From Rules to Meanings: New Essays on Inferentialism 113810261X, 9781138102613

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From Rules to Meanings

Inferentialism is a philosophical approach premised on the claim that an item of language (or thought) acquires meaning (or content) in virtue of being embedded in an intricate set of social practices normatively governed by a special sort of rules—inferential rules. Over the last two decades, inferentialism has established itself as one of the leading research programs in the philosophy of language and also, increasingly, in the philosophy of logic. Though it has grown into a vigorous and ramified branch of philosophical thinking, contemporary inferentialism is only rarely presented in a more systematic and comprehensive manner that explores its diversity. The book fills this lacuna by bringing together new essays on inferentialism that develop, compare, and assess, but also critically react to some of the most pertinent recent trends that would appeal to a wider philosophical readership. Its core chapters have been written by distinguished philosophers contributing to the research in the field. Ondrˇej Beran is a researcher, currently based at the Centre for Ethics (University of Pardubice). His publications, ongoing work, and areas of research interest include the philosophy of language, ethics, the philosophy of religion, and feminist philosophy. He is the author of the book Living with Rules (Peter Lang) and research articles in international journals (Sophia and Ethical Perspectives). Vojteˇch Kolman is Associate Professor of Logic at the Faculty of Arts, Charles University in Prague. His research focuses mainly on themes from the philosophy of mathematics, the history of logic, pragmatism, and the philosophy of the arts. He is author of the book Zahlen (de Gruyter) and numerous articles in international journals (Synthese, Erkenntnis, Hegel-Bulletin, Allgemeine Zeitschrift für Philosophie, and others). Ladislav Korenˇ is the Chair of the Department of Philosophy and Social Sciences at the University of Hradec Králové and a researcher at the Czech Academy of Sciences. His areas of interest include epistemology, philosophy of language, philosophy of logic, philosophy of mind, and philosophy of social sciences. His publications include research articles in international journals (Synthese, Journal of Social Ontology) and Volumes (Routledge).

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Trust in the World A Philosophy of Film Josef Früchtl Taking the Measure of Autonomy A Four-Dimensional Theory of Self-Governance Suzy Killmister The Legacy of Kant in Sellars and Meillassoux Analytic and Continental Kantianism Edited by Fabio Gironi Subjectivity and the Political Contemporary Perspectives Edited by Gavin Rae and Emma Ingala Aspect Perception after Wittgenstein Seeing-As and Novelty Edited by Michael Beaney, Brendan Harrington and Dominic Shaw ature and Normativity N Biology, Teleology, and Meaning Mark Okrent Formal Epistemology and Cartesian Skepticism In Defense of Belief in the Natural World Tomoji Shogenji Epistemic Rationality and Epistemic Normativity Patrick Bondy From Rules to Meanings New Essays on Inferentialism Edited by Ondřej Beran, Vojtěch Kolman, and Ladislav Koreň For a full list of titles in this series, please visit www.routledge.com

From Rules to Meanings New Essays on Inferentialism Edited by Ondrˇej Beran, Vojteˇch Kolman, and Ladislav Korenˇ

First published 2018 by Routledge 711 Third Avenue, New York, NY 10017 and by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business © 2018 Taylor & Francis The right of the editors to be identified as the author of the editorial material, and of the authors for their individual chapters, has been asserted in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Names: Beran, Ondřej, editor. Title: From rules to meanings : new essays on inferentialism / edited by Ondřej Beran, Vojtech Kolman, and Ladislav Koren. Description: 1 [edition]. | New York : Routledge, 2017. | Series: Routledge studies in contemporary philosophy ; 103 | Includes bibliographical references and index. Identifiers: LCCN 2017044429 | ISBN 9781138102613 (hardback : alk. paper) Subjects: LCSH: Meaning (Philosophy) | Inference. Classification: LCC B105.M4 F76 2017 | DDC 121/.68—dc23 LC record available at https://lccn.loc.gov/2017044429 ISBN: 978-1-138-10261-3 (hbk) ISBN: 978-1-315-10358-7 (ebk) Typeset in Sabon by Apex CoVantage, LLC

This volume was put together as a follow-up to the Prague workshop Why Rules Matter that discussed Jaroslav Peregrin’s book Inferentialism, marking a new phase in the inferentialist discussions, and with the aim to celebrate Jaroslav Peregrin’s 60th anniversary.

Contents

Acknowledgmentsx Introduction: Inferentialism’s Years of Travel and Its Logico-Philosophical Calling

1

LADISLAV KOREŇ AND VOJTĚCH KOLMAN

PART I

Language and Meaning

47

  1 Grounding Assertion and Acceptance in Mental Imagery

49

CHRISTOPHER GAUKER

  2 Semantics: Why Rules Ought to Matter

63

HANS-JOHANN GLOCK

  3 Quine Peregrinating: Norms, Dispositions, and Analyticity

81

GARY KEMP

  4 Let’s Admit Defeat: Assertion, Denial, and Retraction

97

BERNHARD WEISS

PART II

Logic and Semantics

113

  5 Inferentialism, Structure, and Conservativeness

115

OLE HJORTLAND AND SHAWN STANDEFER

  6 From Logical Expressivism to Expressivist Logics: Sketch of a Program and Some Implementations ROBERT BRANDOM

141

viii Contents   7 Inferentialist-Expressivism for Explanatory Vocabulary

155

JARED MILLSON, KAREEM KHALIFA, AND MARK RISJORD

  8 Logical Expressivism and Logical Relations

179

LIONEL SHAPIRO

  9 Propositional Contents and the Logical Space

196

LADISLAV KOREŇ

10 Assertion, Inference, and the Conditional

219

PETER MILNE

PART III

Rules, Agency, and Explanation

237

11 Naturecultural Inferentialism

239

JOSEPH ROUSE

12 Inferentialism: Where Do We Go from Here?

249

JAROSLAV PEREGRIN

13 The Nature and Diversity of Rules

261

VLADIMÍR SVOBODA

14 Governed by Rules, or Subject to Rules?

278

ONDŘEJ BERAN

PART IV

History and Present

293

15 Inferentialism after Kant

295

DANIELLE MACBETH

16 Inferentialism, Naturalism, and the Ought-to-Bes of Perceptual Cognition

308

JAMES R. O’SHEA

17 Inferentialism and Its Mathematical Precursor VOJTĚCH KOLMAN

323

Contents  ix 18 Inferentialism and the Reception of Testimony

334

LEILA HAAPARANTA

List of Contributors 347 Index352

Acknowledgments

Work on this volume was supported by grant no. 13-20785S of the Czech Science Foundation (GAČR).

Introduction Inferentialism’s Years of Travel and Its Logico-Philosophical Calling Ladislav Koreň and Vojtěch Kolman

“Alles ist ein Schluss” Georg Wilhelm Friedrich Hegel

Inferentialism, narrowly conceived, is a philosophy of language that treats linguistic artifacts as meaningful by virtue of their being embedded in an intricate set of language-mediated social practices governed by inferential norms. Broadly conceived, it is a philosophical doctrine using the concept of inference as an explanatory key to the matters of human knowledge and its relations to the world of facts, as expressed with the utmost simplicity in the above-mentioned quote by Hegel: everything is an inference. Oscillating between such attitudes of different focus and g­ enerality— the focus on logic being today the most vital and popular one—­ inferentialism found its paradigmatic formulation in Robert Brandom’s (1994) magisterial treatise, Making It Explicit. In the more than twenty years that have followed, the book has proved to be both an important and deep contribution to the existing linguistically oriented philosophical research and a study with a strong intellectual force field of its own. As such, it has not only stimulated new ways of thinking about logic, language, and meaning but also provided a fruitful frame of reference for thinking about knowledge, experience, and normativity in general as well as about the history of their philosophical treatment. Thanks to its broader delimitation, it has opened the path for some old antagonisms to be dissolved and new alliances to be contracted across various philosophical trends and traditions. This also includes a bridging of the unhappy split between analytical and continental philosophy. This anthology wants to address these first twenty years of inferentialism or—in the terminology of Goethe’s coming-of-age stories—let us say its “years of travel.” We think of them as the years in which inferentialism’s corpus has been shaped both within Brandom’s own philosophical work and the work of those who have treated inferentialism as a vital issue, no matter whether in a generally positive or rather critical way.

2  Ladislav Koreň and Vojtěch Kolman While Brandom’s inferentialism has received wide attention in the received philosophical literature, new lines of inquiry that merit recognition and critical appraisal have in the meantime been proposed and developed by inferentialism-friendly thinkers. The impulse for bringing these particular essays together was Peregrin’s book Inferentialism: Why Rules Matter (Peregrin 2014) in which the whole pilgrimage of Brandom’s “early” thought, including its broader analytic context and the various tribulations devised by Brandom’s opponents, have been examined in a particularly instructive and perspicuous way. The workshop Why Rules Matter, organized in Prague in October 2016 and on which some of these essays are based, was devoted to the topics of Peregrin’s book with a particular focus on the matters of (inferential) rules and their relation to meaning. Some essays were written specifically for this volume to cover the other themes of importance. We have decided to call these contributions new essays on inferentialism to express our conviction that inferentialism has entered the phase in which one does not have to explain or justify inferentialist doctrine in extenso for the simple reason that its traveling years are over. This introduction reflects the thematic structure of the anthology and its four parts as well as the narrower and broader shapes of inferentialism mentioned above. Accordingly, in the first three sections we reconstruct inferentialism’s standpoints on specific issues concerning language and meaning (section 1), logic and semantics (section 2), and rules, agency, and explanation (section 3). In the fourth and final section, we step back a bit so as to examine the problems of inferentialism from a broader perspective that covers its philosophical influences, predecessors, and allied streams of thought in contemporary philosophy. In every section, we describe how individual essays in the anthology fit this overall scheme. We often do it within the wider context of themes and topics that are not explicitly dealt with in the volume’s chapters, not only due to the limitations of space, but also because these themes and topics represent challenges to be faced in (to complete our analogy with Goethe) inferentialism’s “master” years to come, as well as in connection with Brandom’s long-awaited commentary on Hegel’s Phenomenology of Spirit that is to appear soon under the name of A Spirit of Trust.

1.  Thought, Language, and Meaning One of the inferentialists’ main undertakings is to shed light on the nature of human cognition in its basic delimitation as thinking or cognizing by means of concepts. What kind of cognitive abilities such conceptual thinking requires, and how they relate to preconceptual modes of cognition on the one hand and language on the other hand, is a vexed issue over which much ink has been spilled. Inferentialists approach it by deciding that the paradigmatic mode of conceptual thought is discursive

Introduction  3 intentionality, exemplified in judging that something is thus and so. As Brandom elaborates it, discursively intentional creatures are sapient in that they are capable of thinking, reasoning, or talking in a propositional mode. Accordingly, paradigmatic conceptual contents are thought of as judgeable-propositional contents or ingredients thereof. Transposed into this particular key, the question of the nature of conceptual thought is a foundational one because what is at stake is an essential piece of our self-understanding: what it takes to think, reason, and talk as we do, eventually allowing better understanding of what it takes to think, reason, and communicate differently. Of course, philosophers have come up with different accounts of what confers on particular episodes the significance of judgments with determinate propositional contents, and what is the relation between them and their constituent conceptual contents. Because inferentialists often advertise their approach as reversing the traditional representational order of explanation, it can be useful to give first a brief characterization of the latter, then detailing why and how inferentialists beg to differ. 1.1. Representationalism As inferentialists portray it, the idea animating the representationalist order of explanation is that contents expressed by judgments constitutively depend on representational (referential, descriptive) powers of their components and the way these are unified in judgments. Though approaches assuming the explanatory priority of linguistic representation are not a ­priori ruled out, representationalists usually proceed by postulating a more fundamental, mind-to-world layer of representational relations supposed to ground linguistic intentionality. Typically, they account for the meanings or contents of sentences by mapping them onto the representational contents of thoughts that the uses of those sentences are taken to express. The contents of such thoughts are in turn explained as being based on the representational contents of concepts that are their ingredients and onto which constituent expressions of corresponding sentences are mappable. This approach fits well in the traditional conception of language as a vehicle for encoding contents antecedently stored in some mental format and transmitting them to a recipient who decodes them into a similar mental format of his or her own. At the semantic level, then, it invites reconstructions of languages that assign referential semantic values of sorts to subsentential expressions, in terms of which truth-conditions of sentences are generated (preferably in a systematic, compositional style). Finally, inferential (paradigmatically ­logical) relations between sentences are accounted for as based on their truth conditions. Along with a number of other opponents, inferentialists are not convinced that this is the only game in town—or the most promising approach

4  Ladislav Koreň and Vojtěch Kolman to pursue. With the benefit of hindsight, it is not unfair to say that representational approaches have failed to explain what they ultimately should explain: what kind of a mental structure does it take to represent some worldly item, rather than something else? Instead of answering the question, some representationalists have begged or avoided it by saying that minds represent what they do by virtue of grasping abstract items in a platonic realm already endowed with representational powers. Here, abstract items endowed with representational powers are unexplained explainers. Moreover, it is a mystery how concrete minds can get in touch with abstract structures. Another way to evade the question by introducing unexplained explainers is to posit primitive, intrinsically representational states realized in brain structures. Most representationalists, however, have attempted to address the challenge head on, typically by providing naturalistic reductions of mental content. Thus causal (or informational) theories hold that mental items represent worldly items that reliably (in a law-like manner) cause (covary with) their tokens in minds, whilst teleological theories propose to explain mental contents as based on evolved biological functions of sorts (cf. Stampe 1977; Dretske 1981; Fodor 1990; Millikan 1984). Ingenious as they might be, such reductions face a number of obstacles that nobody has been able to deal with in a satisfactory way. In particular, it remains unclear whether and how they could account for the phenomenon of misrepresentation (relatedly, for the intuition that contentful items correctly apply only to certain items) without intentional, semantic, or normative notions reentering the stage through the back door. In addition, it remains unclear whether they have enough resources to account for fine-grained contents, including those that characterize propositional thoughts. 1.2.  Space of Reasons Inferentialism offers an alternative approach to conceptual content to be classified as a distinctive version of what has come to be known as ­conceptual-role semantics. The basic idea is often attributed to Wittgenstein (see section 4 of this introduction for details), but it was Sellars who developed it into a systematic proposal (see, particularly, Sellars 1953a; 1954; 1956). In a nutshell, its gist is that there is no intrinsic content (or meaning) and all contentfulness (meaningfulness) is to be accounted for in terms of the use, that is, the role that contentful items play in the economy of reasoning. This is usually further specified by saying that it is the role in inferences (of sorts) that wholly or partly confers contents or meanings on items of thought or language. However, Brandom and other inferentialists elaborate on this line of thought in a distinctive way, parting ways with other conceptual-role theorists at several points. Unlike theorists maintaining the priority of mind-mediated individual reasoning, inferentialists follow Sellars in giving pride of place to a

Introduction  5 language-mediated economy of social reasoning. On this account, for one to be a sapient creature able to conceptualize, one must be able to take part in a social practice of producing and consuming performances having the pragmatic significance of claiming or asserting something. Such performances, in turn, are what they are owing to the role they play in the economy of reasoning embedded in practices of communication and interpretation that have the discursive structure of the game of giving and asking for reasons. The economy, moreover, is rule-governed in a way that renders content-conferring inferential roles normative. That said, inferentialists acknowledge that assertion has two important dimensions. On the one hand, in asserting something, one presents the world as being a certain way. On the other hand, in asserting something, one makes a move in the space of reasons that is apt to provide reasons for or against other moves of its kind (and the other way around). The first dimension captures a representational, objective purport of assertion. The second, inferential dimension captures its role in reasoning. Both dimensions, moreover, come with standards of correctness. In asserting that the world is a certain way, one takes it that what one asserts is correct—the world being the way one presents it to be. Yet, one may be wrong about this. Also, in taking one’s assertion as providing reasons for or against other moves of its kind, one may or may not be correct, depending on the structure of the space of reasons (inferential relations) as determined by the norms of correct inference. Hence, a promising account of assertion, as a linguistic paradigm of conceptual thought, should accommodate both dimensions. But inferentialists propose to account for the inferential dimension first, and then from it also reconstruct the representational dimension. As executed by Brandom (1994, 2000a), this theoretical agenda has two connected parts. First, it provides an account of assertion in terms of a distinctive normative role it plays in the social practice of reasoning. This is the pragmatic part. Based on this, then, it accounts for the contents of assertions (including their objective purport) in terms of their inferential articulation. This is the semantic part. 1.3.  Scorekeeping Model of Language What, then, is the characteristic normative role of assertional performances that creatures have to master practically for their responses to the world and one another to amount to conceptual classifications rather than exercises of their dispositions to differentially and reliably react to environing stimuli? As a first approximation, we can say that to assert something is to produce an expression-involving performance that makes it appropriate to make further moves of its kind by providing a reason for the latter—thereby making them kind of inferable. And it makes it inappropriate to make yet other moves of its kind by providing a reason against the latter—thereby excluding them as kind of incompatible.

6  Ladislav Koreň and Vojtěch Kolman Symmetrically, other moves of its kind are apt to render such a performance appropriate or inappropriate. So it can be provisionally suggested that, at a minimum, concept-mongering creatures must be practically able to treat some performances within their social practice as giving reasons for or against other performances of that kind. Brandom’s normative pragmatism develops this idea as follows: in or by making discursive performances, typified by assertions, performers undertake a special kind of social responsibility and authority (see Brandom 1994, chap. 5). And they could acquire such social-normative standings due to taking part in a shared practice of communication and mutual interpretation, in which performers are treated as responsible or authoritative. More specifically, in Brandom’s deontic scorekeeping model of the practice, practitioners are described as achieving this effect through adopting practical normative attitudes, namely by attributing discursive commitments to performers uttering certain expression-types. Practitioners thereby practically treat performers as undertaking such commitments, as well as what attributors take to be their consequential commitments. By the same token, they treat performers as being precluded from undertaking other commitments that they thereby take to be excluded. In addition, performers are treated as being entitled (or not) to corresponding commitments, having a conditional task-responsibility to inferentially vindicate them if an appropriate challenge arises. In this very sense, practitioners keep score on their respective normative standings (commitments, entitlements) and update it in view of changes effected by utterances of certain expression types in a way that sustains a characteristic pattern of difference to how they perceive their deontic scores before and after such performances. The claim is that in virtue of adopting such scorekeeping attitudes toward performances of one another, they eventually come to practically treat them as having the pragmatic significance of assertional speech-acts making claims. Contents of assertional performances or corresponding expressiontypes are modeled as their specific inferential articulation: their position in the inferential space of reasons implicitly established by scorekeeping activities of this kind. Here, inferentialists insist that contents expressible by (uses of) sentences cannot be identified and individuated independently of contents of a whole lot of other sentences. Sentences always come as a package, being part of a larger system of expressions such that its members owe their semantic identities in part to their inferential relations to other members. Take, for example, a simple English sentence P:  “This is red.” Inferentialists are adamant that one has no—or at best, one has a very poor—idea of what that expression expresses (hence, what its

Introduction  7 sub-expression “red” expresses) if one has no understanding that P is something that appropriately inferentially relates to a host of other expressions such as “This is colored” (which can be inferred from P), “This is crimson” (from which P can be inferred), “This is white” (which is incompatible with, hence excluding coassertibility of P), and so on. Based on holistic considerations of this sort, inferentialists maintain that material inferential links between nonlogical sentences are among the key determinants of conceptual contents of nonlogical sentences and expressions. (Here, Sellars 1953a is a major source of inspiration, but also see section 4 for other details.) They are so called because they do not hold in virtue of forms provided by logical expressions but in virtue of the contents of nonlogical expressions involved in them. Ultimately, however, the contents are explained as being conferred upon the expressions by proprieties governing their use in whole sentences. 1.4.  From Pragmatics to Semantics Brandom elaborates this idea by distinguishing three kinds of consequential relations between normative statuses that practitioners keep score on, eventually constituting three kinds of content-conferring inferential relations. (1) In keeping track of commitment-preserving relations, scorekeepers treat those whom they take to be committed to a claim as being thereby committed to some other claims (commissive consequences). (2) In keeping track of entitlement-preserving relations, scorekeepers treat those whom they take to be entitled to a claim as being thereby entitled to some other claims (permissive consequences). (3) And finally, in keeping track of incompatibility relations, scorekeepers treat those whom they take to be committed to a claim as being thereby precluded from being entitled to some other claims. (3), in turn, grounds incompatibility entailments: assertible p entailing in this sense assertible q if everything materially incompatible with q is materially incompatible with p. These three relations are supposed to generalize (to the material case) respectively deductive inferences, inductive (defeasible) inferences, and counter-factually robust modal inferences. Brandom’s contention then is that when the practice reaches a threshold when practitioners mutually keep score on such relations, it is plausible to interpret them as engaging in a practice of asserting inferentially articulated claimable contents.

8  Ladislav Koreň and Vojtěch Kolman Brandom’s scorekeeping model is designed to connect the pragmatist and the semantic level of description of language: by laying bare the “normative-fine structure” of a rational practice that would warrant its interpretation as a core linguistic-discursive practice apt to be semantically reconstructed in terms of inferential relations. The strategy is to account for what is asserted via proprieties of asserting and inferring reconstructed in terms of deontic-scorekeeping. What content an assertion expresses depends in part on its narrow inferential articulation: its material-inferential links to other assertibles typified by relations referred to above. In addition, to accommodate empirical and practical dimensions of linguistic practice, transitions involving noninferential circumstance or consequences should be given a due recognition, including appropriate making of claims in response to observable events (language-entry transitions such as the correct assertability of “This is red” in the presence of a red object or stuff) and appropriate deliberation and undertaking of actions in response to practical reasons expressible in claims (languageexit transitions, such as the reasonableness of not eating some red stuff when taking it to be toxic while wanting to avoid getting poisoned). So normative roles constituting sentence-types apt to be used to make assertions expressing particular propositional claims—­ derivatively also roles constituting sub-propositional contents that are ingredients thereof—will incorporate such proprieties. We may call this a broad inferential articulation. The justification for this label is that even though such transitions are noninferential, they are still mediated by sentences standing in material-inferential links to other sentences. Moreover, the transitions themselves are not immune to criticism and thus to demands for justification (subject to the default-challenge structure of entitlement). In this sense, observation reports do not form a self-standing language game that one could play without playing an inferential game (see S­ ellars 1954, 1956; Brandom 2015, 124). Accordingly, conceptual competence exhibited by sapient creatures exhibiting discursive intentionality amounts to their practical mastery over such inferential proprieties as well as over proprieties governing language-entry transitions and language-exit transitions issuing into intentional action. 1.5. Contributions Inferentialism is an extremely ambitious theory of meaning and conceptual thought. Brandom (1997a, 189) himself glosses his dialectical strategy in Popperian terms, as one of formulating “the stronger, more easily falsifiable hypothesis to see how far it can be pressed,” that is, whether it can withstand attempts at refutation, eventually what modifications thereof are called for. Commentators have taken Brandom at his word, probing the doctrine from different directions.

Introduction  9 Some criticism has centered on the methodological idea that we could shed light on the representational dimension of assertible content starting with the inferential dimension. The worry here is that once we recognize the two dimensions as interdependent and complementary aspects, any attempt to reduce one to the other (whether in the inferentialist or in the representationalist style) is bound to fail (cf. McDowell 2008; Kremer 2010). Relatedly, it has been charged that Brandom’s deontic scorekeeping model of the assertional language game lacks central features of our practice of staking claims with objective purport, including appropriate attunement to the environment or genuinely objective norms determining correct application of expressions (cf. McDowell 2008; Macbeth 2010). Other critics have specifically challenged the claim that the game of giving and asking for reasons involving just assertions and inferences is the core of any linguistic practice and moreover, an autonomous one in that one can play it while playing no other language game. This has been classified as a version of the “declarative fallacy” (cf. Kukla and Lance 2009). On the semantic level, then, there has been concern that the pervasive holism implicated in the inferential role semantics à la Brandom invites a fatal dilemma: either it forces one to resurrect the discredited analytic/­ synthetic dichotomy, or else it precludes individuation of determinate inferential roles. In addition, it threatens to render interpersonal communication an embarrassing affair of failed attempts to get across a message, because different speakers (scorekeepers) are not going to agree upon what inferences they endorse (cf. Fodor and Lepore 2007). Still other critics have argued that material inferences cannot confer meanings on nonlogical sentences, because inferring operates on contentful sentences as its inputs and outputs in the first place (cf. Boghossian 2014). In addition to this, there is an ongoing discussion of whether meaning or content is indeed constitutively normative (cf. Glüer and Wikforss 2009a, 2009b; Hattiangadi 2006). Needless to say, this is just the tip of the iceberg. Inferentialists have in turn tried to respond to the objections, and the debate is still very much alive. (See particularly Brandom’s various responses to his critics, for example, in Stekeler-Weithofer 2008 and Weiss and Wanderer 2010, as well as Peregrin 2014 for discussions of some of the most notorious objections to inferentialism.) The present anthology is no exception to this general rule. Most of the contributors who address the issue at hand sympathize with particular claims advanced by inferentialists, whilst expressing reservations about other (often bolder) tenets of the doctrine. In Chapter 1, Christopher Gauker agrees with the inferentialists that the traditional referential conception of semantics—often closely linked to the conception of communication as a conveyance of shared ­contents—needs an alternative. However, he worries that inferentialism

10  Ladislav Koreň and Vojtěch Kolman (together with other versions of functional role semantics) is dangerously close to linguistic ­ idealism—what matters are just relations between representations—and specifically, that it leaves us without any basis for explaining the correctness of our linguistic practices. Constructively, he proposes his own preferred account of both conceptual thought and of the norms governing discourse. He first introduces a kind of nonconceptual imagistic thinking in terms of which language learning can be made sense of (and which is available also to nonhuman animals). Based on it, he explains the conditions under which sentences are asserted and accepted. He then argues that, in terms of such conditions, the possibility of successful linguistic exchange in paradigm cases can be explained. And once language is internalized, it becomes a medium of intrapersonal thought. Finally, Gauker suggests that the norms of discourse can be understood as norms that supervise the processes of linguistic exchange so explained. In Chapter 2, Hans-Johann Glock agrees with inferentialists on one basic point: that the meaning of an expression is constituted by the rules for its correct use. Inferentialists emphasize the rules governing the game of giving and asking for reasons. According to him, however, the idea can be elaborated in many different ways. Glock argues that the notion of meaning ought to be clarified by reference to other pertinent notions, which are often neglected or ignored (inferentialists being no exception). In particular, drawing on Wittgenstein, he fleshes out the idea that the meaning of an expression is both what an acceptable explanation of meaning explains and what a competent speaker understands. In the specific case of general terms, Glock submits that their meaning is a matter of rules, provided that the relevant rules specify conditions that something must satisfy to fall under the term rather than specifying which objects actually satisfy those conditions. In Chapter 3, Gary Kemp discusses the relation between inferentialism and a Quinean approach to language and meaning. Quine is an important neopragmatist who taught us that language is a “social art” while denigrating all theories that posit reified, determinate meanings (the “Myth of Museum”). However, even though Quine obviously is a use-theorist of a sort, he is usually interpreted as preferring a naturalistic explanation of linguistic behavior in terms of behavioral regularities or dispositions to overt behavior (particularly, assent and dissent). This reading places him in the camp of those who succumbed to the false allure of regularism about norms of discourse (as both Brandom and Peregrin would put it). Taking issue specifically with Peregrin’s interpretation, Kemp asks whether a Quinean can speak with a straight face of rules that have the normative force envisaged by inferentialists. He then attempts to show that Quine’s linguistic dispositions actually do have the normative force, the force of rules properly speaking. Bernhard Weiss begins Chapter 4 by distinguishing “pure” and “impure” inferentialism. He says that the first aims to capture semantic

Introduction  11 content by attending to the inferential relations between sayings. He finds more plausible, though, impure inferentialism. According to it, propositional content emerges through inferentially articulated assertions, yet assertions, qua speech acts, can be conceptualized prior to and independently of the notion of inference. From this perspective, he submits, the inferential potency of an assertion can be seen to be a product of inferentially generated assertion conditions, which are the focus of semantic theorizing. He then asks whether these assertion conditions should be supplemented by denial conditions, as has recently been suggested by a number of thinkers, and critically evaluates two developments of this idea offered by Ian Rumfitt and Huw Price. He argues for an alternative approach that stresses the role of the practice of retracting previous utterances. And he concludes by comparing this proposal with the approach of Crispin Wright based on the notion of superassertibility.

2.  Logic and Semantics Normative pragmatism invites a congenial semantic perspective on language, viewed primarily in its role of a vehicle required for performances making up practices of giving and asking for reasons. Declarative sentences are given pride of place in the semantic reconstruction of language or some of its fragments, because they provide vehicles for assertions expressing claims apt to play the role of premises and conclusions in material inferences and to stand in material incompatibility relations. For a system of sentences to have a critical semantic mass required of a vehicle of practices of giving and asking for reasons, it must be structured, at a minimum, by appropriate relations of inferability and incompatibility, including material relations as well as proprieties of language-entry transitions and language-exit transitions. Thus generalized, inferential relations can be said to determine inferential potential of declarative sentences: what they follow (can be correctly inferred) from and what follows from them. Contents of expressions in general are accounted for as their specific contributions to inferential potentials of sentences in which they systematically occur as significant constituent parts—that is, their inferential roles. 2.1.  Inferentialism and Logic Inferential-role semantics looks particularly attractive for the case of logical expressions. Many theorists submit that if the whole inferentialist enterprise is going to work at all, chances are that it will work for logical items. Representational approaches are not that appealing when it comes to accounting for the meaning of logical expressions. For what do they represent in the first place? On the other hand, it has some prima facie

12  Ladislav Koreň and Vojtěch Kolman plausibility to hold that in order to know what such expressions mean it is necessary and sufficient to understand (if only implicitly) certain rules governing their manipulation. Specifically, in view of their intimate connection to reasoning, it suggests itself to say that rules governing their use in inference are preeminent determinants of their meanings. In general, logical inferentialists hold that meanings of logical expressions are determined by certain rules of inference that involve them. Influential elaboration of this idea goes back to Gentzen’s (1935) proposal that the meanings of connectives are determined by inference rules of a natural deduction proof system, in particular by the rules of their introduction and elimination, such as the following for conjunction: (∧I)

A  B  (∧E) A ∧ B

A ∧ B , A ∧ B A B

Gentzen’s idea was that elimination rules spell out consequences of the definition of the logical operator provided by means of introduction rules. Faithful to the spirit of normative inferentialism, Brandom and Peregrin interpret this in the style of Dummett (1991): such rules determine the inferential role of conjunction by specifying conditions under which sentences in which conjunction is the main operator can be appropriately asserted—that is, their introduction—and consequences of their appropriate assertability—that is, their elimination. Accordingly, what fixes the inferential role of a given logical operator are the rules of correct inferability governing its use, not actual inferences or dispositions to make or accept them in actual and counterfactual circumstances. A notorious challenge to logical inferentialism in general was spelled out by Arthur Prior (1960). He charged that it makes room for weird operators definable along the following lines: (tonk I)

A (tonk E) A tonk B

A tonk B B

However, given certain minimal demands on a deductive system, a sodefined operator allows deduction of anything (from a nonempty set of premises), rendering the deductive system inconsistent. According to logical inferentialists, what Prior’s considerations teach us is that some plausible constraints must be imposed on inferential rules if these are to determine the inferential roles of logical operators. Thus Belnap (1962) proposed the criterion of conservativeness that requires that the introduction of a logical operator by means of inferential rules must be such as not to forge new inferential links between assertible sentences of the unexpanded language that do not contain it. Conservativeness, though, is a property of the whole deductive system, and as such, it is sensitive to its specifics (in particular, what other operators, governed by

Introduction  13 what rules of inference, the system incorporates before the introduction of a new operator). A number of Gentzen’s followers therefore seek to formulate and justify more local criteria for plausible rules of inference. The criterion of harmony, anticipated by Gentzen himself, is often discussed in this context. Basically, it requires of rules of introduction and elimination that they in effect cancel each other out (cf. Dummett 1991; Tennant 1997). 2.2.  Expressivism and Self-Consciousness It is one thing (though not a small one) to specify rules of inference that determine the inferential roles of distinct logical items. It is another thing to have a story to tell about what logic is for. This question, in fact, pertains to the nature of logic. Brandom splits it into two sub-questions. First, the demarcation question asks what distinguishes specifically logical from nonlogical vocabulary. Second, the correctness question, usually epistemologically motivated, asks what the right logic is. Brandom arrives at a remarkable answer to the first question by transposing it into the pragmatist key: what’s the point of having or introducing into language expressions whose use is governed by rules of their inferential manipulation that yield a conservative extension over the prelogical language or fragment thereof? Here the inferentialist order of explanation proceeds from pragmatics to semantics, and from there to logic. In the first step, normative pragmatics addresses the question of the constitution of pragmatic and content-conferring material-inferential features of core ­linguistic-discursive practices that are claimed to constitute assertional speech acts and their inferentially articulated contents. In the second step, it needs to be explained how such features can themselves be explicitated by means of expressive devices that are pragmatically elaborated from the prelogical practice. This is the raison d’être of broadly expressive notions. Thus, normative notions of commitment and entitlement are suited to make explicit the implicit pragmatic features of scorekeeping practices underlying the assertional practice. Specifically logical notions are suited to make explicit semantic aspects of the prelogical practice responsible for the constitution of assertible contents of nonlogical expressions involved in correct material inferences and incompatibility relations. Paradigmatically, conditionals of the form “If A, then B” allow practitioners to explicitly endorse, in claimable contents, something that they could before practically endorse only in what they do with nonlogical sentences: that is, that B is correctly inferable from A. And negation allows explicit endorsement of implicit incompatibility relations between prelogical claims—for example, in the form of claims, “If A, then not B.” Once we have addressed the demarcation question, the expressive conception of logic leaves us with this task: “For each bit of vocabulary to count as logical in the expressivist sense, one must say what feature of

14  Ladislav Koreň and Vojtěch Kolman reasoning, to begin with, with nonlogical concepts, it expresses” (Brandom, this volume, chap. 6). This presupposes that the primordial game of giving and asking for reasons constituting assertions with propositional contents is prelogical. Logical-expressive devices are latecomers elaborated from it, which enable practitioners to become semantically selfconscious in that they can then make explicit the proprieties governing use of nonlogical expressions sufficient to constitute the game, discursive moves, and their contents. With their help, practitioners can critically discuss and assess their inferential practices so as to eventually revise them. Moreover, consistent with their role of explicitating the implicit inferential relations between (hence contents of) nonlogical sentences, introducing logical items to the prelogical language must not forge new inferential links between them (see Brandom 2000a, 68–69). So, rather than being simply presupposed, or motivated by reference to other demarcation criteria (such as formality or topic-neutrality), the criterion of conservativeness of the introduction of logical expressions into prelogical fragments is itself motivated by the expressive conception of logic. This approach to logic also rejects the “formalist” temptation to reduce all valid inferences to those that are valid on account of their logical form, construing material inferences as enthymemes that need to be supplemented by appropriate bridge-premises to become valid in the preferred sense. In contrast, expressivists take the validity of material inferences as both genuine and more basic, accordingly redefining formally valid inferences in terms of it: namely, as those that remain materially valid under all uniform substitutions of other than their logical elements. 2.3.  Epistemology and Logic The expressive conception of logic ramifies into the debates about the status and epistemology of logic. If one conceives of the basic “laws” of logic as those that codify rules of inference that determine inferential roles of logical expressions, thereby conferring meanings on them, one may stop searching for a queer ontology of logical entities and facts or, for that matter, for a special epistemological basis allegedly required to justify their correctness (see Peregrin 2014 for a thorough discussion of this and related issues). Relatedly, the inferentialist perspective on the demarcation question directly bears on the correctness question. From the expressivist perspective, the question “What is the right logic?” is worth asking only if there are compelling reasons to believe that there is some privileged, fundamental structure of reasoning with nonlogical concepts that is made explicit on the level of logical vocabulary governed by certain rules, all this being codified (or modeled) in some correct system of formal logic (typically deductive). If one doubts that there are such considerations, as Brandom does, the question loses its grip. It becomes replaced by a different question: “What logic does a good (or better) job

Introduction  15 in expressing certain features or structures of reasoning in this or that domain of discursive activity?” Thus one may ask what logic, owing to what features, is better suited relative to this or that domain of mathematical or scientific reasoning. Or one may ask what aspects of our inferential practice are captured by different logics of conditionals. Another issue that deserves to be mentioned concerns the relation between the normativity of logic and reasoning. On the one hand, one traditional view has been that logic somehow guides reasoning processes in that it supplies rules (in the sense of tactics) for what claims or beliefs to hold based on entailment relations to other claims or beliefs. On the other hand, it has been argued that there is no such relationship and that inference and deductive relations are strictly different categories (cf. ­Harman 1999). In particular, logic does not guide reasoning in the sense of compelling one to hold a claim or belief that logically follows from a set of premises, if only because the entailed claim or belief might be implausible (compelling one rather to reconsider one’s allegiance to the premise-set). Inferentialists acknowledge this point when they say that rules of logic are not rules of reasoning but rules that explicitate the material-inferential structure of reasoning. As inferentialists prefer to put it, logic “normatively constrains our reasoning activity, but does not by itself determine what it is correct or incorrect to do” ­(Brandom, this volume, chap. 6; see also Peregrin 2014, chap. 11). 2.4.  Beyond Logic Though many would submit that inferentialism is appealing with respect to logical words, only a few would agree without further ado that it is able to deal with words such as “cat” or “electron” which have some ­empirical—and thus prospectively referential—impact. To account for vocabulary complementary to logical expressions is thus a serious challenge as far as the soundness of the whole inferentialist project is concerned. We will touch on these problems later, in the third and fourth sections respectively; for now, it will be enough to indicate how to inferentially reconstruct the semantics of singular terms, predicates, and demonstratives as they occur in sentences and contribute to their inferentially articulated contents. According to Brandom (1994, 2000a), terms and predicates are explicated in terms of their role in symmetric and asymmetric substitutional inferences respectively, while demonstratives are explicated in terms of their occurrence in anaphoric chains that are subject to substitutional proprieties as well. Admittedly, this proposal does not amount to a systematic semantic theory distributing specific semantic values of appropriate kinds to expressions and sentences of a given language. Here inferentialists might say that it is not their task to construct such theories. That said, to the extent that they offer accounts of how the semantics

16  Ladislav Koreň and Vojtěch Kolman of logical operators, atomic sentences, and their components could, in general outlines, be conceived, they suggest what form a semantic reconstruction of a given language or fragment could take, based on inference, incompatibility, or related notions. In addition to this, since inferentialists aim to reverse the representationalist order of understanding, a vital part of their agenda is to reconstruct intentional and semantic idioms in terms of inferential roles. Thus, on the object level, Brandom (1994, chap. 5) proposed to analyze the talk about reference and truth on the model of anaphoric devices, advertising this as a deflationary strategy in the style of a prosentential theory of truth. On the meta-level, one may attempt to inferentialize occurrences of semantic notions (absolute or relative notions of reference, satisfaction, truth) in semantical systems, treating them, for example, as implicitly defined within the meta-theoretic axiomatic system. In addition, Peregrin (2014) suggests how model-theoretic semantic reconstructions of logical or natural languages could be inferentialized. 2.5. Contributions A number of issues loom large in this currently active area of philosophical and logical research. Some of them are of common interest to logical inferentialists. Others pertain specifically to the expressive conception of logic espoused by Brandom, Peregrin, and other inferentialists. For instance, what harmony exactly comes to, how it relates to conservativeness, and can it be justified as a plausible general condition on admissible rules of inference determining meanings of logical items? Do such structural criteria favor some systems of logic (for example, intuitionistic over classical logic)? What is the relation between the inferentialist perspective on logic and the model-theoretic approach in terms of referential ­relations? For instance, what to make of the fact that semantic consequence outruns derivability by means of finitary methods and inferential rules? Can this be given an inferentialist-friendly reconstruction? As regards the expressive conception of logic, then, how tenable is the claim that logic makes explicit material-inferential relations that are socially instituted before the advent of logical devices? And how does it fare when it comes to providing the semantics of conditionals, and so on, as they are used in everyday linguistic practice? How would extensions of the inferentialist approach to broadly empirical domains of reasoning look like that abound in defeasible material reasoning? What, in general, does this teach us about the relation between reasoning, material-inferential relations, and logic? All the chapters in the second part of this volume address these questions and advance the debate. In Chapter 5, Shawn Standefer and Ole Hjortland start off with a concise overview of the state of the art and proceed by focusing on issues concerning the notion of harmony. To begin with, they discuss

Introduction  17 the relation between conservativeness and harmony, noting that different notions of harmony resurface in the received literature and that they need to be distinguished, compared, and assessed. Importantly, harmony is a system-relative local property in the sense that a logical operator, such as classical negation, that does not have harmonious rules with respect to one deductive system, let us say natural deduction, might have harmonious rules with respect to a different, perhaps not less “natural” deductive system (for example, multiple-conclusion sequent calculus). This has ramifications for the debate about the “correct” logic that they briefly explore. Furthermore, the authors explain that harmony has relevant parameters that can be brought out. They take these to be structural features of a logical system that can be taken to represent aspects of an inferential practice and proceed to consider dropping structural rules of logical systems and enriching logical systems with additional structural elements. Finally, they consider substructural logics and the issue they bring for conservative extensions and harmony. Developing his view that the expressive conception of logic allows us to do logic in a nonorthodox and pluralistic manner, Robert Brandom in Chapter 6 concentrates on how material-inferential relations can be logically explicitated. In the aftermath of the pioneer contributions of Tarski and Gentzen, it has been common to conceive of consequence relation as satisfying reflexivity, monotonicity, and transitivity (or cut). If, however, material-inferential relations normatively constraining defeasible reasoning are both ubiquitous and contribute to conferring meanings on nonlogical (particularly empirical) vocabulary, logical expressivists should reconsider this strategy. Brandom accordingly elaborates an approach to consequence relations (including incompatibility) based on a modification of Gentzen-style substructural proof theory in which they are not globally monotonic or transitive. He shows, accordingly, how to reconstruct the nonmonotonic base material consequence relations between the prelogical atomic sentences and how to conservatively extend them to the logical consequence relations once logical connectives are introduced. The result is a logical explicitation of material consequence relations. Finally, he shows that although neither the material nor the logically extended consequence relations are globally monotonic, there are local regions of the consequence relations that are monotonic, corresponding to the narrowly logical-deductive relations. In their own way, Jared Millson, Khalid Khalifa, and Mark Risjord provide in Chapter 7 a further extension of this line of thinking. Their point of departure is that inferentialism makes it possible to produce more robust and productive explanatory models of how science works. While much attention has been paid to the analysis of logical vocabulary and deductive reasoning, inferences are a constitutive part of the fabric of both our everyday and our scientific reasoning, which is to a considerable extent inductive. Millson et al. propose in their contribution to extend

18  Ladislav Koreň and Vojtěch Kolman the inferentialist-expressivist approach as an explanatory model for the language of inductive reasoning, so far largely ignored. The chapter defines a sequent calculus for a language that contains a logical operator corresponding to the expression “That . . . best explains why . . . ,” regimenting the central kind of inductive inference from empirical evidence to a theory: inference to the best explanation. The authors prove that this calculus conservatively extends the rules of a logic that encodes explanatory arguments and the inference to the best explanation in two distinct classes of consequence relations. Brandom and Millson et al. presuppose the expressive conception of logic and attempt to extend it to new neighborhoods. But is it plausible to claim that the role of logical expressions is to make explicit contentconferring material-inferential relations instituted by normatively governed social practices? In Chapter 8, Lionel Shapiro argues that there are reasons to be skeptical about this. After considering a number of difficulties confronting this account (including the consideration that relations are not suitable entities for nonrelational expressions such as the conditional to express), Shapiro goes on to substantiate an alternative expressive conception of logic. Specifically, he examines the expressive role of the vocabulary by which we ascribe logical relations and argues that this role should be explained in terms of logical operators in a way that undermines the explanation of logical relations in terms of social practice and inverts the usual logical expressivist order of explanation. The expressive conception of logic presupposes that logic is a superstructure over the prelogical layer of language that is pragmatically and semantically self-sufficient. In Chapter 9, Ladislav Koreň develops a challenge to this claim. In the spirit of a conjectural genealogy, he fleshes out a line of argument to the effect that without elaborating some broadly expressive tools for bringing it into the open that something is endorsed (or rejected) as a reason for (or against) something else, prelogical practices (as described by Brandom and other inferentialists) could be, in key pragmatic respects, too ambiguous across practitioners-interpreters to provide for intersubjective norms governing shared practices of giving and asking for reasons, hence constituting propositional contents. If it is on the right track, this argument has ramifications for the explicitating role of logic. Instead of merely making explicit ready-made inferential relations, Korenˇ proposes to view broadly logical expressions (including dialectical devices typified by inference markers and denial) as a means of making the practice more socially coordinated and controlled, hence shared. On the inferentialist view, conditional sentences serve to make explicit material-inferential relations structuring the practices of asserting and inferring operating with nonlogical expressions. In Chapter 10, Peter Milne approaches the relation between assertion, inference, and the conditional from a different perspective. He suggests that assertion is normatively constrained by logical relations—in particular, by consistency and

Introduction  19 by logical consequence—in a way that gives inference a role in the critical evaluation of others (and our own) assertions, allowing us to escape Harman’s challenge that all reasoning is a matter of a reasoned change in view. But he argues that Harman’s distinction between reasoned change in view and logical consequence is crucial to the evaluation of certain patterns of discourse involving indicative conditionals, patterns that are significant for the determination of the semantics of the indicative conditional of natural languages.

3.  The Nature of Rules and the Rules in Nature The philosophical approach to norms or rules exemplified in inferentialism and the discussions connected thereto focuses on the rule-oriented analysis of language, thought, and logic. The core idea, as argued, is that proprieties governing practices of giving and asking for reasons constitute conceptual performances and their meaningful vehicles where the norms are accounted for as creatures of practical normative attitudes adopted by practitioners. Moreover, Brandom does not rest content with this contention but explicates the normative fine structure of the minimal social discursive practice, using to this end the deontic scorekeeping model. This theoretical enterprise promises to illuminate conceptual thought in a distinctive normative vocabulary (of commitments, entitlements, responsibility, authority, and such like), not taking as given any primitive notions belonging to the representational family (intentional or semantic). In this respect, Brandom markedly differs from theorists who are committed to describing representational or inferential roles in a respectable naturalist vocabulary without appealing to any primitive intentional, semantic, or normative notions. Their urge is basically reductionist: allegedly, it must be shown how (if at all) semantic, intentional, or normative phenomena fit into the natural-causal order paradigmatically described and explained by natural sciences. Thus, representationalists refer to causal or teleological aspects, while some conceptual role theorists refer to regularities of actual processes of inferring and still others to dispositions to make or accept certain inferences under both actual and counterfactual circumstances. In contrast, normative inferentialists maintain that content-conferring inferential roles are those that are determined specifically by correct inferences—that is, those that one ought to endorse—where the normative talk about correctness (oughtness) is emphatically not translatable into a nonnormative talk about regularities of or dispositions to behavior. In so far as in describing or modeling these processes inferentialists draw on irreducibly normative notions such as “being correct” or “being appropriate” (or their deontic counterparts such as “being committed” or “being entitled”), they do not attempt a naturalistic reduction of conceptual content.

