence as possible. If I don’t adopt this stance in the relation towards the Other, I will probably tend to one of the following three endings: Either I confine myself to the level of everyday practical communication, without the ambition to understand the other non-trivially. Or I can ignore others and keep focused on myself alone and stay within my “private” (perhaps creative) domain. Or I apply my freedom, i.e. I exploit the irreducible Other to produce a parasitic game. I think that the conclusion from the preceding discussion is twofold. Firstly, it seems obvious that certain types of games (“creative” ones) cannot be treated and explained quite adequately by the inferentialist strategy. Rules more complex than those of the basic grammar cannot be easily and unequivocally identified and made explicit in their case. As a corollary of that, these games are not genuine language games, since they usually cannot be explained, taught and played among more people. In this respect, they resemble the Wittgensteinian picture of private language. But, secondly, if we adopt an expert attitude towards them, which is based on an ethical decision to preserve their distance, they can enrich considerably the space of discourse. It is the decision to let them give us the opportunity to broaden our own language, which broadening is – unlike creative games themselves–already intersubjective.

References Black, Max. 1962. “The Identity of Indiscernibles.” Mind 61: 153-164. Brandom, Robert. 1994. Making It Explicit. Cambridge, MA: Harvard University Press. Heidegger, Martin. 2006. Sein und Zeit. Frankfurt a.M.: Vittorio Klostermann. —. 1960. Unterwegs zur Sprache, Pfullingen: Günther Neske.



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Lance, Mark and W. Heath White. 2007. “Stereoscopic Vision: Reasons, Causes, and Two Spaces of Material Inference.” Philosophers’ Imprint 7: 1-21. Lévinas, Emmanuel. 1980. Totalité et Infini. Haag: Martinus Nijhoff. Wittgenstein, Ludwig. 1958. Philosophische Untersuchungen. Oxford: Basil Blackwell.





CHAPTER NINE INFERENTIALISM AND THE LAWS OF NATURE CONTROVERSY LILIA GUROVA

Introduction Philosophical inferentialism, or the view that the inferential relations among linguistic expressions determine what these expressions mean1, has interesting implications for the laws of nature controversy in contemporary philosophy of science. According to the standard representationalist approach to scientific knowledge, the expressions we call laws of nature (LN) either refer to something in the world and are thus an essential part of scientific knowledge, or they have no real referents and, therefore, their role in science is at best auxiliary, e.g. as tools for building meaningful (having real referents) scientific representations. The problem with the dilemma “LN either have real referents or their role is auxiliary” is that both of its horns seem to end with invincible difficulties. On the one hand, the assumption that LN refers to something that belongs to the real world binds us to the question what exactly are those things which LN supposedly represent. And this question, as we shall see, implies answers presuming highly controversial metaphysical positions. On the other hand, the opposite assumption that the alleged laws of nature do not refer to anything real in the world and, therefore, play at best a subsidiary role in science, does not seem compatible with any good explanation of the fact that scientists, as a rule, highly appreciate their knowledge of laws of nature, a fact which does not fit well with a picture of science allotting to LN a mere instrumental role. The aim of this paper is to demonstrate that an inferentialist account of scientific knowledge successfully avoids the dilemma “LN either have real

 1

See Brandom (2007) and Peregrin (2012, this volume) for a concise introduction to contemporary semantic inferentialism and its varieties.



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referents, or their role is auxiliary”. It will be shown that an inferentialist approach to LN could cope with both the important role that LN play in real scientific practice and the lack of direct referential relations between LN and the physical world. How is that possible? A statement which is central for the inferentialist approach to language suggests the answer: the primary relation that makes a linguistic expression meaningful is not the relation of reference but that of inference. In other words, what X means is not determined by what X stands for but rather by what X implies (or endorses us to accept) and what X itself is an implication of. From the inferentialist point of view, the inferential relations between linguistic expressions are governed by inferential rules. That means that from the inferentialist perspective, inferential rules play the primary meaningformation role and as such they are an extremely important element of knowledge, including scientific knowledge. There are good reasons to assume that the role of what scientists call scientific principles, or laws of nature, is best understood if laws and principles are thought of as meaningforming rules of inference. It is this assumption that explains why LN are so important in science although they do not directly refer to anything that belongs to the real world. The idea that laws of nature are better understood as rules of inference rather than as allegedly true sentences which play the role of general premises in deductive inferential schemas is not new. Its roots, according to Nagel (1954), could be traced back at least to the writings of Charles Peirce. In the 20th century, versions of the same idea have been defended by G. Ryle (1949) and W. Sellars (1953). The most elaborated account of this idea, however, has been proposed by St. Toulmin (1953) and it is his account and the criticism which it provoked, that is used here as a starting point for the discussion. In what follows, the dilemma “LN either have real referents, or their role is auxiliary” will be outlined first as it has been discussed in contemporary philosophy of science. It will be stressed that the representatives of both parties usually presume a representationalist account of scientific knowledge, including the knowledge of laws of nature. The difficulties met by both camps will be traced. In the second part of the paper, Toulmin’s original inferentialist construal of scientific laws as rules of inference will be introduced together with the main critiques which have been raised against it. Special attention will be paid to the fact that Toulmin’s critics have devoted most of their efforts to prove the logical dispensability of the view of LN as rules of inference as well as to denounce Toulmin’s account as “instrumentalist”. It will be shown that the logical dispensability of LN-as-rules-of-inference view is