20  Ladislav Koreň and Vojtěch Kolman 3.1.  Between Regulism and Regularism Inferentialists are adamant that content-conferring norms of discourse are not spooky entities. Here they seek a middle way between (1) regulism and (2) regularism about norms, as Brandom (1994) labels the two extremes that are to be avoided. The former approach, following Plato’s model of knowledge, appears to posit ethereal entities—be it ideas or abstract rules—with mysterious powers to guide behavior, whereas the latter, following Aristotle’s concept of ideas-in-things, would have us reduce norms to law-like patterns of behavior specifiable in a nonnormative vocabulary. Inferentialists, in contrast, think of proprieties as “ought-to-bes” instituted, negotiated, and maintained through ongoing social processes of coordination and calibration of perspectives and normative attitudes that practitioners adopt toward one another’s performances. This is what Brandom calls phenomenalism about norms. At the most fundamental level, then, norms are said to be implicit in practical-normative attitudes of practitioners (practical know how mode) and not codified in stateable principles (theoretical know that mode). One main reason for this claim derives from the famous consideration urged on us by Wittgenstein (1953) and Sellars (1954): if norms confer contents on performances or expressions caught up in practices governed by them, then, on pain of a vicious regress of rules, their primary mode of being cannot be that of being contents of sentences. At the same time, they are explicitable in principle, that is, after elaboration of logico-expressive devices, making it possible to state them as principles apt to be the topic of the game of giving and asking for reasons (but even then, not all of them at the same time). This theoretical battlefield is replete with minefields. We already mentioned controversies about the idea that normativity is a constitutive feature of conceptual contents and linguistic meanings. In what follows, we concentrate on two important issues that have been in the center of many discussions in the aftermath of Making It Explicit. The first issue concerns whether the inferentialist framework can successfully accommodate the distinction between what is correct and what merely seems correct that, by the inferentialists’ own lights, distinguishes the objective dimension of thought and talk, including its representational purport. In other words, can the normativist machinery marshaled by the inferentialists account for normativity of thought and talk be so conceived, and can it achieve this without presupposing representational ideas or taking into account the role of experience? The second issue concerns the status of norms as theorized by Brandom and his fellow travelers. What do we talk about when we talk about norms and their infrastructure supplied by normative attitudes? Why can’t such phenomena be properly theorized by using a disenchanted idiom of natural sciences? Indeed, what, if

Introduction  21 anything, do we explain or illuminate by indulging in such a “dramatic” normativist idiom? Isn’t it, after all, that by helping themselves to primitive normative notions inferentialists take for granted what they should explain or illuminate in the first place? 3.2.  Sociality of Norms Regarding the first issue, the question looms large how normative attitudes (those of practically taking or treating a performance as correct or incorrect) can possibly give rise to a dimension of objectivity independent of individual or communal perspectives—indeed, making it possible to assess them. In general, Brandom’s burden is to show how objective standards of correctness can govern practices that are not hostage to individual or communal attitudes, while, at the same time, they cannot exist without there being social creatures imposing norms based on adopting normative attitudes. In particular, he has to incorporate into his account the normative friction that characterizes the relation that conceptual creatures take to the word so they can be said to be not only responsible for what they do and say but also responsible to something—the world of propertied and related objects. This is related to his ambition to reconstruct the objective-representational dimension (purport) of conceptually articulated talk and thought. Brandom addresses this agenda by attempting to extract objectivity out of an intricate structure of social perspectivality that marks the scorekeeping practice. The argument is too abstract and complex to be spelled out adequately in the limited space. But here is the basic idea in broad outlines. To begin with, recall Brandom’s bold claim: when the scorekeeping practice cashed out in normative attitudes reaches the threshold when practitioners can be described as keeping score on material-­consequential relations linking normative statuses, it is not implausible to interpret them as playing a language game of making assertions with nonlogical sentences. This warrants a semantic account: practitioners can then determine the pragmatic significance of a given performance (how it changes the score) based on assigning a certain inferential role to a corresponding sentence-type and applying this to the context at hand (as determined by the current score—by their lights) (cf. Brandom 1994, 190). However, practitioners update the score in a holistic-perspectival manner. From the perspective of a performer, the score-affecting potential of a given performance varies depending on what commitments she previously acknowledged. Moreover, its significance varies, as a rule, across scorekeepers having different collateral commitments. On this model, then, to understand a performance is to understand how it can acquire different significances from different individual perspectives and to be able to traverse between them in communicative ventures. It is here where

22  Ladislav Koreň and Vojtěch Kolman the social process of establishing norms originates that eventually begets “objectivity,” specifically when scorekeepers become sensitive to the difference between commitments (or entitlements) that are acknowledged by performers and commitments (entitlements) that are undertaken by them. They can attribute to performers the latter based on what they take to be the inferential consequences of the former in light of their own commitments. Scorekeepers might thus attribute statuses that outrun those avowed by performers, thereby developing a basic sense that what is appropriate to do or say (what one is committed or entitled to) does not coincide with what (any) one takes to be appropriate to say or do. Eventually, they can recognize self-other symmetry: their perspective is one among many with this feature (for example, by registering and resolving conflicts between their present and past commitments, updating them in light of evidence). In this way, rudimentary norms enacted the social practice of communication and mutual interpretation emerge in which the objective purport is present, albeit implicitly. These are further refined, up to the point when they can be made explicit by self-conscious creatures equipped with special expressive devices. In particular, building on the substitutional-inferential structure, idioms for ascribing commitments (modeling beliefs) in de re-de dicto style are explained as devices elaborated to make explicit the representational dimension (objective purport) previously implicit in the discourse (cf. Brandom 1994, chap. 8). Crude as this account is, it gives us a grip on how Brandom proposes to account for objective norms. It is fair to say that commentators— including sympathetic ones—have not found his approach equally satisfying. It has been complained that, no matter how complex the structure of scorekeeping attitudes might be, it is difficult to see how they, qua expressions of individual perspectives, could possibly produce genuinely objective standards of correctness in general, and objective purport of judgeable contents in particular (cf. McDowell 2008). Also, it has been charged that when it comes to saying exactly what it means to say that the authority of norms is objective in that it effectively transcends what any individual (even community) treats or takes as correct, we are offered either unilluminating answers smacking of circularity (for example, that normative attitudes are themselves assessable as to their correctness), or we open the door for intentional or semantic notions (cf. Rosen 1997). 3.3.  The Manifest Image of the Scientific Man? The issue of the status of norms can be conveniently introduced as the intellectual legacy that inferentialists inherited from Sellars. Sellars’ (1963) undertaking was to explore the uneasy relation between the manifest image and the scientific image of man. The first image concerns the way we conceive of ourselves as persons thinking, talking, and acting in

Introduction  23 ways that are responsive to the normative force of reasons. As such, it is “fraught with ought.” The scientific image grows out of it. It describes us as belonging to the realm of natural phenomena subject to causal regularities. Science aims to describe and explain its workings by formulating appropriate general laws quantifying over theoretical entities framed in a suitable vocabulary. On the one hand, the manifest image grounds the scientific image and includes normative or prescriptive features of our social operating in the world. From this perspective, it seems to be more basic and hence not amenable to attempts at its complete integration into the scientific image with its specific aims, categories, and methods of description and explanation. On the other hand, Sellars suggests that the scientific image rivals the manifest image, indeed, that science is the ultimate measure of what there is, being the self-correcting enterprise that it inevitably is. From this perspective, then, it might look as though a desirable intellectual project would be, for instance, to provide an illuminating account from within the scientific purview of how creatures like us could have gradually emerged who developed capacities to govern their behavior and reasoning by norms and reasons. Sellars’ big question is whether and how the manifest image “can be reconciled with the idea that man is what science says he is” ­(Sellars 1963, 38). In one form or another, this issue is still with us. Inferentialists have approached it in various ways themselves. The basic problem can be spelled out as follows. Suppose we accept that there are two different perspectives on our place in the world that use such dramatically disparate vocabularies. Then one question that arises for us is whether one vocabulary can be translated into the other without any loss of expressive or explanatory power. Brandom contends that the perspective on conceptual thought emerging from his approach is “norms all the way down” (Brandom 1994, 625) in that the talk about commitments, entitlements, and so on, does not translate into some non-normative vocabulary preferred by naturalists. However, Brandom wants to go further than this. If successful, he suggests, his approach shows that a normative ­vocabulary—which is presumably a part of the vocabulary attached to the manifest image and employed by a theorist who is a second-order interpreter or scorekeeper of first-order scorekeepers—can be used to shed light on what it takes to use any linguistic-conceptual framework whatsoever, including normative or naturalistic frameworks. But it remains to be seen whether naturalistic approaches can pull the rabbit out of the hat. 3.4.  Norms and Nature What about the suggestion that it might be enlightening to give a naturalistic reconstruction of how sapient creatures could have emerged who are capable of making moves in a normative space of reasons? Brandom

24  Ladislav Koreň and Vojtěch Kolman sometimes gives the impression that his approach is consistent with such a project, though he is happy to leave it to others to pursue it. At any rate, he might think philosophical understanding is prior in that it aims to elucidate what structure a social practice must have to be governed by objective norms or normative statuses. Only then will we have an idea of what a natural history of normative creatures is supposed to reconstruct. Anyway, Brandom comes closest to the naturalistic perspective when he says that norms are creatures of normative attitudes, where, at bottom, normative statuses might be instituted by sanctions such as “beating transgressors with sticks,” which are causally efficacious and specifiable in nonnormative terms (see Brandom 1994, chap. 1). At the same time, he hastens to add that such a reductionist strategy is optional and goes on to distinguish external sanctions (negative reinforcing by way of inflicting or threatening to inflict physical harm) and internal sanctions (accounted for as changes in normative statuses attributed by scorekeepers, such as a loss of entitlement to do something consequent on transgressing an implicit norm). He implies that the latter might be indispensable to account for the fact that normative attitudes can themselves be adopted correctly or incorrectly (see Brandom 1994, 42–46, 178–180). That, after all, is the gist of normative phenomenalism: what ultimately matters when it comes to objective norms are not attitudes actually adopted, nor attitudes one is disposed to adopt, but those that it would be correct for one to adopt (Brandom 1994, 627). In addition, accounts of norms in terms of external sanctions face the gerrymandering problem. This threatens all accounts of rules or norms in terms of regularities of behavior or of dispositions to behavior (including sanctioning behavior). The problem is that nonnormatively specifiable behavioral regularities can be made consistent with any number of distinct norms or rules (Brandom 1994, 36). Based on such considerations, Brandom (1994, 626) suggests that the theoretical-interpretive project of reconstructing social practices as discursive and norm-governed is both “norms all the way down” and “begins at home” in that theorists-interpreters cannot but draw on the norms governing their own discursive practices. But then the putative “domestication” of norms in terms of normative attitudes specifiable as features in the causal order would seem to give way to their explication in terms of proprieties of adopting and altering normative attitudes that are not so specifiable. Rather, they are ultimately reconstructed from within the interpreter’s own framework that is always already “fraught with ought.” Brandom’s strategy thus appears to elaborate on the manifest image of human rationality from within it. It does not seem to be reductionist at all, and it is not clear what illumination of the phenomena, if any, it allows us to expect from naturalistic perspectives. Other pragmatists and inferentialists think that there has to be some way to break into this circle. Peregrin (2014), for instance, concurs that

Introduction  25 the normative vocabulary is irreducible, at the same time exploring how inferentialism can be supplemented by viewing the world and our place in it from a naturalized-evolutionary perspective. He elaborates Sellars’ idea that ought-to-bes of pattern-governed behavior are imposed through patterns of normative attitudes, including higher-order, once these start to be inculcated and reproduced via channels of social transmission, including active pedagogy (reminiscent of Sellars’ dialectics of trainers and trainees). This, he notes, has revealing parallels in the recent empirical research on the evolution of norms and norm psychology. ­However, when inferentialists approach the issue in this spirit—that is, by ­talking about the norms as creatures of dispositions to adopt corrective ­(sanctioning) attitudes and to coordinate them into certain patterns—the question comes up as to how this approach to norms is supposed to be superior to various reductionist accounts liable to the gerrymandering problem. Clearly, this is a pertinent issue if their ambition is to avoid the Scylla of regulism and the Charybdis of regularism about norms. 3.5. Contributions In one way or another, all of the chapters in the third part of this volume reflect the background described in the previous parts of this section, revolving around the question of what norms or rules are and what it takes to be a normative creature—one that is governed by or subject to norms or rules. In Chapter 11, Joseph Rouse attempts to turn Brandom’s or Peregrin’s social rationalisms “inside out,” proposing a revisionist evolutionary naturalism. Discursive intelligibility and rationality are presented as scientifically intelligible phenomena in the natural history of a very unusual organism—human beings. His focus is on an alternative account of the normative force of conceptual understanding, emphasizing organismenvironment inter-dependence and using ecological-developmental biology and niche construction theory to circumvent dualistic concepts of nature and normativity. Rouse’s “naturecultural inferentialism” recognizes that discursive performances are materially and practically situated in ways integral to how we think and act, providing an account of conceptual normativity that overcomes the sharp division of the causal (a-rational) from rational normativity. One of the key concepts employed is that of power. Developing ideas that were already surfacing in his recent book Inferentialism: Why Rules Matter, Jaroslav Peregrin explores in Chapter 12 the possibility of a fruitful exchange between Brandomian inferentialism and some naturalistic streams in recent scientific theorizing about the nature of norms considered in close relation to culture, language, and psychology. His idea is that it is “thinking in the normative mode” that might have been the principal evolutionary innovation that has made us

26  Ladislav Koreň and Vojtěch Kolman humans so different from all our animal cousins. Having summarized the current state of the art of such potential extensions of inferentialism, he addresses some objections likely to be raised and offers a view of where it could head in the future. The core of Vladimír Svoboda’s argument in Chapter 13 consists of a conceptual inquiry clarifying concepts that are commonly associated with the terms “rule” and “norm.” He argues that we should carefully distinguish between rules (and norms) understood as social facts and rules (norms) understood as linguistic entities, just as we do between explicit rules and implicit rules. He proposes that we accept a more general account of rules—when compared with Brandom’s or Peregrin’s—based on the concept of a “demandatory” relation between social subjects. The resulting conceptual framework suggests a kind of taxonomy of rules that can help to clarify a number of problems that arise when we study the logic of rules and norms. In Chapter 14, Ondřej Beran attempts to elucidate certain irreducible differences between practices labeled as “following the rule.” While in some practices most or all of the agents’ moves conform to the governing rule (otherwise the practice would cease to exist as such, as with chess), some rules represent rather a standard to live up to (as captured by Sellars’ distinction of “ought-to-be rules”) and the subjection of actions to these rules transpires in discrepancies with the standard. Beran draws on Rhees’ critique of the later Wittgenstein’s conception of language to illuminate the neglected importance of the point of rules-governed practices. The difference between doing well and doing perfunctorily—between whether it matters to the agent or not—is not the difference between following or violating a rule. Any exhaustive description of human normative practices, suggests Beran, must take the variety of the agents’ attitudes toward the point of the practices into account.

4.  The Multiple Layers of Inferentialism The appeal and explanatory breadth of Brandom’s inferentialism is due to what might be called his multilayer approach to philosophy. While stemming from the particular strain of thought nurtured by his teachers Wilfrid Sellars, Richard Rorty, David Lewis, and his fellow traveler John McDowell, Brandom keeps thinking of philosophical problems in terms of bigger and older streams of thought, thus transcending simple assignment to one philosophical trend (such as pragmatism), school (such as analytic philosophy), or discipline (such as epistemology or logic). As a result, in inferentialism one finds a Kantian emphasis on the primacy of judgment, combined with Wittgensteinian and Sellarsian pictures of the normativity of language, a Peircean pragmatist concept of meaning, and a Fregean logocentrism, all alongside Hegel’s overall view of the social nature of reason. For Brandom, of course, Hegel is of a particular

Introduction  27 importance because of his unifying or “absolute” way of thinking which makes his philosophy a System. Against this background, what we call a multilayer approach to philosophy turns out to be simply a philosophical approach worth its name, covering various aspects of philosophy from different points of view such as logic—in Brandom’s case led by the traditional proof-theoretical approach to reasoning and his own idea of this reasoning’s substantial non-­monotonicity, as was particularly developed in his Between Saying and Doing (Brandom 2008)—or both the history of philosophy and the philosophy of history, as sketched in Tales of the Mighty Dead (Brandom 2002). These books on logic and philosophy history are followed by collections of essays devoted to inferentialism’s place in the pragmatic movement (Perspectives on Pragmatism, Brandom 2011), its empirical roots in the work of Sellars (From Empiricism to Expressivism, Brandom 2015), and its broader transcendental background in German idealism and the philosophy of self-consciousness (Reason in Philosophy, Brandom 2009). Presumably, all this will be unified in Brandom’s long-awaited commentary to Phenomenology of Spirit, titled A Spirit of Trust. 4.1.  Fregean Layer Arguably the most significant connection of inferentialism to classical analytic thinking is represented by Brandom’s interpretation of Frege as the first inferentialist stricto sensu. Brandom reads Frege as endorsing Kant’s fundamental insight that the basic unit of discursive thought and rationality—one for which a thinker is distinctively responsible—is ­judgment: but it took Frege to develop the inferential dimension of conceptual content. Though based on a single passage in the introduction of Frege’s Begriffsschrift, the importance of this interpretative move is hard to overstate because it underlies one of the most fruitful readings of the Fregean corpus. Since Tugendhat’s (1970) famous treatment of Frege’s concept of meaning as the so-called truth potential, rather than simply as some pre-given, worldly referent of the word, there exists a minor yet influential tradition of reading Frege as an ambiguous, though sophisticated, advocate of semantic holism. This reading, being at variance with Frege’s overall reputation as an ontological Platonist, is supported significantly by the contextual thesis of his The Foundations of Arithmetic, which Frege himself calls an “axiom” of his inquiry: “Never to ask for the meaning of a word in isolation, but only in the context of a proposition” (Frege [1884] 1950, xxii) and more importantly, by his remark from Posthumous Writings where he explicitly says pace Leibniz and his successors: “I do not begin with concepts and put them together to form a thought or judgement; I come by the parts of a thought by analyzing the thought” (Frege [1969] 1979, 253).

28  Ladislav Koreň and Vojtěch Kolman In the critical passage of Begriffsschrift, this propositional holism is expanded so that the meaning of the word’s meaning depends not only on the sentence in which the word is used but on the whole inference. This makes the meaning of the word its inferential potential. The conceptual content of an expression is something that one can arrive at by making anything that is without significance for logical inference disappear (Frege [1879] 1967, 6). Frege further elaborates on this by means of the substitution technique according to which the sameness of the conceptual content of two sentences (or, in general, of two expressions) A, B, is given by their intersubstitutability within an inference while maintaining its “goodness” (Frege [1879] 1967, 12). On the sentential level, this is a generalization of the substitutability salve veritate which is, according to Tugendhat (1970), the defining condition of expression’s truth potential, the goodness being the expression’s truth-value. Despite the scarce textual evidence, Brandom’s speculative stress on the inferentialist grounding of Frege’s logic allows one to explain its epoch-making success. As Brandom (1994) points out, the notion of substitution plays a pivotal role here, being both the means by which the meaning of expressions is defined as well as the device for a finer sentential analysis. This leads, in turn, to new inferential dependencies and thus to new meanings. With respect to substitution, an expression can assume two basic roles: it can be replaced by or replace another expression within an expression, or it can itself be an expression in which such a substitution occurs. Both these roles—called by Brandom substituted-for and substituted-in, respectively—can be played by a sentence, which is consistent with the supposition that one can work at the beginning with the monolithic sentences only. However, Frege ([1879] 1967) pushes his substitutional strategy much further, stipulating the existence of names as a basic category of sub-sentential substituted-fors. Then, taking sentence as a basic category of substituted-ins, he arrives at the notion of the predicate as a derived category of expressions that one gets by taking out the name or names out of some sentence. These expressions are the so-called substitutional frames. The substitutional procedure allows Frege to use functional metaphor as a way in which he can quite naturally pass from the syntactical substitution to its semantic pendant, in which the predicate represents function assigning truth-values to the given objects represented by given names. It is obvious, however, that this representational picture of language depends heavily on the previous substitutional analysis of sentences and their substitutional interdependence. As Frege keeps stressing, substitutional frame or predicate F(x) does not simply represent some pre-linguistically given or existing object. Its meaning—called a function—is rather a byproduct of the substitutional reading of the sentence F(N) in which name N is replaceable by any other name M, thus connecting all the sentences F(N), F(M), . . . in a single pattern. Here, the sentence F(N) is read as a functional

Introduction  29 application of F(x) at N as one of the given names. See Figure 0.1. In this way, new inferences and inferential patterns can be followed and phrased, especially if one takes into account the possibility of multiple substitutions and the correspondent introduction of relational predicates R(x,y), S(x,y,z), and so on, in combination with quantification over the substitutable terms such as ∀xF(x), ∀x∃yR(x, y), and so on. So interpreted, Brandom submits, all these moves have a significant inferential background, including the very idea and introduction of the category of sub-sentential expressions. In what Brandom (2000a, 41) called “an expressive transcendental deduction of the necessity of objects,” he argues that the reason for having two kinds of sub-sentential expressions—the names and the predicates—consists in the inferential superstructure of the given language and the possibility of its explicitation by expressive-logical devices. As we mentioned previously, Brandom explicates singular terms as those kinds of expressions that are subject to symmetric substitutional inferences, whilst predicates form a category of expressions that are subject to asymmetric substitutional inferences (or rather to what he calls symmetric and asymmetric “substitutioninferential significance” respectively, see Brandom 2000a, chap. 4). Then, quantifiers (∀, ∃) and identity (=) can be accounted for as expressive devices that enable semantic self-consciousness in that they allow making explicit such inferential relations implicitly structuring uses of prelogical sentences and their subsentential constituents. We will not go into the details of Brandom’s argument, which is speculative enough to be the subject of a separate study. See, for example, Rödl (2008). It is mentioned here mainly because it connects the recognition of the sub-sentential structure with the introduction of the linguistic means expressing the relations among sentences such as implication (→) or negation (¬), thus showing how deeply holistic and anti-representationalist Brandom’s approach to semantics is. Even the old-fashioned concept

substituted-in Theaetetus flies

Theaetetus Socrates

x flies

Plato

substituted-for

Figure 0.1 

substitutional frame

30  Ladislav Koreň and Vojtěch Kolman of the world of objects and their properties is treated as something to be understood in connection to a given inferential structure of language. 4.2.  Peircean Layer In the light of the previous paragraphs, one can see inferentialism defined by its opposition to what we called the representational account of knowledge (see the first section). This account consists in grounding the significance of language in its alleged designative relation to the extra-linguistic reality with the words of the language functioning typically as names for pieces of reality. Though not being unfriendly to the representational idea himself, Frege in his substitutional analysis of language suggested a different order of understanding that stresses the intra-linguistic relations of sentences to each other. In this respect, his ideas are mimicked in a particularly interesting way in the philosophy of another important logician and a cofounder of modern logic, Charles Sanders Peirce, with his pragmatic definition of truth and meaning. By defining the meaning of a sentence as its inferential role, one says that two sentences A, B have the same meaning if they have the same class of consequences: in other words, the same sentences can be inferred from A and B. Now, unlike Frege and his analytic followers, Peirce does not think about knowledge in purely linguistic terms, his framework being the more general, though related, concept of semiosis. In this, the key concept of sign is defined structurally as everything that is related to some object and via this to another object—the sign’s interpretant. All the elements of this triad are relative to each other, the interpretant being a sign of its own because of the infinite nature of the whole semiotic process. See Figure 0.2. The semiosis, in fact, works both ways—to the right, interpreting interpretants, and to the left, making interpretants from signs. This idea only develops the former pragmatic maxim according to which the meaning of a sign (event, object, sentence, etc.) is given by its consequences. Again, conceived most generally—that is, not only in a purely linguistic way: Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object. (Peirce 1931–1935, § 5.2) sign

object

Figure 0.2 

interpretant

Introduction  31 The most visible display of Peirce’s pragmatic consequentialism in Brandom’s inferentialism might be seen in the concept of practical inference, leading from the utterance of a sentence, such as “It is raining,” to some action such as taking an umbrella. In this way, inferentialism loses some of its original intellectualist flavor and the suspicion of one-sidedness in that it somehow does not consider the external world we are a part of. Following Sellars, Brandom (2009, 180) refines the whole picture by adjusting the intra-linguistic transfers sentencesentence, which are treated as sufficient by rationalistic philosophies that focus on the role of concepts in reasoning, by two other pillars. The first pertains to the transfers from entry transitions in perception, taken as sufficient by empiricism that takes concepts as functionally defined by their origin in experience. Thus, the use of sentences is traced back to their causal antecedents in the empirical circumstances. The second consists of the exit transition in action where the role of concepts is given by their practical significance. These inferences are those that pragmatism one-sidedly focuses on. By inferentialism, now, the doctrine of inference is meant which covers all these transitions at once. See Figure 0.3. This all-embracing move makes sense only against the overall reorientation of the original linguistic philosophy in the pragmatic direction consisting in a continual deintellectualization of language as some ideal structure detached from the world toward its more embodied version. This proceeds in accord with the overall pragmatist tendency to see the human mind and the empirical world as mutually interacting and adapting to each other, as anticipated in the naturalization of Kantian reason in the philosophy of Hegel. In the tradition of linguistic philosophy, such a move was made by Wittgenstein, who in his Philosophical Investigations contrasted the early Kantian concept of Tractatus, in which the transcendental structures of language are sharply distinguished from the empirical structures of the world, with the Hegelian concept of language games, conceived as

rationalism language

language pragmatism

empiricism perception

action

inferentialism

Figure 0.3 

32  Ladislav Koreň and Vojtěch Kolman a socially employed enterprise or institutions governed by norms. As was already discussed in the first three sections, Brandom also follows Wittgenstein in two further important aspects: (1) He sees language as a specific kind of game, called after Sellars the game of giving and asking for reasons, the rules of which are the rules of inference. Unlike Wittgenstein, however, he views this game as the “downtown” of any linguistic practice worth its name. (2) He thinks even of the intra-linguistic rules as something which is not only a matter of pure linguistic convention in the traditional logical and analytical sense (such as modus ponens or the consequences of explicit definitions), but also takes into account the content of nonlogical expressions. The rules such as “It rains; hence the streets are wet” are thus conceived as inferences sui generis because it is the normative practice and commitments employed in the game of giving and asking for reasons and not some abstract relation of entailment or some abstract logical truths that makes these rules valid. 4.3.  Hegelian Layer Sympathies to Hegel’s philosophy earned Brandom and McDowell the tag of the Pittsburgh Neo-Hegelians. At the current moment, before the appearance of Brandom’s next magnum opus, A Spirit of Trust, devoted to Hegel’s Phenomenology of Spirit, we can only guess how far Hegel’s influence will go. But its core might now already be quite easily identified with one of the most characteristic tasks of Hegel’s absolute idealism: to dissolve the dichotomy of subject-object including its variants such as mind-world, language-meaning, and so on, which leads to various forms of epistemic skepticism, into the relative difference of subject-subject achieved in a relatively stable social equilibrium. It is this very transfer that makes the opposition of representationalism to inferentialism a going concern and that, in fact, finds its linguistic elaboration in the philosophies of Frege, Peirce, and Wittgenstein if understood as transformations of linguistically conceived transcendental idealism (with language and not, for example, mind being the basic precondition of experience) to its absolute variant. Against this background, Brandom’s inferentialism looks like a natural completion of this task, which is also known as a “unity of thinking and being.” The fundamental and quite tangible link between Hegel and linguistic philosophy in Brandom’s choreography is represented by a device of implication and negation, that is, constants with which Frege’s concept of logic was based. By focusing on them, Brandom’s inferentialism appears

Introduction  33 to be a continuous generalization of Frege’s logico-philosophical project. The first step in its development consists in stressing the fact that the primordial role of implication and negation, as well as the role of logic in general is not to introduce some inferences or truths of its own but only to make the whole of inferential practices explicit. According to Brandom, these underlying practices, as captured in the game of giving and asking for reasons, are structured by what he calls material inferences, such as the one from “It rains” to “Streets are wet,” and material incompatibilities, such as “Streets are wet” and “Streets are dry.” As follows from the previous paragraphs, this step is a part of the deintellectualization of language and reason by treating the given transfers as genuine inferences and not some stubs of the “genuine” logical inferences such as “It rains and if it rains then the streets are wet; hence the streets are wet” and “genuine” logical contradictions such as “The street are wet and the streets are not wet.” The reason for this is a logical one, part of what Brandom calls the expressive function of logic. As discussed in the second section, according to the expressivist concept of logic, an implication such as “If it rains than the streets are wet” (A → B) is a mere approval of the underlying practical inference (A; hence B) with modus ponens (A, A → B; hence B) being a second-order rule expressing the fact that to follow the rule is to claim B whenever A obtains and the rule leads from A to B. Similarly, one can obtain negation of A (¬A) as an expression for the claim entailed by everything incompatible with A. Here, both the inferential relations and incompatibility relations are something achieved in the practical coping with the world, that is, not mere intellectual abstractions detached from it. One can even argue that Frege’s logic was devised as an expression of the existing practice of mathematical analysis in which the quantificational dependencies were about to be made explicit for a better understanding and overview of what is going on (see, for example, Kolman 2010, 2015 for details). In this sense, Frege’s project turns out to be a relatively specific one, devoted to the problem of mathematics and as such opened to further generalization. With respect to Hegel, this consists in seeing the implication and negation as instances of the more general vehicles of mediation and contradiction by which the dialectic of knowledge proceeds. This is what Brandom explicitly does when he refers to Hegel’s talk about inference as mediation, which goes both factually and terminologically back to the middle term of the Aristotelian syllogism and the fact that it mediates the relation of premises to conclusion, thus making an inference from them. See Figure 0.4. The whole point, though, is quite general and thus in accord with Peirce’s (1931–1935, § 5.213) definition of intuitive knowledge as the knowledge that was noninferred. Now, according to Hegel, Peirce, and

34  Ladislav Koreň and Vojtěch Kolman Frege implication

negation

Hegel mediation

contradiction

Brandom material inference

material incompatibility

Figure 0.4 

Brandom, no knowledge is immediately given, which cancels the traditional subject-object distinction as based in the immediate contact of mind with the world. Peirce claims this within his concept of infinite semiosis in which every sign is further developed via its interpretant and this interpretant’s interpretant, and so on, with their sum forming the class of the sign’s consequences and hence, its meaning. As already intimated, the whole semiosis also proceeds in another direction, making every sign some other sign’s interpretant, and so on. This does not mean that, as a kind of Zeno’s paradox, one cannot arrive at a fixed meaning of something—that is, use some sign as ­meaningful—but only that this meaning is always subject to further development and, as such, stabilized only within the practices of some society. Along these lines, the subjectobject difference is definitely “sublated” in favor of a socially interpreted subject-subject difference, no matter whether it appears under the label of “Geist,” “Dasein,” “Sprachspiel,” or “the game of giving and asking for reasons.” 4.4.  Sellarsian Layer In inferentialism, the mediacy of knowledge adopts the form of the inferential interdependence of the conceptual content as opposed to the supposition that one can arrive at knowledge on the basis of some nonconceptual content—such as the empirical data—only. Sellars (1956) phrases this ­supposition as the Myth of the Given, to be further specified as the claim that there exists a specific, most fundamental kind of knowledge, the Given, for which the following two conditions hold: (1) the Given “can not only be noninferentially known to be the case, but presupposes no other knowledge either of particular matter of fact, or of general truths,” (2) from the Given, all the other knowledge can be inferred because “it constitutes the ultimate court of appeals for all factual claims—­ particular and general—about the world.”

Introduction  35 Following DeVries (2005), Chauncey Maher (2012, 10) calls these conditions (1) epistemical independence and (2) epistemical efficiency respectively, so as to reconstruct Sellar’s argument against the Given as saying that no knowledge can satisfy both these conditions at once. Adopting the additional supposition that the Given is either conceptual or non-­ conceptual, the argument goes like this: If conceptual, the Given is always dependent on other cognitions simply because one cannot have one concept without having many. And there is no way one can deduce something conceptual from what is nonconceptual simply because, as Sellars, Brandom, and McDowell agree, it cannot serve as a premise for a conclusion, that is, be epistemically efficacious. As a result, the foundational idea of knowledge as something that rests on unshakable ground must be abandoned, as was foreseen—to a greater or lesser extent—in all of the above-mentioned layers of inferentialism, whether it be in Hegel’s stress on the mediacy of knowledge, in Peirce’s claim that there is no intuitive knowledge, or in Wittgenstein’s general thoughts on certainty and its relative nature. The explicit argument for the fallibility of knowledge as a necessary and reasonable penalty for its non-triviality or contentfulness is contained in both Hegel’s masterslave argument and Wittgenstein’s argument against private language, if read to the intent that to achieve independency one must publicly risk something, not only his biological life, but also a certainty of his mental states or feelings (see Kolman forthcoming, for details). In the certainty of private opinions, as Wittgenstein (1953, § 202) argues in his thoughts on rule-following, as well as in certainty in general, there is no difference between what there is (or whether I follow a rule) and what something only seems to be or looks like (or whether I only think I am obeying a rule), which makes the “looks” talk substantially dependent on the “is” talk, and not vice versa, as one of the versions of the Given would like to claim. But this dependency, of course, works both ways, as is demonstrated in the full-fledged social theory of knowledge of Brandom’s (1994) elaboration on Sellars (1956). Using Goldman’s “barn facade” example as his starting point, Brandom (1994, 209–213) argues that the “is” talk, for example, in the case of reports that “There is a barn” in the visual field, not only articulates knowledge if the given reporter is a reliable perceiver of barns per se, but also if the external circumstances in which such a reliability is an issue are suitable. If the barns that the reporter believes to see are in a county where the local hobby is building realistic-looking barn facades, he is, in fact, unreliable, though through no fault of his own. And if it is the other way around, that is, if the county is only one of the many counties in which barns are just barns, then he is reliable again. And so on. According to Brandom, this gerrymandering technique—known also from Wittgenstein’s (1953) thoughts on rule-following and mentioned

36  Ladislav Koreň and Vojtěch Kolman above in the third section—shows that reliability as well as knowledge are not something one can positively have (for example, some states or episodes of mind), but something that can only be attributed to somebody. They are institutions or complex social statuses in which the difference between “There is a barn” and “There seems to be a barn” reflects the moves in the game of giving and asking for reasons. As Brandom put it: In calling what someone has “knowledge,” one is doing three things: attributing a commitment that is capable of serving both as premise and as conclusion of inferences relating it to other commitments, attributing entitlement to that commitment, and undertaking that same commitment oneself. (Brandom 2000a, 119) While the first attribution corresponds to a mere belief in a sense of taking somebody as believing that there is a barn while leaving open the possibility that it only looks like one, in the third part this possibility is excluded by adopting oneself the belief as being true. This repeats the classical definition of truth as justified true belief, with the three parts of Brandom’s definition corresponding to belief, justification, and truth accordingly. See Figure 0.5. Hence, both the inter-content and inter-personal relations—that is, relations between sentences as well as between people that employ them—are necessary for constituting knowledge, which makes it fallible in two possible ways: first, because no individual or particular group of individuals can guarantee the truth of what he or they say or believe; and second, because to know something does not concern a particular set of beliefs as various kinds of foundationalism would claim but the knowledge as a whole. But this absolute quality of knowledge, as Hegel would say, is not something transcendent but stems from its very reflective nature. Following Peirce (1931–1935, § 5.384) and his idea of the

commitment there is a barn entitlement commitment

Figure 0.5 

Introduction  37 scientific method of fixing beliefs, Sellars phrased this old Hegelian idea (with respect to empirical knowledge) like this: [. . .] knowledge, like its sophisticated extension, science, is rational not because it has foundation but because it is a self-correcting enterprise which can put any claim in jeopardy though not all at once. (Sellars 1956, § 38) Our claims are openly placed in the space of reasons to be further justified against others and acknowledged by them. As such, an arbitrary claim might be conceived as inferred from another one, though not necessarily de facto. This redraws the original picture given by Brandom in the sense that language exits and entries are, in fact, already linguistically modified and the differences between intra-linguistics and extra-linguistics transfers are of a gradual rather than categorical nature. Some moves in the game of giving and asking for reasons are more perceptual, others more argumentative, and others are obviously practical; all of them, however, by being inferentially and socially articulated, are conceptually charged and as such open to doubt. 4.5.  Continental Layers and Challenges It is the overall sociality of knowledge, that is, its situatedness in the space of reasons, that makes a cognitive act meaningful as opposed to its being a merely reliable report such as a parrot’s reacting to the color of red by calling it “red” or a thermometer’s displaying the temperature. Brandom (2011, 29–30) thinks of this feature as an answer to what he calls the demarcation question in which he wants to draw the dividing line between sapience and sentience. Unlike Sellars and McDowell, he does not think that this demarcation necessarily contains the phenomenon of self-reflection, which is to say that in order to be in the space of reason one does not have to be able to make all his inferential commitments or entitlements explicit—by means of implication and negation—but only to recognize them in a practical, implicit manner. As in the case of the Given, this does not necessarily mean that one cannot make some part of our practices explicit, but only that he cannot do it for all the practices at once, which blocks any prospective epistemic skepticism as well as the threat of the epistemic regress. The fact that Brandom—unlike Hegel, Heidegger, or McDowell—does not use self-consciousness as the defining feature of knowledge, allows him a rather elegant way of demonstrating the secondary, derived nature of the subject-object distinction as well as its positive discursive function. This lies in making the social structure of our experience—that is, the primordial distinction subject-subject—explicit. Brandom’s route from “reasoning to representing” consists in distinguishing two interpersonal

38  Ladislav Koreň and Vojtěch Kolman

he believes of this barn facade that it is a barn

there is a barn

there is a barn facade

Figure 0.6 

commitments to the same sentence within the given tripartite structure of knowledge. If somebody takes something, such as a barn facade, for something that I believe it is not, let us say a barn, I might not only make his commitment explicit in a sentence like “John believes that the structure before us is a barn,” but I may phrase our difference of opinion by saying “John believes of this barn facade that it is a barn,” contrasting it to another, probably untrue claim that “John believes that this barn facade is a barn.” See Figure 0.6. It is such a differentiation between de re and de dicto ascriptions that according to Brandom (2000a, 181–182) allows us to make the claims of others available for use as premises in one’s own inferences, in order “to be able to tell what their beliefs would be true of if they were true.” By making these differences explicit we grasp the representational content of their claims. Understood as a part of the announced deintellectualization of language, this and similar features of Brandom’s “System” can contribute to find some common points with the continental tradition and other great traditions of Western thinking. This includes, for example, Sartre’s ([1943] 1956, liv) concept of pre-reflective self-consciousness or Heidegger’s ([1927] 1962) concept of objectivity or “presence-at-hand” as a deficient or secondary mode of “Dasein,” and so on. Such similarities and positive comparisons lead, at the same time, to negative delimitations, identifying the alleged lacks and global shortcomings, as phrased, for example, by Bowie (2007, 2013) with respect to the missing link between Brandom’s demarcation criterion and other traditional domains of spirit such as art. Bowie (2007, 122–123) poses his critique as a part of a larger indictment of the “analytical style of philosophy which resulted from the failure of Hegelian ambitions for philosophy to respond to the full spectrum of the demands made by modernity.” He particularly asks what, according to Brandom, differentiates music practitioners as somebody who must understand what they do from blackbirds singing some melody: “It is

Introduction  39 not making music, but what exactly is it that the blackbird has not committed itself to?” Following Adorno’s ([1966] 2004) critique of Hegel, Bowie’s artistic examples turn out to be two-edged: they are to be used not only as signs of the narrowness of Brandom’s system but in the style of negative dialectics, as a means of doubting the very idea of a System or of a philosophy as a conceptual whole. As Bowie puts it: [. . .] what Brandom outlines is a kind of identity philosophy, which Adorno criticizes for its tendency to neglect how the subject’s practices may not be fully transparent to the subject. (Bowie 2013, 123) Spurious or ambivalent as these reproaches might sound to the analytic mind, it is not difficult to see them as part of a legitimate effort to extend the analytic approach “beyond the bounds of academic philosophy” with its rationalistic and all-embracing tendencies. The goal is to stress not only the unifying, rational, or identity side of reality but also its differentiating, discomforting, or even irrational counterpart. In the analytic tradition, such an attitude is noticeably represented in the philosophy of ­ Wittgenstein who—being interested in differences rather than identities— feels himself in this very aspect opposed to Hegel. See Rhees (1984) and Kolman (forthcoming) for details. In adopting Wittgenstein’s concept of language games, Brandom, in what seems to be a quite similar move, deliberately suppresses their alleged plurality. He is a proud proponent of logocentrism who—in contrast to ­Wittgenstein—believes that language has a downtown, namely, the game of giving and asking for reasons (see, for example, Brandom 2000a, 14). But Wittgenstein’s anti-theoretic and anti-rationalistic attitude goes deeper than that, sharing not only Adorno’s mistrust to the healing powers of language, but the whole discomfort with the modern world and the suspicion of final theories and explanations. This attitude, of course, is not completely irrational (merely to be ascribed, for example, to Wittgenstein’s or Adorno’s pessimistic nature) but somehow wants to take into account the very fact of the existential situation of humankind with its unhappy, disquieting features that, according to Adorno, all the system-builders try to sweep under the carpet. How much these objections affect Brandom’s project and whether it is possible or desirable to consider them as valid is, of course, a question sui generis which cannot be addressed here. But the very fact that they have been raised indicates that inferentialism is about to enter its master years, as corroborated by Brandom’s own decision to conceive his second magnum opus as a commentary to the grand structure of Hegel’s Phenomenology in which epistemological arguments are interwoven with literary reminiscences and religious similes. Rather than analytic philosophy with its prevailing orientation toward the positive sciences (with the predominant role played by logic, mathematics, and physics), it is the

40  Ladislav Koreň and Vojtěch Kolman whole pragmatist background, particularly the work of classical pragmatists such as Peirce, James, and Dewey, with their generous attitude to experience in all its flavors, that might be of some inspiration here. To give an example, Meyer’s (1956) work on understanding in music, as based on Dewey’s (1894, 1895) conflict theory of emotions combined with Peirce’s broadly conceived, consequential theory of meaning, is closer to Brandom’s semantic ideas, including the pivotal explanatory role of implication and negation, than the standard analytic approach to these topics, allowing a rather straightforward answer to Bowie’s first challenge (see Kolman 2014a, 2014b for details.) As for negative dialectics and its goal to turn it against itself, maybe Brandom’s stress on the non-monotonicity of reasoning with its systematic tendency to revise already established rules is of some promise here, particularly if one also considers the difficulties met during attempts at its formalization. 4.6. Contributions Having identified a number of layers structuring Brandomian inferentialism, two remarks are immediately in order. First, as Brandom is well aware of, one can interpret his favorite thinkers differently, sometimes even dramatically differently. Second, one can use one’s interpretation of Kant, Hegel, Peirce, Frege, Sellars, or Wittgenstein to make pertinent points of criticism targeting Brandomian inferentialism, or to identify underappreciated developments in them that could supplement an inferentialist approach. This, indeed, is a strategy pursued by contributors in the last section of the ­volume in which some of inferentialism’s layers are reflected upon. It goes without saying that these contributions are only a sample of the different attitudes that can be and in fact, have been adopted toward inferentialism from a broader philosophical point of view. Many others are reflected upon in the existing literature. To name a few, Redding’s (2007) book places Brandom’s philosophy into the broader context of Hegel’s renaissance within the analytic movement. The same holds for Stekeler-Weithofer (1992, 2014, forthcoming) who, moreover, repeatedly confronts Brandom’s inferentialist views with Lorenzen’s socially oriented dialogical logic and the whole tradition of German constructivism (see, for example, Stekeler-Weithofer 2008, 7–34; Kambartel and StekelerWeithofer 2005). There is also an increasing interest in establishing links of inferentialism toward the broadly conceived tradition of continental thinking, going back to Brandom’s reading of Heidegger (cf. Haugeland’s 2005 comments) and his debate with Habermas (see Habermas’ 2000 paper and Brandom’s 2000b reply). Recently, attempts have been made at coherent standpoints toward Brandom’s “System” from the point of

Introduction  41 view of specific philosophical disciplines, such as aesthetics or philosophical standpoints, such as critical theory, see particularly Bowie (2007, 2013). The broader phenomenological perspectives and approaches have been elaborated on, for example, in work by Barber (2011) as well as in volumes edited by Merker (2009) and quite recently, by Čapek and Švec (2017). In Chapter 15 of this volume, Danielle Macbeth continues her ongoing, constructive discussion with Brandom by arguing that we should more carefully distinguish Kant’s and Frege’s inferentialism than inferentialists sometimes do. Broadly speaking, Kantian inferentialism holds that words have meaning (or concepts contents) not by virtue of their relationship to something but instead by virtue of their rule-governed roles in reasoning embedded in a game of giving and asking for reasons. Frege’s inferentialism, she alleges, is of a different sort, not Kantian but instead essentially post-Kantian. For example, she argues that Frege does not replace representationalism with inferentialism, as the Kantian inferentialist does, but instead splits the notion of (sentential) representation into two, into an inferentially articulated sense expressed and a truth-value designated. Further, and connected, Frege does not think of judgment as a matter of making a move in an essentially social game, as Peregrin does; he thinks of it instead as an acknowledgment of (fully objective) truth. Whereas inferentialism in the style of Brandom or Peregrin aims to start not with truth but instead with inference, Frege’s inferentialism takes both inference and truth to be fundamental. Having clarified some of the core differences between these two sorts of inferentialism, Macbeth explores their philosophical significance. James O’Shea begins Chapter 16 by noting that any normative inferentialist view confronts a set of challenges in the form of how to account for the sort of ordinary empirical, descriptive vocabulary that is involved, paradigmatically, in our non-inferential perceptual responses and knowledge claims. Having laid out that challenge, he argues that Sellars’ original multilayered account of such noninferential responses in the context of his normative inferentialist semantics and epistemology shows how the inferentialist can plausibly handle those sorts of cases without stretching the notion of inference beyond its standard uses. Finally, he suggests that for Sellars there were deeply naturalistic motivations for his own normative inferentialism, though the latter raises further questions as to whether this really represents, as Sellars thought, a genuinely scientific naturalist outlook on meaning and conceptual cognition. In Chapter 17, Vojtěch Kolman argues that a transparent precedent to the inferentialist doctrine can be traced back to so-called axiomatism, particularly in the form advocated by Hilbert and implicitly, by Frege. He claims that the dialectical role that axiomatism has played in the history of mathematics provides an important exegetical tool to

42  Ladislav Koreň and Vojtěch Kolman demonstrate the validity of the grounding principles of inferentialist philosophy including, surprisingly, the social perspective on knowledge. Accordingly, he interprets the occurrence of the phenomenon of Gödel incompleteness theorems within Hilbert’s symbolic program as a split of mathematical self-consciousness into two consciousnesses—known in mathematical logic under the names of “truth” and “proof”—to be interpreted as players in the game of giving and asking for reasons. In this, Lorenzen’s transformation of Hilbert’s purely symbolic project of operative mathematics and logic into Lorenzen’s and Lorenz’s dialogical logic is of particular interest, as are Lorenzen’s metamathematical concepts of semi- and full-formalism. In Chapter 18, Leila Haaparanta connects inferentialism to recent epistemological debates about the nature of testimony. Endorsing the socalled commitment theory of assertion proposed by the inferentialists, she elaborates on the idea that the normative attitude emphasized in the inferentialist philosophy of language and the evaluative attitude toward the testifier are interestingly related. She argues that the adoption of a testimonial belief involves the recipient’s seeing the testifier as a certain kind of person; still, the “seeing as,” the evaluative attitude toward the testifier, may or may not have the role of a premise in an inferential chain. This conclusion is related to how inferentialists understand the normative attitude.1

Note 1 Work on this introduction was supported by grant no. 13-20785S of the Czech Science Foundation (GAČR).

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44  Ladislav Koreň and Vojtěch Kolman Hattiangadi, Anandi. 2006. “Is Meaning Normative?” Mind and Language 21 (2): 220–240. Haugeland, John. 2005. “Reading Brandom Reading Heidegger.” European Journal of Philosophy 13 (3): 421–428. Heidegger, Martin. 1962. Being and Time. Translated by John Macquarrie and ­Edward Robinson. Oxford: Blackwell. Original edition, 1927. Kambartel, Friedrich, and Pirmin Stekeler-Weithofer. 2005. Sprachphilosophie: Probleme und Methoden. Stuttgart: Reclam. Kolman, Vojtěch. 2010. “Continuum, Name, Paradox.” Synthese 175 (3): 351–367. Kolman, Vojtěch. 2014a. “Emotions and Understanding in Music: A Transcendental and Empirical Approach.” Idealistic Studies 44 (1): 83–100. Kolman, Vojtěch. 2014b. “Normative Pragmatism and the Language Game of Music.” Contemporary Pragmatism 11 (2): 147–163. Kolman, Vojtěch. 2015. “Logicism as Making Arithmetic Explicit.” Erkenntnis 80 (3): 487–503. Kolman, Vojtěch. Forthcoming. “Master, Slave, and Wittgenstein: The Dialectic of Rule-Following.” Kremer, Michael. 2010. “Representation and Inference.” In Reading Brandom: On Making It Explicit, edited by Bernhard Weiss and Jeremy Wanderer, 227– 246. Abingdon: Routledge. Kukla, Rebecca, and Mark Lance. 2009. “Yo!” and “Lo!”: The Pragmatic Topography of the Space of Reasons. Cambridge, MA: Harvard University Press. Macbeth, Danielle. 2010. “Inference, Meaning, and Truth in Brandom, Sellars, and Frege.” In Reading Brandom: On Making It Explicit, edited by Bernhard Weiss and Jeremy Wanderer, 197–212. Abingdon: Routledge. Maher, Chauncey. 2012. The Pittsburgh School of Philosophy: Sellars, McDowell, Brandom. London: Routledge. McDowell, John. 2008. “Motivating Inferentialism: Comments on Making It Explicit (Ch. 2).” In The Pragmatics of Making It Explicit, edited by Pirmin Stekeler-Weithofer, 209–229. Amsterdam: John Benjamins. Merker, Barbara, ed. 2009. Verstehen nach Heidegger und Brandom. Meiner: Hamburg. Meyer, Leonard. 1956. Emotion and Meaning in Music. Chicago: University of Chicago Press. Millikan, Ruth. 1984. Language, Thought, and Other Biological Categories. Cambridge, MA: MIT Press. Peirce, Charles Sanders. 1931–1935. Collected Papers of Charles Sanders Peirce. Cambridge, MA: Harvard University Press. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan. Prior, Arthur N. 1960. “The Runabout Inference Ticket.” Analysis 21 (2): 38–39. Redding, Paul. 2007. Analytic Philosophy and the Return of Hegelian Thought. Cambridge: Cambridge University Press. Rhees, Rush, ed. 1984. Recollections of Wittgenstein. Oxford: Oxford University Press. Rödl, Sebastian. 2008. “Transcendental Deduction of Predicative Structure in Kant and Brandom.” In The Pragmatics of Making It Explicit, edited by Pirmin Stekeler-Weithofer, 65–82. Amsterdam: John Benjamins.

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Part I

Language and Meaning

1 Grounding Assertion and Acceptance in Mental Imagery Christopher Gauker

1. The Dilemma of Effective Cognition and a Sketch of Its Resolution Here is a simpleminded theory of human cognition. First, the mind perceives an object or some objects before it. For example, the object might be a ripe mango. Then the mind observes that the object has a property or that the objects stand in some relation. For instance, the mind might judge that the mango before it is ripe fruit. Then the mind applies some general knowledge to that observation. For instance, the mind might apply the knowledge that ripe fruit is edible. Finally, the mind draws a possibly useful conclusion: The object before it is edible. If we flesh this out in terms of mental representation, then we seem to be able to explain how thinking is successful in meeting our needs and desires. Roughly, thoughts are in touch with the properties of things, with the relations between things and with the relations between those properties and relations in the sense that it represents them. By virtue of being in touch with the world in this way, the mind can be guided by what is really the case in the world. Changes in the world are registered in the mind in such a way that, by means of its general knowledge, the mind can adapt to those changes. The structure of reality is partially duplicated in structures in the mind, which enables the body that contains these structures to adapt to the structure of the world. Details aside, one major problem with this account is that no one has ever explained what it consists in for the mind to be in touch, in the requisite sense, with one property rather than another. Why should we say that, in having a certain thought, the mind is in touch with the property of being ripe fruit, rather than the property of being a mango or the property of being a yellow and red thing? In other words, what is the representation relation between a mental representation and the things and properties that they represent? Well, we have waited a long time for an answer to this question, without ever getting even a promising start.1 Accordingly, I think that some of us should think about how we might explain successful cognition in a way that does not pose the question.

50  Christopher Gauker Having imagined that success in cognition is explicable given a correspondence between representations and representata, one might engage in the following train of thought: The chain of causes and effects mediating between sensory inputs and behavioral outputs is only the sequence of representations. The properties represented play no causal role. So, really, we can drop them from our explanation and appeal only to the representations themselves considered as meaningless structures. If we find that we cannot explicate the representation relation, that does not matter. We can simply leave it out of the account. If we need to talk about the meanings of representations at all, then we can think of talk of meaning as a more or less indirect way of talking about the proper role of the representations that have those meanings.2 The trouble with this anti-representationalist strategy is that it has a hard time explaining why we should expect the whole system of representations to be successful in meeting our needs and desires. If we no longer think of the system as tracking states of the world, then we can no longer describe it either as adjusted to reality or as achieving a desirable result. We might still say, of the system as a whole, that it was designed by natural selection to enhance our survival. But that explanation does not really answer every question we might like to ask. Regarding some particular transformation of symbolic representations into other symbolic representations that the system performs, we would like to know, why is that a valid or reasonable or justified inference? Since a system can ensure its reproduction well enough, even if it does not do everything as well as can be imagined, we cannot expect to derive an answer to this question from the observation that the system was selected by nature to promote its own reproduction. In short, we seem to face a dilemma—the dilemma of effective cognition. On one horn, we are obligated to do something that no one has been able to do, namely, to explain what it consists in for a mental representation to stand in the representation relation to an object, property, relation, or state of affairs. On the other horn, we need to explain how the manipulation of meaningless symbols can reliably meet our needs. There is a way out of this dilemma, I think. Suppose we can explain how the structure of the world drives our cognition without positing representation relations between mental representations and objects, properties, relations, and states of affairs. When I speak of the structure of the world driving our cognition, what I mean is that the events in cognition are sensitive to the structure of and the structural changes in the world. Then we can say that our thinking is successful because it is driven in this way by the structure of the world. Here is an overall strategy for finding this way out of the dilemma: (1) We restrict our attention to certain cooperative paradigms. It is not the case that the cognition we wish to account for is only that which occurs in these paradigms, but these paradigms will be the cases that

Grounding Assertion and Acceptance in Mental Imagery  51 we can account for most readily and that will serve as our models when we attempt to extend our account to other cases. (2) We posit and explicate a kind of nonconceptual imagistic cognition. By means of mental imagery, we solve problems. This cognition is nonconceptual inasmuch as mental images do not represent the properties of objects or the relations between them. (3) We explain in terms of imagistic cognition the conditions under which sentences are asserted and accepted. (4) We explain how assertion and acceptance by means of spoken sentences could facilitate cooperation in the paradigmatic situations. (5) We explain how the language can become internalized and constitute a medium of intrapersonal thought. (6) We explain how norms of discourse—for instance, rules of logic— can be formulated in terms of structures constructed out of intrapersonal linguistic thoughts. In this chapter, I will sketch some of the details of this strategy up through the first three steps. But I will also provide a kind of formula, the solution to which would take us through the fourth step. I will only briefly sketch the fifth and sixth steps.

2.  First Step: The Paradigms of Communication The cooperative paradigms that ought to be the objects of our initial explanations are situations in which linguistic communication facilitates the achievement of a collective goal. An example would be a hunting scenario. Imagine that there is a group of hunters, and the members of the group have various roles. One is a scout. He goes out ahead of the others to look for game. Another is a tracker. He works with the scout and is expert at recognizing disruptions in the soil and the foliage that indicate that game has passed by. Another is the arrow-maker. Another is the cook, who cooks the meals of the hunters. And so on. The goal of the hunters is to kill game. They eat the meat for basic sustenance, and they make good use as well of the hide and the bones. All of this activity is mediated by language. The hunters agree on where and when to go, when to hunt, and when to rest. They describe what they have seen, they state their needs, and so on. Another paradigmatic scenario would be a case of boat-building in a preindustrial age. Somebody has to design the boat. Somebody has to cut the logs from which the planks are fashioned, and someone has to fashion the planks. Somebody has to build the scaffolding from which the boat will be built. Somebody has to make the pegs or nails by which beams of the planks will be held to together. Somebody has to drill the holes that the pegs will be pounded into. If they are not accustomed to working together, somebody has to direct the activities of these several

52  Christopher Gauker parties. All of this work is mediated by language. Somebody gives the orders. They tell one another when they will arrive. They describe the location where the planks are stored. And so on. For a third example, consider barter trade. People from different parts meet in the marketplace. Some bring grain. Some bring animals. Some bring metal tools. Each declares to the others what he or she has and what he or she will take in return for a quantity of it. Perhaps there is a market manager who arbitrates disputes.

3.  Second Step: Imagistic Cognition All human beings and many nonhuman animals have a capacity to use mental imagery to solve problems.3 For example, if I need to replace a worn-out washer in a faucet, I can take the faucet apart, form mental images of the parts as I do, and record, so to speak, a mental movie of the parts as they come apart. After I have replaced the faulty washer, I can play that mental movie in reverse in order to put the parts back together again. The role of mental imagery in cognition can be made salient by considering cases in which it fails us. I am wrapping Christmas presents. I cut a piece of wrapping paper from a roll, assuming that it is big enough to cover the box before me. But then I discover that it is not. This is a failure in imagination. I imagined the piece I was cutting entirely enveloping the box and then discovered that reality did not conform to what I imagined. Or I might imagine using a wooden chopstick to prop open a window sash. But then I find that when I put the chopstick under the sash and let go of the sash, the sash, because it is too heavy, simply snaps the chopstick. Here again, I imagined—in the sense of mentally picturing—what would happen and then discovered that what I imagined did not happen. The fact that my imagination does not usually fail me in these ways shows that I have a reliable, but imperfect, ability to solve practical problems by imagining, which is to say mentally picturing, how things go. For present purposes, we will need some distinctions between different kinds of mental imagery. One basic distinction is the distinction between what I call commitive (imagistic) representations and what I call (imagistic) representations of fictions. Commitive representations are those that are treated as if they represented something actually existing. That is, the effect of such a representation on behavior is such that one would say that the bearer of the representation acts as if the thing represented actually exists. Representations of fiction are just the opposite; the bearer of the representation treats them as fictions. Commitive representations may be perceptions or memories. But they may also be endogenously generated representations of that which the bearer expects to perceive a moment later (for example, upon going around the corner). An imagistic representation of a fiction, by contrast, is a representation treated as if it

Grounding Assertion and Acceptance in Mental Imagery  53 represented a possibility. To say that a representation is fictitious in this sense is not to say that it is treated as if it represented an impossibility, just that it is not commitive. If we want to compare mental images to pictures, then we have to compare them not to static pictures but to movies. They pictorially represent sequences of events. Among these mental movies, some represent realistically, others fantastically. A realistic mental movie is a movie that we treat as if it represents how things could actually go. For instance, I might represent a dancer dancing across the stage, making only moves such as a human being could actually make. That is not to say that I need ever have observed a sequence of events quite like that which I represent, just that it’s a sequence of a sort that would not surprise me if I actually saw it. That’s also not to say that what I represent in a realistic mental movie could actually happen, only that, perhaps through some error, I treat it as realistic. A fantastic mental movie, by contrast, is a mental movie that we treat as if what it represents could never happen. For example, if I imagine a glass of red wine falling and turning into a bird and flying away before it hits the ground, then that will be what I call a fantastic mental movie. What I call an imagistic hypothesis is a realistic but invented mental movie that begins with a commitive imagistic representation. (It is not throughout its duration a perception or a memory.) For example, an imagistic hypothesis might begin with my current perception of my hand reaching toward a door handle. It might continue with images of my grasping the door handle, my turning the door handle, and my pushing the door in. If one imagistic hypothesis extends another by adding representations of further scenes to it, then I will say that the former is an imagistic elaboration of the latter. In other words, if imagistic hypothesis X is an initial segment of imagistic hypothesis Y, then Y is an imagistic elaboration of X. Further, I will assume that the mind is capable of a kind of imagistic decision-making. (See Nanay 2016 for a closely related hypothesis.) This consists of formulating imagistic hypotheses that may or may not culminate in an imagistic representation of a goal state and then acting so as to perceive the sequence of events represented in one of the hypotheses that culminates in an imagistic representation of a goal state. For example, I might entertain two imagistic hypotheses. In one I imagine myself grasping the door handle without first putting a key in the lock. In the other I imagine myself first turning a key in the lock and then grasping the door handle. If only the latter imagistic hypothesis culminates in an imagistic representation of the interior of my office, then I will turn the key in the lock before grasping the door handle. Imagistic representations, I will assume, are nonconceptual. The term “concept” can mean at least two things. A concept can be a wordlike component in a discursive representation (vehicle), or it can be a

54  Christopher Gauker component of a propositional content. In the latter case, it is a component of a propositional content that stands to an individual word or phrase as a proposition stands to a whole sentence. In denying that imagistic representations are conceptual, I am denying the perceptual representations are conceptual in either of these ways. The vehicles of imagistic representations are not structured into concepts in the first sense, and the contents of imagistic representations (in whatever sense we may properly speak of contents here) are not composed of concepts in the second sense. I have defended this claim in several other publications (Gauker 2011, 2012, 2017a), and so I will not repeat that defense here. Further, imagistic representations stand in relations of similarity to one another. Properly speaking, we might say that the things represented stand in relations of similarity to one another, but the relations of similarity between the things represented can be projected back onto the representations. The similarities I am talking about are always threeplace relations of the form x is more like y than like z. If we had to do with two-place similarity relations of the form x is like y, then we would need to specify a respect in which they were similar (since everything is similar to everything else in some respect). Thinking of similarity as a three-place relation, however, obviates the need to specify a respect of similarity (although we can still confine ourselves to certain dimensions of similarity). This idea that imagistic representations stand in relations of similarity to one another can be developed into a full-blown theory of imagistic representation, but this is another thesis that I have developed in detail elsewhere (Gauker 2011, 2012, 2017a) and will not pursue any further here. One last assumption I have to make about mental images is that they may include auditory images of spoken sentences and that the images of singular terms may be associated with images of particular object-­ representing elements of the image. Alternatively, we can say that the represented occurrences of singular terms themselves may be associated the objects represented in the image. For example, if I form a mental image of a ball in a box and a mental image of an utterance of the sentence, “This is inside of that”, then, “this” may be associated with the ball and “that” may be associated with the box. In view of the fact that an occurrence of “this” in a sentence of the form, “This is F”, may be associated with the object of a mental representation, we may also say that the object is labeled with the predicate F. In other ways as well, objects may be labeled with predicative expressions.

4. Third Step: Grounding Assertion and Acceptance in Mental Imagery The next step is to explain in terms of imagistic cognition the conditions under which a speaker is disposed to utter a sentence and the conditions

Grounding Assertion and Acceptance in Mental Imagery  55 under which a hearer is disposed to accept a sentence. For this purpose, I will assume that we are dealing with a very simple language. It contains demonstrative singular terms, such as “this” and “that”. It contains some monadic and binary predicates. It contains a negation symbol and a disjunction symbol and scope indicators (such as parentheses). It does not contain quantifiers (such as “every”) or modal operators (such as ­“possibly”) or intensional verbs of any kind (such as “believes”). While I will explain the conditions under which a speaker is disposed to utter a sentence, I do not want to suppose that such dispositions are always activated or are activated randomly. There is a general condition under which they are activated, as formulated in the following principle: The Principle of Speaking Up: An agent will utter those sentences that he or she is disposed to utter in response to the things that he or she commitively represents in the course of imagining joint activity in pursuit of goals. I will also explain what it means to accept a sentence. But first I need to lay down the assumption that people do typically accept what they are told. The Principle of Acceptance: Except under conditions C (to be specified), if a speaker utters a sentence P in the course of a cooperative endeavor with a hearer H, then H accepts P. There will be conditions under which hearers do not accept what is told to them (conditions C), but identifying those is not the most pressing challenge, and so I will not try to do so in this chapter. Acceptance is the default. It is not typically the product of a complex reasoning process. The basic schema for a production rule for the assertion of atomic sentences will be this: The Basic Rule of Assertion: For each atomic sentence of L, under conditions D (definable in terms of imagistic representations), a speaker is disposed to utter that sentence. In Gauker (2011) I attempted to flesh out this rule by specifying conditions D (see The Betweenness Rule, Gauker 2011, 234–245). Since that attempt was rather complicated, and even there had only the status of an illustration of the sort of thing one might want to say, I will here confine myself to an example that pertains only to very specific circumstances. Suppose a child has observed some cats, and some of them have, in the child’s experience, been labeled “cat”. That is, in conjunction with the perceptual representation of a cat, the child has sometimes had a perceptual representation of a sentence of the form, “That’s a cat” or “There’s the cat”, accompanied perhaps by some gesture toward the cat, or has

56  Christopher Gauker heard the question, “Where’s the cat?” followed by the perception of someone catching the cat. In accordance with my assumption that images of singular terms may be associated with images of particular object-­ representing elements of the image, let us suppose that the child associates such utterances with the cat. Similarly, the child has observed some dogs, and some of them have, in the child’s experience, been labeled “dog”. Suppose the child now encounters a novel animal and for some reason needs to label it either “cat” or “dog”. Perhaps the child will react to the animal in one way if it decides to label it “cat” and in another way if it decides to label it “dog”, and so the labeling is the child’s method of deciding what to do. In this case, the child can adopt the following heuristic: If its imagistic representation of the novel animal is more similar to the imagistic representations associated with the label “cat” than to those labeled “dog”, the child will be disposed to label the new thing “cat”; if its imagistic representation of the novel animal is more similar to the imagistic representations associated with the label “dog” than to those labeled “cat”, the child be disposed to label the new thing “dog”. My contention is that in this and similar ways, dispositions to label objects with words can be created by the similarity relations that a perceptual representation of the object stands in to other perceptual representations. This account of course will be limited to sentences that we might call observation sentences, by which I mean sentences of a kind such that a disposition to utter one may be grounded more or less directly in perception. It does not say that speakers will be disposed to utter observation sentences only in the manner specified. Even observation sentences may sometimes be theoretically grounded, in the sense that the disposition to utter them may sometimes be grounded in the utterance of other sentences, that, as we say, provide reasons to believe. Acceptance, I have claimed, is a default. But I have yet to say what acceptance consists in. The answer will be different for different kinds of sentences, starting with atomic sentences. Here is where the concept of an imagistic hypothesis comes into play. The Acceptance of Atomic Sentences: An agent accepts an atomic sentence if and only if, as a consequence of hearing or imaginatively entertaining that sentence, the agent confines his or her imagistic hypotheses to those such as would, if commitive, elicit a disposition to utter that same sentence in accordance with the production rules for atomic sentences. For example, if A says to B, “The door is locked”, then B will no longer entertain the imagistic hypothesis that depicts B’s opening the door just by turning the door handle. The reason is that that imagistic hypothesis is not one of those such that if it were commitive and not merely hypothesized, then B would be disposed to utter the sentence, “The door is locked”.

Grounding Assertion and Acceptance in Mental Imagery  57 Next I want to explain the conditions under which speakers of this language will be disposed to utter sentences containing logical vocabulary and the conditions under which they will accept such sentences. In order to do that, it will be useful to define another term: Compatibility: A sentence s is compatible with an imagistic representation X for an agent A if and only if some of A’s imagistic elaborations of X are among the imagistic hypotheses to which the agent would confine him- or herself in accepting s. It will aid understanding to spell out the dual notion of incompatibility as well, thus: Incompatibility: A sentence s is incompatible with an imagistic representation X for A if and only if none of A’s imagistic elaborations of X is among the imagistic hypotheses to which the agent would confine him- or herself in accepting s. For example, if A imagistically represents a sequence of events in which she unlocks a door, opens it, and then closes it again without locking it, then the sentence “That is locked” is incompatible with her imagistic representation, because none of her imagistic elaborations of this representation is among those to which she would confine herself in accepting, “That is locked”. In terms of compatibility and incompatibility we can define a production rule for negations thus: A Production Rule for Negations: An agent will be disposed to utter the negation of a sentence s in response to commitive imagistic representation Z if and only if the agent has occasion to consider whether s is compatible with Z and finds that it is not. For instance, if A commitively imagistically represents herself approaching a door, turning the handle, and opening it without ever imagining herself using a key, then if A has occasion to wonder whether “That is locked” is compatible with the commitive representation (with “that” associated with the door), she will find that it is not and consequently will be disposed to utter, “That is not locked”. Correlatively, an acceptance rule for negations can be formulated thus: An Acceptance Rule for Negations: An agent accepts the negation, ­ ot-s, of an atomic sentence s if and only if, as a consequence of hearn ing or imaginatively entertaining not-s, he or she confines his or her imagistic hypotheses to imagistic representations that are incompatible with s.

58  Christopher Gauker So if A says to B, “That is not locked” and B confines his imagistic hypotheses to such as are incompatible with “That is locked”, such as an imagistic hypothesis in which he imagistically represents himself approaching the door, turning the handle, and opening it, then we can say that B accepts the negation, “That is not locked”. Finally, a production rule and an acceptance rule for negations can be formulated along the same lines: A Production Rule for Disjunctions: An agent will be disposed to utter a disjunction p or q in response to commitive imagistic representation Z if the agent’s imagistic hypotheses containing Z include at least one representation that would dispose the agent to utter p and include at least one representation that would dispose the agent to utter q, and for every one of the agent’s imagistic hypotheses containing Z, either it would dispose the agent to utter p or it would dispose the agent to utter q. An Acceptance Rule for Disjunctions: An agent accepts a disjunction p or q if and only if, as a consequence of hearing or imaginatively entertaining that sentence or one of the disjuncts, he or she confines his or her imagistic hypotheses to the union of those to which he or she would confine him- or herself if he or she accepted p and those to which he or she would confine him- or herself if he or she accepted q. On this account, an agent will not be disposed to utter a disjunction just because he or she is disposed to utter one of the disjuncts. However, the acceptance rule does allow for the acceptance of a disjunction simply as a consequence of accepting one of the disjuncts (since in confining oneself to imagistic hypothesis that would dispose one to utter p one is confining oneself to those that would either dispose one to utter p or dispose one to utter q). In a fuller exposition, I would go on to formulate production and acceptance rules for conditionals, quantified sentences, modal sentences, indirect discourse sentences, and so on. An important further development is that interlocutors must learn to build, on the basis of what they hear, linguistic structures that I call an interlocutor’s take on the context. Only relative to these structures can we define the production and acceptance rules for, for instance, conditional sentences. But again, the basic psychological mechanisms by which these takes on the context are constructed should be definable in terms of imagistic representations.

5.  Cooperation Revisited I have now taken the first three steps of the strategy I announced at the beginning, which are the only steps I promised to work out in some detail. What I want to do now is explain how we might take the next three steps, although I will not actually take them.

Grounding Assertion and Acceptance in Mental Imagery  59 The next step would be to show that a linguistic practice governed by principles of production and acceptance such as I have described could facilitate cooperative action. Here I will take as my example the hunting scenario that I described at the beginning of section 2. Here are some assertions that might contribute to the conduct of a hunt: There are tracks in the sand near the lake. There are no tracks in the valley. Balam has no spear. Spears are in the cave. The enemy is between here and the lake. Namu stays home. Of course, I am cheating already in that I am assuming that the reader knows what these sentences mean, but I will assume also that the reader’s understanding is somehow justified by the same production and acceptance rules grounded in imagistic cognition that would pertain to the language of the hunters. We may suppose that each of the hunters in the hunting party entertains a rich spread of imagistic hypotheses. Each such imagistic hypothesis is rooted in the hunter’s current perceptual representations and develops from there. For instance, Balam may envision forming an advance scouting mission with Namu or staying back with the rest of the hunters; he may imagine going to the hut to get a spear or going to the cave to get a spear; he may imagine heading directly to the lake or may imagine an indirect route to the lake along the ridge over the lake, and so on. We can think of these imagistic hypotheses as forming a tree structure. When Balam imagines two different ways of elaborating on his mental movies, a branch of an imagistic hypothesis splits, to form two imagistic hypotheses that have a stem in common. When a sentence is uttered by someone and Balam accepts it, whole tranches of his tree structure of imagistic hypotheses are erased. For instance, when someone says, “Namu stays home,” all of those imagistic hypotheses depicting an advance scouting mission with Namu are erased. When someone says, “Spears are in the cave,” Balam retains only those imagistic hypotheses that depict him obtaining a spear from the cave. And so on. What I would like to be able to prove, but cannot prove, is that under certain conditions, this process of paring away imagistic hypotheses through the assertion and acceptance of sentences will have the result that each party to the exchange will have an imagistically represented plan of action, such that if each of them engages in the kind of imagistic decision-making of the kind I spoke of earlier, the result will reliably be successful coordination in the pursuit of some goal. In the case of the hunters, each will move his body in such a way that each one ends up with the tools and supplies he needs, and together they move in unison toward the game they need to find.

60  Christopher Gauker I cannot show this, but I can point to some of the key variables that we need to tune so as to make the system work. First, we need to better understand the generation of realistic imagistic hypotheses. We cannot suppose that members of the linguistic community are confined to imagining courses of events that are exactly like those they have experienced. They have to be able to learn from their experience in a way that allows them to imagine what might happen in a way that we would consider realistic, rather than fantastic, as I explained that distinction above. Second, we need to flesh out the schematic basic rule of assertion that I set forth above with something more specific. We need to say, for each atomic sentence, exactly what the conditions are, definable in terms of imagistic representations, such that a speaker is disposed to utter a sentence under those conditions. The effect of a successful linguistic exchange will seldom be that the interlocutors all form the same imagistic hypotheses. The several interlocutors will typically have different roles and responsibilities in their exchange. Since their imagistic hypotheses will be what guide their actions through imagistic decision-making, we should expect that different interlocutors will form correspondingly different imagistic hypotheses. What I am describing is by no means a version of the traditional idea that in communication interlocutors share their mental states.

6.  Glimpses of the Last Two Steps Many people have thought it hard to conceive of the possibility that we literally think in the very languages we speak. Language, they have assumed, may be conceived as a tool by means of which we reveal the contents of our minds to others. But there does not seem to be any point in my revealing to myself the content of my own mind. What could I tell myself that I do not already know? At most the speech we hear could be an impetus to acquiring new concepts and learning new facts, and hearing the sounds of words in our auditory imagination might have a mnemonic function. If we conceive of linguistic communication along the lines I have here described, then thinking in language makes literal sense. It is plausible that when we are engaged in imagistic decision-making, our imaginations draw us in several different directions at once. There is what I expect based on what I observed two days ago, and there is what I expect based on what I saw yesterday. There is what I envision in my capacity as friend, and there is what I envision based on my capacity as citizen. We have various sources of information, and we play various roles in our community. These different streams of our selves can require some coordination. Spoken language may serve as a means by which coordination between these several streams is achieved. For further discussion of this

Grounding Assertion and Acceptance in Mental Imagery  61 conception of thinking in language, see Gauker (2011) and my forthcoming paper on inner speech (Gauker forthcoming). In consequence of both what other people say to others and what people say to themselves, interlocutors can build what I call a take on the context. I call it a take on the context, because we should think of it as an interlocutor’s attempt to find a linguistic structure that really is the context that pertains to the conversation. So for each conversation there will be a context per se. The context per se for a conversation, as opposed to any given interlocutor’s take on the context, is that ideal structure that the interlocutors would indeed all take to be the context if they were communicating most effectively. The norms of discourse are rules that, at various levels, implicitly, unconsciously, or quite consciously, we strive to conform to in order to improve our cooperation by means of language. The rules of logic are norms of discourse in this sense. The rules of logic can be defined in terms of the concept of context, as I have explained it here. We can formulate a recursive definition of the conditions under which the sentences of a language are true (or, as I prefer to say, assertible) relative to a context, and then we can define an argument, considered as a set of premises and a conclusion, to be logically valid if and only if for every context in which the premises are true (assertible), the conclusion is true (assertible) as well. My fullest elaboration of this conception of logical validity is in Chapter 2 of my book on conditionals (Gauker 2005).

Notes 1 The best-known attempt that goes beyond mere hand-waving is Jerry Fodor’s asymmetric dependence theory (Fodor 1987). For my critique of this, see Gauker (2003). A more recent attempt is Sider’s concept of reference magnets (Sider 2011). A cursory glance through the nouns and adjectives across a few pages of a dictionary should quickly persuade one that very few words stand for properties that qualify as reference magnets in his sense. Here are some from the beginning of the “p” ’s: pace, pachinko, pacified, packing, paddle, padlock, paean, pagan. All of these are so far from being reference magnets that it is hard to believe that a preference for reference magnets (ours or nature’s) is doing much of anything to constrain the meanings of our words. 2 This, I take it, is the core thought of the inferentialists such as Jaroslav Peregrin (2014). In saying that meaning characterizes “proper” role I mean to acknowledge that the functions that the inferentialist identifies with meanings are conceived as ought-to-bes, not merely as a sum of the kinds of thing that actually tend to happen. 3 If there are people who claim not to, my guess is that they are simply unaware of it. That is possible, because it is no part of my thesis that mental imagery is necessarily conscious. For evidence that an operation on mental imagery (which I call visual morphing) can account for some results of experiments with monkeys and great apes, see Gauker (2017b).

62  Christopher Gauker

References Fodor, Jerry. 1987. Psychosemantics: The Problem of Meaning in the Philosophy of Mind. Cambridge, MA: MIT Press. Gauker, Christopher. 2003. Words without Meaning. Cambridge, MA: MIT Press. Gauker, Christopher. 2005. Conditionals in Context. Cambridge, MA: MIT Press. Gauker, Christopher. 2011. Words and Images: An Essay on the Origin of Ideas. Oxford: Oxford University Press. Gauker, Christopher. 2012. “Perception without Propositions.” In Philosophical Perspectives 26: Philosophy of Mind, edited by John Hawthorne and Jason Turner, 19–50. Malden, MA: Wiley. Gauker, Christopher. 2017a. “Three Kinds of Nonconceptual Seeing-As.” Review of Philosophy and Psychology 8 (4): 763–779. Gauker, Christopher. 2017b. “Visual Imagery in the Thought of Monkeys and Apes.” In Routledge Handbook of Philosophy and Animal Minds, edited by Jacob Beck and Kristin Andrews, 25–33. London: Routledge. Gauker, Christopher. Forthcoming. “Inner Speech as the Internalization of Speech.” In Inner Speech: Nature, Functions, Agency and Pathology, edited by Peter Langland-Hassan and Augustin Vicente. Oxford: Oxford University Press. Nanay, Bence. 2016. “The Role of Imagination in Decision-Making.” Mind and Language 31 (1): 127–143. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan. Sider, Theodore. 2011. Writing the Book of the World. Oxford: Oxford University Press.

2 Semantics Why Rules Ought to Matter Hans-Johann Glock

The inferentialism of Brandom and Peregrin explains the notion of ­linguistic meaning by reference to rules governing communication. This chapter pursues the same idea, but draws directly on Wittgenstein rather than contemporary inferentialism. It defends the idea that the meaning of an expression is constituted by the rules for its correct use. Such an approach needs to solve at least four formidable and interrelated problems. (a) Assuaging the qualm that linguistic meaning is ultimately a notion we’d be better off without. (b) Addressing arguments against the idea that meaning has an essential normative dimension. (c) Distinguishing those linguistic rules that are constitutive of meaning from others. (d) Spelling out the idea of correct use in a way that is not unilluminatingly circular. I attempt to make some headway toward resolving (b)–(d) by exploiting Wittgenstein’s idea that the notion of meaning ought to be clarified by reference to other pertinent notions. The meaning of an expression is both what an acceptable explanation of meaning explains and what a competent speaker understands. The meaning of general terms is determined by rules specifying conditions of application explained and understood by competent speakers.

1.  Inferentialism, Normativism, and Pragmatism Kant famously characterized metaphysics as a “battlefield of endless controversies” (Kant [1781] 1998, A VIII). The same might be said of philosophical semantics, widespread protestations of professionalism and diagnoses of objective progress notwithstanding. One recent attempt to break the deadlock is “inferential” or “conceptual role semantics.” A particular brand of inferential role semantics is inferentialism. It was inspired distally by Wittgenstein (1953) and proximally by Sellars (1954),

64  Hans-Johann Glock received its emblematic elaboration by Brandom (1994), and is currently being propounded forcefully by Peregrin (2014, chap. 1), among ­others. Inferentialism is distinguished from other versions of conceptual role semantics through its normativism. It explains the notion of linguistic meaning by reference to rules governing communication. My contribution falls into the same general genre. But it does not link up directly with the lively and detailed debate about inferentialism. Instead I shall try to cut an independent track through this conceptual thicket, one that goes back to the letter though not necessarily the spirit of Wittgenstein’s later work. There are also differences of content between inferentialism and my position. For one thing, the latter does not place any special emphasis on rules of transformation, let alone an exclusive one. I shall return to this point in section 3. For another, unlike inferentialism, I accept and set store by the possibility of distinguishing between analytic and synthetic statements, and between conceptual/semantic and factual questions, connections, and arguments. I have defended this heretical break with the Quinean orthodoxy at length elsewhere (for example, Glock 2003, chap. 3) and shall not dwell on it here. Instead I shall try to put both normativism and a conceptual versus factual distinction in the service of what might be called a “use” or “pragmatist theory of meaning.” But in two respects, at least, it is a “theory” only in a minimal sense. First, it investigates the established concept of linguistic meaning as well as related notions, rather than devising a novel one, for example, for the purpose of “naturalizing” meaning or of rendering it more hospitable to being captured by formal systems like the first-order predicate calculus. Second, my theory explicates the notion of meaning in the style of connective conceptual analysis rather than constructing a formal semantic theory generating “meaning-giving” theorems for sentences of a specific natural language. It thereby qualifies as an “analytic” rather than “constructive” theory of meaning (see Glock 2003, 141, 152–153).1 Like inferentialism, my pragmatist theory of meaning and its connection to use is normativist: the meaning of an expression is constituted by rules for its correct use. Such an account needs to confront at least four formidable and interrelated challenges: (a) Assuaging the qualms of Wittgenstein and Quine that linguistic meaning is ultimately a notion we’d be better off without. (b) Distinguishing those linguistic rules that are constitutive of meaning from others, for example, of a syntactic or pragmatic kind. (c) Addressing anti-normativist arguments against the very idea that meaning has an essential normative dimension. (d) Spelling out the idea of correct use in a way that is not circular in an unilluminating way.

Semantics: Why Rules Ought to Matter  65 This essay brackets (a). Contrary to various manifestations of semantic eliminativism and nihilism, I shall assume that the concept of meaning is legitimate and indeed indispensable for everyday, scientific, and philosophical purposes alike. Instead I shall do my best to clear a particular hurdle confronting my approach, which consists in satisfying both (b) and (c) on the one hand, and (d) on the other. I attempt to meet these challenges by exploiting an unduly neglected aspect of Wittgenstein’s writings on this topic. The notion of meaning ought to be clarified by reference to its connections with other pertinent semantic notions. The meaning of an expression is both what an acceptable explanation of meaning explains and what a competent speaker understands. As regards (c), the meaning of general terms is indeed a matter of rules, as long as one pays due heed to the idea that the relevant rules specify conditions that something must satisfy to fall under the term, rather than specifying which objects actually satisfy those conditions. I start by surveying the central connections between meaning, use, and rules. Next, I look more closely at the relation between semantic rules, explanation, and understanding (ad b). To engage with (c), I start by distinguishing different potential dimensions of semantic normativity. This is followed by presenting a popular and prima facie telling objection to the idea of semantic normativity. To overcome that objection, I first introduce the idea of a semantic norm “by mistake,” that is, by specifying a type of error that betokens lack of linguistic understanding rather than factual ignorance. Next, I raise the question of whether correctness is a normative notion, answering it in the affirmative. Finally, I tackle (d) by suggesting how the threat of circularity can be defused, sort of, by a connective analysis linking meaning to use and thence to standards of correctness that are part of acceptable explanations and feature in criteria of linguistic competence.

2.  Meaning, Use, and Rules The negative motivation behind “use theories” is the failure of referential (“Fido”-Fido) conceptions of meaning, according to which the meaning of an expression is an object for which it stands. This conception is doubly wrong. Not all meaningful words refer to objects. The referential conception is modeled solely on proper names, mass nouns, and sortal nouns. It ignores verbs, adjectives, adverbs, connectives, prepositions, indexicals, and exclamations. Moreover, even in the case of referring expressions, their meaning is not the object they stand for. First, if the meaning of a word were an object it stands for, referential failure would have to render a proposition like “Mr. N. N. died” senseless (Wittgenstein 1953, § 40). Second, identifying the meaning of a word with its referent is what Gilbert Ryle (see Ryle 1949, chap. 1; 1971, chap. 27) called

66  Hans-Johann Glock a category mistake, namely of confusing what a word stands for with its meaning. I can fall in love with the referent of “the second wife of Prince Charles,” not with its meaning. There are also positive considerations in favor of linking meaning to use:

• whether an expression like “sesquipedalian” means something in a • •

given language depends on whether it has an established use in a linguistic community; what an expression means depends on how it can be used within that community; we learn what an expression means by learning how to use it, just as we learn how to play chess not by associating the pieces with objects, but by learning how they can be moved.

At the same time, to do justice to the notion of meaning we must avoid reducing linguistic use to a causal process between speakers and hearers after the fashion of causal and behaviorist theories. The meaning of a type-expression does not depend on the actual causes or the actual effects of uttering a token of it, either on a particular occasion or in general (pace causal and behaviorist theories). Nor does it depend on the effects intended by the speaker, however complex and high-order they may be (pace the highly influential Gricean programme in semantics). If I say, “Milk me sugar!” this may well have the result that my hearers stare at me and gape. But it does not follow that this combination of words means, “Stare at me and gape!” It doesn’t even follow if this entertaining effect can be repeated. Indeed, it does not even follow if I utter these words with the intention of bringing about this reaction (Wittgenstein 1953, §§ 493–498). Meaning is a matter not of how an expression is actually used and understood, but of how it is or ought to be used and understood by members of a linguistic community. What is semantically relevant is the correct use of expressions. Accordingly, the linguistic meaning of an expression is determined by rules that lay down how it is to be used correctly.2 However, even a normativist conception of use does not immediately yield a satisfactory account of linguistic meaning. For synonymous expressions can have distinct (rule-guided) uses (see Glock 1996a). “Cop” and “law enforcement agent” are arguably synonymous, yet there are rules against using the former in, for example, a court of law, but no such rules concerning the latter. Consequently, meaning does not determine use. At the same time, use determines meaning not causally, but logically (just as for Frege sense determines reference). While sameness of meaning co­exists with difference of use, every difference in meaning is a difference in use. Given the use of a word, we can infer its meaning without further evidence, but not vice versa. This is plausible. One cannot tell from a

Semantics: Why Rules Ought to Matter  67 dictionary explanation of “cop” whether the term is frequently used by British academics. By contrast, one can write the dictionary entry on the basis of a full description of the term’s employment. If this is correct, we can learn from the use of a word everything there is to its meaning; use remains the guide to meaning, and conceptual analysis a matter of investigating linguistic use. Unfortunately, our modified version does not avoid a problem that has beset the use-oriented approach from its inception, namely that the term “use” in vacuo is too nebulous to be helpful. But it has brought the difficulty into sharper focus. We have settled for the idea that rule-guided use determines meaning, rather than being identical with it. A difference in meaning entails a difference in use, not vice versa. The paramount questions are therefore these: What aspects of our rule-guided linguistic practices are relevant to meaning? And is there any aspect of linguistic practice a difference in which entails a difference in meaning?

3.  Inferences and Speech Act Potential Inferentialism is motivated not least by the first of these questions. Its answer: Only those rules that govern the inferential relations of the expression. On the one hand, however, without something like an analytic/synthetic or conceptual/factual distinction, this is overly permissive, for it would make all inferential relations (deductive, conceptual, inductive) part of the meaning of an expression. It implies, implausibly, that any alteration in general beliefs amounts to a conceptual change, with the consequence that two scientific theories featuring apparently incompatible empirical claims cannot be talking about the same phenomena (see Fodor and Lepore 1992, chap. 1; Glock 2008, 889–891). On the other hand, with an analytic/synthetic distinction restricting semantic rules to those governing inferences runs the risk of being overly restrictive. There are semantic rules for expressions that do not feature in inferences (except of course when they are quoted in assertions)—for example, “hello” and “ouch.” And even for those expressions that do have a role in inferences and the meaning of which is partly determined by those rules, it is far from clear that rules of inference exhaust the semantic dimension. Sellars was alive to this point. In addition to norms governing “intra-­linguistic moves” (Sellars 1974) that qualify as inferences strictu sensu, he also brooked norms for “language entrance” and “language exit transitions.” My approach is more catholic still as regards both the intension and extension of “semantic rule.” In my book, semantic rules encompass anything that, in natural languages, functions as a standard of semantic correctness and hence of linguistic competence and understanding, including explanations of meaning of various kinds. Ostensive definitions, for instance, can function as transformations rules, as Wittgenstein recognized. But they can also be invoked to explain, criticize,

68  Hans-Johann Glock and justify uses that are not inferential, at least as long as that term is not stretched out of proportion (see Glock 1996b, “grammar” and below). This means taking a step back from inferentialism. At the same time my starting point is shared by inferentialism. Neatly summarizing the common normativist perspective, Peregrin (2014, 2 and passim) points out that

• the meaning of an expression is linked to its “role” or function; • role or function is in turn conferred by rules. But how do we identify the pertinent rules? How do we distinguish in particular semantic from pragmatic rules? Formal semanticists in the philosophy of language and representationalists in the philosophy of mind tend to demean the latter as “merely pragmatic,” relying on Grice’s theory of conversational implicatures in their endeavors to keep the notions of meaning and intentional content “pure.” Even for pragmatists who are skeptical about both the motives and the prospects of this project, however, the challenge remains. Semantic rules should treat “cop” as equivalent to “policeman,” pragmatic rules permit use of the latter yet not of the former in a court of law. Appeal to role or function will not solve the problem, since an expression can have different kinds of roles. To mention just a few: syntactic, psychological, social, institutional, and legal roles. Along a different parameter, expressions can have a role in an idiolect or a role in a lexicon, and these roles can coincide or come apart. It would appear that the kind of role we are looking for is one that expressions have in whole natural languages or speech communities. A particularly promising way of pursuing this hint derives from speech act theory. It appeals to the idea of a “speech act potential” (Alston 1964, chap. 2; von Savigny 1983). The sense of a type-sentence is determined by the type of speech-act that uttering it has as a matter of general linguistic conventions; these conventions concern the illocutionary rather than the perlocutionary role in Austin’s well-known terminology. For its part, the meaning of a type-expression is its contribution to the speech act potential of sentences in which it occurs. This line of investigation offers numerous insights, and assessing it fairly is beyond the scope of this essay. Nevertheless, at least in the context of providing a pragmatist account of meaning, it faces a formidable stumbling block. Its conception of meaning via use may be too wide and holistic. For the speech act potential of specific words or sentences is tied to rules or conventions that cannot be counted as part of the lexical meaning of words or the literal sense of sentences. Some of these pertain to communication and communicative competence in general rather than to an individual expression e and the knowledge of e’s meaning. These include the “conversational maxims” highlighted by Grice,

Semantics: Why Rules Ought to Matter  69 which are fueled by “certain general features of discourse.”3 Such rules may contribute to “the total signification of an utterance” (Grice 1989, 41, 118). But they contribute neither to “what the speaker has said” nor to “what is conventionally implicated” by the utterance, that is, “implicated by virtue of some word or phrase which [the speaker] has used.” Instead they determine “what is nonconventionally implicated,” in particular by way of “conversational implicatures.” Such implications fall “outside the specification of the conventional meaning of the words used” (Grice 1989, 39, 26); and the rules that engender them appear to be pragmatic rather than semantic, not just by Gricean standards. It might be feasible to disregard these rules by demonstrating that they have an impact exclusively on the perlocutionary acts that can be performed with e, whereas only illocutionary acts count toward speech act potential. But even if illocutionary roles can be separated with sufficient clarity and precision from perlocutionary ones, a problem remains. There is a second class of rules which contribute essentially to the speech act potential of an expression e, without being part of e’s lexical meaning. These are the very rules around which speech act theory revolves, namely those conventional rules that govern specific types of illocutionary acts. The best-known example is the rules for the speech act of promising that Searle (1969, chap. 3.1) tried to capture. From a pragmatist-cum-normativist perspective, at any rate, these are partly constitutive of the meaning of “promise” and its cognates. But they are not partly constitutive of the meaning of other expressions, all of which have a potential to be used in promises. Mutatis mutandis for semantic competence. Knowledge of these rules is a prerequisite for understanding “promise” and its cognates, yet not for understanding, for example, “chair,” “bachelor,” “drake,” “run,” and “quickly,” not to mention logical operators.

4.  Meaning, Explanation, and Understanding Without leaving behind either the lessons or the difficulties of the idea of speech act potential, I want to pursue an alternative route. It exploits an unduly neglected aspect of Wittgenstein’s reflections on meaning. The more general idea is to elucidate the notion of meaning through its conceptual connections to other pertinent notions. More specifically, Wittgenstein focuses on the connections between meaning on the one hand, and the explanations and understanding of specific expressions on the other. “The meaning of a word is what the explanation of meaning explains.” I.e. if you want to understand the use of the word “meaning,” look at what is called “explanation of meaning.” (Wittgenstein 1953, § 560)

70  Hans-Johann Glock At first sight, this appears to be singularly uninformative. If someone were to clarify what etymology is by saying that it is the history of an expression and then proceeding with “the history of an expression is what the explanation of its history explains,” wouldn’t we regard that as a rather tired joke? Similarly, for “the American Constitution is what the explanation of the American Constitution explains.” But compare this last case to “the British Constitution is what the explanation of the British Constitution explains.” This contrast indicates that a triviality can refer to more or less important and even essential aspects. The British constitution is nothing other than, nothing over and above what is explained by British courts. Similarly for meaning; it does not have an existence independently of being explained and understood. And that is why the passage just quoted, though literally trivial, captures an essential feature of the idea of meaning. To home in on this essential feature, one needs to embed the truism in a context of follow-up elucidations. The first of these is that the explanation at issue is not causal, at least in the sense of efficient causation. The explanation that is connected to meaning in a way that is both conceptual and illuminating is not an explanation why (an expression e means what it does). Instead it is an explanation of what (e means) and how (e is to be used). There are meta-semantic lessons one can draw from the truism thus understood. First, the meaning of “meaning” is connected to that of “explanation.” Second, and in consequence: meaning has a normative dimension since semantic explanations have a normative status. They function as standards of semantic correctness and competence. There is also a semantic lesson, that is, a lesson for determining the meaning of specific expressions: if you want to know which rules for e are semantic, look at which rules are invoked to explain the meaning of e. Does that solve the problem of distinguishing semantic from other rules? Yes, at least up to a point. Acceptable (notably lexical) explanations of “cop” distinguish conditions of correct application from, inter alia, characterizations of legal legitimacy and social propriety. This is evident from, among other things, the entries in standard lexica. The explanans of such an entry explains or specifies the meaning of the explanandum at the start of the entry. That explanans will specify conditions of application, but not other rules concerning the explanandum. To be sure, after the explanandum, there may be additional information about its use in parentheses. Some of these will be syntactic or morphological, for example, “(adj.).” But others will specify features of use that qualify as pragmatic, for instance, ­“(colloq.)” or “(pej.)” or “(anc.).” Even a parenthesis of that kind, however, falls way short of specifying specific rules concerning the impropriety of “cop” in a legal context. This is another respect, therefore, in which following up our apparently stale truism is illuminating: lexica provide a well-established, clear, and

Semantics: Why Rules Ought to Matter  71 generally reliable, though by no means fail-safe, way of distinguishing semantically pertinent from other features of use. Wittgenstein’s strategy for clarifying meaning also appeals to how competent speakers understand an expression. The meaning of e cannot transcend the understanding of competent speakers. Meaning is immanent rather than “hidden” (Wittgenstein 1953, § 126–128). It is determined by how competent speakers understand e. The connection of meaning to semantic competence and knowledge of meaning furnishes a second way of demarcating semantic rules: to single out semantic rules, consider whether a speaker needs to be familiar with them to count as a competent user, in the sense of knowing what e means. Like the connection to explanation, it also highlights a normative aspect: competent speakers, users, or uses are those satisfying certain standards.