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not a problem for this view insofar as the main reasons to support it are epistemological rather than logical. It will be shown as well that the inferentialist account of LN looks “instrumentalist” only if one takes a representationalist perspective on scientific knowledge. The paper will end with a summary of the epistemological merits of the inferentialist construal of LN as material rules of inference.

The laws of nature controversy In the contemporary discussion, the central question “What is to be a law of nature?” (Carroll 2006) is typically followed by a referentialist analysis which transforms this initial asking into the following one: “What do the statements that are supposed to express laws of nature refer to?” The standard realist answer of this question which has been broadly accepted by current philosophers of science, is that law-statements refer to „tendencies and regularities that preexist our attempts to describe them” (Harré 2000, 213) and that these tendencies and regularities are present in one or another way in experience. From this perspective, the law statements are viewed as generalizations drawn on observed phenomena, phenomena which appear to us in regular patterns. The laws-asgeneralizations view, however, faces two serious problems which have provoked extensive discussions. The first problem is related to the fact that at least some of the most prominent laws (e.g. Newton’s first law of motion) could hardly be conceived as generalizations from facts insofar as they appeal to reality which no one could directly observe. Newton’s first law, for example, states that „Every body perseveres its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon” (Newton 1848, 11). However, no one can ever come across a moving body without any forces acting upon it. Thus, strictly speaking, this law statement is not a generalization built on observations. Such counterfactual law statements seem to be a serious challenge not only for the laws-as-generalizations view but for any representational (referential) account of laws of nature in general, insofar as such law statements do not refer to anything that exists (or ever existed) in the real world. It is even questionable whether they refer to a possible world.



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The second problem which has challenged the laws-as-generalizations view is connected to the fact that not all true generalizations seem to be laws of nature. For example, it is true that gold spheres bigger than a kilometer in diameter do not exist but hardly anyone would accept that this truth is a law of nature. At the same time, a similar statement about uranium spheres (that all uranium spheres are less than a kilometer in diameter) is recognized as expressing, or implied by, a law of nature (see Carroll 2006). What’s the difference between these two statements? In other words, what additional feature do law statements possess along with being generalizations of observed regularities or tendencies? Those who have tried to solve this problem have mostly appealed to the idea of necessity2. The fact that all golden spheres are less than a kilometer in diameter is contingent, they have said, there is no any necessity behind it. Nothing in the world prevents the existence of bigger gold spheres, it has just happened that all existing gold pieces are smaller than a kilometer in diameter. In contrast, it is a necessary truth that all uranium spheres are smaller than a kilometer in diameter, because a uranium sphere of this size exceeds the critical mass necessary for the initiation of a nuclear reaction which would transform uranium in a different chemical element. What is the nature of the supposed necessity? How is it discovered? What feature of the law statement refers to the alleged necessity? The lack of acceptable answers of all these questions casts shadows on the referentialist analysis of laws of nature. This situation has led some philosophers to one or another kind of anti-realism about the laws discussion in science. Giere, for example, provided the following answer to the question “What is the status of claims that are typically cited as ‘laws of nature’– Newton’s Laws of Motion, the Law of Universal Gravitation, Snell’s Law. Ohm’s law, the Second Law of Thermodynamics, the Law of Natural Selection?” (Giere 1999, 90): “Close inspection, I think, reveals that they are neither universal nor necessary–they are not even true” (Giere 1999, 90).