5.  Connective Analysis In sum, we have arrived at the following two conceptual connections: Meaning-Explanation (ME): The linguistic meaning of an expression e is what the explanation of e (as opposed to an explanation of the phenomena e refers to or applies to) explains. Meaning-Understanding (MU): The linguistic meaning of an expression e is what a competent speaker or user of e (as opposed to someone who knows everything about the phenomena e refers to or applies to) understands by e. Both ME and MU provide criteria for identifying rules as semantic in a particular language. Alas, it is blatantly obvious that appeal to these criteria does not provide a noncircular explanation of what “meaning” means. For in the sense pertinent to ME, “explanation” must be understood as explanation of meaning, whether directly (“what the explanation of meaning explains”) or indirectly (“as opposed to causal explanations . . . ”). Mutatis mutandis for MU and “understanding.” The attempt to single out semantic rules appeals to conventions that can only be separated from other rules governing language by presupposing the notion of meaning. It would appear that the desideratum of demarcating semantic from other rules and the desideratum of analyzing the concept of meaning are mutually exclusive. It is at this juncture that we should appeal to a distinct conception of conceptual analysis. Strawson has distinguished between “atomistic,” “reductive,” and “connective” analysis (Strawson 1992, chap. 2). Atomistic analysis seeks to break down concepts and propositions into components that are absolutely simple. Strawson regards atomistic analysis as “distinctly implausible” (Strawson 1992, 20). Reductive analysis tries to explain complex concepts in terms that are regarded as more

72  Hans-Johann Glock perspicuous or less problematic, for example, from an empiricist or naturalistic perspective. Strawson resists this ambition on the grounds that the fundamental concepts with which his descriptive metaphysics deals “remain obstinately irreducible, in the sense that they cannot be defined away, without remainder or circularity, in terms of other ­concepts” (Strawson 1995, 16). Strawson is right on both counts. Atomistic and reductive analysis seeks to break down concepts into simpler (in the case of atomistic analysis, ultimate) components and to unearth the concealed logical structure of propositions. Developments in the wake of Wittgenstein and Quine cast doubt not just on the quest for simpler let alone ultimate components, but also on the idea of definite logical structures. Strawson has good reasons, therefore, to abandon the idea that philosophical analysis decomposes or dismantles a complex phenomenon, and thereby the analogy to chemical analysis. His connective analysis is the description of the rule-governed use of expressions, and of their connections with other expressions by way of implication, presupposition, and exclusion. Connective analysis need not result in definitions; it can rest content with elucidating features that are constitutive of the concepts under consideration, and with establishing how they bear on philosophical problems, doctrines, and arguments. “Only connect”: Strawson transposes E. M. Forster’s maxim for the understanding of human life to the understanding of our conceptual framework (see Strawson 1992, 17–19; 1995, 15–17). We were faced with a circularity involved in explaining meaning by reference to rules to be demarcated from other rules by appeal to linguistic-semantic explanation and understanding. But all explanations of meaning eventually move in a circle, either directly or indirectly. What is to be avoided is not explanatory circles as such, but only those that are too narrow or unilluminating for other reasons. The circles—in turn interconnected—­summarized by ME and MU, respectively, are not of this kind. They shed light on the problematic notion of meaning by reference to notions that do not invite reification and which seem to be less confusing in philosophical contexts. Both of them also highlight normative dimensions of the concept of meaning of the kind that normativism (whether inferentialist or not) is keen on. At this juncture, however, we now need to face the challenge that the appearance of these normative dimensions is deceptive. The remainder of this chapter will address some of the numerous questions and objections brought forth by this challenge.

6.  Semantic Normativity and Its Discontents All claims of semantic normativity involve the idea that a certain phenomenon which is semantic in a highly general sense entails the existence

Semantics: Why Rules Ought to Matter  73 of certain normative phenomena. The following are directly relevant to the nature of linguistic meaning: Bare Normativity of Meaning (BNM): Expression e is meaningful ⇒ there are conditions for e’s correct use. Ruly Normativity of Meaning (RNM): e is meaningful ⇒ there are rules for the use of e. Prescriptive Normativity of Meaning (PNM): e is meaningful ⇒ there are prescriptions for the use of e. Most anti-normativists grant BNM. That an expression has a specific meaning implies that there are conditions for its correct use. At the same time they confront normativism with a dilemma: either these semantic principles are not really normative; or they are not in fact constitutive of meaning, that is, they do not follow from an expression being meaningful (Glüer and Wikforss 2009). BNM is supposed to fall under the first horn; RNM and especially PNM under the second. In this essay I shall exclusively consider BNM as applied to general terms. A popular way of capturing the idea that general terms require conditions of correct application is (BNM1): e means F ⇒ ∀x(it is correct to apply e to x ↔ x is f ), (where “e” is a general term, “F” gives its meaning, and “f ” is that feature in virtue of which e applies to an object x). The consequent of BNM1 provides the scheme for a “semantic principle” of the kind employed in formal semantics: (SP): ∀x(it is correct to apply e to x ↔ x is f ). For the sake of argument, I shall stick to such principles, even though they are rather alien to everyday parlance and by no means exhaust the range of candidates for semantic rules, least of all from a catholic Wittgensteinian perspective. At the same time, to preserve some connection with the reality of linguistic exchange, I shall ignore the disquotational principles beloved by formal semanticists and address principles that are at least suitable as explanations of meaning in actual practice. For “drake,” such a principle might read: (SPD): ∀x(it is correct to apply “drake” to x ↔ x is a male duck).

74  Hans-Johann Glock The first anti-normativist objection runs: “correct” in BNM1 is not genuinely normative, since it is simply a place-holder for “true”; “it is correct to apply e to x,” in other words, boils down to e holds true of x (Boghossian 2005; Hattiangadi 2007, 51–61). One cannot counter this objection by pointing out that semantic principles give rise to norms. For the same holds for descriptive statements. For one thing, they can give rise to technical norms or rules, given additional premises of a normative kind. That compact fluorescent lamps consume less energy than standard light-bulbs may give rise to norms requiring the fitting of compact fluorescent lamps, given a prior norm requiring energy savings. For another, one can criticize statements and actions by reference to empirical statements no less than by reference to semantic principles. At the same time, by dint of its connection with truth, holding true is what Parfit (1997) calls “normatively relevant.” A proposition being true (or a predicate holding true of something) can have implications for what it is correct to believe or do, implications that depend on fundamental features of human thought and action rather than specific empirical or normative premises. We need to modify, that is, “correct” our beliefs and activities in the light of what is the case, of things being thus-and-so. This in turn reflects the fact that how things are is essential to how we should pursue our goals (Horwich 1998, 44–46; Glock 2003, 131–136). Furthermore, the anti-normativist objection assumes that semantic norms would have to be norms of truth, norms to the effect that one ought to think and state what is true. That assumption has also been accepted by most normativists (for example, Blackburn 1984, 281–282). But the contrast between correct and incorrect applies to language in a variety of ways, and their connection to the notion of meaning differs. In particular, one can use a word meaningfully, in a sentence with a sense that expresses a thought, without that thought being either true or justified. This difference between truth and meaning emerges when we consider different types of mistakes that people can make in using words. First, in the run-up to a by-election to the House of Commons a candidate once said: (1) I know that I cannot win this seat. There was nothing wrong with (1) either linguistically or factually. Yet, she made a dreadful mistake, because it is not politic to admit to such dim prospects. Next consider Tony Blair’s notorious statement in the House of Commons: (2) Iraq is capable of deploying weapons of mass destruction within 45 minutes of an order by Saddam Hussein.

Semantics: Why Rules Ought to Matter  75 There is nothing wrong linguistically with (2), yet it is both unjustified and false. Now consider George W. Bush’s: (3) You teach a child to read, and he or her will be able to pass a literacy test. Here we are confronted with a linguistic mistake. But it is of a syntactic rather than semantic kind. In fact, once we correct for that error, (3) is analytic, at least on a certain understanding of “teach” and “literacy.” In spite of involving a solecism, therefore, this example shows Bush at the very height of his semantic powers. That is more than can be said of: (4) I am mindful not only of preserving executive powers for myself, but for my predecessors as well. Here Bush’s travails are semantic. (4) betokens not lack of factual knowledge, but an insufficient grasp of the meaning of at least one of the two terms “preserving” and “predecessors.” There is a fundamental contrast between saying something false or unjustified—as in (2)—and saying something meaningless—as in (4). ­ Some uses of words are mistaken solely because of what these words mean, irrespective of any other facts, syntactic rules or social expectations. Conversely, one can apply a word in a way which is semantically correct—based on a proper understanding of its meaning—without applying it correctly in the sense of saying something true, namely if one errs about pertinent facts (but see Whiting 2016). Even if semantic rules are understood as principles that specify conditions for making a true statement—application/truth-conditions—their violation does not consist simply in saying something false. The proper distinction between semantically correct and incorrect does not amount to that between true/false but is (closer to) that between meaningful on the one hand, meaningless or nonsensical on the other. Or perhaps even more appositely and in the spirit of MU: there is a difference between using an expression with understanding and using it to say something true and with the knowledge that what is said is true. A semantic principle like SPD specifies not what “drake” actually applies to, but the conditions under which it applies to an object x. Whether it actually applies then depends on whether x satisfies these conditions; it is a matter of fact rather than meaning. One commits a factual error if one applies “drake” to x on the mistaken assumption that x is a male duck. One commits a semantic mistake if one applies “drake” to x on grounds other than x being a male duck. In both cases, one does something that is assessable as incorrect against a standard, but only in the latter case is the standard (the mistake) semantic.

76  Hans-Johann Glock

7.  Correctness and Normativity Once this point is recognized, the semantic dignity of our principles or explanations is unassailable. However, the anti-normativist can switch to the other horn of the alleged dilemma and ask: Is correctness a normative notion? When I first encountered this question at a workshop on meaning and rule-following in Berlin in 2002, I was bemused: Is the pope ­catholic? I am not alone. It is widely assumed that notions like “correct” or ­“mistaken” are normative (Blackburn 1984, 286–287), even among those skeptical about the normativity of meaning (Boghossian 2003, 35; Fodor 2008, 205). But there is a prima facie credible source of doubt. A serviceable explanation of correctness runs as follows: (COR): x is correct ↔ x is in accordance with an acknowledged standard. This standard may be part of a specific system of evaluation appropriate to x, as when we speak of correct academic dress. Or it may be a general standard expressing certain demands, for example, on prudential or moral conduct. Either way, there must be a standard specifying conditions under which x counts as correct. At this juncture, it is tempting to argue that calling x correct is merely to state that it satisfies these conditions, and hence that the concept has no normative implications after all. However, in characterizing x as correct we do not just ascribe to x the features specified in the relevant standard. We also characterize x as meeting a standard of positive evaluation. The term “correct” is not purely descriptive or factual, but evaluative. What is more, unlike other evaluative terms, for example, “good,” it carries the further implication that failure to meet this standard is not just undesirable, but provides grounds for intervention. After all, the verb “to correct” means: to set right, rectify, or amend. Applying terms used in the standard may be purely descriptive, but applying the term “correct” is not. And to call something incorrect is not only to evaluate it negatively; if something is incorrect, then one has grounds for correcting it. To appreciate this difference, consider the following statements: (5) (6) (7) (8) (9)

Glock is not wearing a cap and gown. Glock is not dressed correctly. Glock is dressed badly. Glock had to change his dress, because it was incorrect. Glock didn’t have to change his dress, because it was correct.

No normative force attaches to (5). But in certain contexts, for instance a graduation ceremony, not wearing a cap and gown counts as not being dressed correctly. And (6), which records this fact, does have normative force. It is not just a negative evaluation like (7). According to my family,

Semantics: Why Rules Ought to Matter  77 (7) is what Quine calls a standing sentence. It holds true most of the time. But (8) doesn’t. I am happy to say that my attire rarely gives license to correction. But this is precisely the force of (8). In the envisaged case, it entitles the stewards to insist that I either put on cap and gown or absent myself from the procession. If “correct” and “incorrect” no longer served these normative purposes, their meaning would have altered by any standards. For example, if (8) and (9) became unacceptable while (8’) Glock had to change his dress, because it was correct. (9’) Glock didn’t have to change his dress, because it was incorrect. were to become acceptable locutions, then “correct” and “incorrect” would have reversed their meaning. This lesson carries over to semantic normativity. According to antinormativists, “to say that some use of a term is ‘correct’ is [. . .] merely to describe it in a certain way—in light of the norm or standard set by the meaning of the term” (Hattiangadi 2006, 225). To categorize something by reference to the defining features of a drake has no normative implications per se. To deny that an object x possesses the defining features of a drake, for instance, is not to characterize x as fit for correction. At the same time, the “norm or standard set by the meaning” of “drake” makes reference to these features, just as the standard for correct academic dress makes reference to cap and gown. If a neophyte applies “drake” to an animal on the grounds that it is a female fox and we classify this as “incorrect,” this second statement has direct normative implications, since it characterizes the initial application of “drake” as fit for correction. More generally, to assess an assertion or belief as false is to present it as fit for epistemic correction. Equally, to assess an utterance as meaningless, nonsensical or a malapropism is to present it as fit for semantic correction. To be sure, on particular occasions a speaker may aim to make false assertions, to commit linguistic mistakes, or to utter nonsense. In that case what she does may be correct relative to a different standard—a prudential or moral one, for example. If that standard is more important in that situation, what she does may also be correct in an “all things considered” sense. But this does not detract from the fact that she is violating semantic or epistemic norms. In semantic principles like SPD “correct” is not used in the all things considered sense. Conversely, the general norms of reason presupposed in that usage are not constitutive of the meaning of specific terms, although they feature in the semantic norms governing terms like “reasonable” or “rational.”

8.  Concluding Thought on Circularity This demonstrates the normative character of BNM. But in the context of explaining what meaning is it comes at a steep price. Once again

78  Hans-Johann Glock normativism seems to be in a bind. To avoid reducing the incorrectness involved in violating semantic principles to falsehood, we have explained it in explicitly semantic terms—“meaningless,” “nonsensical,” “senseless,” “without understanding,” and so on, and so forth. The desideratum of identifying the semantically relevant features of use and the desideratum of pinpointing the normative dimension of meaning seem to stand in a potentially fatal tension. Once again, however, we can take comfort from the aforementioned method of connective analysis. And as in the fifth section above, we can appeal to nontrivial and important conceptual connections between meaning, explanation, and understanding. Explanations of meaning play normative roles in teaching, justifying, and criticizing linguistic use, yet they specify conditions under which e applies or is true of, not whether it applies to or is true of a given case. By the same token, understanding a sentence requires knowing the conditions under which it true, rather than knowing its truth-value. Using words in ways that fall foul of recognized explanations and betrays misunderstanding is a ground for correction. While this is not all there is to the normativity of meaning, it is enough to justify the normativist perspective in the spirit of Wittgenstein, Sellars, Brandom, and Peregrin.

Notes 1 Before Davidson, a theory of meaning was supposed to provide an analysis—in a suitably lose sense—of the concept of meaning. Theories of meaning in this analytic sense are, for example, the referential theory, behaviorist and causal theories like that of Quine, verificationist theories, Wittgensteinian accounts of meaning as use, speech-act theories influenced by Austin, and Grice’s theory of communication intentions. By contrast, Davidson envisaged a constructive theory, which differs from analytic theories of meaning roughly in the way in which Tarski’s truth-theory differs from traditional theories of truth. Such a theory does not directly explain what meaning is. Instead, it generates for each actual or potential sentence s of a particular language a theorem “that, in some way yet to be made clear, ‘gives the meaning’ of s,” and shows in particular how that meaning depends on that of its components (Davidson 1984, 23). Analytic theories of meaning should be compatible with the way the meaning of particular sentences is specified or explained; but unlike constructive theories they do not prescribe an algorithm for generating such specifications. 2 This idea underlies both Wittgenstein’s approach to meaning and contemporary inferentialism. It is also raised by Ryle’s unjustly forgotten distinction of use and usage, in “Use, Usage and Meaning” (Ryle 1971, chap. 31). The semantically relevant notion of use is that of a way of using an expression, its method of employment. By contrast, usage is constituted by the prevalence or nonprevalence of this method of employment in a certain linguistic community. As thus explained, use is of interest to philosophers, usage to empirical linguists. The former has a normative dimension, the latter doesn’t. There is the misuse of expressions, but there is no such thing as the “misusage” of an expression.

Semantics: Why Rules Ought to Matter  79 3 All discourse, he maintains, is governed by a Cooperative Principle: “Make your conversational contribution such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged” (Grice 1989, 26). Speakers who follow this principle will abide by maxims like: • say what is required, and no more; • say it when and how it is required.

References Alston, William. 1964. Philosophy of Language. Englewood Cliffs: Prentice-Hall. Blackburn, Simon. 1984. “The Individual Strikes Back.” Synthese 58 (3): 281–301. Boghossian, Paul. 2003. “The Normativity of Content.” Philosophical Perspectives 13 (1): 31–45. Boghossian, Paul. 2005. “Is Meaning Normative?” In Philosophy-Science-­ Scientific Philosophy, edited by Christian Nimtz and Ansgar Beckermann, 205–218. Paderborn: Mentis. Brandom, Robert. 1994. Making It Explicit: Reasoning, Representing, and Discursive Commitment. Cambridge, MA: Harvard University Press. Davidson, Donald. 1984. Inquiries into Truth and Interpretation. Oxford: Oxford University Press. Fodor, Jerry. 2008. LOT 2: The Language of Thought Revisited. Oxford: Oxford University Press. Fodor, Jerry, and Ernest Lepore, eds. 1992. Holism: A Shopper’s Guide. Cambridge: Blackwell. Glock, Hans-Johann. 1996a. “Abusing Use.” Dialectica 50 (3): 205–223. Glock, Hans-Johann. 1996b. A Wittgenstein Dictionary. Oxford: Blackwell. Glock, Hans-Johann. 2003. Quine and Davidson on Language, Thought and Reality. Cambridge: Cambridge University Press. Glock, Hans-Johann. 2008. “Analytic Philosophy and History: A Mismatch?” Mind 117 (468): 867–897. Glüer, Kathrin, and Åsa Wikforss. 2009. “The Normativity of Meaning and Content.” In The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta. https://plato.stanford.edu/archives/spr2016/entries/meaning-normativity. Grice, Paul. 1989. Studies in the Way of Words. Cambridge, MA: Harvard University Press. Hattiangadi, Anandi. 2006. “Is Meaning Normative?” Mind and Language 21 (2): 220–240. Hattiangadi, Anandi. 2007. Oughts and Thoughts. Rule-Following and the Normativity of Content. Oxford: Oxford University Press. Horwich, Paul. 1998. Truth. 2nd ed. Oxford: Oxford University Press. Kant, Immanuel. 1998. Critique of Pure Reason. Translated and edited by Paul Guyer and Alan W. Wood. Cambridge: Cambridge University Press. Original edition, 1781. Parfit, Derek. 1997. “Reasons and Motivation.” Proceedings of the Aristotelian Society, Supplementary Volume 71 (1): 99–130. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan.

80  Hans-Johann Glock Ryle, Gilbert. 1949. The Concept of Mind. London: Hutchison. Ryle, Gilbert. 1971. Collected Papers, Volume II. London: Hutchison. Searle, John. 1969. Speech Acts: An Essay in the Philosophy of Language. Cambridge: Cambridge University Press. Sellars, Wilfrid. 1954. “Some Reflections of Language Games.” Philosophy of Science 21 (3): 204–228. Sellars, Wilfrid. 1974. “Meaning as Functional Classification: A Perspective on the Relation of Syntax to Semantics.” Synthese 27 (3–4): 417–434. Strawson, Peter Frederick. 1992. Analysis and Metaphysics: An Introduction to Philosophy. Oxford: Oxford University Press. Strawson, Peter Frederick. 1995. “My Philosophy.” In The Philosophy of P. F. Strawson, edited by Pranab Kumar Sen and Roop Rekha Verma, 1–19. New Delhi: Allied Publishers. von Savigny, Eike. 1983. Zum Begriff der Sprache: Konvention, Bedeutung, Zeichen. Stuttgart: Reclam. Whiting, Daniel. 2016. “What Is the Normativity of Meaning?” Inquiry 56 (3): 219–238. Wittgenstein, Ludwig. 1953. Philosophical Investigations. Oxford: Blackwell.

3 Quine Peregrinating Norms, Dispositions, and Analyticity Gary Kemp

Jaroslav Peregrin characterizes the basics of inferentialism as follows: The approach of inferentalism is quite radical: It requires us to ­dispense with the persistent intuition that words are symbols, and that they stand for their meanings or that they become meaningful by representing something. Instead of this, inferentialism puts forward the picture that meaningfulness is essentially a role, a role that a word acquires if it is made to function within a virtual space delimited by a system of [. . .] inferential rules. (Peregrin 2014, 238) My thesis is that Peregrin’s inferentialism is available to a Quinean.1 Quine himself would have applauded the rejection of the “persistent intuition that words are symbols [. . .] that they become meaningful by representing something.” But can a Quinean speak with a straight face of rules? I think the answer is yes and will devote most of this essay to explaining why. What of “a virtual space”? Does it mean that “a system of [. . .] inferential rules”—a language—is an abstract object, which would seem to represent semantic determinacy, so famously rejected by Quine? This is connected with the matter of analyticity, and as I will explain, I’m not convinced that this is a problem.2 Peregrin says that the evidential basis provided by Quine’s behaviorism is too meager to account for language—that it is unworkable to conceive language as entirely consisting in dispositions to overt behavior, where this is limited to assent and dissent. I shall try to show that Quine’s linguistic dispositions, harmlessly widened, do have the normative or ruletheoretic force that Peregrin counts as vital to language. In addition I’ll make the following claims: (1) that Quine in fact explicitly accepts the reality of norms; (2) that there is no obvious barrier to Quine’s tolerating the full gamut of norms requisite for Peregrin’s purposes; (3) that Quine is indeed within his self-imposed rights to accept normativity. I will close with some remarks about the place of inferentialism in Quine’s general architecture of science, of how a “system of norms” might fit into his picture of reality, which one might well think too austere to allow it.

82  Gary Kemp

1. Analyticity Here is the kernel of an inferentialist account of language, crudely matched up to Quine’s alternative.3 The inferentialist view of sentential conjunction is that if one accepts S and one accepts S* then one is aware of the propriety of inferring “S and S*,” and similarly for the other direction. And similarly for the other truth-functional sentential connectives. Aside from the absence of the notion of “propriety,” Quine’s treatment of the sentential connectives in terms of “verdict tables” is comparable (although Quine thinks of the verdicts—dispositions to assent and ­dissent—as not quite being sufficient for the truth-functional connectives proper, but let us set this aside).4 What Quine conceives as observation sentences are for the inferentialist conceived in terms of what Sellars calls “language-entry” rules, for example, as one’s “inferring” (in a certain extended sense) the propriety of “It’s red” from a certain perceptual situation, and “language-exit” rules, for example, as one’s recognizing the propriety of choosing the red Lego piece from the command “Take the red one.” For the inferentialist, other sorts of general terms are explained by the mastery of a great interlocking fund of such inferences as x has bill and fur ⊢ x is a platypus (“interlinguistic inferences” in Sellars-speak). Ed Becker (2012, 260–267) has recently argued that Quine can consistently recognize these as well: again roughly, we ask the subject such questions as “Would an animal with a bill and fur be a platypus?” or “Could a thing without a bill be a platypus?” You might think of objections but let us suppose that Becker is right. It would be natural to wonder whether a key difference between the two views might be their contrasting views of analyticity—that whereas Peregrin accepts it, Quine rejects it. But the case is rather the reverse, and any clash on the issue is unlikely to be decisive. Peregrin holds that the proprieties of certain patterns of inference play “meaning-constitutive” roles. They are rules of language, criteria for the use of the words. But he denies that inferentialism is thereby committed to a strict doctrine of the analyticity of such inferences, thus flirting with circularity (since an analytic truth is widely thought to be “true-according-to-meaning”). Meaning is explained rather in terms of a wider notion of normativity. And the matter of precisely which inferences have this normative status is somewhat fluid and variable (indeed he accepts semantic holism): in any given conversational context, one typically presupposes clusters of rules, but these are without sharp boundaries, and within limits, they can change from context to context. Peregrin does not make this point so far as I’m aware, but the influence of such rules is typically subterranean: semantical smooth sailing is normally taken for granted (children for the most part are not overtly taught language; they learn largely by listening and imitation). But the spell is sometimes broken, and especially revealing is the local, adult case where a bit of language is indeterminate and

Quine Peregrinating: Norms, Dispositions, and Analyticity  83 we have to extemporize a rule. You and I might explicitly decide, for the purpose of a conversation about music, on an exact rule governing the expression “the blues” so as not to allow any tacit semantic disagreements to masquerade as factual disagreement. The case is exactly what one would expect if there were a vast but largely tacit and somewhat indefinite complex of rules underlying language. Quine came round to accepting, by the time of Roots of Reference (Quine 1974), that many or perhaps most sentences which others such as Grice and Strawson (1956) insisted are analytic can indeed be called “analytic,” in his newly formulated sense of the term. For the individual: if one accepts “Bachelors are unmarried men” in the course of learning—acquiring the relevant dispositions with respect to—the term “bachelor,” then that, for you, is an analytic truth (Quine 1974, 80). Generalized to the linguistic community: “a sentence is analytic if everybody learns that it is true by learning its words” (Quine 1974, 79). Logical truths can also be classed as analytic, if we think of the status as being transmitted via logical inference and the axioms are themselves classed as analytic. The idea also makes sense of cases which depend on implicit relational structure, such as Chomsky’s “If she persuaded him then he was not coerced” (or the analytic inference from “She persuaded him” to “He was not coerced”). Presumably it is doubtful whether this “vegetarian” explication of analyticity can bear anything like the burden of the epistemological burden which Carnap and others envisaged for the notion of analyticity, because for Quine—to cut a long story short— there is no such thing as a commitment-free stipulation. Choice of language is always substantive, and there are no purely “external questions,” free choices of what language to use, in the manner of Carnap.5 But it does go some way to relieving any lingering Gricean/Strawsonian itches (cf. Quine’s treatment of the terms “necessarily” and “possibly” in Quine 1964).

2.  Quine’s Acceptance of Normativity So I don’t think that any difference with respect to “true-by-meaning” will itself signify very much. Rather, the most visible difference between the two views, as indicated at the outset, is that Quine uses the notion of linguistic disposition whereas Peregrin uses the idea of propriety, rulegovernedness, or norm. I’ll discuss their respective takes on norms presently but as a way in the subject, I will first make a point on linguistic dispositions. Peregrin supposes Quine to be unable to provide norms in a substantive enough sense for the purposes of inferentialism. I think this is a mistake. The apparent source of this is that Peregrin repeats Chomsky’s error of assuming that by a disposition with respect to an observation

84  Gary Kemp sentence—for example, “Lo, a spider”—Quine means a disposition to utter the sentence in certain non-linguistic circumstances: [As a Quinean we] claim that the meaning of sentence is a matter of a disposition to utter the sentence; and we reduce dispositions to specific behavior in specific situations. In this case, however, we are unable to specify the relevant circumstances other than as those circumstances in which the relevant sentence is really uttered, hence we say, in effect, that the meaning of a sentence is a matter of uttering the sentence in those situations in which it is really uttered [. . .] the concept of a disposition [. . .] seems to do no work than the ill-famed concept dormitive power within the explanation “Opium makes one sleepy because it has dormitive power.” I think that the dispositional elaboration of the use theory of meaning therefore leads us up a blind alley. (This makes us part our way with Quine.) (Peregrin 2014, 48) As Chomsky says, for almost any observation sentence the probability of its utterance is vanishingly low even in the right nonlinguistic circumstances. In that sense the idea that linguistic dispositions add up to meaning or a facsimile of meaning is a nonstarter. But that isn’t Quine’s idea, as he stressed in his reply to Chomsky (1969). Quine’s idea is that of the disposition to assent to the observation sentence if asked; Quine calls the method of identifying such dispositions the method of “prompted assent” (so one is counted competent with the sentence only if one has a conditional or second-order disposition: a disposition to become disposed to assent to the sentence under certain non-linguistic circumstances). For example, a subject will have a disposition to assent to “Rabbit” just in case some subset of the subject’s sensory receptors are stimulated (ceteris paribus). This mistake fuels Peregrin’s response to the question of whether specifically linguistic norms can be understood in terms of dispositions: In a sense, the answer may be positive. Invoking a suitable concept of disposition, anything that a human subject does can be said to be a matter of dispositions [. . .]. But even if we accept this way of looking at things, the concept of disposition necessary to account for normative attitudes is much thinner, and hence less problematic, than that needed to account for linguistic behaviour. (Peregrin 2014, 75–76) Reading “thicker” for “thinner,” when Peregrin says that the envisaged thicker dispositions are “less problematic” than the unsubstantive ones Quine uses to account for linguistic behavior, he is assuming as Chomsky did the near-vacuous or trivial conception of Quinean dispositions.

Quine Peregrinating: Norms, Dispositions, and Analyticity  85 But the question is not whether dispositions in the near-vacuous sense can explain meaning or do the duty of meaning, but whether proper Quinean dispositions, hypothetical or higher-order dispositions, can do the trick. Now to norms themselves. Norms are the alpha and omega that inferentialists point to as that which displays our rationality, which are necessary for meaning proper, which display our spontaneity as users of fully fledged language. These are necessary for the “space of reasons” to open up. Peregrin likens such norms to the rules of a game: just as there would be no game of chess were the players not to observe the rules of chess, so there would not be meaning did we not take ourselves to be bound by certain norms, for example, the rules of inference for conjunction. It is not sufficient, for playing the game of chess, that one behave in the right way, that one’s behavior accord with the rules of chess. That can happen by chance, or on the part of a computer, or a trained creature who has no idea of what he’s doing. Something more is required: one has to treat the rules as rules, which involves one’s appreciation that it is incorrect to break a rule, even if it never happens. If we shift now to language (language-games), and require further that one master not just a few but a great many interlocking language-games, then the idea is that one’s mastery of language as a whole is expressible by the use of explicitly normative vocabulary. And these norms ramify at least up one level: it’s incorrect to call a bat a “bug,” or to infer a disjunct from a disjunction, but it is also wrong to let such transgressions go unremarked (Peregrin 2014, 121). Quine is often thought not to have room for normativity, but he made it quite clear in later years that he embraces normativity, even if he didn’t use the term “normativity” or “norms” until the 1970s. The presence of the idea in Quine’s writings goes back at least to the “Two Dogmas” (Quine 1951) claim that the standards for theory-revision are holistic. According to his “no first philosophy” view of philosophy present in his writings of the 1950s—what later he would call his naturalism— there are no standards for knowledge, or for responsible belief or theory, other than those operative within natural science. Those are ideas about norms. In The Web of Belief (Quine and Ullian 1970, 64 ff) he spoke of various further norms (calling them “virtues”) aimed at characterizing good ­science—rules of thumb, ideals, or guidelines, for the formation of fruitful hypotheses, including generality, simplicity, conservatism (the “maxim of minimal mutilation”), refutability, and modesty (there are other virtues of scientific theory that define a theory’s overall “scientific value,” which is a wider notion than a theory’s empirical content; see Quine 1992, 18, 95–96). This is not just gas. In later writings— the books The Roots of Reference, Pursuit of Truth, From Stimulus to Science, and various essays and responses—Quine speaks explicitly of

86  Gary Kemp normative claims as being for him “part of heuristics generally” (Quine 1992, 20). More generally: The most notable norm of naturalized epistemology actually coincides with that of traditional epistemology. It is simply the watchword of empiricism: nihil in mente quod non prius in sensu. This is a prime specimen of naturalized epistemology, for it is a finding of natural science itself, however fallible, that our information about the world comes only through impacts on our sensory receptors. And still, the point is normative, warning us against telepaths and soothsayers. (Quine 1992, 19) In his reply to Morton White of 1986 he writes: Naturalization of epistemology does not jettison the normative and settle for the indiscriminate description of ongoing procedures. For me normative epistemology is a branch of engineering. It is the technology of truth-seeking, or, in a more cautiously epistemological term, prediction. Like any technology, it makes free use of whatever scientific findings may suit its purpose [. . .]. There is no question here of ultimate value, as in morals; it is a matter of efficacy for an ulterior end, truth or prediction. The normative here, as elsewhere in engineering, becomes descriptive when the terminal parameter is expressed. (Quine 1986, 664–665) And in a late piece: Naturalistic epistemology [. . .] is viewed by Henri Lauener and others as purely descriptive. I disagree. Just as traditional epistemology on its speculative side gets naturalized into science [. . .] so on its normative side it gets naturalized into technology, the technology of scientizing. (Quine [1995] 2008a, 468) He speaks also of the gambler’s fallacy as a simple example of a mathematical fact being transmuted into a norm, which collectively constitute the “technology of scientizing” (Quine [1995] 2008a, 468), illustrating further his idea that the engineering of scientific success is a place where norms enter in (see Decock 2000). He intends the “norm of empiricism” as an ultimate parameter of science, in a certain sense a non-conditional or “categorical” norm. Indeed he has a Wittgensteinian moment in citing “predictions as the checkpoints of science” as definitive of the “language-game of science”

Quine Peregrinating: Norms, Dispositions, and Analyticity  87 (Quine 1992, 21). In calling it a “non-conditional norm,” I am not making a point of logic but a pragmatic point: the hypothesis in such a statement as “If knowledge is your aim, then you ought to maximize predictive success” normally goes without saying. Normally it goes without saying that one in certain circumstances is playing the language game of science, of striving for knowledge. These norms make as explicit as possible how to make artful guesses in framing hypotheses, and more generally how to do good science. If Quine is entitled to those then there is no evident reason that he cannot also have linguistic norms or even Gricean cooperative maxims and the like; there would appear not to be an impediment in principle to a Quinean embrace of inferentialism (see Baghramian 2016 for another verdict on this). He can accept the more specific norms that pertain to the use of language, that there is an “implicit normative structure” guiding our use of language. In particular, the vast structure of norms, of rules, underlying language as mentioned above is largely unspoken, covert or tacit. It is only when someone violates such a rule—when we observe someone saying of a bat in plain view that it’s a bug—that they come to the surface. We are disposed to correct such behavior—to say, “That’s wrong!” and so on, or to assent to, “The statement is incorrect”—when we observe such transgressions. That is just more behavioral dispositions, dispositions to corrective behavior.6 But is he so entitled? In the remainder I want to ask whether, despite what I have just said, the appeal to norms is after all consistent with Quine’s stringently naturalistic conception of science. If normative statements are a part of science, must they not be capable of being expressed by extensional means, for Quine? Mustn’t they, despite appearances to the contrary, be capable in some sense of being reduced to “mere facts,” perhaps to higher-level generalizations about linguistic practice or to dispositions in some other sense? I think that the answers to these questions are no: even for Quine, extensionality and reducibility are not required.

3.  Norms and Values One might think of Quine as allowing normativity only if it can be reduced to generalizations about dispositions. And are not the prospects for an actual reduction bleak? In particular, Peregrin is surely right that the behavioural patterns will display complicated feedback loops corresponding to the fact that a rule is always ‘in the making’,” which make a “practice such a complicated behavioural pattern (a motley of patterns?) that any attempt to capture it in the idiom of natural science [. . .] appears foolhardy. (Peregrin 2014, 114; Peregrin’s emphasis)

88  Gary Kemp But that a task is extremely complicated, or too much so to carry out, is consistent with its being possible in principle. Further, Quine accepts sciences whose vocabulary cannot be expressed in the severe language of physics. He does think that ontology is just the ontology of physics, but such extremes of complexity do not themselves entail anything new ontologically. He finds room for disciplines—“sciences”—which cannot as a matter of principle be reduced to physics which nevertheless treat of physical objects whose behavior is just too complex to be expressed in that austere vocabulary (biology, to take a notable example). I’ll say more about this at the end, as I will of the looser idea that norms might admit explanation in terms of behavior as opposed to reduction to behavior. For now we can just note that for Quine, the irreducibility of a certain notion or cluster of notions to the hard sciences is consistent with their finding a place in science. The key is irreducibility at the level of laws, or statements; or to put it in an idiom Quine favored, the irreducibility is not ontological but “ideological.” In Quine’s one essay about moral philosophy—“On the Nature of Moral Values”—he is explaining his way of thinking of action as depending on belief and value by considering a dog, a turnip, and a tree between them (also there is the brief section of the book Roots of Reference, Quine 1974, 49–52). Why doesn’t the dog go get the turnip? Either he doesn’t want it, or he’s unaware of it.7 Quine goes on: The duality can be traced back to the simplest conditioning of responses. A response was rewarded when it followed stimulus a and penalized when it followed b; and thereafter it tended to be elicited by just those stimulations that were more similar to a than to b according to the subject’s inarticulate standards of similarity. Observe then the duality of belief and valuation: the similarity standards are the epistemic component of habit formation, in its primordial form, and the reward-penalty axis is the valuative component. (Quine [1978] 1981, 55) Much of rest of the essay is devoted to moral values proper, distinguishing them from “aesthetic values” and “sensual values.” He points out that just as we must have an innate predilection to inductive inference for learning to be possible, so we must have some innate values. Thus we are born liking to be caressed, fed, and so on (and disliking pain, sour milk, and so on). Quine also cites the possibility of a behavioral test for values in an individual, in the same spirit as the test he had sketched in the Roots of Reference for subjective similarity spaces involving an animal pecking at levers (simplifying somewhat): a chicken learns to get food by pressing lever A; he is now faced with two levers B and C; if the chicken presses B rather than C then B is more similar to the chicken to A than C is (likewise for C rather than B). He remarks (Quine [1978] 1981, 56)

Quine Peregrinating: Norms, Dispositions, and Analyticity  89 that characterizing the “reward-penalty axis” is likely to be much simpler than characterizing the similarity space, since not only does it seem straightforward for example to formulate a criterion for which kind of food the chicken prefers, unlike the reward-penalty axis, subjective similarity realistically has to be relativized to “respects” of subjective similarity (for example carrots and oranges have like colors but unlike shapes). Quine describes specifically moral values as follows: We learn by induction that one sort of event tends to lead to another that we prize; and then by a process of transfer we may come to prize the former not only as a means but for itself [. . .]. The transmutation of means into ends [. . .] is what underlies moral training. Many sorts of good behavior have a low initial rating on the valuation scale and are indulged in at first only for their inductive links to higher ends: to pleasant consequences or the avoidance of unpleasant ones at the preceptor’s hands. Good behavior, insofar, is technology. But by association of means with ends we come gradually to accord this behavior a higher intrinsic rating. We find satisfaction in engaging in it and we come to encourage it in others. Our moral training has succeeded. (Quine [1978] 1981, 57) He speculates further: The penalties and rewards by which the good behavior was inculcated may have included slaps and sugar plums. However, mere show of approval and disapproval on the parent’s part will go a long way. It seems that such bland manifestations can directly induce pleasure and discomfort already in the very young. Perhaps some original source of sensual satisfaction, such as a caress, comes to be associated very early with the other more subtle signs of parental approval, which then come to be prized in themselves. (Quine [1978] 1981, 57) The point we need is just that Quine does have room in his conception of reality for value, and can formulate at least the beginnings of behavioral tests for it. He points to a parallel with linguistic value, by implication linguistic norms: Language, like the moral law, was once thought to be God-given. The two have much in common. Both are institutions for the common good. They reflect, somewhat, the primitive duality of belief and valuation on which I remarked at the beginning. Language promotes the individual’s inductions by giving him access to his neighbor’s observations and even to his neighbor’s finished inductions. It also helps

90  Gary Kemp him influence his neighbor’s actions, but it does this mainly, still, by conveying factual information. On the other hand the moral law of a society, if successful, coordinates the actual scales of values of the individuals in such a way as to resolve incompatibilities and thus promote their overall satisfaction. In language there is a premium on uniformity of usage, to facilitate communication. In morality there is a premium on uniformity of moral values, so that we may count on one another’s actions and rise in a body against a transgressor. (Quine [1978] 1981, 61; emphasis added) That language is an institution “for the common good,” that it reflects, “somewhat, the primitive duality of belief and valuation” (Quine [1978] 1981, 61), strongly suggests that there are at least general norms at work in all communication such as the premium on the uniformity of usage, truth-telling, and the like. But still there is a difference between values as Quine describes them and norms. They are of course very close: if one accepts that there is a norm to accept or bring about such and such, then ordinarily it’s because one either values such and such directly, or values something that such and such leads to (or disvalues what failure to realize it leads to). But what sort of behavior counts as the criterion for one’s accepting a normative statement? As far as I know, this is not a subject that Quine wrote on directly, so the following is merely reconstructive, or speculative, even if the general idea may strike the Quinean as relatively obvious. Our target-schema is “One ought to Φ.” We are asking how it can be satisfactorily explicated in Quinean terms. Suppose that the non-­normative “Those who get V in situation S are those who Φ” is confirmed, where “V” names something valued (realistically, we should say “tend to get V” rather than “get V”). This becomes the normative “In order to get V in situation S, one ought to Φ.” How? Presumably Quine would envisage community-wide behavioral tests for finding out, so to speak, whether the “is” is treated as an “ought”: say showing displeasure at transgressors, or punishing them, and rewarding or praising the compliant. Suppose then that V is indeed a “terminal value”—a thing such as empirical adequacy whose value goes without saying—and that we are considering a situation in which S is satisfied. Then we infer the target-schema “One ought to Φ.” In other words, a Quinean envisages us as behaving in ways that tend to enforce certain normative claims. That is what normativity is for the Quinean. On this, as on so many things, Quine is a follower of Hume: we derive the “ought” from the “is” not logically—that’s ­impossible— but by being disposed to behave in certain ways. We envisage normativity in general as being embodied in our dispositions to assent to certain types of sentences in suitable occasions, and our exhibiting certain behavioral patterns. The takeaway is just there is no deeper fact to normativity; although we are stopping short of an outright behavioral

Quine Peregrinating: Norms, Dispositions, and Analyticity  91 reduction or definition of normativity, norms are not something additional to which our acting in those ways is a response (although we would have to add that the norm must be recognized by a significant portion of the community; more on this below). Our tendency to make the transition from “is” to “ought”—in certain cases—is much like our tendency to perform induction. It’s not logic, but it is part and parcel of our being the sort of rational creatures we are. A certain distinction can be drawn among norms. Values are categorically unlike empirical generalizations—the outputs of induction—in that they are freestanding. Quine writes: “whereas we can test a prediction against the independent course of observable nature, we can judge the morality of an act only by our moral standards themselves” (Quine [1978] 1981, 63). Norms can be of either type: some—for example, the norms of scientific and linguistic practice—can be tested against their tendency or lack of it to bring about, for example, truth. Other norms—the moral norms, to name another example—go with moral value. But either way, they are not unamenable to behavioral explication. At this point we need to have before us a certain complication for Quine’s so-called linguistic behaviorism. In later years, Quine accepted what is more explicitly a “proximate” account of language, an “individualistic” account (to speak obliquely of another theorist with whom on other matters Quine had a contentious relationship, namely Noam Chomsky). Quine does not, strictly speaking, found the objectivity of speech on our referring to common objects, or on our having similar “stimulus meanings” for observation sentences. The first is ruled out by the inscrutability or indeterminacy of reference, and the second is ruled out by the seeming irrelevance of any such similarity to actual communication (in fact, as Quine came to point out, there is evidently no such similarity, at least not such as would allow one to speak with any precision of intersubjective stimulus patterns). Accordingly, he came to define the stimulus meaning of an observation sentence for an individual languageuser in terms of some subset of the user’s sensory receptors being activated, the layout of which may vary across the population. What makes communication possible is rather what Quine calls the “pre-established harmony” of perceptual standards: Having certain natural needs and interests, and living in a common environment, our species has evolved common standards of salience—for example, to track and pay attention to various things immediately in view rather than others (this has many parallels in the work of psychologists; for example, in studies of object constancy in infants). Thus, for example, you and I are programmed by natural selection to tend to respond to such things as a rabbit emerging into view, and not typically a random bit of sky, even though the precise anatomical details will differ between us. Fundamentally it’s no different from the fact that despite our anatomical differences, we equally learn to walk, prefer to ingest sugar rather than turpentine, and recoil at loud

92  Gary Kemp noises. That is what makes communication possible, what makes it fruitful to define a sentence as observational for the community as its being observational for each member and the members’ agreement on verdicts in the relevant circumstances. Now I said above that it seems that norms, or linguistic norms at any rate, are inherently social. Peregrin stresses this. Wittgenstein also emphasized it—that coaching, training, and more generally the corrective reactions and guidance on the part of others in the linguistic community are needed for linguistic rules to have their effect, and hence for meaningfulness. And on the face of it, the apparent social nature of linguistic norms sits ill with Quine’s neurological privacy—with the doctrine of stimulus meaning, which, as we noted, turns out to be individualistic, therefore not social, or at least not straightforwardly so. I will try to relieve the pressure by saying more about how normative sentences would function within Quinean semantics. Instances of the general schema “If x is in situation S, then in order to get V, x ought to Φ” do not have stimulus meanings; they are standing sentences, not occasion sentences (and so not observation sentences). To get an occasion sentence of the form “A ought to Φ,” we have to instantiate the schema, and detach the antecedents of the conditionals (so assume that A is indeed in situation S and V is a terminal parameter). The occasion of the resulting occasion sentence is just A being in S, a non-­normative matter. Normativity enters into the response of the individual subject when he or she accepts the sentence with respect to A’s behavior. If the subject does accept this sentence, then he or she will tend to approve or be satisfied if A does Φ, and will tend to disapprove or be dissatisfied if A does not Φ. So provided there is something narrowly psychological about approval and disapproval, or satisfaction and dissatisfaction, the proximate behavioral approach can at least get a grip. I said that (an instance of the type) “A ought to Φ” as just described is an occasion sentence, but not that it has a well-defined stimulus-­meaning, not that it’s an observation sentence. This is because the appropriate situations for the sentence are situations that tend to cause approval or disapproval in the subject, which, though psychological, are not just matters of the firing of the subject’s sensory receptors. However, in the basic or elementary case, “A ought to Φ” is appropriate in a special sort of circumstance: where A is observed in situation S, where S is in some perceptual condition. The challenge here does not come from the normative vocabulary, but from the need to show how the sort of statement “A is in S” might be explained in proximate terms. It is relevant then that in Pursuit of Truth of 1992, when Quine made empathy an essential part of his account of language-teaching and learning (you see that the baby sees the cat, you say, “Kitty!”), he did not see it as incapable in principle of being explained in proximate terms. (Quine 1992, 42; see Ebbs 2016, 22–23). In fact, as psychologists have pointed out the evidence is strong that we

Quine Peregrinating: Norms, Dispositions, and Analyticity  93 are as innately tuned to read faces and gestures as we are to notice rabbits. Quine can thus appeal to the slightly later (Quine 2016) and more satisfactory and more general doctrine of preestablished harmony: it stands to reason that just as natural selection makes us peculiarly attentive to rabbits, so it makes us peculiarly attentive to the perceptual states of others. Although he doesn’t quite make the point, he hints somewhat in this direction in “On the Nature of Moral Values”: By the same token [the theory presented here] represents each of us as pursuing exclusively his own private satisfactions. Thanks to the moral values that have been trained into us, however, plus any innate moral beginnings that there may have been, there is no clash of interests as we pursue our separate ways. Our scales of values blend in social harmony. (Quine [1978] 1981, 60)

4.  Grades of Objectivity Finally, for a quite different angle on the problem of normativity, we can look to Quine’s two-sorted conception of science, as dividing Class A from Class B (see Quine 1960, 218–232; Davidson and Hintikka 1969, 335). Class A consists of a single, empirically answerable, extensional, regimented, first-order theory directed at “limning the true structure of reality” (Quine 1960, 221). It is as near to being absolutely objective and precise as humanly possible. The paradigmatic example is physics, which “discover[s] the ultimate constituents of the world and their regularities” (Quine [1986] 2008b, 166). We might call this the metaphysical aspect of science (I call it such because the ontology of science is exhausted by class A; class B expands only the “ideology” of class A—its predicates). Class B consists of statements of various idioms that are practically and even scientifically indispensable but that cannot, usually for featuring nonextensional statements, ascend to Class A; statements explicitly involving causation, de re propositional attitudes, necessity and possibility, dispositions, and meaning itself have, as Quine points out, invaluable functions, but admit of explanation as so to speak markers, pointers to regions of reality without themselves being of Class A standard. Dispositions themselves are a clear example: by a “disposition” Quine means them in the orthodox sort, expressed non-extensionally in counterfactual conditionals, as in “If x were Ψ then x would Φ.” For Quine, these are promissory notes for standard extensional generalizations describing the underlying mechanism (for example, if the disposition is solubility in water then the mechanism concerns molecular structure). Class B statements point to the existence of those of Class A, even if the latter are unknown. We might call this the pragmatic aspect of science.8 And I submit on behalf of Quine that statements of normativity are of this sort (not least

94  Gary Kemp because their logic is intensional): they do not pertain to reality “as it is in itself”—whatever precisely that means—but they are indispensable to human beings collectively aiming to know reality. What is here important for the Class A/B distinction, again, is that statements’ being of Class B does not imply that they are dispensable, humanly dispensable, or otherwise unimportant. For Quine, statements made by the ineliminable use of indexicals are of this sort; so are statements ascribing de re propositional attitudes. Inside our ordinary conceptual scheme, such statements can reasonably strike us as unavoidable, even if from outside that scheme, from a hypothetical, abstract, and impersonal point of view, they would ultimately be merely pragmatic or relative. John Divers (conversation) speaks of “anthropocentric necessity” as a way of characterizing the modal aspects of Class B statements (Quine of course disallows modality from Class A). Chris Hookway speaks, in a way intended to buttress Quine’s view of things, of “expressive function” as opposed to “descriptive function” (Hookway 1988, 65–66). For Hume himself causal statements are a sort of subjective projection. So it’s not asking anything new among defenders of that austere conception of reality to find a place for normativity. So this is how Quine’s chicken might try to take flight with Peregrin’s falcon.9

Notes 1 I stick to Peregrin; of course, other models are provided by Brandom and Sellars. 2 Quine’s account of language is heavily filtered by his explicit philosophical interests. His wishes to account systematically for the minimal parts of language requisite for the expression of scientific doctrine, to make out the thesis that extensional first-order language is adequate for science, and to elucidate the relation of evidence to theory. Peregrin’s account is not quite so filtered, but I do not see this as a fundamental impediment to the comparison. 3 Neither Peregrin nor Quine have much to say about statements of desire or of intention, competence with which one might think equally basic to the possession of language. Presumably an account of these will have to connect one’s disposition to say or assent to such a statement—like “I want ice cream”—to the presence of the desire or subsequent behavior (looking for ice cream, etc.). See Canfield (1996) and my reply to him, Kemp (2014). 4 For example, in some cases one is disposed to accept “S or S*” but not either disjunct (for example put p for S and not-p for S*; or for S put “The democrat will win the US election” and for S* put “The republican will win the US election”). So the verdict tables don’t match up with the truth-tables. 5 For this point I thank Peter Hylton. 6 For more on Quine’s attitude to the normativity question, see his reply to Stoutland in Orenstein and Koťátko (2000). 7 The parallel with Davidson’s story “Action, Reasons and Causes” (Davidson 1963) is evident, but in this piece Quine does not acknowledge the article. 8 See Kemp (2014). 9 I thank John Divers, Matej Drobňák, Paul Horwich, Peter Hylton, and Andrew Lugg for conversation.

Quine Peregrinating: Norms, Dispositions, and Analyticity  95

References Baghramian, Maria. 2016. “Quine, Naturalized Meaning and Empathy.” Argumentia 2 (1): 25–42. Becker, Edward. 2012. The Themes of Quine’s Philosophy. Cambridge: Cambridge University Press. Canfield, John. 1996. “The Passage into Language: Wittgenstein Versus Quine.” In Wittgenstein and Quine, edited by Robert L. Arrington and Hans-Johann Glock, 118–143. London: Routledge. Chomsky, Noam. 1969. “Quine’s Empirical Assumptions.” In Words and Objections: Essays on the Work of W. V. Quine, edited by Donald Davidson and Jaakko Hintiikka, 53–68. Dordrecht: Reidel. Davidson, Donald. 1963. “Actions, Reasons and Causes.” The Journal of Philosophy 60 (23): 685–700. Davidson, Donald, and Jaakko Hintikka, eds. 1969. Words and Objections: Essays on the Work of W. V. Quine. Dordrecht: Reidel. Decock, Lieven. 2000. “Domestic Ontology and Ideology.” In Quine: Naturalized Epistemology, Perceptual Knowledge and Ontology, edited by Lieven Decock and Leon Horsten, 189–206. Amsterdam: Rodopi. Ebbs, Gary. 2016. “Introduction to ‘Preestablished Harmony’ and ‘Response to Gary Ebbs’.” In Quine and His Place in History, edited by Frederique JanssenLauret and Gary Kemp, 21–28. Basingstoke: Palgrave. Grice, Paul, and Peter Frederick Strawson. 1956. “In Defense of a Dogma.” The Philosophical Review 65 (2): 141–158. Hookway, Christopher. 1988. Quine: Language, Experience, and Reality. Palo Alto, CA: Stanford University Press. Kemp, Gary. 2014. “Pushing Wittgenstein and Quine Closer Together.” Journal of the History of Analytical Philosophy 2 (10): 1–18. Orenstein, Alex, and Petr Koťátko, eds. 2000. Knowledge, Language and Logic: Questions for Quine. Dordrecht: Kluwer Academic Publishers. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan. Quine, Willard Van Orman. 1951. “Two Dogmas of Empiricism.” The Philosophical Review 60 (1): 20–43. Quine, Willard Van Orman. 1960. Word and Object. Cambridge, MA: MIT Press. Quine, Willard Van Orman. 1974. The Roots of Reference. La Salle, IL: Open Court. Quine, Willard Van Orman. 1981. “On the Nature of Moral Values.” In Theories and Things, 55–66. Cambridge, MA: Harvard University Press. Original edition, 1978. Quine, Willard Van Orman. 1986. “Reply to Morton White.” In The Philosophy of W.V. Quine, edited by Lewis Edwin Hahn and Paul Arthur Schilpp, 663–665. Chicago: Open Court. Quine, Willard Van Orman. 1992. Pursuit of Truth. 2nd ed. Cambridge, MA: Harvard University Press. Quine, Willard Van Orman. 2008a. “Naturalism; Or, Living within One’s Means.” In Confessions of a Confirmed Extensionalist and Other Essays, edited by Dagfinn Føllesdal and Douglas B. Quine, 461–472. Cambridge, MA: Harvard University Press. Original edition, 1995.

96  Gary Kemp Quine, Willard Van Orman. 2008b. “The Way the World Is.” In Confessions of a Confirmed Extensionalist and Other Essays, edited by Dagfinn Føllesdal and Douglas B. Quine, 66–71. Cambridge, MA: Harvard University Press. Original edition, 1986. Quine, Willard Van Orman. 2016. “Preestablished Harmony.” In Quine and His Place in History, edited by Frederique Janssen-Lauret and Gary Kemp, 29–32. Basingstoke: Palgrave. Quine, Willard Van Orman, and Joseph S. Ullian. 1970. The Web of Belief. New York: Random House.

4 Let’s Admit Defeat Assertion, Denial, and Retraction Bernhard Weiss

1. Introduction Let me say a few words in opening about how this chapter meshes with the inferentialist project as articulated preeminently by Brandom (1994, 2008) and Peregrin (2014). Pure inferentialism aims to capture semantic content by attending to the inferential relations between sayings. I have my doubts about the prospects of pure inferentialism because I think that we fail to capture propositional content unless we conceive of the sayings as assertions. So I think we need an impure inferentialism, which views propositional content as emerging through inferentially articulated assertions, which, as speech acts, can be conceptualized prior to and independently of inference. The inferential potency of an assertion can, in turn, be seen to be a product of inferentially generated assertion conditions. So the focus of semantic theorizing shifts from inference toward assertion conditions. The interest in this chapter is whether these should be supplemented by denial conditions.

2.  Rumfitt on Denial Ian Rumfitt argues that an inferentialist account of the logical connectives ought to focus on the twin notions of assertion and denial. He motivates the position as cohering with aspects of our everyday practice of inferring. For, he claims, on occasion we are prone to frame arguments in terms of questions calling for a yes or no response. He borrows an example from Frege (see Rumfitt 2000, 799): If the accused was in Berlin at the time of the murder, could he have committed it? No. Was the accused in Berlin at the time of the murder? Yes. So: Could he have committed the murder? No. Though he doesn’t claim that such arguments are common, the fact that we are able to mount them demonstrates that a general account of the

98  Bernhard Weiss connectives ought to be sensitive both to conditions of assertion and those of denial. He goes on to explain his understanding of the yes/no responses. These are to be understood as responses to the question “Is it the case that A?” So, where the truth of A carries a presupposition, denial of the corresponding question includes the situation in which the presupposition fails. Though in this clarification he mentions A as a declarative sentence, one supposes that a similar account will apply to conditionals. Thus the first premise of this argument should be understood as: Is it that case that if the accused was in Berlin at the time of the murder then he could have committed it? No. So the answer no is a rejection of the truth of the conditional and thus amounts to the claim that the accused was in Berlin at the time of the murder, and he could not have committed the murder. At least, this is clear if the conditional is a material conditional, which is what Rumfitt goes on to treat in his bilateral system. However, so interpreted, this clearly distorts the argument as it is intended, for on this reading the second premise becomes redundant. It’s clear that the question involving the conditional is doing something other than asking for a verdict on the “Is it the case?” question. What it is asking for is an answer to the question “Could he have committed the murder?” under the assumption that he was in Berlin at the time of the murder; that is, it is asking an “Is it the case?” question about the consequent on the supposition that the antecedent is true. And the point of this is that it is aimed at establishing—even tacitly—that a conditional holds.1 In this case: “If he was in Berlin at the time of the murder, then he could not have committed the murder,” that is, a conditional with the antecedent of the original interrogative conditional and a consequent determined by whether the answer is yes or no. Two things follow from this. First, it is likely that the conditional is something other than the material conditional and so, strictly, is not relevant to Rumfitt’s project. But second, and more importantly here, the proper account of the inference is not one where denial plays an intimate role in the inference. Rather the role of the question and response is simply to establish the truth of a certain conditional statement. I don’t think this is just an incidental feature of the example. Other cases of reasoning by means of questions—those involving logically simple sentences and those involving non-conditional compounds—are easily seen as stylistic variants of inference via assertion or assertion of negations. So the proposal is under-motivated. I think we can see that it unravels too. Rumfitt symbolizes the force of assertion with the plus sign: “+”; and the force of denial with the minus sign: “–.” He then characterizes the logical constants in terms of introduction and elimination rules in

Let’s Admit Defeat: Assertion, Denial, and Retraction  99 the context of each mode of force. If he is genuinely a bilateralist, then he must hold that denial conditions cannot be derived from assertion conditions. But I think that, given his system, it plausibly follows that if one is not in a position to assert A then one is in a position to deny it. So denial conditions follow just from failure of assertion conditions. Here’s how. Accept these object to meta-language coordination principles: (i) From +A infer +(A is assertible) and vice versa. (ii) From −A infer +(A is deniable) and vice versa. In the system: (−¬E) (+¬E)

From −¬A infer +A. From +¬A infer −A.

Then: From −¬A infer +(A is assertible), by (−¬E) and the left to right part of (i). From −¬A, +(A is not assertible) infer ⊥, since it is absurd to assert any sentence and its negation. From +(A is not assertible) infer +¬A, by Reductio. From +(A is not assertible) infer −A, by (+ ¬ E).2 Denial conditions follow from failure of assertion conditions, or more strictly, from assertion that assertion conditions fail. I think Rumfitt’s likely reply is pretty obvious. Unlike the intuitionist, he denies that truth coincides with assertiblility.3 So he will distinguish truth from assertiblity by rejecting the inference from A to “It is assertible that A” (though he accepts the converse); and thus seemingly he will want to reject the object to meta-language coordination principles. But this is just what he cannot do. What he wants to say is that you can’t infer the assertibility of A from its truth. But his own system precludes him saying this, since the system requires him to argue not from a proposition but from a proposition either asserted or denied. I think this is retrograde. Logic interests itself with consequential relations between propositions, not relations between assertion and denial of them.4 However, given that all inference begins with assertions or denials, I cannot see how Rumfitt can say what he wants to say about truth coming apart from assertibility and how he can resist the coordination principles. And then bilateralism collapses into an implausible unilateralism. At § 4.062 of the Tractatus Wittgenstein asks, Can we not make ourselves understood with false proposition just as we have done up till now with true ones?—So long as it is known that they are meant to be false.

100  Bernhard Weiss And he responds, No! For a proposition is true if we use it to say that things stand in a certain way, and they do; and if by “p” we mean ¬p and things stand as we mean that they do, then, construed in the new way, “p” is true and not false. (Wittgenstein [1921] 1961, § 4.062) I think that this speaks to a crucial problem with the attempt to take denial as basic in an account of sense. How so? We might put the problem like this. Let’s consider utterances in the form “A?Yes” and “A?No.” For a given sentence A, each of these forms of utterance is supposed to be correlated with a distinct set of correctness conditions; and jointly these serve to capture the sense of A. This cannot, of course, be all there is to say because it needs to be understood that the conditions correlated with utterance of “A?Yes” are those which relate to the truth of A; whereas those correlated with utterance of “A?No” relate to the falsity of A, or, better, A’s failure to be true. The answer presumably lies in the fact that “A?Yes” is correlated with conditions warranting assertion; whereas “A?No” is correlated with conditions warranting denial. But we’ve been given no account of what assertion and denial are, and if we take these to be distinguished by the syntactic makeup of the utterance, we face two problems. The first is that this achieves precisely nothing: conditions in which “A?Yes” is appropriately used are those of assertion, that is, conditions in which an utterance of the form “A?Yes” is appropriately used. The second is that there is no natural syntactic form corresponding to assertion and denial on Rumfitt’s scheme: his forms are artificial constructs, and this contrasts markedly with the natural association of declarative form with assertion. The problem is acute because the kind of commitment involved in assertion and denial is so similar: in both cases the speaker commits herself to the obtaining of certain conditions. So we can’t distinguish the acts from one another, as we might distinguish asserting from questioning or ordering, by appeal to broad features of the kinds of commitment involved. In part this seems to be what Wittgenstein is getting at in the above quote; and in part it is a feature that recommends the plausibility of the bilateral approach: we are, after all, seeking conditions which jointly determine the sense of declarative sentences. The Wittgensteinian point can be applied like this. As long as we take assertion and denial as basic and as on “all fours” then there can’t a be a reason for saying that “A?No” relates to its conditions of use through denial whereas “A?Yes” relates to its conditions of use through assertion. There might be such a reason were we able to appeal to the sense of A; but since the conditions are precisely supposed to determine A’s sense, there cannot be any progress along that route.

Let’s Admit Defeat: Assertion, Denial, and Retraction  101 I think we need to give up taking assertion and denial as basic and as on “all fours.” As we’ll now see, this is what Price does, even if there’s little reason for thinking he shares my motivation.5

3.  Price on Denial It seems that the failure to focus logic on propositions is a product of the way Rumfitt develops his proposal, namely, by introducing objectlinguistic force markers which frame every sentence. Price’s earlier work on a similar proposal is quite different. There he uses the meta-­linguistic predicates “is assertible” and “is deniable” to say what it is about a sentence that we are specifying when we specify its sense in terms of its assertion and denial conditions. And this seems exactly right: having characterized the assertion and denial conditions of logically complex sentences in terms of those of their components, we then justify a choice of introduction and elimination rules period, not introduction and elimination rules in the context of each of assertion and denial. One might, however, worry that this observation won’t suffice to extricate Price from the presented argument. For the metalinguistic predicates are iterable; so could we not simply run the argument using these predicates? Our coordinating principles would then read: (i) From “A is assertible” infer “ ‘A is assertible’ is assertible” and vice versa. (ii) From “A is deniable” infer “ ‘A is deniable’ is assertible” and vice versa. The difference, however, is that now we can appeal to a distinction between truth and assertibility to resist each claim. But this makes apparent an inadequacy in the proposal, namely, that assertibility isn’t itself a decidable property of sentences. Were it so, we would be able to iterate the predicate “is assertible” salva veritate; so, if we reject iterability, we reject the decidability of assertibility. I don’t pretend that any of this is news, nor that it is particularly problematic. The very same feature emerges in the intuitionistic account of the logical constants in intuitionistic developments of mathematics. There the notion of provability is not taken to be decidable, and so the focus of the account is not a recursive characterization of provability conditions but a recursive characterization of the proof relation; and the relation is ­decidable—that is, it is claimed that it is always decidable whether a presented construction is or is not a proof of a given mathematical sentence.6 So, strictly, if he intends his account to be congenial to anyone persuaded by Dummettian constraints on a theory of meaning—as he does—Price should interest himself not with assertibility and deniability but with the relation of something’s being a warrant for assertion/denial

102  Bernhard Weiss of a given sentence. To repeat, I don’t claim that this is any more than a friendly emendation of the proposal. Price seems to acknowledge the Wittgensteinian point above, which calls for an account of the significance of assertion and denial, respectively. He writes as follows: [T]he origin of the notion of denial is in the practice of disagreement with the utterance of a previous speaker. We have already distinguished, in effect, two kinds of negative response to an assertion: that of declining to agree, which is appropriate when one regards a previous utterance as unjustified; and that of disagreeing. (Price 1983, 169) Speakers become competent speakers by internalizing assertion and denial conditions. This both involves grasp of conditions that warrant assertion and denial respectively and that those conditions are conditions of assertion and of denial. Theorists will thus need to be able to theorize these conditions in a way that renders them plausible as explanatorily basic in speakers’ competence. In contrast to Rumfitt, Price seems to suggest that denial is an emergent phenomenon, one that arises from the practice of reacting, in speech acts, to a previous utterance (assertion), thereby disagreeing with it. I don’t think that Price’s account can be made plausible, since disagreement is a very complex phenomenon, one that can’t adequately be reflectively understood prior to a good deal of semantic theorizing and that thus cannot be grasped by speakers without attributing to them a good deal of semantic sophistication. To be brief, one disagrees with an utterance by making another utterance that, as uttered from one’s own perspective, is incompatible with the previous utterance. But what renders one utterance incompatible with another will thus depend on how a piece of syntax employed in one context relates semantically to a piece of syntax employed in a different context. I don’t see how one could have a general understanding of these systematic linkages between the truth-values of sentences employed in different contexts without having considerable insight into the mechanics semantic theory aims to uncover. So, I don’t think that the notion of disagreement is available as a basis for such theorizing. Nor do I think that a sensitivity to the significance of denial—through sensitivity to disagreement—can be theorized as a basic semantic competence. What I think this shows is that we need to follow Price in thinking about the appraisal of a previous speech act but cannot do so in terms of an object linguistic phenomenon such as disagreement. (Since, as I argued above, this will presuppose the very semantic relations and competencies we are aiming to elucidate.) But we can instead think of the appraisal as,

Let’s Admit Defeat: Assertion, Denial, and Retraction  103 in a sense, meta-linguistic, as a way of changing the normative status of the act. My suggestion is that we bring into the picture the practice of retracting previous utterances.

4.  Defeat and Retraction Retraction is a more suitable notion to focus on because it is, arguably, a primitive normative move—that is, one inherent in any normative practice. Accept that any such practice will include moves of correction— moves that commend and condemn. And now ask what distinguishes such a practice from one that merely includes moves that encourage and discourage other moves in the practice. I take it that practices of the latter sort exist—let’s call them practices involving mere peer pressure— and that, though they might well be precursors to genuinely normative practices, they are not themselves normative. I think it is plausible to think that social animals herd and feed in ways subject to peer pressure, without these being genuinely normative behaviors. It seems that what distinguishes a correction from, say, a discouragement is that the latter is aimed purely at bringing about a change in future behavior, it is entirely forward-looking, whereas the former, though it likely has this forwardlooking dimension, also involves a normative assessment of the past performance. I don’t see how this retrospective aspect of the assessment is brought into the practice unless there is a way in which it can be acknowledged and accepted. And it can be acknowledged and accepted via retraction. The role of retraction, in turn, is to forestall (further) correction; it makes it so that, although one ϕed, one counts normatively as not having ϕed. My claim is that retraction is a feature of normative practices, as such. It is thus a notion available prior to and so can be explicable of normative practices that have distinctively semantic purport. A prime motivation for supplementing assertion with denial conditions is that there appear to be coassertible sentences that differ in meaning. Dummett thinks of this as a difference in what he calls content (or we might say, free-standing) sense and ingredient sense.7 As has been remarked by others,8 the need to see this distinction in terms of a feature of sense that only emerges when one considers the sentence as embedded (in such contexts as conditionals and negations) arises out of blinkering one’s view of the potential determinants of sense to assertion-conditions alone. Widen that view to include denial-conditions and the problem disappears: the sentences “A” and “A is assertible,” though coassertible, are not codeniable and thus can be distinguished as having different senses, if the latter are included as determinants of sense. But retraction conditions can do the same work, if slightly differently. An assertion made by uttering “A” in context C is to be retracted in different circumstances from an assertion of “A is assertible” also made in context C. So if retraction

104  Bernhard Weiss conditions are included as determinants of sense, then the two sentences can be distinguished as having different senses. Let me say a few words about defeat and retraction. Intuitively retraction conditions are wider than defeating conditions. For an assertion of A ought to be retracted when either one discovers that the assertion conditions of the original assertion, in fact, failed to hold or when, though they did hold, they are now seen no longer to warrant the assertion. An example of the first sort of case is when one asserts, “The cat is on the mat” on the basis, so one takes it, of seeing the cat on the mat. It later turns out that what one took to be the cat was, in fact, a puppy. So what one took to be a warrant for assertion was no such warrant. The second sort of case is illustrated by assertion of “It has rained” on the basis of the ground being wet. When one discovers that the cause of the wet ground may well have been something other than rain, the warranting function of the wet ground is undercut, despite there being no doubt about the ground being wet. I shall call the latter defeat of assertion conditions and the former failure of assertion conditions. The phenomenon of defeat seems to require a supplement to assertion conditions as determinants of sense; the phenomenon of failure does not: one simply needs a general stipulation that an assertion is undermined if its assertion conditions are no longer held to obtain. I want here to align my notion of retraction with that of defeat; so in that sense, it perhaps differs from the wider pretheoretic notion. Now, though I’ve framed my proposal as a friendly emendation of the proposal to combine assertion with denial conditions, a substantial difference appears to manifest itself in the choice and justification of logic. Both Rumfitt and Price believe they can justify application of classical logic, and each sees his task as characterizing both the assertion and denial conditions of logically complex sentences in terms of their components. On the current proposal, we don’t need to move beyond assertion conditions in our account of logic, because the logical constants do not introduce a source of defeat. The details are provided in the appendix. So the account of logic is thus. In effect, intuitionistic and is uniform in the move from mathematical to empirical discourse; it is simply that considerations of defeasibility fall away completely in the former case. If this is right then the movement from unilateralism to bilateralism doesn’t usher in a revised account of the meanings of the logical connectives, which is congenial to classical logic. Rather at least one form of bilateralism about sense is unilateralist about logic and adopts an orthodox intuitionism.

5.  Wright on Truth Let me change tack slightly now to consider an (epistemic) truth-­ conditional account of sense. Wright attempts to recruit a special kind

Let’s Admit Defeat: Assertion, Denial, and Retraction  105 of assertion condition in the service of a truth-conditional account of meaning. In essence, we could view his account as offering an epistemic ­conception of truth and then using truth, so-explained, in a ­(Davidsonian) truth-conditional account of meaning. An identification of truth with provability in the mathematical realm doesn’t immediately collapse because proof provides an indefeasible warrant. But we cannot identify truth with assertibility in the empirical realm because warrants for assertion are, in general, defeasible. Wright claims that the lesson we should learn is that we need to find a special type of indefeasible warrant in the empirical realm and to use this as a conception of truth. So he explains that a sentence is superassertible when it is enduringly assertible, that is, when we have warrant for its assertion and where, as it happens, that warrant is not defeated by the upshot of any investigation, no matter how extensive. Having characterized truth as superassertibility, Wright takes himself to be in a position to adopt the machinery of a Davidsonian truth-conditional account of meaning. I think both legs of this proposal are lame, but I want to focus on the second leg, which we might think of as characterizing meaning in terms of superassertion-conditions.9 Let’s begin with a statement of Wright’s conception of superassertionconditions: “P” is superassertible just in case the world will, in sufficiently favorable circumstances, permit the generation in an investigating subject, S, of a set of beliefs, {B1, . . . , Bn} with the following characteristics: (a) S has adequate grounds for regarding each of {B1, . . . , Bn} as an item of knowledge. (b) The status of each of {B1, . . . , Bn} as an item of S’s knowledge will survive arbitrarily close and extensive investigation. (c) The state of information constituted by {B1, . . . , Bn} warrants the assertion of “P.” (d) The case provided by {B1, . . . , Bn} for “P” is not in fact defeasible, that is, no {B1, . . . , Bn, . . . , Bz} containing {B1, . . . , Bn} and satisfying (a) and (b) for some S, yet failing to warrant “P,” can be achieved in this world, no matter how favorable the circumstances for the attempt. (Wright 1986, 414–415)10 The question to ask is whether such conditions are capable of playing a role in an account of meaning. The nub of the problem is that superassertion-conditions are conditions that a particular utterance of a sentence may either fulfil or fail to fulfil, and there’s no generalizing from a statement of an utterance’s superassertion-conditions to a meaningful kind of condition that would

106  Bernhard Weiss characterize the use of a type of sentence. Compare, for instance, with a standard Davidsonian schema: An utterance of “I am cold” by S at t is true if and only if S is cold at t. Though what we characterize is the truth-condition of particular utterances of the sentence, the clause specifies these conditions in a manner that is generalized relative to selected parameters of the utterance and thus can be taken to specify the meaning of the type of sentence, “I am cold.” In contrast, Wright’s account captures a set of conditions, namely, a set of beliefs possessing certain properties, which are designed to guide speakers’ use but then either we build indefeasibility into the properties of the beliefs—which makes the conditions unavailable to speakers—or we don’t, but then we fail to be able to generalize, since qualitatively identical conditions might be defeasible in one circumstance and not in another. In point of fact, Wright seems to opt for the first horn of this dilemma and to allow that superassertibility conditions are undecidable, but whose grasp is manifested in the combination of the speaker’s propensities both to assert and to retract. But if so, then clause (d) needs to be revised. Though what we aim to characterize is the superassertion-conditions of an utterance of a sentence, we need to formulate these appropriately so as to think of the grasp of these conditions as constituting speakers’ capacities in relation to a type of sentence. We’d leave such a capacity thoroughly indefinite if we simply talked about the evolution of the set of beliefs to include further (unspecified) beliefs that cease to provide warrant. Put differently, we’ve crafted the clauses in such a way that S might be sensitive to her possession of a set of beliefs {B1, . . . , Bn} but clause (d) then simply specifies a property of those beliefs—their indefeasibility relative to accumulation of further beliefs—without saying what kind of accumulation might lead to defeasibility. So this leaves it imprecise as to what capacity a speaker would have were she sensitive to defeat of her warrant; thus the character of speakers’ understanding would remain imprecise. After all, the defeating conditions of the assertion made by uttering “P” are presumably determined by the meaning of “P,” and until we specify these conditions, we’ve failed adequately to characterize that sentence’s meaning. Finally, we need to acknowledge a temporal element to the whole process. Defeating conditions may impact on speakers at times distinct from the time of assertion. So, as stated, clause (d) misses out the diachronic change in warranting status of beliefs. In ignoring this aspect of our use of language, it enables itself simply to talk about warrant for “P.” But once we bring in the diachronic element, we can’t simply talk about a set of beliefs which, at a different time, fail to warrant “P.” (Actually

Let’s Admit Defeat: Assertion, Denial, and Retraction  107 sentences themselves aren’t warranted; rather speech acts deploying a sentence may or may not be warranted.) The reason is obvious: “The cat is on the mat” may cease to be warrantedly assertible (when Tibby moves to the sofa) without that defeating the previous warranted assertion of “The cat is on the mat.” Most sentences do not have stable assertion conditions. So we need to acknowledge that the defeating conditions will be conditions that develop at some time t1 and that mandate retraction of the assertion of “P” at t. But having followed the development of superassertion-conditions thus far, we can quickly see that their use is redundant, for it seems that, if superassertion-conditions have a role to play in the account of meaning, then they rely on characterizing assertion-conditions and retraction-­conditions. However, in that case they have no role to play since meaning—speakers’ use of sentences—can be adequately captured in terms of direct specifications of assertion- and defeating-conditions, that is, the meaning of a sentence (type) is characterized in terms of those conditions warranting its assertion and those conditions that would defeat that assertion. Two final points (made rather too quickly): First, although I think that superassertion-conditions cannot themselves be used in an account of sense, nor do I think we can aim for a recursive theory of superassertion-­conditions, I see no bar to treating superassertion—in the sense of the property of being enduringly assertible—11as an explication of truth. If so, then we might think of the joint specification of assertion- and defeating-­ conditions as indirectly feeding into an account of the sentence’s truth-conditions. So arguments that see assertion as aimed at truth and thus correctness of assertion as (largely) determined by its truth and thus that link sense to truth-conditions can be accommodated nicely in this framework. But second, if this proposal is right then it provides a new reason for being suspicious of direct truth-conditional accounts of sense. The reason is that more than one pattern of assertion- and defeating-conditions is compatible with a given truth-condition. For one might think of the truth-condition as constituted from the obtaining of assertion-conditions combined with failure of the defeating-conditions. But then whether a condition counts as the obtaining of an assertion-condition or the failure of a defeatingcondition will be up for grabs. That is, there seem to be many ways in which the same truth-condition might be constructed out of assertionand defeating-conditions. So there is no reading off from mere truthconditions the use of a sentence in terms of when it is permissible to assert it and when it is obligatory to retract such an assertion. Since an account of sense should deliver an account of the norms of permission and obligation governing use of a sentence, a truth-conditional account of meaning is inadequate.

Appendix

1.  General Pattern Permission to assert: ϕ warrants assertion of P in C. Obligation to retract: δ defeats assertion of P in C on the basis of ϕ.

2. Logic Conjunction

• ϕ warrants assertion of P ∧ Q in C if and only if ϕ warrants as•

sertion of P in C and ϕ warrants assertion of Q in C. δ defeats assertion of P ∧ Q in C on the basis of ϕ if and only if δ defeats assertion of P in C on the basis of ϕ or δ defeats assertion of Q in C on the basis of ϕ.

Disjunction

• ϕ warrants assertion of P ∨ Q in C if and only if ϕ warrants as•

sertion of P in C or ϕ warrants the assertion of Q in C. δ defeats assertion of P ∨ Q in C on the basis of ϕ if and only if (if ϕ warrants assertion of P in C then δ defeats assertion of P in C on the basis of ϕ) and (if ϕ warrants assertion of Q in C then δ defeats assertion of Q in C on the basis of ϕ).

Conditional

• ϕ warrants assertion of P → Q in C if and only if (if θ is a war-

•

rant for assertion of P in C then either there is a δ such that δ defeats assertion of P in C on the basis of θ or ϕ can be applied to θ to yield a warrant for assertion, ϕ(θ), of Q in C). δ defeats assertion of P → Q in C on the basis of ϕ if and only if (there is a θ such that θ is an undefeated warrant for assertion of P in C and δ defeats assertion of Q in C on the basis of ϕ(θ)).

Negation

• ϕ warrants assertion of ¬P in C if and only if (if θ warrants as-

sertion of P in C then there is a δ such that δ defeats assertion of P in C on the basis of θ).

Let’s Admit Defeat: Assertion, Denial, and Retraction  109 This can be seen as arising out of application of the clause for the conditional to P → ⊥—the second disjunct is vacuous in the clause for warrant and the defeating condition cannot be satisfied, since there are no such θs: there are no defeaters and so no need for defeating conditions unless we contemplate defeaters of defeaters.

3.  Introduction and Elimination Rules Plan: to show warrant for premises transmits warrant to conclusion; and, if the conclusion is defeated, then it must fail to be warranted in those circumstances by the premises. (∧I) A  B (∧E) A ∧ B

A ∧ B,  A ∧ B A B

From the clause for warrants right to left, warrants for the premises, A and B, provide a warrant for A ∧ B; if the conclusion, A ∧ B, is defeated then by the clause for defeat left to right warrant for at least one of the premises is defeated. So the premises no longer jointly provide warrant for the conclusion. So (∧I) is justified. From the clause for warrants left to right, warrant for A ∧ B is warrant for A and for B. If warrant for A(B) is defeated then by the clause for defeat right to left warrant for the premise, A ∧ B, is defeated. So the warrant it provides for the conclusion is defeated. So (∧E) is justified. (∨I)

A, B (∨E) A ∨ B A ∨ B

A A ∨ B C C

B C

From the clause for warrants right to left a warrant for either of the premises will provide warrant for the conclusion. From the clause for defeat left to right if the conclusion, A ∨ B, is defeated then any premise providing that warrant for the conclusion is defeated. So neither any longer warrants the conclusion. So (∨I) is justified. We can assume the subproofs of C from A and B respectively preserve warrants and entail that when C is defeated so too are A and B. From the clause for warrants left to right if there is a warrant for A ∨ B then there is a warrant for one of A and B. By our assumption this entails that there is a warrant for C. So (∨E) is warrant preserving. If C is defeated then so too are the warrants for A and for B, thus whichever provides warrant for A ∨ B (possibly both) is defeated and, by the clause for defeat right to left, A ∨ B is defeated. So (∨E) is justified. (→I)

A (→E) A  A → B B B A→B

110  Bernhard Weiss If there is an undefeated warrant to assert A then assuming that the proof of B from A is warrant preserving there is a warrant for asserting B. So appending this proof to the warrant for assertion of A provides a means of converting a warrant for A into a warrant for B. Thus by the clause for warrants right to left, A → B is warranted. If A → B is defeated, then by the clause for defeat left to right there is an undefeated warrant for assertion of A, yet the warrant provided by appending the proof of B from A to this warrant is defeated. But this contradicts the assumption that when the conclusion of this sub-proof is defeated so too is the premise. It counterexemplifies the subproof. So within the logical system the clause for defeat is satisfied but is vacuous. In insisting that the warrant for B from A emerges via proof, rather than some defeasible reasoning we fail to exploit the full meaning of the conditional. However (→I) is faithful to the meaning of the conditional and is thus justified. If there is a warrant to assert A and warrant to assert A → B then by the latter there is a procedure that can be applied to the former to yield a warrant for B. So (→E) is warrant preserving. If warrant for B is defeated and there is no undefeated warrant for A then (→E) cannot, for that reason, provide warrant for B. So we’re done. Suppose, therefore, that there is an undefeated warrant for A. Then by the clause for defeat right to left, warrant for A → B is defeated. Thus in no circumstance does (→E) provide warrant for the defeated B. So (→E) is justified. (¬I) A (¬E) ⊥ ¬A

A   ¬A ⊥

If we simply treat absurdity as that which can never be warranted then the subproof of absurdity from A shows that if A had an undefeated warrant then so too would absurdity. Thus A has no undefeated warrant and by the clause for warrant right to left, ¬A is warranted. So (¬I) is justified. If we had undefeated warrants for the premises in (¬E) we would both have undefeated warrant for A and by the clause for warrant left to right have no undefeated warrant for A. So (¬E) never transmits warrant for assertion of ⊥. Thus (¬E) is justified. Note: ¬A ⊥ A This rule is not justified because being able to rule out that every warrant for A is defeated, does not provide warrant for A. So it is not warrantpreserving. Our logic is thus intuitionistic.

Let’s Admit Defeat: Assertion, Denial, and Retraction  111 It is not surprising that the logic is no stronger than intuitionistic because it needs to be warrant preserving and so is constrained in similar fashion to intuitionistic logic. What is slightly surprising is that it is as strong as intuitionistic logic, because this seems to show that the added constraint—that is, requiring that when the conclusion is defeated it is not simultaneously warranted by the proof rule—is vacuous. But this is not, on reflection, all that surprising because the point is that logically complex sentences, though defeasible, are relatively indefeasible. That is, the logical machinery introduces no additional source of defeasibility; the defeating condition of the complex is entirely determined by those of its components. The one case where this might not be true is where the conditional is established by defeasible reasoning from the antecedent to the consequent. But this was an aspect of its meaning that was not unpacked here.

Notes   1 This seems right when you fill in the context of the inference. Imagine that this is a dialogue between two detectives. It then seems appropriate to think of them as working out that the conditional mentioned in the text holds. While, if you imagine the case to be an advocate questioning a witness, then the advocate is at least pretending to be ignorant of the conditional so as not to be seen to be leading the witness.   2 Or we could also say that from its being deniable that A is assertible it follows that A is deniable. But as Price (1983, 167) points out, we should want to maintain a distinction here.   3 He makes this point in response to Dummett (see Dummett 2002).   4 See Kurbis (2015, 83) and in more detail, Kurbis (forthcoming, chap. 6) for arguments to similar effect. In correspondence, Kurbis has suggested a proof that the first coordination principle commits Rumfitt to the view that every proposition is either assertible or its negation is.   5 There are also very plausible doubts about the speech act of denial. See Dickie (2010) for a good discussion of what she calls the “messiness” of denial.   6 See the debate between Tennant and Weir: Tennant (1981, 1984, 1985), Weir (1983, 1985).   7 See Brandom (1976). Price (1983, 163) seems to be discussing the same problem but there he raises it not as a difference between the meaning of different sentences but in terms of distinguishing a sentence’s content from its assertibility.   8 See Price (1983) and Brandom (1976).   9 For complaints about the first leg see Weiss (2007). 10 I shall continue to speak, with Wright, of beliefs warranting assertion; though, as will emerge, I am happier to think more neutrally about circumstances in which an assertion is warranted. 11 As Bob Brandom noted at the conference Why Rules Matter, the concept of belief seems ill-fitted to play this role in an account of truth, because it is either extensionally inaccurate or presupposes true beliefs and thus presupposes truth. I think it is ill-fitted too in explicating meaning.

112  Bernhard Weiss

References Brandom, Robert. 1976. “Truth and Assertibility.” The Journal of Philosophy 78 (6): 137–149. Brandom, Robert. 1994. Making It Explicit: Reasoning, Representing, and Discursive Commitment. Cambridge, MA: Harvard University Press. Brandom, Robert. 2008. Between Saying and Doing: Towards an Analytic Pragmatism. Oxford: Oxford University Press. Dickie, Imogen. 2010. “Negation, Anti-Realism, and the Denial Defence.” Philosophical Studies 150 (2): 161–185. Dummett, Michael. 2002. “ ‘Yes’, ‘No’ and ‘Can’t Say’.” Mind, New Series 111 (442): 289–295. Kurbis, Nils. 2015. “What Is Wrong with Classical Negation?” Grazer Philosophische Studien 92 (1): 51–85. Kurbis, Nils. Forthcoming. Negativity in Proof Theoretic Semantic. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan. Price, Huw. 1983. “Sense, Assertion, Dummett, and Denial.” Mind 92 (366): 161–173. Rumfitt, Ian. 2000. “ ‘Yes’ and ‘No’.” Mind 109 (436): 781–823. Rumfitt, Ian. 2002. “Unilateralism Disarmed: A Reply to Dummett and Gibbard.” Mind 111 (442): 305–312. Smiley, Timothy. 1996. “Rejection.” Analysis 56 (1): 1–9. Tennant, Neil. 1981. “Is This a Proof I See Before Me?” Analysis 41 (3): 115–119. Tennant, Neil. 1984. “Were Those Disproofs I Saw Before Me?” Analysis 44 (3): 97–105. Tennant, Neil. 1985. “Weir and Those ‘Disproofs’ I Saw Before Me.” Analysis 45 (4): 208–212. Weir, Alan. 1983. “Truth Conditions and Truth Values.” Analysis 43 (4): 176–180. Weir, Alan. 1985. “Rejoinder to Tennant.” Analysis 45 (1): 68–72. Weiss, Bernhard. 2007. “Anti-Realist Truth and Anti-Realist Meaning.” American Philosophical Quarterly 44 (3): 213–228. Wittgenstein, Ludwig. 1961. Tractatus Logico-Philosophicus. Translated by David F. Pears and Brian F. McGuinness. London: Routledge and Kegan Paul. Original edition, 1921. Wright, Crispin. 1986. Realism, Meaning and Truth. Oxford: Blackwell.

Part II

Logic and Semantics

5 Inferentialism, Structure, and Conservativeness Ole Hjortland and Shawn Standefer

1. Introduction Logical inferentialism is, roughly, the view that the meaning of a logical connective is determined by the inference rules governing that connective. For example, in systems of natural deduction the introduction and elimination rules for a connective fix its meaning. The paradigmatic example is conjunction, governed by the following rules. A B A∧B

(∧ I )

A∧B A

(∧ E)

A∧B B

(∧ E)

The conceptual content of conjunction is given, not by a truth-condition, but by the inferential role specified by the inference rules governing it. The introduction rule tells us under what conditions we are entitled to assert a conjunction, namely when we are entitled to assert its conjuncts, and the elimination rules tell us what we commit ourselves to when we assert a conjunction, namely, to both conjuncts. However, it is well known that some combinations of rules for a ­connective can result in disaster. The most famous example is Prior’s (1961) tonk, :1 A A  B

( I )

A  B B

( E)

The inference rules for tonk lead to a trivial consequence relation where any conclusion is derivable from any (non-empty) set of premises. So if logical inferentialism is correct, there has to be some constraint on which inference rules can confer meaning on a connective. In an early response to Prior, Belnap (1962) suggested a constraint that has proved influential: the inferentialist should require that the addition of logical vocabulary to a consequence relation should be a conservative extension. An extension L′ of a theory L is conservative when the language of L′ contains that of L and X ⇒Lʹ A only if X ⇒L A, when X and A are in the language of L. The condition will rule out tonk as a legitimate expression, assuming that the original theory has a nontrivial standard consequence relation.

116  Ole Hjortland and Shawn Standefer Robert Brandom, following the work of Michael Dummett, endorses conservativeness as a requirement. Among the reasons Brandom gives for requiring that extensions be conservative is the expressive role of logic: But the expressive account of what distinguishes logical vocabulary shows us a deep reason for this demand [of conservative extension]; it is needed not only to avoid horrible consequences but also because otherwise logical vocabulary cannot perform its expressive function. Unless the introduction and elimination rules are inferentially conservative, the introduction of the new vocabulary licenses new material inferences, inferences good in virtue of the concepts involved rather than their form, and so alters the contents associated with the old vocabulary. So if logical vocabulary is to play its distinctive expressive role of making explicit the original material inferences, and so conceptual contents expressed by the old vocabulary, it must be a criterion of adequacy for introducing logical vocabulary that no new inferences involving only the old vocabulary be made appropriate thereby. (Brandom 2000, 68–69) The distinctive feature of logical vocabulary, on Brandom’s view, is that it makes explicit aspects of a community’s inferential practice. According to Brandom, the conceptual content of nonlogical expressions is determined by the material inferences they license. Logical expressions serve to make explicit this implicit content. So if the addition of new logical vocabulary results in new inferences in the old vocabulary becoming valid, then the inferential connections of the old vocabulary have been altered. Even if conservativeness can be motivated as a constraint on logical vocabulary, it has limitations. One issue is that conservativeness is a global property of a logical system. Consequently, whether an extension is conservative can depend on what other connectives are already in the system. As a result, logical inferentialists have attempted to impose a local property on inference rules that prohibit problematic connectives like tonk. Following Dummett, such a local constraint is often called harmony. Harmony, whatever the formal details, is a local property that holds, when it does, in virtue of the rules governing a given connective.2 As recent work has shown, however, there are distinct concepts of harmony, even in the work of Dummett, and not all of these imply that certain additions will be conservative.3 A further point, on which we will focus, is that harmony itself has relevant parameters that can be brought out. These background or structural features of a logical system can represent aspects of an inferential practice, so they are of interest to a Dummettian-Brandomian logical inferentialist. In section 2, we will present some background on harmony,

Inferentialism, Structure, and Conservativeness  117 normalization, and cut elimination. Once we have this background in place, our discussion will have two streams: dropping structural rules of logical systems and enriching logical systems with additional structural elements. In section 3, we will consider substructural logics and the issues they bring for conservative extensions and harmony. The substructural setting introduces a bifurcation of logical connectives, leading to a wellknown problem, namely the failure of a distributive law relating one form of conjunction and disjunction. We will present this issue in section 4 and consider plausible inferentialist responses, leading to the suggestion of enriching the sequent structure. Enrichment of sequent structure will be further considered in section 5 as a general response to problems with harmony and modal operators. Let us turn to the background.