What’s the role, then, of the expressions which have been called “laws of nature”? According to Giere, the alleged laws, which should better be called “principles”3,

 2

See, for example, (Armstrong 1983). Giere reminds us that in fact both words “laws” and “principles’ have often been used as synonymous in scientific practice and that Newton himself has chosen the title for his main book “The Mathematical Principles of Natural Philosophy”.

3



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“should be understood as rules devised by humans to be used in building models to represent specific aspects of the natural world. Thus Newton’s principles of mechanics are to be thought of as rules for the construction of models to represent mechanical systems, from comets to pendulum. They provide a perspective4 within which to understand mechanical motions. The rules instruct one to locate the relevant masses and forces, and then to equate the product of the mass and acceleration of each body with the force impressed upon it.” (Giere 1999, 94-5).

However, by thus disconnecting laws from the reality which these laws otherwise so cleverly instruct us how to model, Giere has put himself in a position of not being able to answer the pressing question why, then, some “laws” are better rules for building models than others. Let’s see now how Toulmin managed to avoid the problems of representationalist realism about laws of nature without embracing any version of outrageous instrumentalism.

Toulmin’s inferentialist account of laws of nature Contemporary inferentialists do not mention Toulmin among the predecessors of their movement5. However, two assumptions underlying Toulmin’s analysis of laws of nature reveal how close his approach is to that of semantic inferentialism. The first assumption is that a scientific principle should always be understood “in the context of its use”6. This assumption characterizes Toulmin as a proponent of the so-called use theory of meaning which roots could be traced back to the writings of the later Wittgenstein7. In addition, semantic inferentialism has been broadly

 4

The notion of perspective is central for Giere’s later development of his methodological position which he called “perspectivism” (see Giere 2006). 5 Neither the key figure of contemporary semantic inferentialism Robert Brandom and his followers–see (Brandom, 2000; 2007; Peregrin 2012), nor any of the scholars who have commented on this philosophical movement from outside (see Horwich 1998) have ever related the present inferentialist ideas to those of Toulmin. 6 Because, Toulmin wrote, “looked at against this background, its force will be clear enough: divorced from all practical contexts and left to stand on its own, its meaning will be far from clear, and it will be open to all sorts of misunderstanding and misapplications” (Toulmin 1953, 57). 7 Let us recall that Toulmin was a student of Wittgenstein and at many places declared a “special debt” to his teacher. Wittgenstein, for example, is mentioned first in the acknowledgements section in the Preface of (Toulmin 1953).



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recognized as a species of the use theory of meaning8. The second of Toulmin’s assumptions is about the difference between the language of scientists who use it for describing what they are studying, and the language of the “onlookers” in which “the roles of the scientist’s symbolic techniques are not left unexamined, but stated explicitly” (Toulmin 1953, 59). In Toulmin’s perspective, the logicians are such “onlookers” who use logical techniques to “state explicitly” what is implicit in the practice of scientists. That reminds us about another important characteristics of contemporary semantic inferentialism–it is similar to Toulmin’s expressivist view about logic9. Thus, for Toulmin, in order to answer the question what LN are, one should reveal what LN mean for real scientists in the first place. The meaning of LN could be found only in their real use. However, the meaning of LN could not simply be depicted. It is not directly given to us and the meaning should be logically explicated. Here comes Toulmin’s original suggestion: the logical explication of LN which best fit to the real practice of scientists represents the law statements as rules of inference rather than as general premises. In support of this suggestion, Toulmin stated an argument which speaks directly against the laws-as-generalizations view. The argument is based on a careful observation of the history of some laws of nature. Toulmin’s main example is Snell’s Law, which in one of its simplest formulations states that “whenever any ray of light is incident at the surface which separates two media, it is bent in such a way that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is always a constant quantity for those two media” (Toulmin 1953, 59).

Or, if “i” is the angle of incidence and “r”–the angle of refraction: sin i/sin r = const. Toulmin’s most important remark concerning Snell’s Law is that the regularity that is supposedly summarized by this law statement had been known for a long time before Snell succeeded in formulating the law in its present form. If the law were simply derived from observational data,

 8

See (Horwich 1998). According to Brandom, the task of logic is not to study the patterns of formally valid inference, rather its task is to make explicit “the inferences that are implicit in the use of ordinary, nonlogical vocabulary” (Brandom 2000, 30).