2. Conservativeness We will begin by discussing the conditional. One reason for this focus is that the conditional is Brandom’s paradigm of logical vocabulary. Conditional claims—and claims formed by the use of logical vocabulary in general, of which the conditional is paradigmatic for the ­inferentialist—express a kind of semantic self-consciousness because they make explicit the inferential relations, consequences, and contents of ordinary nonlogical claims and concepts. (Brandom 2000, 21) Consider the standard natural deduction introduction and elimination rule for the conditional:4 [ A]u . B A→B

(u)(→I )

A→B A B

(→E)

The leftmost rule is a hypothetical rule: If we can infer B from the assumption A, we can conclude that A → B and discharge the assumption A. The rule is also known as conditional proof. In Brandomian terms, it encapsulates the idea that the conditional A → B makes explicit an inferential connection between A and B. Correspondingly, the rightmost rule (→E) (Modus Ponens) allows us to infer B from A and A → B. There is an intuitive harmony between the inference rules. The elimination rule allows us to infer B from A, thus unpacking the inferential connection. The question is how we can make the intuitive idea of harmony between inference rules precise. What is it in general that is required for the introduction rules and elimination rules of a logical expression to be

118  Ole Hjortland and Shawn Standefer in harmony? One preliminary way of spelling it out is by invoking what Prawitz (1965) calls reduction conversions. Consider the following derivation (where Π0, Π1 are subderivations): [ A]1 1 [ A] ∏0 ∏0 B ∏1 B (1) A→B A A→B B B

∏1 A

The above derivation has an application of (→I) immediately followed by an application of (→E). Prawitz notes that such a derivation can be converted into a derivation that avoids a detour: [ A]1 1 [ A] ∏0 ∏0 B (1) B (1) A→B A→B B

B

∏1 ∏1 A ∏1 ∏0 A A  B

Since the original derivation already had a derivation of A, and a derivation of B from A, the detour through the applications of (→I) and (→E) is unnecessary. This is the reduction conversion for the conditional. The existence of the conversion is a decisive component in the proof of normalization. Suppose the natural deduction system only has the inference rules (→I) and (→E). Then we can show that every derivation can be transformed into a corresponding derivation in normal form (i.e. a derivation without any formula occurrence A → B that is both the conclusion of an (→I) application and the major premise in a (→E) ­application). That in turn leads to the sub-formula property, the fact that if A is derivable from Γ, there is a derivation where every node is a subformula of A or some B ∈ Γ. Normalization and the subformula property can also be proved if we add the standard introduction and elimination rules for ∧ and ∨. The subformula property then furthermore entails the separation property: if A is derivable from Γ, there is a derivation that only applies inference rules for connectives occurring in A or some B ∈ Γ. So, extending a language consisting of some members of {∨, ∧, →} to the language L    ∨,∧,→, and extending the proof system with the corresponding rules, always yields a conservative extension. Conversion reductions are, in other words, a way of ensuring that the addition of standard connectives will be conservative extensions. It is natural to think that the idea can be generalized to a template for harmony as a local constraint on inference rules. In turn, the formal harmony

Inferentialism, Structure, and Conservativeness  119 constraint should entail conservativeness. Harmony can then serve as a recipe for how to construct inference rules for new logical vocabulary in a way that does not alter the conceptual content of the original vocabulary. Although the idea works well for a limited set of connectives, it runs into trouble when extended to more interesting languages. One reason is that there are connectives that have reduction conversions but whose introduction leads to nonconservativeness. Consider for example the following connective, bullet:5 [•]u . ⊥ • • (u)(•I ) • ⊥

(• E)

With the rules (•I) and (•E) we can give the following reduction conversion: [•]1 [[A [••]]1]11 Π0 ∏ ΠΠ00 0 ⊥ (1) ⊥ (1) Π Π11 B⊥Π1(1) (1) • • •• •• A→B  ⊥ ⊥⊥ B

Π1 •∏ 1 Π0 A   ⊥

ΠΠ11 •• ΠΠ00 ⊥⊥

Nonetheless, (•I) and (•E) leads to inconsistency in a straightforward manner (i.e., it allows a derivation of ⊥). [•]1 [•]1 ⊥ (1) •

⊥

[•]2 [•]2 ⊥ (2) •

To apply the reduction conversion, one branch, say the leftmost, needs to be pasted onto each of the discharged assumptions of the other branch. It is not too hard to see that repeated applications of the reduction conversion will not terminate. So, the existence of a reduction conversion does not guarantee conservativeness. Further, given the usual rules governing ⊥, this then leads to triviality: the addition of bullet, governed by the rules (•I) and (•E) results in every formula being provable. It is tempting to blame the problem on the relative strangeness of a connective like •. Not unlike tonk, it is designed to lead to inconsistency. Perhaps there are other conditions the inferentialist could apply in order to block connectives of this sort. But unfortunately there are other, less

120  Ole Hjortland and Shawn Standefer artificial connectives that also resist an analysis in terms of reduction conversions. Negation is a case in point. The good news is that intuitionistic negation can also be conservatively added to the previous language with ∨, ∧, and →. Take the following standard introduction and elimination rule for the intuitionistic negation: [ A]u [ A]u   ⊥ ⊥ ¬A ¬A

(u)(¬I ) (u)(¬I )

¬A A ¬A A ⊥ ⊥

(¬E) (¬E)

The rules give rise to a conversion reduction just like the one we saw for the conditional above: [ A]1 1 [ A] Π0 ∏0 ⊥ (1) Π1 B (1) ¬A A A→B ⊥ B

Π1 ∏1 A 

A Π0 ⊥

The resulting proof system has the separation property. Unfortunately, this is where the good news ends. Although the separation result holds for intuitionistic negation, it cannot be straightforwardly extended to classical negation. The standard inference rules for classical negation do not have a reduction conversion.6 Indeed, when classical negation is added to the negation free fragment we get a nonconservative extension. In the presence of classical negation, we can derive theorems in the conditional language that aren’t derivable without the negation rules. The most famous example is Peirce’s Law, ((A → B) → A) → A. In fact, this is crucial for the formalization of classical logic, as without classical negation, the inference rules (→I) and (→E) only give us the weaker intuitionistic conditional. Put differently, the natural deduction rules for classical logic appear to violate the spirit of logical inferentialism. The introduction and elimination rules for the conditional aren’t alone sufficient to prove the class of theorems in the →-fragment of the language. That is, they aren’t sufficient to determine the conceptual content of the classical conditional. For that classical negation is required. Dummett, Prawitz, and other intuitionists have argued that the nonconservativeness of classical negation shows that the classical inference rules fail to fix a conceptual content at all. Classical negation, they conclude,

Inferentialism, Structure, and Conservativeness  121 is semantically dysfunctional. That leads to a revisionary inferentialism where the harmony constraint points in favor of intuitionistic negation. However, classical logicians have pointed out a number of problems with the revisionary argument. First, the argument relies on the assumption that the conceptual content of a logical expression is determined by the inference rules for that connective alone, what Paoli calls operational meaning. In contrast, an inferentialist who is willing to accept a form of semantic holism could accept that connectives only acquire their content in the context of a full system of logical connectives, Paoli’s global meaning.7 Second, even if classical negation fails to satisfy the harmony constraint, it doesn’t follow that intuitionistic negation is the only alternative. And third, it turns out that the nonconservativeness of classical negation depends on formal properties of the proof system in question. This third objection points to a more severe limitation with nonconservativeness as a constraint on logical expressions. In a sequent calculus system, the inference rules for connectives is given in a multiple conclusion form. An operational rule in sequent calculus has a finite set of premise sequents Γ1 ⇒ ∆1, . . . , Γn ⇒ ∆n and a conclusion sequent Γ ⇒ ∆, where Γ, ∆ are finite multisets of formulas. The operational rules for the classical conditional and negation can then be presented as follows: Γ ⇒ A, ∆ Γ ′,B ⇒ ∆ ′ Γ , Γ ′A → B ⇒ ∆ , ∆ ′ Γ ⇒ A, ∆ (L¬) Γ, ¬A ⇒ ∆

(L →)

Γ, A ⇒ B, ∆ Γ ⇒ A → B, ∆ Γ, A ⇒ ∆ (R¬) Γ ⇒ ¬A, ∆

(R→)

It is easy to see that in the presence of the standard structural rules (identity, weakening, contraction), (L→) and (R→) are sufficient to prove Peirce’s Law.8 In fact, every classical consequence in the →-fragment is derivable using the rules. In the sequent calculus system, there is a counterpart to the reduction conversions and normalization of natural deduction. One shows that the conclusion of a proof that uses the cut rule, Γ ⇒ ∆, A A, Σ ⇒ Θ Γ, Σ ⇒ ∆ , Θ

(cut )

can be obtained in a way that does not use the cut rule. Let us say that a rule R S1 , . . . , Sn S

( )

is admissible in a sequent system if and only if: the premiss sequents S1, . . . , Sn are derivable, then the conclusion is derivable. The standard

122  Ole Hjortland and Shawn Standefer proofs that cut is admissible rely on the following type of reduction conversions, which are the counterparts of reduction conversions:9 Π′ Π Γ, A ⇒ ∆ Γ ′ ⇒ A, ∆ ′ Π′ Π Γ ′ ⇒ A, ∆ ′ Γ, A ⇒ ∆ Γ ⇒ ¬A, ∆ Γ ′, ¬A ⇒ ∆ ′  Γ, Γ ′ ⇒ ∆ , ∆ ′ Γ, Γ ′ ⇒ ∆ , ∆ ′ Showing that cut is admissible in a sequent system without it is a standard technique for obtaining conservative extension results for sequent systems. Cut admissibility, or elimination, theorems are the sequent analogues of normalization theorems in the natural deduction setting. Cut is distinguished in many sequent systems as the only rule in which a connective disappears. If a sequent that is derivable with cut is derivable without cut, then it is derivable using rules in which formulas and connectives do not disappear, moving from premiss to conclusion. The cut admissibility theorem entails the separation property as a corollary. So, in a multiple conclusion sequent system, the addition of classical negation with its standard operational rules is a conservative extension of the →-fragment, unlike in the natural deduction case. It should be clear that conservativeness depends on the choice of proof system. There are logical expressions whose addition in a sequent calculus yields a conservative extension but whose addition in natural deduction, with corresponding rules, yields a nonconservative extension. What is more, by allowing multiple conclusions in natural deduction, it is also possible to formalize classical negation and conditional with the separation property.10 This raises an important question about which formal framework for inference rules best captures a given inferential practice. It is true that introducing sets (or multisets) of conclusions is a further complication, but it is not one that lacks a philosophical interpretation. In fact, Restall (2005) has provided an account of multiple conclusion sequents that is potentially a good fit with logical inferentialism. On this interpretation, derivable sequents provide information about norms of assertion and denial: a derivable sequent A1 , ... , An ⇒ B1 , ... , Bm says that one cannot coherently assert all the antecedent formulas while denying all the succedent formulas. We then get corresponding interpretations of the operational rules presented above. The rule (R¬), for example, encodes a norm saying that if one cannot assert all the members of Γ and A while simultaneously denying every member of ∆, then one cannot assert all the members of Γ while simultaneously denying ¬A and every member of ∆. If we simplify by dropping the auxiliary formulas, it says that if you cannot assert A, then you cannot deny ¬A.

Inferentialism, Structure, and Conservativeness  123 While some philosophers have objected to the use of multiple conclusion sequent systems (Dummett 1991, 40–41; Tennant 1997, 319–320; and Steinberger 2011b), we think that the inferentialist still has reason to adopt them.11 Additionally, although much of the focus of Brandom (1994) is on assertion, including both assertion and denial in the description of the inferential role of expressions can accommodate much of Brandom’s view. The stakes for the inferentialist are greater than just the conservativeness of classical negation. Many connectives are only conservative given certain assumptions about the structural properties of the proof system. Once the inferentialist can vary the structural properties of the proof system to capture different inferential practices, well-behaved connectives might prove problematic, and ill-behaved connectives might become legitimate.

3.  Practice and Parameters For a second example of structural properties, we can stick with the conditional. Recall the standard inference rules for the intuitionistic conditional, (→I) and (→E). There are structural properties built into the (→I) rule we would like to highlight. The rule is hypothetical—that is, it allows us to discharge assumptions. Hypothetical rules are governed by discharge policies, in particular that in an application of (→I), one discharges 0 or more occurrences of an assumption A. That leads to two special cases of (→I), vacuous and multiple discharge respectively.

B A→B

[ A]u ... [ A]u  . . . . B (u) A→B

In the leftmost derivation, (→I) is applied without discharging any copies of the antecedent A, while the rightmost derivation discharges multiple copies of A. These special discharge policies are not logically idle. Without the former we cannot derive A → (B → A) in the →-fragment, and without the latter we cannot derive (A → (A → B)) → (A → B). It should be clear, therefore, that (→I) and (→E) only axiomatize the intuitionistic conditional if the discharge policies are permitted.12 The reduction conversions are also affected by the presence of the special discharge policies.13 Suppose that the proof Π0 in the unreduced proof example above has two occurrences of A that are discharged by (→I). Then, in the reduced proof, there will be two copies of Π1 in the resulting proof, one for each assumption of A that is being replaced. We said that the discharge policies were implicit in the natural deduction system. They are implicit in the sense that they are not notationally

124  Ole Hjortland and Shawn Standefer marked. For our purposes, it will be easier to work with sequent calculus systems, in particular the multiple conclusion rules (L→) and (R→) ­displayed above. In addition to these rules and the axioms, A ⇒ A, standard sequent calculus systems have structural rules that correspond roughly to the discharge policies in natural deduction:14 Γ⇒∆ Γ, A ⇒ ∆ Γ, A, A ⇒ ∆ Γ, A ⇒ ∆

(LK )

(LW )

Γ⇒∆ (RK ) Γ ⇒ A, ∆ Γ ⇒ A, A, ∆ (RW ) Γ ⇒ A, ∆

The topmost rules—antecedent and succedent weakening—correspond to vacuous discharge of assumptions, while the bottommost rules—­ antecedent and succedent contraction—correspond to multiple discharge of assumptions.15 These structural rules reflect features of inferential practices, and there are practices in which these rules may not be appropriate.16 An inferential practice in which the rules (RK) and (LK) do not reflect the structure of the practice is suggested in the motivating comments of relevant logicians, such as Anderson and Belnap (1975).17 A community might require that, in a good argument, all the premises are used in a substantive way in obtaining the conclusion(s). There can be no idle premises. If we are trying to formalize the inferential practice of this community, we should not use the weakening rules, which permit inferences rejected by the community.18 Similarly, there are examples of inferential practices that, arguably, reject the rule of contraction. One example is the geometers of the early twentieth century.19 The geometers were concerned to mark how many times they appealed to certain assumptions, evaluating arguments differently depending on how many times the assumptions were used. It is a small step of idealization to a community that requires that whenever an argument uses an assumption multiple times, the assumption has to be made multiple times, which is to say that they reject the structural rules (LW) and (RW). Another example is supplied by Barker (2010). Barker argues that the phenomenon of free choice permission is best understood by appeal to the distinction between connectives that emerges when contraction is dropped. If he is right, then contemporary English speakers, at least sometimes, engage in inferential practices best formalized without (LW) and (RW). These examples show how the structural rules reflect aspects of an inferential practice. Different practices may require the adoption or rejection of different sets of structural rules.20 An inferential practice need not manifest the structural rules in an overt form. They may remain implicit in the practice, in the sense that no one explicitly engages in an inference whose form matches that of the rule. Still, an explicit regimentation of the practice may contain the rules. Since the presence or absence of the

Inferentialism, Structure, and Conservativeness  125 structural rules results in different logics, the different conditionals make explicit different sorts of inferential practices. One familiar consequence of dropping weakening and contraction is that classically equivalent operational rules become distinct. To stick with the conditional, consider the two following implicational connectives  and . Γ ⇒ A, ∆ Γ, B ⇒ ∆ Γ, A ⇒ ∆ Γ ⇒ B, ∆ (L ) (Ri ) Γ, A  B ⇒ ∆ Γ ⇒ A  B, ∆ Γ ⇒ A  B, ∆ Γ ⇒ A, ∆ Γ ′, B ⇒ ∆ ′ Γ, A ⇒ B, ∆ (L) (R) Γ , Γ ′, A  B ⇒ ∆ , ∆ ′ Γ ⇒ A  B, ∆

(Rii )

The connectives  and  are equivalent in the presence of weakening and contraction. Indeed, they are just two variants of the classical conditional. However, once we drop either of the structural rules, they come apart. A similar bifurcation happens for conjunction and disjunction. In general, the substructural logics allow for distinct context-sharing (additive) and context-independent (multiplicative) connectives. The substructural systems also produce nonconservative extensions with connectives that are conservative in the fully structural systems. Certain connectives reintroduce structural rules, thereby allowing the derivation of new sequents in the original language. An example is conditionals defined by mixing the context-sharing and context-independent operational rules above. Suppose we have a system with  and , but without contraction. We then extend the system with a new conditional, : Γ ⇒ A, ∆ Γ, B ⇒ ∆ Γ, A  B ⇒ ∆

(L )

Γ, A ⇒ B, ∆ Γ ⇒ A  B, ∆

(R )

The new conditional  has the left-rule of  but the right-rule of . The result is that, provided we have (LK) and (RK), we can derive a restricted version of (LW) where there is at least one succedent formula (B below): A, A ⇒ B A⇒ AB ⇒ A  (A  B)

A⇒ A B⇒B A⇒ A A ⇒ A, B A, B ⇒ B A, A  B ⇒ B A ⇒ A, B A, A  (A  B) ⇒ B A⇒B

The presence of the restricted contraction rule will affect which sequents are derivable for the other conditionals. For example, suppose we have a sequent system with  and the weakening rules, but not the contraction rules. In the extension with , we can derive the sequent ⇒ (A  (A  B))  (A  B), which was underivable in the original system.

126  Ole Hjortland and Shawn Standefer Similar nonconservative extensions with weakening can be produced by combining (R) and (L). The result is a conditional,, that allows the reintroduction of a restricted version of weakening.21 Next, let us look again at Read’s connective bullet, •. The rules for bullet normalize, as Read indicates. The addition of bullet to, say, intuitionistic logic would result in inconsistency and so nonconservative extension. However, the derivation of inconsistency crucially uses contraction, or multiple discharge. It could be added to a non-contractive system in a conservative way. This is an instance of a broader point, made by Restall (2010), that the context of deducibility, which encompasses the structural rules, has far-reaching consequences for logical issues, such as conservative extension and definability. In substructural logics, the context of deducibility is modified from that of classical and intuitionistic logic. One example that is sometimes held up as a counterexample to the claim that harmony implies conservative extension is the truth predicate.22 While not a connective, there is some reason to think that the truth predicate is logical, accorded distinguished status along with identity, and the rules A T A

(TI )

T A A

(TE)

are invertible and seem harmonious. Adding these rules to classical arithmetic, without any restrictions, results in inconsistency, and so nonconservative extension.23 In a noncontractive logic such as RW, one can add these rules without restriction to arithmetic nontrivially.24 As far as we know, the question of whether the extension is conservative remains open.25 Next, we will return to the example with which we started, tonk. A, Γ ⇒ ∆ A  B, Γ ⇒ ∆

(L )

Γ ⇒ ∆, A Γ ⇒ ∆, B  A

(R )

In the presence of all the structural rules, neither bullet nor tonk can be added conservatively. As we have seen above, however, the inferentialist can salvage bullet through rejection of the structural rule of contraction. The question, then, is whether something similar is possible for tonk. In fact, there is another structural rule to discuss, namely cut. Ripley (2015) has argued that tonk is acceptable to the inferentialist provided that cut is rejected. Indeed, the addition of tonk to a system whose only rules are contraction and weakening, together with the axioms, will be conservative, although cut will not be admissible. As with the other structural rules, cut corresponds to features of inferential practices. Cut is sometimes described as encoding the use of

Inferentialism, Structure, and Conservativeness  127 lemmas in proofs. Something is proved once and cited as needed, without reproducing the proof of the lemma in the course of the reasoning. The inferential practice of classical mathematics, on one construal, would be well formalized using the cut rule. Another example is supplied by Restall (2005). Taking the rule contrapositively, Restall says, “It tells us that if A is undeniable in the context of [coherently asserting Γ and denying ∆] then it is coherent to assert A, provided that [asserting Γ and denying ∆] is already coherent.”26 On Restall’s view, cut codifies a certain sort of coordination of assertions and denials.27 If, by the rules of logic, A is undeniable in a given context, then it is coherently assertible in that context, and if A cannot be coherently asserted in that context, then it is undeniable. One can imagine inferential practices in which assertion and denial are not coordinated in the way that Restall describes. Ripley motivates the failure of cut by appeal to the same bilateralist interpretation of sequents as Restall. On Ripley’s view, there is more leeway between assertion, denial, and claims that are out of bounds than on Restall’s view.28 A claim being undeniable as a matter of logic in a given, coherent context does not thereby mean the claim is coherently assertible in that context, and similarly, an unassertible claim is not forced to be deniable. There can be gaps between the assertible and the undeniable and between the undeniable and the unassertible. On this view, assertion and denial each split into strict and tolerant forms, which interact in interesting ways. It appears, then, that the presence or absence of cut, as admissible or primitive, also codifies different norms at play in inferential practices.29 We will close this section echoing a point made by Ripley (2013b). If all one wants in one’s choice of sequent system is a guarantee of conservative extension, then cut should not be taken as a primitive rule. Provided that formulas from the premises of a rule do not disappear in the conclusion, then extension of the system with rules for new connectives will be conservative, since any newly derivable sequent will have an occurrence of the new connective in it. If formulas disappear in the conclusion of a rule, however, one will not have this assurance, as demonstrated by Wansing’s super-tonk.30 Admissible rules may not be preserved under extension, whereas a primitive rule of a system will be preserved. When cut is not a primitive rule, one may be in the position of having cut admissible in the system prior to extension but no longer admissible post-extension. Whether the loss of cut is a major problem will depend on one’s interpretation of sequents and views about logical consequence, such as whether cut is a primitive rule of the system, and whether cut admissibility is a part of the harmony constraint for sequent systems. We bring up these questions to emphasize that cut is another parameter of inferential practice that should be specified when considering what one wants in harmony. We now turn to issues of proof-theoretic structure.

128  Ole Hjortland and Shawn Standefer

4.  Distribution and Structure Classical negation provides motivation to adopt multiple conclusion sequents, as it is difficult to add to a single-conclusion system with a conditional in a harmonious way.31 Multiple conclusions can be seen as an enrichment of the single conclusion sequent structure. There are other forms of structure with which one can enrich sequents. In this section, we will motivate one sort of enrichment in a substructural setting. In the previous section, we presented context-sharing (additive) and context independent (multiplicative) forms of rules for implication. The distinction extends to other connectives, and we present the rules for conjunction here, the disjunction rules being straightforward duals. Γ, A, B ⇒ ∆ Γ, A  B ⇒ ∆ Γ, A ⇒ ∆ Γ, A ∧ B ⇒ ∆

(L)

(L ∧)

Γ ⇒ A, ∆ Σ ⇒ B, Θ (R) Γ, Σ ⇒ A  B, ∆, Θ Γ, B ⇒ ∆ Γ ⇒ A, ∆ Γ ⇒ B, ∆ (L ∧) Γ ⇒ A ∧ B, ∆ Γ, A ∧ B ⇒ ∆

(R ∧)

In intuitionistic and classical logic, where we have all the structural rules, the additive and multiplicative are equivalent, in the sense that both A  B ⇒ A ∧ B and A ∧ B ⇒ A  B are derivable.32 When either of weakening or contraction is dropped, the two connectives come apart, in the sense that one of the two sequents will not be derivable. Consider a community that uses a conditional, but does not permit vacuous introduction and so rejects weakening. The community encounters conjunction and disjunction, understood according to their additive rules, and adopts them. A sequent system that represents their inferential situation uses the conditional, additive forms of conjunction and disjunction, with the rules above, and contraction, but not weakening. The resulting system is known to have cut admissibility, but the law of distribution is not derivable.33 A ∧ (B ∨ C) ⇒ (A ∧ B) ∨ (A ∧ C) This system yields the positive fragment of the relevant logic R minus distribution.34 There is an intuition that if additive disjunction and conjunction are to mean the same thing in the substructural setting as in the classical, then they should obey distribution. After all, the additive rules yield distribution in the presence of contraction and weakening. This intuition has motivated some to add a primitive rule of distribution.35 A ∧ (B ∨ C) (A ∧ B) ∨ (A ∧ C)

(Dist )

Inferentialism, Structure, and Conservativeness  129 It is not clear that this is open to the inferentialist. It can spoil normalization, and it does not fit neatly into the dichotomy of introduction and elimination rules, while clearly not being a structural rule. We will briefly look at three ways of responding to this issue. The first is to maintain that the additive rules alone determine the meaning of conjunction and disjunction, and that is insufficient to secure distribution. So, additive conjunction and disjunction do not obey distribution. The fact that they distribute in classical logic is a side effect of the structural rules, rather than the meaning determined by the operational rules.36 While this view is open to the inferentialist, we will set it aside to look at some options that maintain the intuition that additive conjunction distributes over additive disjunction. An alternative response begins by noting that the problem with deriving distribution is that one is restricted as to what additional assumptions are available for use in the (L∨) step, or (∨E) in natural deduction. The response then is to adopt a natural strengthening of the additive disjunction elimination rule.37 According to this rule, one is permitted to freely use side premises in the subproofs for (∨E) that the major premiss disjunction depends upon.38 This system enjoys normalization and permits the derivation of distribution. The strengthened form, however, results in a logic properly stronger than (positive) R but still weaker than classical logic. The difference between the two rules is whether they permit the use of formulas in (∨E) that depend on the same assumptions as the disjunction. In classical logic, there are no restrictions on what side premises are used in (∨E), but in the substructural setting the added flexibility matters. The third response takes the view that distribution should be derivable for the target vocabulary and it secures this by enriching the sequent system with additional structural connectives governed by their own structural rules.39 In the basic sequent systems we have been discussing, the comma is the only structural connective. Once the distinction between additive and multiplicative connectives becomes important, as in substructural logics, it is natural to see them as reflecting different structural features of inferential practices. Let us then add to the sequent system a structural connective, “;”, in addition to the comma. The two structural connectives can be governed by different sets of structural rules. In particular, the comma, but not the semicolon, obeys (LK) and (RK), and both obey (LW) and (RW). The connective rules are changed to reflect the differing roles of these structural elements, with the conditional and multiplicative conjunction going with semicolon and conjunction going with comma, as in the following examples.40 A⇒ A B⇒B A; B ⇒ A  B (L) AB ⇒ AB

(R)

A⇒ A (LK ) A, B ⇒ A A ∧ B, A ∧ B ⇒ A A∧B⇒ A

(L ∧) (LW )

130  Ole Hjortland and Shawn Standefer A sequent system for positive R using two structural connectives enjoys cut admissibility and permits the derivation of distribution.41 The question this option raises for the inferentialist is whether the new structural element can be understood in terms of inferential practices. The two structural elements are different ways of combining premises (or conclusions).42 The semicolon is an intensional way, appropriate when one is extracting information from a conditional via modus ponens. The comma, on the other hand, is extensional, appropriate for simply pooling information from some premises.43 The inferentialist can understand these structural connectives in terms of practices, and their addition can secure some of the desired formal properties, such as cut admissibility, for certain logics. The third response uses an idea that we will discuss further, namely enriching the basic proof-theoretic structure. For the remaining discussion, we will turn to systems for classical logic, focusing on extensions with modal vocabulary.

5.  Modality and Structure We have, so far, considered systems in which some of the fundamental structural rules have been dropped. These properties are important for normalization, cut admissibility, conservative extension, and harmony. In this section, we will look at enriching sequent systems with additional structure. Modal connectives provide initial motivation for additional structure. There are a wide variety of modal logics, but it is notoriously difficult to provide satisfactory proof systems for them. One recalcitrant example is the modal logic S5. One of the first sequent systems for it was provided by Ohnishi and Matsumoto (1957). The modal rules are the following. A, Γ ⇒ ∆ A, Γ ⇒ ∆

(L)

Γ ⇒ ∆, A Γ ⇒ ∆, A

(R)

In the (R) rule, Γ is A1, . . . , An, where Γ is A1, . . . , An. Ohnishi and Matsumoto point out that certain sequents are only derivable using cut. Their (R) rule has a strong restriction on the form of side formulas, which requires one to introduce a box at one step in the derivation and then use cut on a side formula to insert a side formula that does not have the appropriate form. Further, as Read points out, the natural deduction introduction and elimination rules for the box A A

(I )

A A

( E)

Inferentialism, Structure, and Conservativeness  131 and diamond

A ◊A

( ◊I )

[A]u Π ◊A B B

(u) (◊E)

are intuitively not in harmony.44 While the (E) rule permits the transition from A to A, (I), in S4 and S5, does not let one move from A to A unless certain side conditions are satisfied. In Prawitz’s formulation, the side condition is that the open assumptions on which the premise of (I) depends must be appropriately modal. The minor premiss of the rule (◊E) is subject to a similar restriction as (I), namely, that all assumptions of the subproof, apart from the assumed A, are appropriately modal. Although the S4 rules (I) and (E) normalize and their addition to classical logic is conservative, they are not in harmony.45 Both S4 and S5 have the same rules for the modal operators, differing only in the side conditions. As Read (2008) puts the point, we should expect that since the logics are different, the rules should differ. The (E) rule in harmony with the (I) would be one weakened to reflect the side condition on (I). On the possibility side, the (◊E) rule in harmony with the (◊I) rule would be one without a side condition, but this rule trivializes the modality, as well as being insensitive to the differences between S4 and S5, which share a (◊I) rule. A natural diagnosis of the issue that arises both with natural deduction and sequent presentations of modal logic is that there are not enough parts to the basic structure, whether formulas or sequents, variations of which permit the distinctions needed by the different modal operators. A suggestion from Read is to enrich the system with additional structure, namely labels for worlds, A : i, and special formulas relating worlds, Rij.46 The rules for ◊ then become the following.

A : j Rij ◊A : i

( ◊I )

[Rij, A : j ] Π ◊A : i B: k B: k

(u) (◊E)

In the (◊E) rule, i ≠ j ≠ k, and no assumptions of minor premiss subproof are labelled with j besides the displayed ones. The rules for  can be adjusted similarly. These rules normalize. The distinction between S4 and S5 is brought out by the different rules added to the system for the Rij formulas. One can add labels to sequents, along with special formulas indicating relations between the labels.47 As in the natural deduction system, different modal logics are accounted for using structural rules on the relational

132  Ole Hjortland and Shawn Standefer formulas. As an alternative to labels, one can enrich sequents in the direction of hypersequents, which we will now discuss.48 A hypersequent, X1 ⇒ Y1 | ... | Xn ⇒ Yn , is a multiset of sequents. Restall (2007) provides a hypersequent system for S5 that enjoys cut elimination.49 For the move to hypersequents to be appealing to the Brandomian, there needs to be a feature of the inferential practice that, in some sense, corresponds to the proposed structure. Such a feature has been supplied by Restall. As we saw above, multiple conclusion systems can be understood in terms of norms of assertion and denial. The additional hypersequent structure can be understood in terms of consideration of alternatives.50 Derivable hypersequents present norms governing assertion and denial in alternative situations. The necessity rules are the following. H  ∑ ⇒ Θ A, Γ ⇒ ∆ 

H A, ∑ ⇒ Θ Γ ⇒ ∆ 

(L)

H Γ ⇒ ∆ ⇒ A H[Γ ⇒ ∆, A]

(R)

In these rules, H is a hypersequent that contains the components displayed in the brackets. Cut is admissible in this system, unlike that of Ohnishi and Matsumoto (1957). The system has the subformula property, so the addition of the S5 modalities to classical logic is a conservative extension. S5 is one of the standard philosophical modal logics. The inferentialist has, we think, strong reason to provide a treatment of S5 that is acceptable by her lights. This has proved difficult to do in the basic, unaugmented sequent setting.51 It shows up as the distinguished modal logic of Brandom’s incompatibility semantics.52 Brandom says, “S5 accordingly has some claim to being the modal logic of consequence relations, whether material or logical.”53 The added structure of hypersequents permits the codification of norms dealing with assertion and denial in various alternatives. Consideration of alternatives is natural in inferential practices. The necessity operator makes explicit claims whose assertion or denial affects coherence across alternatives. Some claims can be denied in certain alternatives, in combination with other assertions and denials. Some assertions and denials have a modal force that extends beyond a particular hypothetical situation. There can be different sorts of consideration of alternatives, which naturally motivates a further enrichment of the hypersequent structure. As investigated by Restall (2012), one can extend the hypersequents with another type of hypersequent separator, representing a second dimension to the consideration of alternatives. These two-dimensional systems

Inferentialism, Structure, and Conservativeness  133 provide a representation of a practice of considering indicative and subjunctive alternatives.54 Further operators can be introduced to make explicit features of the inferential practice represented by this richer system, such as a priori knowledge and actuality. These systems enjoy cut admissibility and so the addition of these operators is conservative. A community’s inferential practices may broadly concern not just inference and assertion, but also consideration of hypothetical alternatives, as well as being sensitive to considerations not covered here, such as time and explicit concern with deontic statuses. The basic sequent structure may be sufficient for representing features of a relatively simple inferential practice, but a richer practice may need a richer sequent structure to adequately make the features of the practice explicit. We now turn to our general conclusions.

6. Conclusion The rules for tonk present a problem for the logical inferentialist: there needs to be a principled way to separate the acceptable combinations of rules from the unacceptable. Dummett’s proposal, harmony between the introduction and elimination rules, offers a way to demarcate these collections, provided there is some further analysis of harmony. Brandom tentatively endorses Dummett’s view, with respect to logical connectives, although it appears that harmony is merely a means to the end of securing conservative extensions.55 What we have argued is that the concept of harmony has several parameters that need to be settled to apply the concept. The very notion of a problem case depends upon this. As we saw above, classical negation appears to be a problem when single conclusion sequents and natural deduction are under consideration, but it is fine in multiple conclusion frameworks. Further, the connective bullet can be added conservatively in a contraction-free framework. Indeed, if cut is up for grabs, then even tonk can be embraced by the inferentialist. These observations point to a more general dynamic. If structural rules are dropped, then standard connectives that can be added conservatively when all structural rules are present may yield nonconservative extensions, depending on the formulation of the rules. Even the conditional, which sits at the heart of Brandomian inferentialism, makes explicit different material inferences depending on the structural rules. The move to a substructural setting brings with it distinctions between previously equivalent connectives. We noted the well-known fact that a form of the distribution law for conjunction and disjunction is underivable with the additive rules. One response to this is to enrich the proof system with additional sequent structure. This move will be appealing to the inferentialist if one can understand the addition in terms of features of an inferential practice. The addition can be so understood: the

134  Ole Hjortland and Shawn Standefer additional structural connective captures an additional way to combine premises. Substructural logics can be sensitive to which premises were used in a derivation in a way that classical logic is not. The richer inferential setting of substructural logic motivates the addition of a richer sequent structure. Mirroring the structure of inferential practice in sequent structure is not restricted to substructural logics. Modal logics naturally motivate an enrichment of natural deduction and sequent structure. Hypersequent structure can be understood in inferential terms, namely the consideration of alternatives. A richer inferential practice, one involving considerations of different alternatives, temporal relations, or explicit deontic or epistemic evaluation, could call for the use of additional or different sequent structure. The richer sequent structure suggests a path to making explicit the relevant features of the target inferential practice.56

Notes   1 The notation is our own.   2 Harmony is typically viewed as ensuring that the elimination rules do not outstrip the introduction rules. The converse relation, that the introduction rules do not outrun the elimination rules, is sometimes called stability. Stability and similar concepts have been the focus of much recent work on logical inferentialism. See Pfenning and Davies (2001), Jacinto and Read (2016), and Dicher (2016) for further discussion.   3 See Read (2000) and Steinberger (2011a).   4 See Gentzen (1935) and Prawitz (1965).   5 See Read (2000; 2010).   6 There are many ways of formalizing classical negation. One could add any of the following rules to the rules for intuitionistic negation: [ ¬A]u . A ∨ ¬A

(LEM)

⊥ A

(u)(CRAA)

¬¬A A

(DNE)

  7 See Paoli (2003) for discussion of the distinction between global and operational meaning.   8 The structural rules will be introduced in the next section.   9 The proof of Gentzen (1935) uses these types of conversions with a strengthening of cut. See Negri et al. (2001) or Bimbó (2015) for proofs using reduction conversions on cut. 10 Cf. Read (2000), and Francez (2014c). 11 For a treatment of assertion and denial in a single-conclusion natural deduction setting, see Smiley (1996), Rumfitt (2000), or Francez (2014b). See Humberstone (2000) for further discussion. 12 Although in the presence of other connectives, that might change. Consider for instance the following derivation.

Inferentialism, Structure, and Conservativeness  135

[ A]

2

[B]1

A∧B A (1) B→ A

A → (B → A)

(2)

13 See Francez (2014a) for details on the reduction conversions involved when vacuous discharge is disallowed. 14 See Negri et al. (2001, chap. 8) for more on the correspondence. 15 Here we follow Restall (2000), and other logicians in the tradition of combinatory logic, in using the labels “K” and “W” for weakening and contraction, respectively. 16 See also Paoli (2002) for an overview of different motivations for dropping structural rules. 17 Lance and Kremer (1996) motivate a related logic of relevant commitment entailment, on Brandomian inferentialist grounds. 18 As an aside, we note that dropping structural rules, particularly weakening, has reper- cussions for incompatibility-based inferentialism. Suppose that one introduces a connective, ⊥, into the language to mark when some premises are incompatible. A natural axiom for it to obey is the following: ⊥ ⇒ ∅. In the presence of (RK), ⊥ entails everything. One can define a negation using this and the conditional: ¬A is A → ⊥. The negation of A is then guaranteed to be incompatible with A, in the sense that the following will be derivable. A⇒ A

⊥⇒⊥

A, ¬A ⇒ ⊥

(L →)

Cutting on the ⊥ axiom followed by an application of (RK) yields that incompatible formulas, here contradictory formulas, entail everything, giving sets of incompatible premises a distinctive inferential role. This fact is exploited, under a different presentation by Brandom (2008) and Peregrin (2015). It is an underlying assumption of their approaches that incompatibility persists through the addition of premises, which is a form of weakening. In some substructural settings, such as the relevant logic R, one can adopt the view that the conditional makes explicit moves from premises to conclusions while denying that sets of incompatible premises have a distinctive, explosive role. A modified definition of incompatibility entailment is needed for such substructural settings. In addition to weakening, cut and contraction are built into the structural assumptions of incompatibility semantics. See, for example, Brandom (2008, 137). If either of cut or contraction is unavailable, other complications may be needed, but we leave this open here. 19 The details are supplied by Pambuccian (2004). 20 There are further structural rules one can distinguish, such as permutation, by taking structures on each side of the sequent separator to be sequences or more general structures, but we will focus on contraction, weakening, and cut. 21 See Hirokawa (1996), Humberstone (2007), and Rogerson (2007) for more on rules that permit the derivation of structural rules in substructural contexts.

136  Ole Hjortland and Shawn Standefer 22 See Read (2000). For a dissenting view, see Steinberger (2011a). 23 The truth predicate needs a theory of syntax to supply sentence names, and we are here taking that theory to be arithmetic. 24 See Restall (1992) or Petersen (2000). 25 Depending on the rules governing the syntactic theory and negation, the addition of the truth predicate and the syntactic theory to pure logic may be nonconservative in a noncontractive logic. 26 Restall (2005, 196–197). 27 We are treating assertion and denial as aspects of an inferential practice, following Brandom (1994, 206), who says, “For asserting and inferring are two sides of one coin; neither activity is intelligible except in relation to the other.” 28 See Cobreros et al. (2011) and Ripley (2013a, 143–144) for discussion. 29 One might, following French (2016), wonder about the identity sequents, A ⇒ A. After all, the starting points of derivations are, in a broad sense, structural features. If one thinks it is sometimes coherent to assert and deny the same sentence, then, given the interpretation of sequents in terms of assertion and denial, identity sequents will not generally be acceptable. We note that French considers a different interpretation of sequents, due to Malinowski, than we consider here. 30 The rules for super-tonk, provided by Wansing (2006), are the following. Γ⇒∆

Ψ ⇒ super−tonk

Ψ ⇒ super−tonk

Γ⇒∆

For further discussion, see Ripley (2015). 31 Note that we are not claiming that it is impossible. 32 See, for example, French and Ripley (2015). 33 One can see the appeal to weakening in the following derivation. A⇒A

(LK )

B⇒B

A, B ⇒ A A, B ⇒ B A, B ⇒ (A ∧ B)

(LK )

A⇒A

(LK )

C⇒C

A, C ⇒ C A, C ⇒ A A, C ⇒ (A ∧ C)

(LK )

A, B ⇒ (A ∧ B) ∨ (A ∧ C) A, C ⇒ (A ∧ B) ∨ (A ∧ C) A,(B ∨ C) ⇒ (A ∧ B) ∨ (A ∧ C) A ∧ (B ∨ C), A ∧ (B ∨ C) ⇒ (A ∧ B) ∨ (A ∧ C) A ∧ (B ∨ C) ⇒ (A ∧ B) ∨ (A ∧ C) 34 See Thistlewaite et al. (1988) for details. 35 This is the route adopted by Anderson and Belnap (1975). 36 See Paoli (2007; 2014) and Hjortland (2014) for discussion. 37 See Prawitz (1965), Charlwood (1981), and Giambrone and Urquhart (1987). We omit the rule since it requires either a lengthy side condition or the use of subscripts on formulas, conventions for which would take more explanation than is justified by the point at hand. 38 We focus on the natural deduction system, since it is easier to give a feel for the rule strengthening. In the sequent system, the strengthening is implemented through the use of a restricted weakening rule that lessens the impact of the context-sharing features of the additive disjunction rules. 39 See Belnap (1982), Read (1988), or Slaney (1990) for examples. 40 We omit general statements of the rules, as that would require some further notational details that would take us a bit afield. 41 See Belnap et al. (1980) or Dunn and Restall (2002) for more.

Inferentialism, Structure, and Conservativeness  137 42 This view is elaborated by Slaney (1990). 43 These structural elements can nest, so it would be more correct to say that they are ways of combining structures, or bunches, of formulas. 44 Read (2008). 45 See Prawitz (1965) and Medeiros (2006). 46 See Read (2008). 47 Negri (2005). 48 For discussion of the relative philosophical merits of the use of labelled formulas, see Poggiolesi (2009), Humberstone (2011, 111–112), and Read (2015). 49 Poggiolesi (2008) also provides a hypersequent formulation of S5. See Bednarska and Indrzejczak (2015) for a survey of the area. 50 Restall (2012). 51 See Poggiolesi (2011), especially chap. 1, for discussion. 52 See Brandom (2008, 141–175). 53 Brandom (2008, 139), the original is bolded for emphasis, which we omit here. 54 See Lance and White (2007) and Restall (2012) for more on the consideration of alternatives. 55 We say “tentatively,” since Brandom registers some criticisms of Dummett’s view. See, e.g., Brandom (2000, 72–76). 56 We would like to thank Greg Restall, Rohan French, and Kai Tanter for discussion and comments on earlier versions of the material. Shawn Standefer’s research was supported by the Australian Research Council, Discovery Grant DP150103801.

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6 From Logical Expressivism to ­Expressivist Logics Sketch of a Program and Some Implementations Robert Brandom 1. Introduction Jarda Peregrin’s fabulous book Inferentialism (Peregrin 2014) brings into conversation two contemporary movements of thought that have hitherto had little to say to one another: inferentialism in semantics and inferentialism in logic. It embeds that conversation philosophically in a broader normative framework that articulates what is most distinctive of us as persons. It is the book of a lifetime, and only he could have written it. Jarda and I deeply see the world the same way—both the real world of talking, reasoning persons, and the philosophical world that both participates in and tries to understand that other world. So what I have to say today should be understood as an attempt to push forward a common enterprise. I start with an observation: the well-expressed, well-argued, and welltaken semantic and logical inferentialism of the two halves of Jarda’s book are revolutionary in their philosophy, but relatively conservative in their logic. I think the inferentialist motivations we share should also motivate us to do logic a bit differently than we traditionally have. What I want to report here is how surprisingly little one needs to give up in one’s logic—as opposed to one’s conception of it—in order to gain a great deal of expressive power. Traditionally, two principal issues in the philosophy of logic are the demarcation question (what distinguishes specifically logical vocabulary?) and the correctness question (what is the right logic?). One of the binding agents tying together semantic and logical inferentialism is a distinctive philosophy of logic: logical expressivism. This is the view that the expressive role that distinguishes logical vocabulary is to make explicit the inferential relations that articulate the semantic contents of the concepts expressed by the use of ordinary, nonlogical vocabulary. If one offers this logically expressivist, semantically inferentialist answer to the demarcation question, the correctness question lapses. It is replaced by a concrete task. For each bit of vocabulary to count as logical in the expressivist sense, one must say what feature of reasoning,

142  Robert Brandom to begin with, with nonlogical concepts, it expresses. Instead of asking what the right conditional is, we ask what dimension of normative assessment of implications various conditionals make explicit. For instance, the poor, benighted, and unloved, classical two-valued conditional makes explicit the sense of “good inference” in which it is a good thing if an inference does not have true premises and a false conclusion. (At least we can acknowledge that implications that do not have at least this property are bad.) Intuitionistic conditionals in the broadest sense let us assert that there is a procedure for turning an argument for the premises of an inference into an argument for the conclusion. C. I. Lewis’ hook of strict implication codifies the sense in which it is a good feature of an inference if it is impossible for its premises to be true and its conclusion not to be true. And so on. There can in principle be as many conditionals as there are dimensions along which we can endorse implications. In spite of its irenic neutrality concerning the correctness question, one might hope that a new approach to the philosophy of logic such as logical expressivism would not only explain features of our old logics but ideally also lead to new developments in logic itself. I think this is in fact the case, and I want here to offer a sketch of how.

2.  Prelogical Structure I take it that the task of logic is to provide mathematical tools for articulating the structure of reasoning. Although for good and sufficient historical reasons, the original test-bench for such tools was the codification of specifically mathematical reasoning, the expressive target ought to be reasoning generally, including, for instance and to begin with, its more institutionalized species, such as reasoning in the empirical sciences, in law-courts, and in medical diagnosis. We can approach the target-notion of the structure of reasoning in two stages. The first stage distinguishes what I’ll call the “relational structure” that governs our reasoning practices. Lewis Carroll’s fable “Achilles and the Tortoise” vividly teaches us to distinguish, in John Stuart Mill’s terms, “premises from which to reason” (including those codifying implication relations) from “rules in accordance with which to reason,” demonstrating that we can forego the latter wholly in favor of the former. Gil Harman sharpens the point in his argument that there is no such thing as rules of deductive reasoning. If there were, presumably a paradigmatic one would be: If you believe p and you believe if p then q, then you should believe q. But that would be a terrible rule. You might have much better reasons against q than you have for either of the premises. In that case, you should give up one of them. He concludes that we should distinguish relations of implication, from activities of inferring. The fact that p, if p then q, and not-q are incompatible, because p and

From Logical Expressivism to Expressivist Logics  143 if p then q stand in the implication relation to q, normatively constrains our reasoning activity, but does not by itself determine what it is correct or incorrect to do. The normative center of reasoning is the practice of assessing reasons for and against conclusions. Reasons for conclusions are normatively governed by relations of consequence or implication. Reasons against conclusions are normatively governed by relations of incompatibility. These relations of implication and incompatibility, which constrain normative assessment of giving reasons for and against claims, amount to the first significant level of structure of the practice of giving reasons for and against claims. These are, in the first instance, what Sellars called “material” relations of implication and incompatibility. That is, they do not depend on the presence of logical vocabulary or concepts, but only on the contents of non- or prelogical concepts. According to semantic inferentialism, these are the relations that articulate the conceptual contents expressed by the prelogical vocabulary that plays an essential role in formulating the premises and conclusions of inferences. Once we have distinguished these relations from the practice or activity of reasoning that they normatively govern, we can ask after the algebraic structure of such relations. In the 1930s, Tarski and Gentzen, in the founding documents of the model-theoretic and proof-theoretic traditions in the semantics of logic, though differing in many ways in their approaches (as Jarda Peregrin discusses in the second half of his book), completely agree about the algebraic structure of logical relations of consequence and incompatibility. Logical consequence satisfies Reflexivity, Monotonicity, and Idempotence (Gentzen’s “Cut,” sometimes called “Cumulative Transitivity”). In Tarski’s terms: X ⊆ Cn(X), X ⊆ Y ⇒ Cn(X) ⊆ Cn(Y), and Cn(Cn(X)) = Cn(X). Logical incompatibility satisfies what Peregrin calls “explosion”: the implication of everything by logically inconsistent sets. (Peregrin builds this principle in so deeply that he takes the functional expressive role of negation to be serving as an “explosion detector.”) Perhaps these are, indeed, the right principles to require of specifically logical relations of consequence and incompatibility. But logical expressivists must ask a prior question: what is the structure of material relations of consequence and incompatibility? This is a question the tradition has not thought about at all. But the answer one gives to it substantially shapes the logical enterprise when it is construed as expressivism does. We can think of statements of implication and incompatibility as expressing what is included in a premise-set and what is excluded by it. In a semantic inferentialist spirit, we can say that the elements of a premise-set are its explicit content, and its consequences are its implicit content—in the literal sense of what is implied by it. It is reasonable to

144  Robert Brandom suppose that what is explicitly contained in a premise-set is also part of its implicit content. It is accordingly plausible to require that material consequence relations, no less than logical ones, be reflexive. Monotonicity, by contrast, is not a plausible constraint on material consequence relations. It requires that if an implication (or incompatibility) holds, then it holds no matter what additional auxiliary hypotheses are added to the premise-set. But outside of mathematics, almost all our actual reasoning is defeasible. This is true in everyday reasoning by auto mechanics and on computer help lines, in courts of law, and in medical diagnosis. (Indeed, the defeasibility of medical diagnoses forms the basis of the plots of every episode of “House” you have ever seen—besides all those you haven’t.) It is true of subjunctive reasoning generally. If were to strike this dry, well-made match, it would light. But not if it is in a very strong magnetic field. Unless, additionally, it were in a Faraday cage, in which case it would light. But not if the room were evacuated of oxygen. And so on. The idea of “laws of nature” reflects an approach to subjunctive reasoning deformed by a historically conditioned, Procrustean ideology whose shortcomings show up in the need for idealizations (criticized by Cartwright 1983 in How the Laws of Physics Lie) and for “physics avoidance” (diagnosed by Wilson 2006 in Wandering Significance on the basis of the need to invoke supposedly “higher-level” physical theories in applying more “fundamental” ones). Defeasibility of inference, hence nonmonotonicity of implication relations, is a structural feature not just of probative or permissive reasoning, but also of dispositive, committive reasoning. Ceteris paribus clauses do not magically turn nonmonotonic implications into monotonic ones. (The term for a Latin phrase whose recitation can do that is “magic spell.”) The expressive function characteristic of ceteris paribus clauses is rather explicitly to mark and acknowledge the defeasibility, hence nonmonotonicity of an implication codified in a conditional. The logical expressivist (including already—as I’ve argued elsewhere— Frege (1879) in the Begriffsschrift, at the dawn of modern logic) thinks of logical vocabulary as introduced to let one say in the logically extended object-language what material relations of implication and incompatibility articulate the conceptual contents of logically atomic expressions (and, as a bonus, to express the relations of implication and incompatibility that articulate the contents of the newly introduced logical expressions as well). There is no good reason to restrict the expressive ambitions with which we introduce logical vocabulary to making explicit the rare material relations of implication and incompatibility that are monotonic. Comfort with such impoverished ambition is a historical artifact of the contingent origins of modern logic in logicist and formalist programs aimed at codifying specifically mathematical reasoning. It is to be explained by appeal to historical causes, not good philosophical reasons.

From Logical Expressivism to Expressivist Logics  145 Of course, since our tools were originally designed with this task in mind, as we have inherited them, they are best suited for the expression of monotonic rational relations. But we should not emulate the drunk who looks for his lost keys under the lamppost rather than where he actually dropped them, just because the light is better there. We should look to shine light where we need it most. Notice that reasons against a claim are as defeasible in principle as reasons for a claim. Material incompatibility relations are no more monotonic in general than material implication relations. Claims that are incompatible in the presence of one set of auxiliary hypotheses can in some cases be reconciled by suitable additions of collateral premises. Cases with this shape are not hard to find in the history of science. What about Cut, the principle of cumulative transitivity? It is expressed in Tarski’s algebraic metalanguage for consequence relations by the requirement that the consequences of the consequences of a premise-set are just the consequences of that premise-set, and by Gentzen as the principle that adding to the explicit premises of a premise-set something that is already part of its implicit content does not add to what is implied by that premise-set. Thought of this way, Cut is the dual of what is usually thought of as the weakest acceptable structural principle that must be required if full monotonicity is not.1 “Cautious Monotonicity” is the structural requirement that adding to the explicit content of a premise-set sentences that are already part of its implicit content not defeat any implications of that premise-set. (Even though there might be some additional premises that would infirm the implication, sentences that are already implied by the premise-set are not among them.) We can think generally about the structural consequences of the process of explicitation of content, in the sense of making what is implicitly contained in (or excluded by) a premise-set explicit as part of the explicit premises. Cut says that explicitation never adds implicit content. Cautious Monotonicity says that explicitation never subtracts implicit content. Together they require that explicitation is inconsequential. Moving a sentence from the right-hand side of the implication-turnstile to the left-hand side does not change the consequences of the premise-set. It has no effect whatever on the implicit content, on what is implied. (Explicitation can also involve making explicit what is implicitly excluded by a premise-set.) Explicitation in this sense is not at all a psychological matter. And it is not even yet a logical notion. For even before logical vocabulary has been introduced, we can make sense of explicitation in terms of the structure of material consequence relations. Noting the effects on implicit content of adding as an explicit premise sentences that were already implied is already a process available for investigation at the semantic level of the prelogic.

146  Robert Brandom It might well be sensible to require the inconsequentiality of explicitation as a structural constraint on logical consequence relations. But just as for the logical expressivist there is no good reason to restrict the rational relations of implication and incompatibility we seek to express with logical vocabulary to monotonic ones, there is no good reason to restrict our expressive ambitions to consequence relations for which explicitation is inconsequential. On the contrary, there is every reason to want to use the expressive tools of logical vocabulary to investigate cases where explicitation does make a difference to what is implied. One such case of general interest is where the explicit contents of a premise-set are the records in a database, whose implicit contents consist of whatever consequences can be extracted from those records by applying an inference engine to them. (The fact that the “sentences” in the database whose material consequences are extracted by the inference engine are construed to begin with as logically atomic does not preclude the records having the “internal” structure of the arbitrarily complex datatypes manipulated by any object-oriented programming language.) It is by no means obvious that one is obliged to treat the results of applying the inference-engine as having exactly the same epistemic status as actual entries in the database. A related case is where the elements of the premise-sets consist of experimental data, perhaps measurements, or observations, whose implicit content consists of the consequences that can be extracted from them by applying a theory. In such a case, explicitation is far from inconsequential. On the contrary, when the CERN supercollider produces observational measurements that confirm what hitherto had been purely theoretical predictions extracted from previous data, the transformation of rational status from mere prediction implicit in prior data to actual empirical observation is an event of the first significance—no less important than the observation of something incompatible with the predictions extracted by theory from prior data. This is the very nature of empirical confirmation of theories. And it often happens that confirming some conclusions extracted by theory from the data infirms other conclusions that one otherwise would have drawn. Imposing Cut and Cautious Monotonicity as global structural constraints on material consequence relations amounts to equating the epistemic status of premises and conclusions. But in many cases, we want to acknowledge a distinction, assigning a lesser status to the products of risky, defeasible inference. In an ideal case, perhaps this distinction shrinks to nothing. But we also want to be able to reason in situations where it is important to keep track of the difference in status between what we take ourselves to know and the shakier products of our theoretical reasoning from those premises. We shouldn’t build into our global structural conditions on admissible material relations of implication and incompatibility assumptions that preclude us from introducing logical vocabulary to let us talk about those rational relations, so important for confirmation in empirical science.

From Logical Expressivism to Expressivist Logics  147 The methodological advice to not unduly limit the structure of rational relations to which the expressive ambitions of our logics extend applies particularly forcefully to the case of incompatibility relations. The structural constraint, the classical tradition for which Gentzen and Tarski speak, imposes on incompatibility relations is explosion: the requirement that from incompatible premises anything and everything follows. This structural constraint corresponds to nothing whatsoever in ordinary reasoning practices, not even as institutionally codified in legal or scientific argumentative practices. It is a pure artifact of classical logical machinery, the opportune but misleading translation of the two-valued conditional into a constraint on implication and incompatibility that reflects no corresponding feature of the practices that apparatus—according to the logical expressivist—has the job of helping us to talk about. It is for that reason a perennial embarrassment to teachers of introductory logic, who are forced on this topic to adopt the low invocations of authority, pressure tactics, and rhetorical devices otherwise associated with commercial hucksters, con men, televangelists, and all the other sophists from whom since Plato we have hoped to distinguish those who are sensitive to the normative force of the better reason, whose best practices, we have since Aristotle hoped to codify with the help of logical vocabulary and its rules. In the real world, we are often obliged to reason from sets of premises that are explicitly or implicitly incompatible. (An extreme case is the legal practice of “pleading in the alternative.” My defense is first, that I never borrowed the lawnmower, second, that it was broken when you lent it to me, and third that it was in perfect condition when I returned it. You have to show that none of these things is true. In pleading this way, I am not confessing to having assassinated Kennedy. Examples from high scientific theory are not far to seek.) We should not impose structural conditions in our prelogic that preclude us from logically expressing material relations of incompatibility that characterize our actual reasoning.

3.  The Expressive Role of Basic Logical Vocabulary The basic claim of logical expressivism in the philosophy of logic is that the expressive role characteristic of logical vocabulary is to make explicit, in the object-language, relations of implication and incompatibility, including the material, prelogical ones that, according to semantic inferentialism, articulate the conceptual contents expressed by nonlogical vocabulary, paradigmatically ordinary empirical descriptive vocabulary. The paradigms of logical vocabulary are the conditional, which codifies relations of implication that normatively structure giving reasons for claims, and negation, which codifies relations of incompatibility that normatively structure giving reasons against claims. To say that a premise-set implies a conclusion, we can write in the metalanguage: “Γ ⊢ A.” To say that a premise-set is incompatible with a conclusion, we can write in the metalanguage “Γ, A ⊢ ⊥.”

148  Robert Brandom To perform its defining expressive task of codifying implication relations in the object language, conditionals need to satisfy the Ramsey Condition:  Γ ⊢ A → B if and only if Γ, A ⊢ B.

That is, a premise-set implies a conditional just in case the result of adding the antecedent to that premise-set implies the consequent. A conditional that satisfies this equivalence can be called a “Ramsey-test conditional,” since Frank Ramsey first proposed thinking of conditionals this way. To perform its expressive task of codifying incompatibility relations in the object language, negation needs to satisfy the Minimal Negation Condition:  Γ → ¬A if and only if Γ, A ⊢ ⊥.

That is, a premise-set implies not-A just in case A is incompatible with that premise-set. (It follows that ¬A is the minimal incompatible of A, in the sense of being implied by everything that is incompatible with A.) We should aspire to expressive logics built onto material incompatibility relations that are nonmonotonic as well as material implication relations that are nonmonotonic. That means that just as an implication Γ ⊢ A can be defeated by adding premises to Γ, so can an incompatibility. Γ, A ⊢ ⊥ can also be defeated, the incompatibility “cured,” by adding some additional auxiliary hypotheses to Γ. And while, given the role negation plays in codifying incompatibilities, an incompatible set, Γ ∪ {A}, where Γ, A ⊢ ⊥, will imply the negations of all the premises that are its explicit members, it need not therefore imply everything. In substructural expressive logics built on Gentzen’s multisuccedent system, the condition that emerges naturally is not ex falso quodlibet, the classical principle of explosion, but what Ulf Hlobil calls “ex fixo falso quodlibet.” This is the principle that if Γ is not only materially incoherent (in the sense of explicitly containing incompatible premises) but persistently so, that is incurably, indefeasibly incoherent, in that all of its supersets are also incoherent, then it implies everything. In a monotonic setting, this is equivalent to the usual explosion principle. In nonmonotonic settings, the two conditions come apart. One conclusion that might be drawn from expressive logics is that what mattered all along was always ex fixo falso quodlibet—classical logic just didn’t have the expressive resources to distinguish this from an explosion of all incoherent sets. The basic idea of expressivist logic is to start with a language consisting of nonlogical (logically atomic) sentences, structured by relations of material implication and incompatability. In the most general case, we think of those relations as satisfying the structural principles only of Contexted Reflexivity—not Monotonicity, not Cautious Monotonicity, and not even transitivity in the form of Cut. We then want to introduce logical

From Logical Expressivism to Expressivist Logics  149 vocabulary on top of such a language. This means extending the language to include arbitrarily logically complex sentences formed from the logically atomic sentences by repeatedly applying conditionals and negations, and then extending the underlying material consequence and incompatibility relations to that logically extended language in such a way that the Ramsey Condition and the Minimal Negation Condition both hold. (In fact, we’ll throw in conjunction and disjunction as well.) A basic constraint on such a construction is set out by a simple argument due to Ulf Hlobil (2016). He realized that in the context of Reflexivity and a Ramsey Condition, Cut entails Monotonicity. For if we start with some arbitrary implication Γ ⊢ A, we can derive Γ, B ⊢ A for arbitrary B—that is, we can show that arbitrary additions to the premise-set, arbitrary weakenings of the implication, preserves those implications. And that is just Monotonicity. For we can argue: Γ ⊢ A

Assumption,

Γ, A ⊢ B → A

Ramsey Condition Right-to-Left,

Γ, B ⊢ A

Ramsey Condition Left-to-Right.

Γ, A, B ⊢ A

Contexted Reflexivity,

Γ ⊢ B → A

Cut, Cutting A using Assumption,

Since we want to explore adding Ramsey conditionals to codify material implication relations that are reflexive but do not satisfy Cut—so that prelogical explicitation is not treated as always inconsequential, we will sacrifice Cut in the logical extension. It is a minimal condition of logical vocabulary playing its defining expressive role that introducing it extends the underlying material consequence and incompatibility relations conservatively. (Belnap motivates this constraint independently, based on considerations raised by Prior’s toxic “tonk” connective. The logical expressivist has independent reasons to insist on conservativeness: only vocabulary that conservatively extends the material relations of consequence and incompatibility on which it is based can count as expressing such relations explicitly.) So there should be no implications or incompatibilities involving only old (nonlogical) vocabulary that hold or fail to hold in the structure logically extended to include new, logical vocabulary, that do not hold or fail to hold already in the material base structure. Since that material base structure is in general nonmonotonic and intransitive, satisfying only reflexivity, so must be the global relations of consequence and incompatibility that result from extending them by adding logical vocabulary.

150  Robert Brandom

4.  Basic Expressivist Logics We now know how to do that in the context of Gentzen-style substructural proof theory. I will be summarizing technical work by recent Pitt PhD Ulf Hlobil, now at Concordia University (on single-succedent systems) and current Pitt PhD student Dan Kaplan (on multisuccedent systems). We produce substructural logics codifying consequence and incompatibility relations that are not globally monotonic or transitive by modifying Gentzen’s systems in three sequential stages. Gentzen’s derivations all begin with what he called “initial sequents,” in effect, axioms, (which will be the leaves of all logical proof trees) that are instances of immediate reflexivity. That is, they are all of the form A ⊢ A. We impose instead a structural rule that adds all sequents that are instances of contexted reflexivity—that is (in the multisuccedent case), all sequents of the form Γ, A ⊢ A, Θ. Making this change does not really change Gentzen’s system LK of classical logic at all. For he can derive the contexted version from immediate Reflexivity by applying Monotonicity, that is Weakening (his “Thinning”). One remarkable thing we have discovered is that Gentzen does not need the stronger principle of unrestricted monotonicity in order to get the full system LK of classical logic. He can make do just with the very restricted monotonicity principle of Contexted Reflexivity, which allows arbitrary weakening only of sequents that are instances of reflexivity, that is, which have some sentence that already appears on both sides of the sequent one is weakening. Since all Gentzen’s initial sequents are instances of immediate reflexivity, being able to weaken them turns out to be equivalent to being able to weaken all logically derivable sequents. (The weakenings can be “permuted up” the proof trees past applications of connective rules in very much the same way Gentzen appeals to in proving his Cut-Elimination Hauptsatz.) Substituting the stronger version of Contexted Reflexivity for Gentzen’s version accordingly allows dropping the structural requirement of Monotonicity. We also do not impose Cut. But Gentzen’s Cut-Elimination Theorem will still be provable for all proof-trees whose leaves are instances of (now, contexted) Reflexivity. So the purely logical part of the system will still satisfy Cut. The next step in modifying Gentzen’s systems is to add axioms in the form of initial sequents relating logically atomic sentences that codify the initial base of material implications (and incompatibilities). Whenever some premise-set of atomic sentences Γ0 implies an atomic sentence A, we add Γ0 ⊢ A to the initial sequents that are eligible to serve as leaves of proof-trees, initiating derivations. (We require that this set of sequents, too, satisfies Contexted Reflexivity. We will be able to show that the connective rules preserve this property.) This is exactly the way Gentzen envisaged substantive axioms being added to his logical systems so that those systems could be used to codify substantive theories—for instance,

From Logical Expressivism to Expressivist Logics  151 when he considers the consistency of arithmetic. The crucial difference is that he required that these sequents, like those governing logically complex formulae, satisfy the structural conditions of Monotonicity and Cut—and we do not. We will introduce logical vocabulary to extend material consequence and incompatibility relations that do not satisfy Monotonicity, and that are not idempotent. The third stage in modifying Gentzen’s systems is accordingly to extend the prelogical language to include arbitrarily logically complex sentences formed from that prelogical vocabulary by the introduction of logical connectives. Gentzen’s connective rules show how antecedent consequence and incompatibility relations governing the logically atomic base language can be systematically extended so as to govern the sentences of the logically extended language. Gentzen’s own rules can be used to do this, with only minor tweaks. Basically, we need to use the versions Ketonen introduced, so as to make Gentzen’s rules invertible. These are the versions standardly used in Gentzen-style systems today. They are all equivalent to Gentzen’s own rules in the presence of a global structural rule of Monotonicity. But in nonmonotonic settings, they come apart. So, for instance, Gentzen’s left rule for conjunction allows us to move from Γ, A ⊢ C to Γ, A ∧ B |~ C. That builds in monotonicity on the left. We can’t have that, since in the material base, it can happen that adding B as a further premise defeats the implication of C by Γ and A. We allow instead only the move from Γ, A, B ⊢ C to Γ, A ∧ B ⊢ C. (A similar shift is needed in his right rule for disjunction: where he allows derivation of Γ |~ A ∨ B, Θ from Γ |~ A, Θ, building in monotonicity on the right, we allow instead only the move from Γ ⊢ A, B, Θ to Γ ⊢ A ∨ B, Θ.) I said above that from a logical expressivist point of view, for the conditional to do its defining job of codifying implication relations in the object language, it needs to satisfy the Ramsey condition. In Gentzen’s setting, this amounts to the two principles: (CP)

Γ, A ⊢ B   and (CCP) Γ ⊢ A → B

Γ⊢A→B Γ, A ⊢ B.

The first is Gentzen’s right-rule for the conditional. The second rule is not one of his. And it cannot be. For it is a simplifying rule. The only simplifying rule he has is Cut, and it is of the essence of his program to show that he can do without that rule: that every derivation that appeals to that single simplifying rule can be replaced by a derivation that does not appeal to it. Ketonen-style invertibility of connective rules, which makes root-first proof searches possible, though, requires not only Conditional Proof but the simplifying rule Converse Conditional Proof. And it is possible to show that this rule, too, like Cut is “admissible” in Gentzen’s sense: every derivation that uses it can be replaced by a derivation that does not.

152  Robert Brandom It can be shown that our versions of Gentzen’s connective rules produce a conservative extension of any nonmonotonic material base consequence relation (including nonmonotonic incompatibility relations incorporated in such consequence relations) that satisfies the structural condition of extended (contexted) Reflexivity. That is, in the absence of explicitly imposing a structural rule of Monotonicity (Weakening or Thinning) and Cut, the connective rules do not force global monotonicity. So the resulting, logically extended consequence relation is nonmonotonic. And the nonmonotonicity extends to logically complex formulae, for instance, as we have seen, in that from the fact that Γ, A ⊢ C it does not follow that Γ, A ∧ B ⊢ C, so that from Γ ⊢ A → C it does not follow that Γ ⊢ (A ∧ B) → C. The logical language that results permits the explicit codification using ordinary logical vocabulary of arbitrary nonmonotonic material consequence relations in which prelogical explicitation is not inconsequential. And yet, the system is supraclassical. All the theorems of Gentzen’s system LK of classical logic can be derived in this system. For if we restrict ourselves to derivations all of whose leaves are instances of Contexted Reflexivity, that is, are of the form Γ, A ⊢ A, Θ, the result is just the theorems of classical logic. It is only if we help ourselves to initial sequents that are not of that form, the axioms that codify material relations of consequence and incompatibility, that we derive nonclassical results. What Dan Kaplan discovered is, astonishingly, that Gentzen never needed to require monotonicity, his “Thinning,” as a global structural rule. He could just have used initial sequents that correspond to Contexted Reflexivity instead of immediate reflexivity. That gives him all the weakening behavior he needs. Further, if we look only at sequents that are derivable no matter what material base relation we extend, sequents such as Γ, A, A → B ⊢ B, hence Γ ⊢ (A ∧ (A → B)) → B, we find that the “logic” of our system in this sense, too, is just classical logic. Perhaps not surprisingly, if, following Gentzen, we use essentially the same connective rules but restrict ourselves to single succedent sequents, the result is a globally nonmonotonic supraintuitionist logic. I have been talking about the logical extension of nonmonotonic material consequence relations and not about the logical extension of nonmonotonic material incompatibility relations. But the latter are equally well-behaved. The multisuccedent connective rules for negation are just Gentzen’s. But it is not the case that any materially incoherent premiseset implies every sentence. Such premise-sets imply both the sentences they explicitly contain and the negations of all those sentences. But they do not imply everything else. If a premise-set explicitly contains both A and ¬A for some sentence A, then it implies everything. But that is because persistently or monotonically incoherent premise-sets explode— that is, sets that are not only incoherent themselves, but such that every superset of them is incoherent. This is what Ulf Hlobil calls “ex fixo falso quodlibet.” No specific stipulation to this effect needs to be made.

From Logical Expressivism to Expressivist Logics  153 It arises naturally out of the connective rules. If monotonicity held globally, ex falso quodlibet and ex fixo falso quodlibet” would be equivalent. Outside of derivations all of whose leaves are instances of contexted reflexivity, in our systems, they are not. So in a clear sense, the logic is monotonic and transitive—indeed, classical or intuitionistic, depending (as with Gentzen) on whether we look at multisuccedent or single-succedent formulations—but the logically extended consequence and incompatibility relations in general, are not.2 The logic of nonmonotonic consequence relations is itself monotonic. Yet it can express, in the logically extended object language, the nonmonotonic relations of implication and incompatibility that structure both the material, prelogical base language, and the logically compound sentences formed from them, as they behave in derivations that substantially depend on the material base relations. Substructural expressivist logics suitable for making explicit nonmonotonic, nontransitive material consequence and incompatibility relations are accordingly not far to seek. They can easily be built by adding to Gentzen’s system nonlogical axioms codifying those material relations of implication and incompatibility. It turns out that the relations of implication and incompatibility that hold in virtue of their logical form alone are still monotonic and transitive, even though the full consequence and implication relations codified by the logical connectives is not. So if you want Cut and Weakening, you can still have them—for purely logical consequence. Remember that from the point of view of logical expressivism, the point of introducing logical vocabulary is not what you can prove with it (what implications and incompatibilities hold in virtue of their logical form alone) but what you can say with it. Expressivist logics let us say a lot more than is said by its logical theorems. If I had more space, I would talk about the next step. We can also introduce a modal operator that marks, in the object-language, implications that hold persistently, that is, monotonically—no matter what further collateral premises one adds. Thus within a sea of material consequences that are not globally monotonic, it lets us explicitly mark off local regions where monotonicity does hold. From this point of view, ordinary monotonic logics show up as what you get if you identify all sentences with their monotonicity necessitations. We can now express also the un-necessitated contents. These monotonicity-modal expressivist logics implement technically the central methodological principle of expressivist logics: don’t presuppose Procrustean global structural requirements on the material relations of consequence and incompatibility one seeks to codify logically. Instead, relax those global structures and introduce vocabulary that will let one say explicitly, in the logically extended object language, that they hold locally, wherever in fact they still do. But that story will have to wait for another day.

154  Robert Brandom

Notes 1 On holding onto both Cut and Cautious Monotonicity, see Gabbay (1985). Gabbay agrees with the criteria of adequacy laid down by the influential KLM approach of Kraus et al., (1990). 2 When I talk about “the logic” here this can mean either the theorems derivable just from instances of Contexted Reflexivity (following Gentzen) or what is implied by every premise-set for every material base relation of implication and incompatibility that satisfies Contexted Reflexivity.

References Cartwright, Nancy. 1983. How the Laws of Physics Lie. New York: Clarendon Press. Frege, Gottlob. 1879. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: L. Nebert. Gabbay, Dov M. 1985. “Theoretical Foundations for Nonmonotonic Reasoning in Expert Systems.” In Logics and Models of Concurrent Systems, edited by Krzysztof R. Apt, 429–459. Berlin and New York: Springer. Hlobil, Ulf. 2016. “A Nonmonotonic Sequent Calculus for Inferentialist Expressivists.” In The Logica Yearbook 2015, edited by Pavel Arazim and Michal Dančák, 87–105. College Publications: London. Kraus, Sarit, Daniel Lehmann, and Menachem Magidor. 1990. “Nonmonotonic Reasoning, Preferential Models and Cumulative Logics.” Artificial Intelligence 44 (1–2): 167–207. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan. Wilson, Mark. 2006. Wandering Significance: An Essay on Conceptual Behavior. Oxford: Clarendon Press.

7 Inferentialist-Expressivism for Explanatory Vocabulary Jared Millson, Kareem Khalifa, and Mark Risjord

1. Introduction While most of our inferential lives traffic in the inductive, surprisingly little work has been done to develop an inferentialist approach to inductive vocabulary. In contrast to the detailed inferentialist treatments of deductive vocabulary (Dummett 1991; Peregrin 2014; Prawitz 1965; Schroeder-­Heister 2006), inferentialist discussions of inductive vocabulary (Brandom 1994, 2008, 2015; Sellars 1957, 1963) are mostly programmatic. Admittedly, the induction literature as a whole (inferentialist or otherwise) is not as well-developed as its deductive counterpart. However, this only licenses a more cautious, piecemeal inferentialist approach to inductive vocabularies, rather than widespread avoidance. In keeping with this cautious application of inferentialism to inductive language, we focus on explanatory vocabulary—not just “explains” and its cognates, but the rich, concrete, material language with which we account for why things happen. An inferentialist approach to explanatory vocabulary has several initial attractions. Explanation is deeply embedded within science’s inductive apparatus through its relationship to causation, probability, and laws of nature. Inferentialism about explanatory vocabulary can marshal earlier inferentialist treatments of laws and causality (Lange 2009; Reiss 2015), so as to develop a kind of scientific realism that avoids substantive metaphysical commitments to laws and causes over and above commitment to those entities and processes characterized in lawful, causal terms. This stands opposed to traditional semantic analyses that tend to suffer from ontological bloat as a result of characterizing the meanings of explanatory, nomological, and causal vocabulary in terms of the objects that they represent. All alone, however, inferentialism is not enough. The inferential role of expressions like “law” or “cause” are themselves characterized in modal terms. If modal vocabulary remains representational, inferentialism merely trades one set of dubious metaphysical commitments for another. Expressivism about some vocabulary X is the view that X’s function is not to describe or represent features of the world, but rather

156  Jared Millson, Kareem Khalifa et al. to express or to make explicit attitudes that would otherwise remain implicit, tacit, or latent (Blackburn 1993; Brandom 1994, 200, 2008; Gibbard 2003; Peregrin 2014). Expressivist treatments of a vocabulary’s function need not be wedded to an inferentialist account of its meaning. Nonetheless, the two approaches have a natural affinity. Both eschew traditional linguistic approaches that privilege representational concepts and descriptive functions by taking word-world relationships as fundamental. More importantly, an inferentialist account of the meaning of vocabulary X goes some way toward explaining why X has the peculiar expressive function that it does. For instance, the introduction and elimination rules for the conditional in classical logic permit the derivation of the Deduction Theorem (A ⊢ B if and only if ⊢ A → B), which can be thought of as articulating the expressive function of the conditional— the theorem says that an object-language operator gives expression to or makes explicit what would otherwise be given as a rule of inference in the meta-­language. It thereby illustrates how inferentialism can support a particular brand of expressivism, one distinguished by the claim that the expressive role of the target vocabulary is to make explicit speakers’ commitments to inferences. In this essay, we extend earlier inferentialist-expressivist treatments of traditional logical, semantic, modal, and representational vocabulary (Brandom 1994, 2008, 2015; Peregrin 2014) to explanatory vocabulary. From this perspective, Inference to the Best Explanation (IBE) appears to be an obvious starting point. In its simplest formulation, IBE has the form: A best explains why B, B; so A. It thereby captures one of the central inferential features of explanation. An inferentialist-­expressivist treatment of “best explains” would treat it as a logical operator. Analogous to the inferentialist-expressivist treatment of other logical operators, this essay aims to provide introduction and elimination rules for “best explains.” Indeed, by exhibiting a form of detachment, IBE superficially looks like an elimination rule. The sequent calculus LEA+, described in section 5 below, makes good on this intuition. By showing how “A best explains why B” is related to the underlying, scientific inference “A, so B,” we can purchase the inference ticket of IBE for no more than the cost of science’s material inferences.

2.  Best Explains as a Logical Operator We aim to show that certain explanatory locutions enable speakers to express their commitments to explanatory arguments, rather than to describe features of the world. The vast literature on explanation in the philosophy of science has gone a long way toward characterizing the topography of explanatory argumentation. Before developing a sequent calculus for “best explains,” we must tour those parts of explanatory practice that we aim to make explicit.

Inferentialist-Expressivism for Explanatory Vocabulary  157 2.1.  Explanatory Vocabulary The expression “best explains” admits of potential ambiguities. For instance, “A explains why B” is typically factive. On a simple reading, then, “A best explains why B” is also factive. After all, it is natural to think of our best explanations as a proper subset of the totality of actual explanations. However, our chief aim is to capture the meaning of “A best explains why B” as it functions as a major premise in IBE. As IBE’s foremost defender, Peter Lipton (2004, 58), argues, to treat “A best explains why B” as factive or “actual” in this case is “like a dessert recipe that says start with a soufflé.” For this reason, Lipton suggests that the best explanation ought to be construed as the best potential explanation.1 Following a common convention among philosophers of science, let us stipulate that “A potentially explains why B” requires neither “A” nor “B” to be true. Then the notion of “A best explains why B” that we seek to capture is not factive, but must still provide good inductive grounds for detaching the explanans, A, when the explanandum, B, obtains. In addition to being nonfactive, the sense of best explanation that we aim to represent is immediate and exhaustive. A is an immediate explanation of B so long as it does not explain B merely by explaining something else, C, which in turn explains B. In other words, we assume that explanations are not transitive. By “exhaustive,” we mean that nothing needs to be added to A in order for it to explain B. The target of our account is thus expressed by the locution “is the best potential, immediate, exhaustive explanation of why.” To avoid having to repeat this phrase, we will henceforth speak of best explanations or simply explanations and will use “►” to symbolize this relationship in our object language. In the vein of Carl Hempel’s famous model of explanation, we hold that explanations are a type of argument or inference—what we call explanatory arguments. Of course, we are interested in the type of inference that can be identified with our best explanations and are thus investigating our “best explanatory arguments.” As we shall see, however, this evaluative feature is actually integrated with other properties of this as-yet-unspecified, consequence relation. Therefore, we will continue to refer to our target as “explanatory arguments,” and will refer to them in our metalanguage with a modified turnstile  . Since our aim is to have our best-explains-why operator exhibit the properties of best explanations, and since we treat explanations as a kind of argument, in order to make progress in this aim, we must specify the properties of explanatory arguments that distinguish them from other inferences. Explanatory arguments are intransitive, and the account of best explanation we seek to capture requires these arguments to exhibit the form of detachability associated with IBE. What else distinguishes explanatory arguments from other inferences? Careful reflection suggests five

158  Jared Millson, Kareem Khalifa et al. further features: irreflexivity, premise consistency, minimality, defeasibility, and stability. While previous attempts to base an account of explanation on inference have relied primarily on classical logic, explanatory arguments behave non-classically in many ways. For instance, they do not tolerate irrelevant premises. They are minimal in the sense that there is no logically weaker version of their premises that would provide explanation. For example, if the liquid’s acidity explains why the litmus paper turns red, then it does not follow that the liquid’s acidity and its potability explains why the litmus paper turned red, even if the liquid is in fact potable. Reflexive explanations, such as “the litmus paper turned red because it turned it red,” are clearly nonstarters. Indeed, even partial self-­ explanations seem unacceptable. A ∧ B ⊢ A and its ilk do not qualify as explanatory arguments, even though they are classically valid.2 In addition, contradictions do not explain; ex contradictione quodlibet is not a pattern of explanatory reasoning. Explanatory arguments must therefore have consistent premises. Below we refer to irreflexive and premise consistent inferences as nontrivial. Since discovering that a premise is false defeats an explanation, premise consistency is a special case of defeasibility. Defeasibility also can take other forms. For instance, while the claim that “the liquid’s acidity explains why the blue litmus paper turned red” may constitute a good explanation, strengthening the explanans can easily produce a bad one: “the liquid’s acidity and the presence of chlorine gas explains why the blue litmus paper turned red.” In this case, the additional information is logically consistent with the explanans but incompatible with the explanandum (since chlorine prevents litmus paper from turning red). In other cases, however, new information undercuts the explanatory relation itself. For instance, that the match was struck may explain why the match lit, but if it is discovered that the match was damp, then the striking no longer, by itself, explains why it lit (perhaps the match was dried before it was struck). In both sorts of cases, we say that the explanatory arguments in question are defeated. Finally, explanations are stable. Philosophers of science have analyzed stability in different ways (Hempel 1965; Lange 2009; Mitchel 2003; Skyrms 1980; Woodward 2003). In its most general form, X is said to be stable if X remains unchanged as other conditions C change. For instance, suppose that a patient’s rash is explained by a particular bacterial infection, though an alternative potential explanation is that the rash is caused by an allergic reaction. The explanation is stable insofar as she would have a rash regardless of whether she had had an allergic reaction. Typically, the fundamental bearers of stability are taken to be laws or generalizations. By contrast, as inferentialists, we take explanatory arguments to be the fundamental bearers of stability. In what follows, we develop a distinctively inferentialist brand of stability that we

Inferentialist-Expressivism for Explanatory Vocabulary  159 call “sturdiness.” Sturdiness is a comparative property among defeasible, nontrivial inferences. An inference is sturdy just in case it succeeds when all other nontrivial inferences that share its conclusion fail, where by “failure” we mean defeat and by “success,” the absence of defeat. The challenge of providing an inferentialist-expressivist account of explanatory vocabulary, then, is to properly characterize the underlying inferences. The list of desiderata—intransitivity, detachability (IBE), irreflexivity, premise consistency, minimality, defeasibility, and stability—is sufficiently daunting that one might doubt the project’s feasibility. Inferentialist-expressivist accounts of classical logic are plausible at least in part because the Deduction Theorem (A ⊢ B if and only if ⊢ A → B) is so well understood. It is the aim of this essay to define a set of consequence relations that map onto the features of explanatory arguments, and show that “A best explains why B” can be treated as an operator within that system. 2.2. LEA and LEA+: An Inferentialist-Expressivist Treatment of Best Explains In the remainder of this essay, we develop sequent calculi for explanatory arguments and the vocabulary that makes them explicit. We begin by introducing our base logic, LEA, defined over a standard propositional language, L . LEA is composed of two parts: LKΘ and LE►. The first part, LKΘ, is developed in section 3. It is based on LKS, a variant of Gentzen’s sequent calculus for classical logic proposed by Piazza and Pulcini (2017). The aim of LKS was to represent nonmonotonicity in terms of an inference’s context-sensitivity. Although we have altered the key concepts and definitions with which Piazza and Pulcini (2017) introduced their calculus, the rules of LKΘ are nearly identical to those of LKS and thus we inherit the latter’s cut-­elimination theorem. Our modifications are intended, on the one hand, to represent a concept of defeat more appropriate to the behavior of explanations, and, on the other, to extend the axioms of the system to nonlogical, material inferences. In section 4, we develop the second part, LE►. We introduce an additional class of sequents and rules that govern the interaction between LE► and LKΘ, including a rule corresponding to IBE. Finally, in section 5, we describe a system LEA+ defined over L ► that extends L  to include an objectlanguage connective, ►, that makes commitments to explanatory arguments explicit. The need for a base logic that includes two consequence relations stems from the observation that IBE cannot itself be an explanatory argument, if the function of locutions like best explains why is to express commitment to explanatory arguments, and if IBE is a legitimate rule of inference. This counterintuitive claim arises from the way that implicit inference rules and the explicit operators interact in an inferentialist-expressivist

160  Jared Millson, Kareem Khalifa et al. account. Suppose that the locution A best explains why B makes explicit a commitment to an explanatory argument. Now suppose (for reductio) that IBE is also an explanatory argument. From these suppositions it follows that the best-explains-why connective expresses an explanatory argument from B to A, since this is the only way for there to be a good explanatory argument with the form of IBE: A best explains why B, B; so A. But if IBE is an explanatory argument, it follows that such an inference can also be made explicit by the best-explains-why connective, thereby yielding the sentence [(A best explains why B) ∧ B] best explains why A. Insofar as sentences of this form are even intelligible, it is far from obvious that they claim what an application of IBE shows. Thus, we should not treat IBE as an explanatory argument. Rather, IBE belongs to one class of inferences and explanatory arguments belong to another. This means that any logical system designed to represent both explanatory arguments and IBE must appeal to two distinct consequence relations. In recognition of this point, LEA contains two consequence relations, or more precisely, two classes of consequence relations. The class whose rules are given by LKΘ (table 7.1) is intended to represent the broad set of inferences to which both IBE and candidate explanatory arguments belong. The class of consequence relations introduced by LE► and denoted by  (table 7.2) is supposed to capture the behavior of explanatory arguments themselves. The chief results of sections 3, 4, and 5 are that (a) the provable sequents of LEA that are constructed with  exhibit all of the properties associated with explanatory arguments, (b) LEA can be extended to LEA+ (table 7.3), including an object-­language expression for making explicit commitments to explanatory arguments (Theorem 2), and (c) this extension is conservative (Corollary 4.1).

3.  LKΘ: A Sequent Calculus for Defeasible Inference In what follows, we assume a propositional language, L , for classical logic, that consists of a countable set of atomic sentences whose elements are denoted p, q, r, etc., and the standard connectives ∧, ∨, ¬. Formulas are defined recursively as usual and are ranged over by A, B, C. Sets of formulas are ranged over by Γ, ∆, Θ, ᴪ, Σ, Λ; sets of sets of formulas by S, T; and sets of atoms by X, Y. All of the latter sets are assumed to be finite. We begin by employing the standard sequent notations, for example, Γ, A ├ B, ∆. Formulas on the left side of the turnstile are called the antecedent; on the right side, they are called the succedent. Commas in the antecedent are read conjunctively and those on the right are read disjunctively. The formula with the connective in a rule is the principal formula of that rule, and its components in the premises are the active formulas.

Inferentialist-Expressivism for Explanatory Vocabulary  161 3.1.  Defeasible Sequents The sequents in our calculi, what we will call defeasible sequents, depart from the standard form in two respects: just below our turnstile we add a set of formulas, Θ, called a defeater set and to the far left of the turnstile we add another, Σ, called a background set. Defeasible sequents thus have the following form:3

Defeater sets contain information whose addition to the premises defeats the inference represented by the sequent. Roughly put, a sequent is defeated whenever its antecedent or background set contains a formula that is logically equivalent to a subset of the defeater set. Thus, as the name suggests, defeater sets are sets of inference-defeaters. As noted, we adopt and modify the sequents and rules of the calculus LKS developed by Piazza and Pulcini (2017). The general idea captured by this calculus is that any application of the rules along a derivation ought to preserve not only the validity, but also the defeat-status of sequents. In our system, LEA, this means that for any derivation tree, π, constructed by recursive applications of the rules (excluding cut), the following holds: if a defeated sequent occurs in a branch of π, then all sequents below it are also defeated. By tracking the defeat of sequents, our proof theory can identify if and when a line of defeasible reasoning goes astray. We interpret background sets as consisting of information that a reasoner is beholden to when she draws an inference, but which does not serve as a premise and from which the conclusion is not said to follow. Having such a device in our formalism enables us to capture an important aspect of defeasibility, namely that the introduction of new information may jeopardize prior inferential commitments even when that information does not serve as fodder for new inferences in its own right. These sets also serve a technical role in our system. They often expand in the course of a derivation, picking up traces of those formulas shifted from the left to the right side of the turnstile (see ¬ ├ in table 7.1). It is this latter feature which permits the implementation of a Gentzen-style normalization procedure and proof of cut-elimination. Indeed, by keeping a record, so to speak, of formulas that have moved from the antecedent in a premise to the succedent of a conclusion, background sets ensure that all the sequents in a cut-free derivation are undefeated just in case its end-sequent is undefeated.4 Because the provability of any sequent in LEA depends, in part, upon the contents of its defeater set, there is not one or two, but P   (L   )-many consequence relations represented by the calculi. Some are classical, that is, Θ = ∅; many are nonmonotonic, that is, Θ ≠ ∅; others defy even the

162  Jared Millson, Kareem Khalifa et al. most ubiquitous structural properties, such as reflexivity, that is, ∆ ⊆ Θ. By manipulating the contents of defeater sets, the rules of our calculi are able to exploit this panoply so as to home in on the class of consequence relations bearing precisely those properties we associate with explanatory arguments. Proofs in LKΘ preserve both validity and defeat-status. However, since the rules of LE► are not deductive, it cannot be deductive validity that is preserved through proofs in the complete calculus, LEA. Instead, we follow Brandom (2008) and treat the sequents that belong to a proof as inferences that preserve entitlement. In keeping with this view, we offer the following reading of the defeasible sequent above: Anyone entitled to (every member of ) Γ is entitled to (at least one member of ) ∆, given the background of Σ. Informally, defeat should be a kind of incompatibility between the set of premises, Γ, the background, Σ, and the defeater set, Θ. This relationship is characterized formally in Definitions 1 and 2. Definition 1 (D  (Θ)). Let D  (Θ) be the closure of Θ under double negation, De Morgan’s Laws, as well as the commutativity, associativity, and distributivity of conjunction and disjunction. In addition, the set is closed under the following D -rules: D  ∧ : A ⇒ A ∧ B D  ∨ : A and B ⇔ A ∨ B Definition 2 (Defeat). A defeasible sequent is said to be defeated just in case the conjunction of the members of the background set and the antecedent is included in the D  -closure of the defeater set, that is, is defeated if and only if ÙΣ∪Γ ∈ D  (Θ). Example 1.

is defeated.

Example 2.

is undefeated.

Example 3.

is defeated.

Example 4.

is undefeated.

D  (Θ) is designed to generate closed sets of formulas whose occurrence in the antecedent defeats the sequent to which the defeater set is attached. Since a formula of the form A ∧ B defeats an inference just in case one or more of its constituents belongs to the defeater set, a set closed under

Inferentialist-Expressivism for Explanatory Vocabulary  163 D  ∧ will contain all those conjunctions for which at least one member of the original set, Θ, is a conjunct. Conversely, if the defeater set contains a conjunction but neither of its conjuncts, then we know that the two formulas together defeat the sequent but not whether either formula by itself would defeat it. (The need for defeat to occur when both conjuncts appear on their own in the antecedent is handled by the conjunction in the left-hand side of Definition 2.) Thus, unlike the other rules that define D (Θ), D  ∧ only permits the construction of more complex formulas— hence the absence of a biconditional in its formulation. In contrast, a disjunctive formula defeats an inference only when both of the disjuncts occur in its defeater set. The D  ∨-rule captures this intuition—read left-to-right—by constructing disjunctions when both disjuncts are present in the defeater set. Conversely, a disjunction in a defeater set means that the presence of either disjunct in the antecedent will defeat the sequent. Thus, the D ∨-rule is formulated—from right-toleft—so that a disjunction in the D -closure of a defeater set will contain both disjuncts. The result of comparing the antecedent (and background set) with the closure of the defeater set under the D -rules is an intuitive conception of inference-defeat. 3.2.  Proofs in LKΘ We now turn to the sequent calculus for defeasible sequents. Proofs take the form of trees that begin from one or more axioms. Rules for the construction of proofs in LKΘ are listed in table 7.1. Definition 3 (Proof, Paraproof ). For a rooted, finitely branching tree π whose nodes are sequents of LKΘ (LEA+), and which is recursively built up from axioms by means of the rules of LKΘ (LEA+), if each sequent in π is undefeated, then π is said to be a proof of LKΘ (LEA+), otherwise π is called a paraproof. The axioms of LKΘ come in two varieties. Logical axioms consist of single identical propositions on either side of the turnstile, and while they may contain nonempty defeater sets, their background sets are always empty. As in the classical sequent calculus, the role of the logical axioms is to introduce single atomic propositions into proof trees.5 Proper axioms, on the other hand, are sequents composed of nonempty, nonoverlapping sets of atoms on the left and right of the turnstile.6 These sequents are intended to represent the nonlogical, material inferences that figure in various types of scientific reasoning. Since such inferences are often the products of concrete empirical inquiries, we insist that they be introduced with non-empty background sets of (possibly complex) formulas that reflect the epistemic context of their use.

164  Jared Millson, Kareem Khalifa et al. Table 7.1  Rules for LKΘ

LKΘ has some interesting, even exotic, features. First, with the exception of the DE rule (which stands for Defeater Expansion), single-premise rules have no effect on defeater sets, while all the two-premise rules yield defeater sets in the conclusion that are the union of those in the premises. This fact guarantees that no information about potential defeaters is lost along a derivation (Proposition 1). Exempting DE from this requirement is justified by the idea that reasoners ought to be able to add new, extralogical information about defeaters to their arguments as it becomes available. DE allows one to do so as long as it does not defeat the sequent in question.

Inferentialist-Expressivism for Explanatory Vocabulary  165 Proposition 1. (a) If π is a tree whose root is occurs in the leaves of π and A ∈ Θ, then A ∈ Θ′; (b) If π is a tree whose root is occurs in the leaves of π and A ∈ Θ, then A ∈ Θ′.7 Second, all of the rules either transfer or combine background sets from premises to conclusions, except for BE and ⊢ ¬. The former (whose name abbreviates Background Expansion) permits the addition of arbitrary formulas to a sequent’s background set. At one level, this rule simply captures the way new contextual information is added in the course of scientific reasoning. But at a deeper level, it attempts to represent the way reasoners might probe the defeasibility of an inference by discharging it in different contexts. In this sense, BE codifies certain patterns of experimental reasoning. On the other hand, ⊢ ¬ adds the active antecedent of the premise to the background set of the conclusion. This behavior is of a piece with the explanation given for background sets above—they act as a kind of record of those formulas that have been shifted from the left to the right of a turnstile.8 An informal interpretation of the rule (read upward) can be given as follows: if one is entitled to ¬A while A is in one’s background set of entitlements, then one is entitled to whatever follows from A once it has been removed from that background set and entitlement to its negation has been renounced. The formulation of ⊢ ¬ in this manner is critical to the upwards preservation of undefeatedness in cut-free proofs. Proposition 2. Any cut-free paraproof in LKΘ is a proof if and only if its end-sequent is undefeated, that is, undefeatedness is preserved upwards in cut-free proofs. The preservation of undefeatedness in cut-free proofs is, in turn, critical to cut-elimination because by permuting cut upward in derivations, the normalization procedure occasionally turns proofs into paraproofs.9 Proposition 2, however, ensures that for any such paraproof, there is a cut-free proof of its end-sequent. Lemma 1. Any sequent that is provable in LKΘ has a cut-free proof. Cut-elimination is crucial to the project of this paper. Our aim is to demonstrate that a logic of explanatory arguments can be conservatively extended to include a best-explains-why operator in the object-language. Showing that this extension preserves cut-elimination is a straightforward way of demonstrating conservativeness.