9



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Toulmin asked, why did it take such a long time to do that? According to him, to discover a law is not the same as to discover a regularity. The law does not stand for a regularity, it is rather a logical tool that allows us to express the form of that regularity. Toulmin’s most important evidence in support of his claim that lawstatements are neither true nor untrue is also taken from real practice in science. It is a regular practice in science, he wrote, for the law itself to be stated separately from its scope of application: “To every law there corresponds a set of statements of the form “X’s law has been found to hold, or not to hold, for such-and-such systems under such-and-such circumstances.” (Toulmin 1953, 78)

But, he sais, these statements do not coincide with the law itself. Thus being a law, according to Toulmin, is a logical matter. Before recognizing Snell’s formula as a law, it has been treated as a hypothesis the truth of which had to be checked in different situations. “But very soon–indeed, as soon as its fruitfulness has been established–the formula in our hypothesis comes to be treated as a law, i.e. as something of which we ask not ‘Is it true?’ but ‘When does it hold?’ When this happens, it becomes part of the framework of optical theory, and is treated as a standard” (Toulmin 1953, 79).

It is easy to recognize when we are at the law-talk stage: the cases in which the alleged law does not stand (as double refraction or anisotropic refraction) are called anomalies and the way scientists try to explain them differ from the way they explain “normal” refraction (looking for the cause of the departure from the law). Why do scientists defend some of their statements by calling them laws and thus preserving them from attempts to prove that they are not true? One reason for that which Toulmin especially stressed is that “laws of nature are used to introduce new terms into the language of physics” (Toulmin 1953, 80). In the case of Snell’s law such a term is “refractive index”. (The “refractive index” of a particular transparent substance is the constant quantity for refraction out of air to this substance.) “Notice one thing in particular: that questions about refractive index will have a meaning only in so far as Snell’s Law holds, so that in talking about refractive index we have to take the applicability of Snell’ Law for granted – the law is an essential part of the theoretical background against which alone the notion of refractive index can be discussed” (Toulmin 1953, 80).



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The most interesting part of Toulmin’s analysis of LN which is also the most neglected and/or misunderstood by his critics, is that in which he explicitly distinguished his views from the seemingly similar views of some notorious instrumentalists. The fact, he wrote, that laws of nature are neither true nor untrue does not imply that scientists are not interested in truth. It only implies that some of the statements which scientists deal with “need to be logically assessed in different terms” (Toulmin 1953, 80). “This, of all things, is most often overlooked in the logical discussion of the physical sciences; it is therefore essential to insist on it.” (Toulmin 1953, 80).

According to Toulmin, by calling laws of nature “instructions”, “directions” and “rules” instead of “principles”, the instrumentalist like Schlick and Ramsey snap the link between the laws of nature and the world and make it appear that laws “do solely with physicists and their conduct” (Toulmin 1953, 102). “But to snap this link is … an extremely misleading thing to do. Through their whole logical apparatus the laws of physics still speak about the objects of the world; and the fact that some inferences rather than others come to be licensed usually tells us much more about the world than about the physicist and his methods” (Toulmin 1953, 102-103).

Despite these comments, why was Toulmin recognized as instrumentalist not only by his critics but also by those who were in sympathy with his approach to theoretical knowledge10? The following seems to be a plausible answer: in the representationalist perspective, an expression which is claimed to have no real referent could have only an auxiliary, instrumental role; Toulmin insisted that LN do not directly refer to any real entity; therefore, his commentators said, he allotted to them nothing but an instrumental role. Most of Toulmin’s critics, however, considered the main challenge for his position to be the fact that, logically, laws of nature could be construed both as premises in a deductive argument and as material rules of inference. In fact, Toulmin’s critics said, in their practice scientists rely on both modes of logical use11. And insofar as a central premise in Toulmin’s argument for laws-as-rules-of-inference is the claim that scientists use

 10

See, for example, (Suppe 1977; Musgrave, 1980), and more recently, (Kuipers 2007). 11 See (Nagel, 1954; Scriven, 1955).



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them in this way in their practice, and insofar as scientists seemingly do not use LN exclusively as rules of inference, Toulmin’s argument has been broadly recognized as invalid. Is it invalid, indeed? Fortunately not. Toulmin’s critics missed something important, something that stems immediately from his views about the difference between the language of scientists and the language of the onlookers. They missed that Toulmin’s account of LN as rules of inference is not descriptive but explicatory and is part of the onlookers’ language. Toulmin had never insisted that LN could not be logically explicated as premises in a deductive argument; he only insisted that viewing LN as rules of inference as better than viewing them as premises in a deductive argument explains the real behavior of scientists. Insofar as this point is crucial for the understanding of the epistemic merits of the inferentialist approach to laws of nature, and it has not been clarified enough by Toulmin himself, it will be discussed in more detail in the next (last) part of the paper.

What Toulmin’s critics didn’t see, or the epistemological merits of the inferentialist construal of laws of nature Toulmin’s critics were right that from a logical point the view, there is no difference whether laws of nature will be construed as sentences that serve as premises in deductive arguments or as material rules of inference. If one sticks to the laws-as-premises view, however, and faces a case when a particular law, taken together with some initial conditions, implies a prediction which is false, logically she has two possibilities: to admit that the law-premise is not true (at least not universally true) or to assume that the initial conditions have not been properly accounted for. As there is no logical way to decide between these two possibilities, the proponents of the laws-as-premises view finally end with the famous problem of underdetermination. There have been many objections to the problem of underdetermination in a sense that it is an artificial problem, created by philosophers who have stuck to a particular (deductivist) picture of science (Laudan 1990). We see here that such objections are not unreasonable: the underdetermination appears as a problem only if one conceives LN as premises in a deductive schema. What happens if instead we take an inferentialist stance to LN? Suppose, we have the law X such that if X is applied as an inferential rule to the description |S1| of the situation S1, the result is the description |S2| which, however, does not fit the real situation S2. In this case one can definitely conclude that the law X does not hold in S1. There is no ambiguity in this conclusion and thus no underdetermination.



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To summarize, the epistemological merits of the inferentialist account of laws of nature are twofold. In the first place, the construal of LN as material rules of inference relieves us of the burden of looking for peculiar referents of the alleged law statements; in the second, it dissolves the underdetermination problem by revealing that the latter is an artifact that matters only if one takes the deductivist stance of the laws-as-premises view. These epistemological merits of the inferentialist approach to one of the most essential parts of scientific knowledge suggest that the implications of inferentialism for philosophy of science look highly promising and deserving further exploration.

References Armstrong, David. 1983. What Is a Law of Nature? Cambridge: Cambridge University Press. Brandom, Robert. 2000. Articulating Reasons. Cambridge, MA: Harvard University Press. —. 2007. “Inferentialism and Some of Its Challenges.” Philosophy and Phenomenological Research 74 (3): 651-691. Carroll, John. 2006. “Laws of Nature.” In Stanford Encyclopedia of Philosophy, edited by Edward Zalta. Retrieved September 18, 2010, from http://plato.stanford.edu/entries/laws-of-nature. Giere, Ronald. 1999. Science without Laws. Chicago: University of Chicago Press. —. 2006. Scientific Perspectivism. Chicago: University of Chicago Press. Harré, Rom. 2000. “Laws of Nature.” In Companion to the Philosophy of Science, edited by William Newton-Smith. London: Blackwell. Horwich, Paul. 1998. Meaning. Oxford: Clarendon Press. Kuipers, Teo. 2007. “Laws, Theories, and Research Programs.” In General Philosophy of Science: Focal Issues, edited by Teo Kuipers. Amsterdam: Elsevier. Laudan, Larry. 1990. “Demystifying Underdetermination.” Minnesota Studies in the Philosophy of Science 14: 267-297. Musgrave, Alan. 1980. “Wittgensteinian Instrumentalism.” Theoria 46: 65-05. Nagel, Ernest. 1954. “Review.” Mind 63 (251): 403-412. Newton, Isaac. (1848) 2002. Principia. London: Running Press. Peregrin, Jaroslav. 2012. “What is Inferrentialism?” In Inference, Consequence, and Meaning: Perspectives on Inferentialism, edited by Lilia Gurova. Newcastle upon Tyne: Cambridge Scholars Publishing.



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Ryle, Gilbert. (1949) 2000. The Concept of Mind. Chicago: The University of Chicago Press. Scriven, Michael. 1955. “Review.” The Philosophical Review 64 (1): 124128. Sellars, Wilfrid. 1953. “Inference and Meaning.” Mind 62: 313-338. Suppe, Frederick, ed. 1977. The Structure of Scientific Theories. Illini Books. Toulmin, Stephen. 1953. Introduction to the Philosophy of Science. London: Hutchinson.





CONTRIBUTORS

OndĜej Beran is Researcher at the Institute of Philosophy of the Academy of Sciences of the Czech Republic. He is the author of the books Our Language, My World (2010, in Czech) and Private Languages (forthcoming, in Czech). He also translated some of Ludwig Wittgenstein’s writings into Czech. Boris Grozdanoff is Assistant Professor at the Institute for the Study of Societies and Knowledge of Bulgarian Academy of Sciences. He is the author of the book Thought Experiments and Science (2010, in Bulgarian) and the papers “Fregean One-to-One Correspondence and Numbers as Object Properties” (2010) and “Reconstruction, Justification and Incompatibility in Norton’s Account on Thought Experiments” (2007). Lilia Gurova is Associate Professor at the Department of Cognitive Science and Psychology of New Bulgarian University. She has published two books in Bulgarian: The Role of Problems (1998) and The Psychologism – Anti-Psychologism Debate (1999, with D. Tsatsov). Her most recent papers include “Fodor vs. Darwin: A Methodological FollowUp” (2011), “Sparse and Dense Categories: What They Tell Us about Natural Kinds” (2011), “Assuming Essences and Refuting Them” (2008). Anita Kasabova is Associate Professor at the Department of Anthropology of New Bulgarian University. She has published papers in journals such as Archiv für Geschichte der Philosophie, British Journal for the History of Philosophy, History of Philosophy Quarterly, History and Theory, Lexia and recently contributed to the series Boston Studies in the Philosophy of Science. She is also the author of the book On Autobiographical Memory (2009, CSP). Rosen Lutskanov is Assistant Professor at the Institute for the Study of Societies and Knowledge of Bulgarian Academy of Sciences. His major publications include: “Whitehead’s Early Philosophy of Mathematics and the Development of Hilbert’s Formalism” (2011), “On the Intricate Interplay of Logic and Ontology” (2011), “Hilbert’s Program: the Transcendental



144

Contributors

Roots of Mathematical Knowledge” (2010), “What is the definition of logical constant?” (2009). Nenad Mišþeviü is Professor at the Department of Philosophy of the University of Maribor, Slovenia and recurrent Visiting Professor at Central European University, Budapest. He has published papers in the journals Erkenntnis, Dialectica, Monist, Topoi, Pragmatics and Cognition, Philosophical Studies, Studies in East European Thought, International Studies in the Philosophy of Science, Acta Analytica, Croation Journal of Philosophy. He has also edited the book Nationalism and Ethnic Conflict: Philosophical Perspectives (2000, Carus Publishing). Jaroslav Peregrin is Professor at the Institute of Philosophy of the Academy of Sciences of the Czech Republic and at the Faculty of Philosophy, University of Hradec Králové. His research is located at the intersection of logic, analytic philosophy, and semantics and he has authored papers in these areas for Australasian Journal of Philosophy, Erkenntnis, Journal of Philosophical Logic, Pragmatic and Cognition, Philosophia, Philosophical Topics, Studia Logica etc. Aside of a couple of books in Czech, he is the author of Doing Worlds with Words (1995, Kluwer) and Meaning and Structure (2001, Ashgate). Anguel Stefanov is Professor at the Institute for the Study of Societies and Knowledge of Bulgarian Academy of Sciences. He has published 11 books and over 140 papers in Bulgarian, English, and Russian. His latest books are About Science and Its Applicability (2010, in Bulgarian), Philosophy of Time (2008, in Bulgarian), The Challenge of Incommensurability (2000, in Bulgarian). He is also the author of “On Kant’s Conception of Space and Time” (2003). Vladimír Svoboda is Researcher at the Institute of Philosophy of the Academy of Sciences of the Czech Republic. He has co-authored the books Logic and Ethics (1997, in Czech), From Language to Logic (2009, in Czech) and Logic and Natural Language (2010, in Czech). Some of his recent papers are „Logic and Values” (2009), „Causation, Interpretation and Omniscience: A note on Davidson’s Epistemology” (2004, with Tim Crane), „Forms of Norms and Validity” (2003). Since 1987 V. Svoboda has coorganized the Annual International Symposia LOGICA.







INDEX

algebra 21-22, 25-29 Boolean 21, 26-27, 29 constraint infon 25 Heyting 25-27, 29 infon 27-28 antecedent 86-87, 89-90, 101 and consequent 86-87, 89-91, 99 a priori 47, 49, 55, 59-61, 65 Aristotle 90-93, 98 assertion 8-9, 33-36, 59 authenticity 119 Barwise, K. J. 24-25, 27-29 Belnap, N. 6 Benacerraf, P. 69-74, 77, 79-80 Benacerraf’s dilemma 69-70, 76, 80 Bolzano, B. 85-96, 98-99 Brandom, R. ix-xi, 3-4, 8-11, 13, 19-20, 22-24, 28-29, 31, 34-35, 37-38, 47-62, 64-66, 86, 107109, 131, 135-136 Carnap, R. 12 command 37, 41-45 commitment 20, 37, 45, 51, 54, 57, 59, 61-62, 64 and entitlement 8-9, 29 communication 9, 11, 33-36, 40, 107, 123, 126-128 concepts 24, 35, 47-66, 76-77, 106, 109, 111-112 non-empty 48, 65 non-logical 49-51, 109 pejorative 47, 51, 53, 55-57, 62-63 representational vs. inferential theory of 47-66 theoretical 57-58, 108



consequence 29, 38, 57, 86-88, 9094, 99-101 content 5, 8-9, 19, 23-24, 33, 36, 120 conceptual 3, 4, 20, 28, 49-51, 59, 61, 64, 108-110 propositional 24, 33-35, 87, 89, 108 Davidson, D. 31 deducibility 87-90, 92 discourse 29, 31, 33-34, 37, 39-42, 45-46, 54, 121, 123, 127-128 assertoric 31, 34, 37, 39 prescriptive 31, 33, 39-42, 46 Dummett, M. 6, 8, 32, 48-51 enthymeme 90 probative 90 explication 9, 37, 42, 136 explicitation 20-21, 23-24, 29 expressivism about logic 136 rationalist 22 Feyerabend, P. 105 fictionalism 71 Fodor, J. x, 10-11 Frege, G. 4, 48, 69, 76-78, 87 Gentzen, G. 5, 7 giving and asking for reasons 4, 8, 24, 33, 35, 37, 40 ground 47-48, 55, 57, 59, 61-62, 64, 85-87, 90-94, 98-100, 110 harmony 7, 51 Hegel, G. W. F. 19-20, 22-24, 2829 dialectical logic of 19, 23, 29

146 Heidegger, M. 117-121 Hilbert, D. 5, 72, 78 Hume, D. 39 imperative 40-41 implication 22, 52, 56, 87, 89-90, 99, 119, 132 material 87, 89-90 impossible worlds 29 incommensurability xii, 105-106, 110 individuality xii, 115-121, 127 critical 118-121, 127 numerical 118, 127 inference ix-xii, 4-6, 8-13, 21-22, 24-25, 27-29, 31, 33-34, 36-37, 39-41, 47-48, 52-55, 57, 59-66, 86-87, 89-90, 107-109, 116-132, 136-138 formal 28, 61, 118, 127 logic of x, 19-21, 29 material xii, 28, 37, 49, 59, 6162, 107-108 “materially bad” 49, 51, 65 rules of ix, xii, 3-5, 9-12, 38, 40, 49-50, 61, 63-65, 108, 126, 132-133, 136, 138-140 inferentialism ix-xiii, 3-14, 23-24, 27-29, 31, 85-86, 105, 108-110, 112-113, 115-116, 131, 135136, 140 hyper-, strong, and weak 11-12, 108-109 normative vs. causal 8-11 and representationalism 3-4, 11, 13, 58, 64-65, 131-133, 135, 138 inferentially native operators vii, 21 intersubjectivity 29, 115-117, 122124, 127-128



Index Kafka, F. 121 Kuhn, T. 105 Lance, M. ix, 13, 31 language 3-6, 8-13, 21-24, 31-34, 37-39, 42, 44, 62, 69-71, 77-79, 86-87, 90, 115-128, 139 embodiment of 13 meta- 21 philosophy of xii-xiii, 115, 117 prescriptive 31-32, 34, 40, 42, 45 private xii, 115, 124-125, 128 of science 69, 71, 106-107, 111, 136-137, 139 theory of natural x, 13-14, 24, 34, 77-79, 115-128 language games xi, 4, 8, 32-34, 36, 45, 118-128 assertive 34-35 creative xii, 123-124 intersubjective 127 parasitic 127 successful vs. unsuccessful 39 laws of nature xii, 13, 105, 108, 131-140 inferentialist account 132, 135140 instrumntalism about 134-135 representationalist account 133134 Toulmin’s view 132, 135-139 Lepore, E. x, 10-11 Lewis, D. 13, 42-44 logic 4-8, 13, 19-29, 61, 77-78, 136 classical 5, 29 deontic 41 intuitionistic 5, 22, 28-29 philosophy of x, xiii, 3 relevant 29, 89 substructural x, 6

Inference, Consequence, and Meaning: Perspectives on Inferentialism logical constants 5-8, 22, 50 logical vocabulary 11, 20-21, 24, 108 meaning ix-xi, 3-13, 24, 31, 34-42, 45, 49-52, 56, 62, 70, 73, 76, 78-79, 90, 95, 105-112, 116118, 126-127, 131-132, 135-137 change 106, 108, 110 contextual theory of 107 inferentialist theories of ix-x, 413, 39, 42, 107 representationalist theories of ix-x, 3 of terms use theory of 135-136 memory xii, 85, 95-98 autobiographical 99 episodic xii, 85, 95, 98, 100101 trace 95-97 metaphysics xi, 70, 72, 76-77, 7980, 94 Mill, J. S. 76 Montague, R. 13 Nagel, E. 132, 138 Newton, I. 71, 108, 113, 133-135 normative 8-11, 19, 33, 44, 59, 6162, 64-65 attitude 10, 61 commitment 61, 64 pragmatics 12 situation 44-45, 122 objects xi, 13, 21, 29, 37, 76, 88, 90, 92-93, 97, 100, 110-112, 138 abstract 71, 73-74 physical xi, 69-71, 73-75, 78



147

Peirce, C. S. 132 pejoratives xi, 47-58, 63-66 permission 33, 39, 42, 44 poetry 120 pragmatic turn 12 Prawitz, D. 7 prescription 33, 37, 39, 41-42, 45 Prior, A. 5-6, 12 proof 5, 7, 85-86, 91-92, 94 theory x, 5-8, 13-14, 86 properties 26, 50, 63, 70-71, 75-77, 79, 88, 110, 112, 118 provability 28 Quine, W. V. O. 23, 31, 55, 60, 72 Ramsey, F. 138 reason 4, 8-9, 24, 33, 35, 37, 40-41, 61, 85-87, 91-92, 98-100 recollection xii, 92, 95-101 reference 4, 52, 55-56, 61-62, 69, 73-74, 77-80, 132 referentialism 55 relation xi-xii, 9, 24, 73-74, 77, 85101, 108-112, 131-132 “because” 86, 97-98, 101 causal xii, 91-92, 99 demandatory 39 grounding xii, 85-101 inferential xi, 9, 11, 21, 33-34, 37, 108-109, 112, 131-132 semantic xii, 97 representation, scientific 110-111, 131 inferential conception of 110, 113 Ross paradox 41 Ryle, G. 132 Schlick, M. 138 Sellars, W. x, 4, 11-12, 23, 31, 40, 62, 64, 108, 132

148 semantics x-xi, 3-4, 6-13, 19, 22, 48, 64-66, 69-80, 85-86, 109, 115 conceptual role 10 homogeneous xi, 69-80 inferentialist x, 12-13, 19, 24, 29 model-theoretical 13 of scientific knowledge 73 situation x, 19, 24-25, 27-29 sense 48, 50-54, 56, 65-66, 69, 7879, 95-96, 98 sentences 6, 8, 11, 13, 20, 33, 36, 41, 53, 86-89, 107-109, 132, 139 imperative xi, 38-39 Snell’s law 134, 136-137 space 13 of discourse 121, 127-128 of meaningfulness 13 and time 69-71, 73-75, 79, 111, 117



Index sphere of permissibility 42-43, 45 sublation 23 surrogative reasoning 112-113 syntax 12 Tarski, A. 69-72, 78-79, 87-89, 97 time 69-71, 73-75, 79, 99-100, 125 Toulmin, S. 132, 135-39 truth 6, 28, 33, 37, 40-41, 53, 59, 65, 69-70, 76-77, 85-87, 90-94 conceptual 48, 60, 77 conditions 53, 69-70, 79, 87 in science 134, 137-138 mathematical 76 tables 5-6, 12, 107 values 33, 40-41, 59 underdetermination 139-140 Wittgenstein, L. 4, 8, 10, 31-32, 98, 115, 117, 119-121, 124-126, 128, 135