166  Jared Millson, Kareem Khalifa et al. LKΘ has one of the key features we associate with explanatory arguments, specifically defeasibility. This property is not only represented by the basic sequent notation, it is also preserved through proofs in LKΘ. To demonstrate this, we invite the reader to consider the rules for LKΘ in table 7.1. These rules are designed to generate trees that preserve validity downward and undefeatedness upward. When read bottom-up, the rules say that, “If [the conclusion sequent] is undefeated, then so is/are [the premise sequent/s].” Alternatively, the rules may be read top-down as permitting the conclusion, given the premises, so long as the former is not defeated. On either reading, the rules are formulated to ensure that a cut-free derivation whose end-sequent is undefeated will contain only undefeated sequents throughout. This property is important both for the establishment of cuteliminability and more primitively, for the fact that proofs in a system for defeasible reasoning should not contain defeated sequents. The same mechanism that allows us to track defeat among sequents also permits us to realize the remaining characteristics of explanatory and create a arguments. To do so, we must add further restrictions to second class of consequence relations.

4.  LE►: A Sequent Calculus for Explanatory Arguments With the rules for LKΘ now in place, we can turn to the other part of our base system, LE►, where we introduce a class of consequence relations, denoted by , that represents explanatory arguments. We will call sequents constructed with this turnstile ►-sequents. The rules for LE► are presented in table 7.2. Table 7.2  Rules for LE►

Inferentialist-Expressivism for Explanatory Vocabulary  167 The structural rules and the logical rules need little discussion. The structural rules for LE► are just the DE and BE rules, modulo the ► turnstile. As before, these characterize the probing of defeasibility and background information typical of scientific inference. Note that no structural rules correspond to LW or RW. If the antecedents of ►-sequents could be arbitrarily weakened, then the minimality condition, which STR secures, would be compromised. Right Weakening, on the other hand, does not directly conflict with the properties of explanatory arguments; rather, we deny it because the weakening of explananda by arbitrary disjuncts appears to us as both unnatural and unreasonable. The fact that our target vocabulary expresses the notion of immediate explanation motivates the absence of a structural rule corresponding to cut. Moreover, without a cut rule, the intransitivity of ►-sequents follows immediately. It is entirely possible that are provable in LEA, but is not. The logical rules of LE► are just the left and right rules for conjunction in LKΘ, modulo ►-sequents. Out of an abundance of caution, we have chosen to restrict the logical operations permitted on ►-sequents to just these rules. To our ears, inferences from conjunctive explanantia and to conjunctive explananda sound far more natural than those involving disjunctive or negated explanatia/explananda. Insofar as negations or disjunctions play a role in explanatory arguments, these propositions need to be built up through applications of the rules of LKΘ, not through manipulation of ►-sequents. The mixed rules of STR and ABD are both the most unusual—as they contain two different types of consequence relations—and the most important for the purposes of representing explanatory arguments. As mentioned above, “sturdiness” is our proposal for how to understand the property of stability associated with explanations. In slogan form, inferences are sturdy just in case they succeed where all others fail. To say that one inference succeeds when another fails, we can imagine the following procedure: Step 1: Line up all of the nontrivial inferences that have the explanandum, B, as their conclusion. For each of these inferences, all other nontrivial inferences leading to B are its “competitors.” Step 2: For each A that has B as a nontrivial consequence, suppose that all of A’s competitors’ premises are false. Step 3: If the falsehood of any of these competitors defeats the inference from A to B, then the latter is not sturdy; otherwise, it is sturdy. Our STR rule aims to formalize this procedure. To capture the first step, we need a formal definition of a competitor. To arrive at this definition, we must introduce a few preliminary concepts.

168  Jared Millson, Kareem Khalifa et al. Definition 4 (Set Negation, ¬(Γ)). Let ¬(Γ) stand for the following operation: ¬(Γ) = df {¬A : A ∈ Γ} . The operation easily extends to sets of sets: ¬(S) =df {¬(Γ) : Γ ∈ S} .

Definition 5 (Λ ⊥ ). Let Λ ⊥ stand for the following set: Λ ⊥ = df {A ∧ ¬A : A ∈ L Λ = df {A ∧ ¬A : A ∈ L } . ⊥

By definition, D (Λ ⊥) contains all of the contradictions in L . Thus, when the defeater set of a sequent whose antecedent is Γ includes Λ ⊥, the sequent will be defeated if Γ is inconsistent. Definition 6 (Non-trivial Antecedent Set, S∆). Let S∆ stand for the following set:   LK Θ S∆ = df Ω i : Σ i Ω i ∆ ⊥ Ψi ∪ Λ ∪ ∆   where i ∈ N and LKΘ above a turnstile indicates that the sequent is provable in LKΘ. Despite its complex appearance, S∆ is nothing more than the set containing the antecedents of all those provable nontrivial sequents of LKΘ that have ∆ as its conclusion. For ease of reference, the definition indexes background sets and defeater sets by the antecedents of the relevant sequent. Naturally, a candidate for sturdiness should not compete against itself. Thus, to generate a set of proper competitors for some antecedent Γ we must remove Γ and its logical equivalents from S∆. The next two definitions allow us to do so. Definition 7 (Classical Equivalence Set, TΓ). Let TΓ stand for the following set: TΓ = df {Λ : Γ  Λ and Λ  Γ} where ├ denotes the consequence relation of LK.

The members of TΓ are just those sets that are provably equivalent to Γ in classical logic, that is, LK. Definition 8 (∆\\ Γ ). ∆ ∆ \\ Γ = df  ∆ \ Γ

if ∆ ⊂ Γ, otherwise.

We extend the definition to sets of sets as follows: S \\ T =df {∆ \\ Γ : ∆ ∈ S a S \\ T =df {∆ \\ Γ : ∆ ∈ S and Γ ∈ T} .

Inferentialist-Expressivism for Explanatory Vocabulary  169 The set denoted by S \\ TΓ consists of those members of S that are proper subsets of Γ (and its logical equivalents) and the set-complements relative to Γ (and its logical equivalents) of those members that are not. While this definition is needed to arrive at a suitable definition of competitor, it will also prove critical in securing minimality. As we explain below, we must not allow candidates to compete against sets of formulas that contain a disjunction of one its members with an arbitrary formula. To prevent such a scenario, we introduce an operation that removes or “deletes” arbitrary disjunctions from a set.

{

}

Definition 9 (Disjunction Deletion, ∨S). ∨ S =df ∆\ {A ∨ B} : ∆ ∈ S and A ∈  S

{∆\{A ∨ B} : ∆ ∈ S and A ∈  S}

The set denoted by ∨S is the result of “deleting” from the members of S any disjunction one of whose disjuncts belongs to a member of S. We at last have the means to precisely define what counts as a set of competitors, thus completing the formalization of the first step in the procedure described above. Definition 10 (Competitor Set). For any non-trivial sequent, the competitor set of its antecedent, Γ, is  ∨ S∆ \\ TΓ. The second step of the sturdiness procedure is captured by the fact that the set defined by  ¬(∨ S∆ \\ TΓ ) appears in the background set of the premise sequent for STR. Roughly put, this set contains the negations of all the antecedents of nontrivial inferences whose succedent is ∆, with the caveat that the members of Γ and their equivalents are removed from any antecedent that is a superset of Γ. The appearance of  ¬(∨ S∆ \\ TΓ ) in the background of the premise for STR thus guarantees that the negations of the competitors are part of the background of a candidate explanatory argument. If the sequent remains undefeated under these circumstances, then it represents an inference that goes through even if the antecedents of all competitors are false. Under these conditions, the third step of sturdiness is reached. The inference is an explanatory argument, and the premise sequent carries down into the conclusion where it appears with the explanatory-argument-denoting turnstile, that is, . The rules for LKΘ defined a class of defeasible consequence relations. We propose that STR captures the stability of explanatory arguments. As we shall now show, STR also guarantees that the class of consequence relations has four of the remaining properties we associate with explanatory arguments: premise consistency, irreflexivity, minimality, and intransitivity.

170  Jared Millson, Kareem Khalifa et al. STR restricts premise sequents to those whose defeater sets contain Λ ⊥ . It follows that if the antecedents of ►-sequents are inconsistent, the sequent is defeated. Sequents of the form are therefore not provable in LEA.10 Undefeated ►-sequents are thus premise-consistent. The STR rule also prevents ►-sequents from being reflexive. It does so by restricting the defeater sets of premise sequents to those which contain the succedent. Sequents of the form are not provable in LEA. Both partial and complete self explanations are thus prohibited from LE►. Less obvious than the achievement of premise-consistency and irreflexivity is the fact that STR also ensures that ►-sequents are minimal in the sense that no logical consequence of the premises of an explanatory argument is explanatory unless it is logically equivalent to those premises. There are four cases to consider in establishing minimality. First, it must be the case that no proper subset of these premises is explanatory (of the same explanandum). Such a scenario is blocked by the fact that the set-theoretic operation S \\ T only removes the elements of T from those elements of S that are supersets of the former. As a consequence, a candidate explanans is never sturdy when one its proper subsets is. Lemma 2. If the sequent

is provable in LEA, then

is not. Second, formulas derived by disjunction introduction from the premises of an explanatory argument must also be blocked. In other words, a disjunctive candidate explanans must never be sturdy when one or more of its disjuncts is a competitor. Lemma 3. If the sequent

is provable in LEA, then

is not. The third and fourth cases cover formulas that are derived by conjunction introduction and double negation, respectively. is provable in LEA if and only if

Lemma 4. is.

is provable in LEA if and only if

Lemma 5. is.

Inferentialist-Expressivism for Explanatory Vocabulary  171 Since these four cases cover all the logical consequences of the premises of an explanatory argument that are not logically equivalent to those premises, the minimality



is thereby established.

Theorem 1. If

are provable in LEA and

Lemma 3 entails that a disjunctive candidate is never sturdy when it must compete against its disjuncts. Unfortunately, without a special constraint, disjunctive competitors would also block their disjuncts from obtaining sturdiness. Fact 1.

 ¬ ({{A ∨ B}} \\ {A}) ∈D (¬A)

In order to prevent this unwanted result, we deploy Disjunction Deletion (Definition 9) in the formulation of STR. Thus, as the following proposition states, a candidate explanans is never forced to compete against a set that contains its disjunction with an arbitrary formula. Proposition 3. If the sequent is the premise in an application of STR, then for any formula B. The provisos on STR are intended to prevent applications of the rule in cases where there is no genuine comparison between a candidate explanans and its competitors—for example, if a candidate explanans were to be smuggled into the background set of a competitor (Γ ⊆ Σ i ) or vice versa (Ωi ⊆ Σ). Similarly, the requirement that the background set of the candidate explanans form a subset of those of its competitors (Σ ⊆ Σi) provides a common set of assumptions against which comparisons can be made. Thus, these provisos provide a level playing field on which candidate explanans may compete for sturdiness. In combination with Definition 10, this last constraint enables the set of competitors to be culled. For instance, one can prevent an antecedent, Ωi , from belonging to S∆ by constructing a background set for the candidate that includes information that defeats the inference from Ωi to ∆. This procedure of culling the competitor set describes how a reasoner goes about holding certain pieces of information, such as those regarding actual causes, “fixed.” We turn now to the ABD rule. As the name suggests, this rule is intended to capture the detachability of the premises of explanatory arguments via abductive inference. Roughly put, ABD says that if Γ and A explain ∆, and Γ ′ provides evidence for ∆, then together, Γ and Γ ′ license the

172  Jared Millson, Kareem Khalifa et al. inference to A. Since A only forms part of the explanatory argument for ∆, we may read ABD as licensing the detachment of a partial explanation of ∆—though still the “best” partial explanation.11 The formulation of the rule thus makes detachability a manifest property of ►-sequents. Several peculiarities of the rule deserve discussion. First, the explanandum (∆) disappears from the conclusion, leaving only the partial explanans. This feature accords with our desire to present IBE in the strongest form possible. If IBE only licensed inferences to best explanations or their explananda, its legitimacy would hardily have roused debate—though its utility might have. Unfortunately, the absence of the explananda in the succedent of ABD’s conclusion means that information is lost in any derivation that contains an application of the rule. The effect, like that of proofs that employ cut, is that proofs in which ABD is applied fail to be analytic—that is, some derivations will contain formulas that are not subformulas of those in the end-sequent. The loss of the subformula property is not all that surprising given the standard characterization of IBE as a form of ampliative inference. We are reassured by the fact that despite this loss, the cut-elimination theorem holds for LEA (Theorem 3). Second, the defeater set attached to the second premise indicates that the inference that entitles us to the explanandum must be nontrivial. This restriction is justified on the grounds that a tautology should never count as evidence for an explanandum’s obtaining. Third, the proviso on ABD prevents the antecedents of the premises from overlapping. This constraint follows from the idea that abductive inferences are only licensed when one has evidence for the explanandum that is independent of the explanans. Note that this means that the second premise of ABD will contain a sequent whose antecedent may have competed with the explanans for sturdiness. This is as it should be, since the competitors include not only potential explanations, but also nonexplanatory, evidential inferences. Finally, in addition to appearing in the succedent of the conclusion, the (partial) explanans also appears in the background set. This feature is consistent with our understanding of these sets as keeping track of formulas that have shifted from the left to the right of the turnstile. We have seen that the provable ►-sequents of LEA exhibit all of the properties associated with explanatory arguments. We therefore propose captures explanatory argumentation. What remains is to show that that we can treat explanatory vocabulary as expressive of these underlying inferences.

5.  LEA+: Introducing the Best Explains Why Operator We shall now demonstrate how the system LEA and the language L    over which it is defined may be extended to include an object-language

Inferentialist-Expressivism for Explanatory Vocabulary  173 expression for best explains why. We begin with the syntax of the extended language L ►. Definition 11 (Syntax of L ►). If A ∈L  then A ∈L ►. If A, B ∈ L then A ► B ∈L ►. The expression “A ► B” is intended to be read as “A best explains why B.” Note that the syntactic definition for ► is not recursive with respect to L ►. Consequently, the operator ► is noniterative. We impose this syntactic constraint on the grounds that, as argued in section 2, the “best explains why” locution does not appear to iterate in natural languages—at least not in English. The rules in table 7.3 define the calculus LEA+ over L ►. While the rules of LKΘ apply to all the formulas in L ►, the rules for LE► are restricted to the fragment L   ∩ L  ►. This restriction is intended to prevent the generation of ill-formed formulas along a derivation, such as A ► (B ► C). Table 7.3  Rules of LEA+

As promised, the extension LEA+ provides introduction (right) and elimination (left) rules for the best-explains-why operator, that is, ►. The ►├ rule ought to be familiar—it is essentially the ABD rule with the abducible formula joined to a member of the succedent of the second premise (i.e., B) by the ►-connective and appended to the antecedent of the conclusion. In fact, the ►├ rule is derivable from ABD and LW. The ├► rule, on the other hand, represents something quite novel. While it resembles the right rule for → in LK, it is distinguished by two features. First, the active formula in the antecedent of the premise occurs in the background set of the conclusion. This peculiarity is justified by the need to preserve undefeatedness upward, much in the way that ├ ¬ does. Second, while the premise is a ►-sequent, the conclusion is not. This feature captures the sense in which formulas whose main operator is ► are explicitly explanatory claims. As such, these claims can enter into reasoning patterns that do not consist in the making of explanatory

174  Jared Millson, Kareem Khalifa et al. arguments, and thus they belong to the class of sequents whose turnstile is unadorned by ►. We are now in a position to make good on our promise to provide an expressivist treatment of explanatory vocabulary. Since the deduction theorem serves as the model for logical expressivist theses, it is incumbent upon us to show that a similar theorem holds in LEA+. As we have argued, any uniform proof theory that formalizes both explanatory arguments and IBE must appeal to two distinct (classes of) consequences relations. It follows that we will not be able to establish a traditional deduction theorem—that is, one that says that an object-language expression makes explicit a rule of inference in the meta-language. Instead, we establish what we can call a quasideduction theorem. Theorem 2 (Quasi-Deduction Theorem).

is provable

in LEA if and only if +

Such a theorem says that an expression used in one logic (that of the unadorned turnstile, ) encodes the rules of another logic ( ). In other words, the theorem tells us that anyone who can reason on the basis of a rule for one type of inference can explicitly undertake a commitment to that rule as the conclusion of another type of inference. Plainly, the quasideduction theorem establishes the expressive role of the ► operator. We now show that LEA+ is a conservative extension of LEA. To do so, we must ensure that any sequent provable in the former that does not contain ► must (already) be provable in the latter. Since the new rules in LEA+ are just those of the ► connective, the only way a new sequent with formulas drawn exclusively from L  might be validated in LEA+ would be through an application of cut to a formula whose main operator is ►. In other words, we need only concern ourselves with proofs in which a formula is cut from the conclusions of ►├ and ├ ►. If the cut-elimination theorem holds for both calculi, then we know that any sequent in LEA+ whose proof involves such an application of cut will have a cut-free proof in LEA. We will therefore demonstrate the conservativeness of LEA+ with respect to LEA by proving cut-elimination. We first prove that the cut-elimination theorem holds for LEA and then extend this result to LEA+. While there is no cut► rule, proofs in LEA contain an application of cut that is not available in LKΘ, namely, one where the cut formula appears in the succedent that follows the application of ABD. Fortunately, the cut-elimination theorem can be extended to cover these cases. Theorem 3. Any sequent provable in LEA has a cut-free proof.

Inferentialist-Expressivism for Explanatory Vocabulary  175 Proof. Lemma 1 gives us cut-elimination for the proofs in LKΘ. The following reduction covers the one application of cut that appears in proofs of LEA that does not appear in proofs of LKΘ.

 By proving that the cut-elimination theorem holds for LEA+, we can show that LEA+ is a conservative extension of LEA. Theorem 4. Any sequent provable in LEA+ has a cut-free proof. Proof. Since Theorem 3 establishes cut-elimination for LEA, we need to show that every application of cut that occurs in proofs of LEA+ but not in proofs of LEA is eliminable. There is only one such application, namely, that which cuts the formula A ► B from the conclusions of ►├ and ├ ►. The following reduction covers this application.

176  Jared Millson, Kareem Khalifa et al.

The conservativeness of LEA+ follows immediately from cut’s eliminability. Corollary 4.1. Every sequent provable in LEA+ that only contains formulas from L  is provable in LEA.

6. Conclusion In this paper, we have argued not only that there is a viable inferentialistexpressivist treatment of explanatory vocabulary, but that its inferential foundation can be given a precise treatment in terms of sequent calculi. While we have not provided formal proofs of the propositions, lemmas, and theorems mentioned above, we hope to have described the system LEA+ in sufficient detail to show that it captures all of the commonly recognized features of explanatory arguments. Even more significantly, LEA+ demonstrates that IBE can be represented by a sequent calculus without treating IBE as a primitive form of inference. Ultimately, the particular scientific arguments licensed by IBE are underwritten by sturdy inferences. The reliability of IBE in a particular usage thus depends entirely on the reliability of the material inferences (proper axioms) from which it derives. This paper has also argued that the language L   can be conservatively extended to L ►, given the rules of LEA+. This means that we can treat “best explains” on analogy with inferentialist-expressivist treatments of the classical deductive operators. This result has important ramifications for the theory of explanation in the philosophy of science. Explanation is not a sui generis feature of scientific practice. Like IBE, explanation derives its power from the underlying scientific inferences.12

Notes  1 Lipton also argues that IBE should construe the best explanation as the “loveliest” explanation, and then vaguely describes “loveliness” as a combination of various “theoretical virtues,” such as simplicity, scope, fit with background belief, etc. While our view does appeal to some superlative— what we call “sturdiness”—it appears to be something quite different than this. A detailed comparison of loveliness and sturdiness exceeds the scope of the current paper.   2 While a nonreflexive system would be one in which the principle of reflexivity fails on at least some occasions, an irreflexive system is one in which no instance of reflexivity holds.

Inferentialist-Expressivism for Explanatory Vocabulary  177   3 In the special case where Σ = ∅, we write: .   4 In Piazza and Pulcini (2017) what we call background sets are simply referred to as repositories. While they play the same technical role, they are not provided with a substantive interpretation.  5 If axioms are restricted to logical axioms where Θ = ∅ and the rules DE and BE are omitted, then the consequence relation characterized by LKΘ is classical.   6 It is well-known that the addition of nontautological axioms to the system of classical logic will lead to inconsistency if those axioms are taken to be closed under universal substitution (US). Even if closure under US is abandoned for proper axioms, their addition to a sequent system such as LK, threatens the cutelimination theorem. Fortunately, Piazza and Pulcini (2016) have shown how to generate nonlogical axiomatic extensions of classical propositional logic that admit cut elimination. While such extensions are obviously not complete—they are post-complete—axioms can be formulated so as to preserve consistency. The trick to doing so is to ensure that the empty sequent does not belong to the set of proper axioms—see Theorem 3.7 in Piazza and Pulcini (2016). Our proper axioms have been formulated in conformity with this constraint.   7 Formal proofs of propositions and lemmas have been omitted for the sake of space. These results, along with proofs of other features of this system, will appear in Millson (forthcoming).   8 By this same reasoning, the cut rule also ought to add the active formula in its premises to the background set of the conclusion. However, the cut rule is exempted on the grounds that such a rule is just a statement about the conditions under which information may be removed from a proof.   9 See Piazza and Pulcini (2016, 19) for an example. 10 Again, while the results here and below admit of proof, formal details have been omitted for the sake of space. Proofs will appear in Millson (forthcoming). 11 Proofs will appear in Millson (forthcoming). 12 Mark Risjord’s work on this chapter was supported by the joint Lead-Agency research grant between the Austrian Science Foundation (FWF) and the Czech Science Foundation (GAČR), Inferentialism and Collective Intentionality, No. I 3068-G24.

References Blackburn, Simon. 1993. Essays in Quasi-Realism. Oxford: Oxford University Press. Brandom, Robert. 1994. Making It Explicit: Reasoning, Representing, and Discursive Commitment. Cambridge, MA: Harvard University Press. Brandom, Robert. 2000. Articulating Reasons: An Introduction to Inferentialism. Cambridge, MA: Harvard University Press. Brandom, Robert. 2008. Between Saying and Doing: Towards an Analytic Pragmatism. Oxford: Oxford University Press. Brandom, Robert. 2015. From Empiricism to Expressivism: Brandom Reads Sellars. Cambridge, MA: Harvard University Press. Dummett, Michael. 1991. The Logical Basis of Metaphysics. Cambridge, MA: Harvard University Press. Gibbard, Allan. 2003. Thinking How to Live. Cambridge, MA: Harvard University Press. Hempel, Carl G. 1965. Aspects of Scientific Explanation: And Other Essays in the Philosophy of Science. New York: Free Press.

178  Jared Millson, Kareem Khalifa et al. Lange, Marc. 2009. “Why Do the Laws Explain Why?” In Dispositions and Causes, edited by Toby Handfield, 286–321. New York: Oxford University Press. Lipton, Peter. 2004. Inference to the Best Explanation. New York: Routledge. Millson, Jared. Forthcoming. “A Logic for Best Explanations.” Mitchell, Sandra D. 2003. Biological Complexity and Integrative Pluralism. Cambridge: Cambridge University Press. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan. Piazza, Mario, and Gabriele Pulcini. 2016. “Uniqueness of Axiomatic Extensions of Cut-Free Classical Propo-Sitional Logic.” Logic Journal of IGPL 24 (5): 708–718. Piazza, Mario, and Gabriele Pulcini. 2017. “Unifying Logics via Context-Sensitiveness.” Journal of Logic and Computation 27 (1): 21–40. Prawitz, Dag. 1965. Natural Deduction: A Proof-Theoretical Study. Stockholm: Almqvist and Wiksell. Reiss, Julian. 2015. Causation, Evidence, and Inference. New York: Routledge. Schroeder-Heister, Peter. 2006. “Validity Concepts in Proof-Theoretic Semantics.” Synthese 148 (3): 525–571. Sellars, Wilfrid. 1957. “Counterfactuals, Dispositions, and the Causal Modalities.” In Minnesota Studies in the Philosophy of Science, Vol. II, edited by Herbert Feigl, Michael Scriven, and Grover Maxwell, 225–308. Minneapolis, MN: University of Minnesota Press. Sellars, Wilfrid. 1963. Science, Perception and Reality. Edited by Robert Colodny. Atascadero, CA: Ridgeview Publishing. Skyrms, Brian. 1980. Causal Necessity: A Pragmatic Investigation of the Necessity of Laws. New Haven: Yale University Press. Woodward, James. 2003. Making Things Happen: A Theory of Causal Explanation. New York: Oxford University Press.

8 Logical Expressivism and Logical Relations Lionel Shapiro

1. Introduction A central motivation for expressivism about logic has been to avoid a view of logical vocabulary as serving to map the layout of a special domain of facts whose bearing on discursive practice remains mysterious.1 Logical expressivists adopt, instead, a pragmatist stance: they seek to explain the role of logical vocabulary in terms of discursive practice. In the form pioneered by Brandom and elaborated and extended by Peregrin, logical expressivism adopts a specific version of this stance. According to both philosophers, logical vocabulary lets us endorse broadly-speaking inferential relations, which are said to hold in virtue of socially instituted norms of discursive practice. Specifically, talk of consequence and incompatibility has such relations as its subject matter. And logical operators, such as conditionals and negation, give us an indirect way to endorse consequence and incompatibility relations. In this chapter, I’ll suggest an alternative version of logical expressivism. On my proposal, logical vocabulary doesn’t serve to let us endorse discursive-practical relations. Rather, it serves to let us express discursivepractical attitudes.2 One upshot will be a different view of the importance of relational locutions such as “is a consequence of” and “is incompatible with.” Brandom and Peregrin give these a central explanatory role: it is in terms of the socially constituted relations attributed using consequence talk and incompatibility talk, they hold, that we must understand the expressive function of logical operators. According to the logical expressivism I’ll propose, by contrast, the relational locutions have no such explanatory role. Indeed, I’ll argue that the expressive role of the relational locutions undermines the plausibility of a reduction of logical relations to socially instituted norms of discursive practice. In the second section, I begin by isolating two theses that are components of Brandomian logical expressivism: implicit-content expressivism and inferential-attitude expressivism. Focusing on conditionals, the third section critically examines the versions of implicit-content expressivism found in Brandom and Peregrin. The fourth section then proposes a ­version of inferential-attitude expressivism that differs from Brandom’s.

180  Lionel Shapiro On the view I sketch there, the expressive role of a logical operator (here the conditional) is explained without invoking any logical relation (thus without invoking consequence). In the fifth section, I turn to logical relations and give a deflationary account of the expressive role of our talk of consequence. The sixth section then argues that this account poses a challenge to an expressivism according to which the function of logical operators is to make explicit socially instituted logical relations.

2.  Two Components of Logical Expressivism Here’s one way Brandom summarizes the substance of his logical expressivism: Logic transforms semantic practices into principles [. . .]. [It] provid[es] the expressive tools permitting us to endorse in what we say what before we could endorse only in what we did [. . .]. (Brandom 1994, 402, emphasis added; cf. Peregrin 2008, 268; 2014, 187) This characterization is ambiguous between two theses, both of which I believe Brandom intends to affirm. Each corresponds to a different way of identifying the kind of item that, in the absence of logical vocabulary, is endorsable only in practice, but that can also be endorsed by stating a principle once logical vocabulary is available.

• On one disambiguation, what can be endorsed implicitly is what

•

Brandom calls a “claimable content” (for example, Brandom 1994, 330). To come to endorse a content “explicitly” (that is, “in what we say”) is simply to come to assert the content. On another disambiguation, what can be endorsed implicitly is, broadly speaking, an inference. To come to endorse an inference “explicitly” (that is, “in what we say”) is to come to endorse it by asserting some claimable content.3

We can thus formulate the theses combined in the quoted passage as follows: Implicit-content expressivism: Logical vocabulary lets us endorse a content explicitly (that is, by asserting that content), a content that we already endorsed implicitly. Inferential-attitude expressivism: Logical vocabulary lets us endorse an inference explicitly (that is, by asserting a content), an inference that we already endorsed implicitly. My aim is to recommend a version of inferential-attitude expressivism. To set the stage, however, I’ll first critically examine the versions of implicit-content expressivism found in Brandom and Peregrin.

Logical Expressivism and Logical Relations  181

3.  Making Explicit a Practice-Endorsed Content To make sense of implicit-content expressivism, we must answer two questions.

• What content does a given piece of logical vocabulary let us endorse •

explicitly? In what sense can this content be implicitly endorsed in what we do?

Consider the case of a conditional sentence. According to one way of answering these questions found in Brandom and Peregrin, the content a conditional sentence lets us endorse is a claim about an inferential relation. Specifically, it’s a claim that there’s a good inference from some premise to some conclusion. And there are two senses in which this claim can be implicitly endorsed. First, one can implicitly endorse the claim by treating premise and conclusion as inferentially related, even if in fact they aren’t so related. (Someone might treat as good the inference from “There was just lightning” to “The gods are angry.”) But according to both Brandom and Peregrin, a second kind of implicit endorsement is more basic. The claim that an inferential relation holds can be endorsed in one’s social practice, in the sense that the practice can make that claim true by instituting the respective inferential relation. Now the good inferences Brandom and Peregrin are concerned with aren’t formally valid; they are “material inferences” such as that between “There was just lightning” and “There will soon be thunder.” These are inferences whose goodness Brandom and Peregrin hold to be partly constitutive of the words “thunder” and “lightning” possessing their conceptual contents (Brandom 1994, 97–98; Peregrin 2014, 26). In what follows, I’ll speak of material consequence instead of goodness of material inference. But Brandom and Peregrin understand material consequence in terms of norms of social practice that qualify as “inferential” in some suitably loose sense—they play some role in constraining, though not prescribing, a process of inferring.4 Understood this way, logical expressivism holds that in asserting a conditional, one states a claim about material consequence, where if one speaks truly this will be a claim one had previously endorsed in virtue of being a user of certain nonlogical concepts, such as those of thunder and lightning. Numerous passages from Brandom support this interpretation: [T]he strategy pursued [. . .] is to focus on the use of logical vocabulary to permit the explicit expression, as the content of sentences, of relations among sentences that are partly constitutive of their being contentful [. . .]. [Conditionals] permit the assertionally explicit expression of material-inferential relations. (Brandom 1994, 401–402)

182  Lionel Shapiro Before introducing [the conditional], one can do something, namely endorse an inference. After introducing the conditional, one can now say that the inference is a good one. (Brandom 2000, 81; also 1994, 22, 108, 115; 2000, 21; 2010, 353; 2008b, 151) Peregrin, too, speaks of a conditional operator as allowing what is already implicit in discursive practice to “find an explicit expression (in the form of a sentence stating that the inference holds)” (Peregrin 2014, 203). Yet, understood this way, the expressivist’s claim about conditionals can’t be correct. First, as Brandom elsewhere notes, asserting a conditional isn’t a matter of using explicitly normative vocabulary. To assert that if p then q isn’t “to say that an act of inferring is permissible” (Brandom 2008a, 46 n). But it also isn’t to affirm a “material-inferential relation” of consequence between the sentences “p” and “q” (or their contents),5 even if that relation is only ultimately understood in normative terms. The reason is a basic one. A conditional isn’t a relational expression: it’s a sentential operator, not a predicate. I conclude that implicit-content expressivism should identify the content endorsed in practice as a conditional claim, not as a claim about a relation of consequence. On this view, a discursive practice—in virtue of instituting a material consequence relation—can implicitly endorse the claim that if there was just lightning, there will soon be thunder. Once practitioners come to deploy a conditional, they are then in a position to endorse this claim explicitly. In what sense, though, might a practice implicitly endorse a conditional claim? An answer is suggested by Peregrin’s discussion. Although a conditional doesn’t state a claim about consequence, a discursive practice can nonetheless ensure that the conditional states a truth by making the corresponding consequence hold. Consider how Peregrin explains the conditional’s expressive role. He writes: “We need a sentence which expresses the fact that B is inferable from A” (Peregrin 2014, 187). Since he has in mind a conditional sentence, I’ll assume that “expressing” the fact about inferability doesn’t mean stating that relational fact itself, but rather stating a suitably related conditional content. He continues: “But what does it take for a sentence [of the object language] to express this? Presumably to be true if and only if B is inferable from A.” We now have a way to understand a conditional A ⇒ B as stating a claim endorsed by the discursive practice in which sentences A and B are used:6 (*) A ⇒ B states a claim that’s true if and only if B is a material consequence of A.7

Logical Expressivism and Logical Relations  183 Recall that Peregrin is interested in a consequence relation that’s ­meaning-constitutive. Suppose that ⇒ meets his condition (*) for expressing such consequence. Then it had better not be the conditional of classical or intuitionistic logic. Where → is one of those conditionals, A → B will be true if B is true. But Peregrin isn’t willing to allow that each true sentence is a meaning-constitutive consequence of every other sentence (Peregrin 2014, 196–197). So the conditional ⇒ that “does the expressive work” by satisfying (*) must be a different one. Perhaps, he suggests, it will be a strict conditional definable using a modal operator, so that A ⇒ B is (A → B).8 In what follows, I’ll assume that the conditional operator under discussion satisfies condition (*).9 Drawing on Peregrin, I have arrived at what I think is the best formulation of implicit-content expressivism about conditionals. In at least two ways, this view gives priority to consequence talk over conditionals. First, the purpose of the conditional is one that would be served more perspicuously using a consequence predicate.10 This calls to mind Carnap’s account of the relation between claims of logical consequence (“L-consequence”) and corresponding object-language conditionals (Carnap 1934, § 63, § 69). According to Carnap, a language can have a binary sentential operator “LImp” such that “LImp(A, B)” is inferentially equivalent to the consequence predication “ ‘B’ is an L-consequence of ‘A’.” Yet the former conditional is said to be a “quasi-syntactical sentence,” whose role would be played more perspicuously by the latter, its “correlated syntactical sentence.” We can put this in Carnap’s “material mode”: such a conditional serves as a convenient means for talking indirectly about consequence. Likewise, according to the content-expressivist version of logical expressivism under discussion, conditionals serve as a convenient means for talking indirectly about material consequence. Here’s another way to explain how consequence locutions enjoy priority over conditional operators according to Brandom and Peregrin: consequence talk plays an explanatory role in their accounts of the function of the corresponding conditional operator. In the rest of the chapter, I’ll argue against giving consequence locutions priority over operators. Let’s start by considering how Brandomian logical expressivism understands material consequence as something that can bear explanatory weight: namely, as a relation that obtains in virtue of a structure of norms governing a discursive practice. Suppose we grant a sense (however vague or context-sensitive) in which “There will be thunder soon” is a consequence of “There is lightning now.” Should we agree with Brandom and Peregrin that this holds in virtue of norms of social practice? For an initial sense of why I think we should be skeptical, it should help to compare the relation of material consequence with the property of truth. Unlike Brandom, Peregrin accepts an analysis of truth in

184  Lionel Shapiro terms of meaning-constitutive rules (Peregrin 2014, 83, 236). He cites with approval Sellars’ claim that to be true is “to be assertible [. . .] in accordance with the relevant semantical rules, and on the basis of such additional [. . .] information [namely, about empirical circumstances] as these rules may require” (Sellars 1967, 101). Against such views, I would urge, adapting a remark by Quine (1953, 437), that the “notion of truth is a far less dubious starting point” than any notion of semantic rule in terms of which one might seek to explain truth.11 As I’ll discuss later, Quine’s doubts are substantiated by his subsequent “deflationary” account of the expressive function served by a truth predicate.12 Now I believe that what I’ve said about truth and semantic correctness goes equally for material consequence and inferential correctness. The claim that “There will be thunder soon” follows from “There is lightning now” strikes me as a far less dubious starting point than any claim about what’s correct or incorrect according to socially instituted inferential norms. And just as in the case of truth, I’ll argue that the reason can be seen once we examine the expressive role of the predicate “follows from” (or “is a material consequence of”). For the time being, I hope to have made it worth asking this chapter’s key question, which is as follows. Can there be a version of logical expressivism that not only follows Brandom in rejecting explanations of truth in terms of social-practical correctness, but also rejects explanations of material consequence in terms of social-practical correctness?13

4.  Making Explicit One’s Endorsement of an Inference For this purpose, I turn now to a different way of understanding how logical vocabulary makes explicit something implicit in what one does. According to inferential-attitude expressivism, what asserting a conditional makes explicit is one’s endorsing of an inference. This is certainly a claim Brandom makes: Saying that if something is copper then it conducts electricity is a new way of doing—by saying—what one was doing before by endorsing the material inference from “That is copper” to “That conducts electricity” [. . .]. Where before one could only in practice take or treat inferences as good or bad, after the [. . .] introduction of conditionals one can endorse or reject the inference by explicitly saying something. (Brandom 2008a, 45–46) [Introducing conditionals] will let one say something, the saying of which is taking some inferences to be good and other ones not good. (Brandom 2008a, 47)14

Logical Expressivism and Logical Relations  185 Understood this way, logical expressivism explains the role of conditionals using a sense of “express” distinct from what Sellars calls the “logical (or semantical) sense” in which what is expressed is a content (Sellars 1969, 521). Rather, the relevant sense of “express” is a pragmatic one.15 By asserting a conditional that semantically expresses a certain content, one pragmatically expresses one’s endorsing of an inference. Brandom points out the connection to Ryle’s account of conditionals as “inference licenses” (Brandom 2008a, 104; Ryle [1950] 2009).16 In explaining the function of some target vocabulary in terms of a pragmatic sense of expressing, inferential-attitude expressivism stands in the tradition Price (2011a) calls “Humean expressivism” (and also resembles the “neo-expressivism” of Bar-On 2004).17 Compare a Humean expressivist who holds that when one asserts that a thing is good, what one is doing is expressing one’s valuing of it. Such a theorist isn’t explaining the assertion as the endorsement of a content whose truth is determined by facts about what the asserter, or anyone else, values (or should value). Similarly, if asserting a conditional expresses one’s endorsing of an inference, this needn’t mean that the conditional’s truth is determined by facts about the inferential attitudes anyone has (or should have). However, Brandom’s version of inferential-attitude expressivism won’t do for my purposes. The problem concerns the practical attitudes expressed by conditionals. According to Brandom, to endorse an ­inference—to “treat [it] as good”—is to attribute to practitioners that constellation of normative statuses in which, on Brandom’s theory, material consequence consists. Going this route would open up inferentialattitude expressivism to the doubts I raised earlier. But I see no reason why an explanation of the role of conditionals in endorsing inferences must describe the asserter of a conditional as implicitly affirming any relation of consequence. What, then, do I mean by endorsing an inference? Here’s a rough sketch. Following Brandom (1994), I’ll conceive of discursive practice as a “game of giving and asking for reasons” in which practitioners undertake commitments to defend their assertions in response to appropriate challenges. Again like Brandom, I propose that the conditional I’m describing makes explicit something essential to participation in any such game (Brandom 2008a, 53, 26). In asserting “If p, then q,” I suggest, a speaker of English (here “the subject”) expresses dispositions that are manifested as follows in an exchange with an interlocutor:18

• when an interlocutor has challenged the subject’s assertion that q, the •

subject treats her own adducing of a warranted assertion that p as meeting that challenge,19 when the subject has challenged an interlocutor’s assertion that q, she treats that interlocutor’s adducing of a warranted assertion that p as meeting her challenge,20

186  Lionel Shapiro

• when an interlocutor has asserted that p, the subject treats her own •

rejection of the claim that q as challenging that interlocutor’s assertion, and when the subject has asserted that p, she treats an interlocutor’s rejection of the claim that q as challenging her own assertion.

Furthermore, in virtue of asserting the conditional, the speaker licenses hearers to do likewise, on the asserter’s authority. Crucially, however, this needn’t mean that the asserter regards manifesting the above-described dispositions as in any sense correct for a participant in the linguistic practice. Consider one of Brandom’s favorite examples (Brandom 1994, 634). Suppose I assert, speaking about a certain tractor, “If this tractor is completely green, then it is made by John Deere.” And suppose that, in an unrelated conversation, Barack Obama asserts that the tractor in question is completely green. I need not, merely in virtue of having asserted my conditional, take it to be correct, in any sense, for Obama to treat his interlocutor’s rejection of the claim that the tractor is made by John Deere as a way to challenge his assertion. To see this point, it should help to compare assertion in general. On the Brandomian view adopted here, in asserting that p, I license my hearers to assert that p. But that doesn’t give rise to any sense in which I must regard the proposition that p as correctly assertible by speakers of my language. I have now sketched an account of the expressive role of a conditional that agrees with Brandom and Peregrin in viewing the conditional as making explicit something implicit in any discursive practice. To flesh out this proposal, I would need to discuss other logical operators, but space doesn’t allow that here. Instead, I’ll turn to logical relations, specifically material consequence.

5.  The Function of Consequence Talk Unlike Brandomian logical expressivism, the approach I’ve proposed doesn’t start with a relation of material consequence, instituted by a social practice. What, then, can I say about material consequence, about the sense in which “There will soon be thunder” follows from “There was just lightning”? Ryle, whose view of conditionals as inference licenses we have been developing, asks: “But just how does the [material] validity of the argument require the truth of the hypothetical statement [that is conditional]?” (Ryle [1950] 2009, 247). Though he never explicitly answers his question, his idea seems to be that for a single-premise inference to be correctly performed (the “conclusion [. . .] legitimately drawn from the premiss”), the conditional that would license it must be true. I’ll argue that we can maintain a Ryleian view of conditionals without understanding

Logical Expressivism and Logical Relations  187 validity/consequence in terms of correctness of inference. This requires a radically different answer to Ryle’s question. Here I think the key move is to turn away from asking what material consequence consists in, and instead pose the more expressivist question: what is the expressive role of consequence locutions? What purpose do they serve in our linguistic practice?21 To answer this, let me start by considering locutions that express a relation of single-premise material consequence between claimable contents. Elsewhere (Shapiro 2011), I have argued that there would be no need for consequence talk if it weren’t for our need to express certain kinds of generalizations.22 In place of “The claim that there will soon be thunder is a material consequence of the claim that there was just lightning,” we could use a conditional “If there was just lightning, then there will soon be thunder.” What consequence locutions allow us to do is to achieve the effect of quantifying into sentence position by instead quantifying over contents or their bearers. Thus we can formulate generalizations such as (a) She denied a material consequence of something he asserted. (b) If a claim is a material consequence of each of two other claims, then it is a material consequence of their disjunction. Claim (a) can take the place of an existential generalization over all sentences of the form “He asserted that p, and she denied that q, and if p then q.” Claim (b) can take the place of a universal generalization over all sentences of the form “If it’s the case that if p then r and it’s also the case that if q then r, then it’s the case that if p or q then r.” Next, consider multipremise consequence locutions. Again, if it weren’t for our interest in expressing generalizations, we could make do with conditionals with conjunctive antecedents. In place of “The claim that a rainbow can be seen is a joint material consequence of the claims that it’s raining and that the sun is shining” we could say “If it’s raining and the sun is shining, then a rainbow can be seen.” But multipremise consequence talk lets us formulate lots of useful generalizations, which we can then subject to critical assessment. Here are three examples: (c) What Brandom claims follows from something said by Kant together with something said by Sellars. (d) One ought to believe the joint consequences of any set of claims one believes. (e) If claim Q follows from claim P together with the claims in set X, and P follows from the claims in set Y, then Q follows from the claims in the union of X and Y. (This is a version of the cut rule.)23 Let me contrast this proposal with what Peregrin says about the relation between conjunction and multipremise consequence. According to him,

188  Lionel Shapiro an important expressive role of conjunction lies in allowing us to talk indirectly about what follows from a number of premises taken together. By asserting the conditional (A ∧ B) ⇒ C, I can make explicit what’s implicit in (the claim expressed by) C’s being a consequence of (the claim expressed by) A taken together with (the claim expressed by) B.24 Peregrin describes conjunction as an operator that serves as “amalgamator” for premises. It does so by satisfying the principle (Am) For all sentences A, B, and C, and every set X of sentences, X, A ∧ B ⊢ C if and only if X, A, B ⊢ C.

Here ⊢ is used to express the relation of material consequence that can obtain between a set of premises and a conclusion. Peregrin also suggests a second way conjunction makes explicit structural features of consequence. He says that it “marks” or “reveals” a relational feature a sentence possesses considered as an element of an “inferential structure,” namely the feature of being an “inferential supremum.” Here’s one way of understanding Peregrin’s claim: by asserting the biconditional (A ∧ B) ⇔ C, I make explicit in the form of an assertion what’s already implicit in C’s being an inferential supremum for the sentences A and B. This explicitation will be possible provided conjunction satisfies the principle (Sup) For all sentences A and B and every set X of sentences, X ⊢ A ∧ B if and only if both X ⊢ A and X ⊢ B.

According to Peregrin, then, Došen (1989, 366–367) is right that conjunction as well as the conditional are operators that serve as “a kind of substitute in the object language” for talk of consequence and its “structural features.”25 My proposal inverts the perspective of Došen and Peregrin. I have argued that our talk of consequence (and its structural features) has as its expressive role allowing us to formulate generalizations over sentences involving certain operators. In particular, the expressive role of talk about a claim being the consequence of several premises taken together lies in allowing generalization over conditionals with conjunctions as antecedents. The biconditional (Am) doesn’t explain the expressive role of conjunction. Instead, it explains how the multipremise consequence locution X ⊢ A can play its expressive role.26 The biconditional (Sup) then makes use of this expressive role. Let me pause to deflect an objection. Since I’m characterizing the role of consequence talk as lying in how it lets us generalize over conditionals, it would be accurate to say, using Brandom’s words, that my proposal “trades primitive goodnesses of inference for the truth of conditionals.” And that’s precisely what Brandom says is done by the “formalist

Logical Expressivism and Logical Relations  189 approach to inference” he himself convincingly criticizes (Brandom 1994, 98, 112). But my proposal doesn’t in fact involve the formalist idea that’s the target of Brandom’s criticism. This is the idea that the material entailment from “There was just lightning” to “There will soon be thunder” must be accounted for in terms of a formal consequence involving as an additional premise the conditional “If there was just lightning then there will soon be thunder.” On the current proposal, the connection between conditionals and inferences isn’t explained in terms of the role of conditionals as premises in inferences. Rather, just as on Brandom’s own Ryleian approach, conditionals serve to let us express our endorsing of inferences.

6.  Consequence as a Merely Logical Relation I can now explain why I’m skeptical about a logical expressivism according to which logical operators serve to indirectly talk about material consequence, understood as a socially instituted relation. This is because the above explanation of the expressive role of consequence talk gives reason to doubt that consequence is such a relation. Here I draw on an analogy with deflationism about truth proposed in Shapiro (2011). According to the brand of deflationism I find attractive, the functions that give the predicate “true” its raison d’être are very limited.

• We use “true” to semantically express generalizations that achieve •

the effect of quantification into sentence position, for example, “None of his claims about Russia are true.”27 We use “true” to pragmatically express something essential to our ability to ascribe claimable contents in the first place. That is our disposition to conclude that p on the basis of our taking our informant to have asserted the claim that p, a disposition we express when we assert “What she claimed is true.”28

To understand how the predicate “true” serves each these functions, it’s enough to know that for all sentences S in our language, freestanding or logically embedded, (T) S can be replaced by “the claim that S is true,” or vice versa, with no effect on the game of giving and asking for reasons. I agree with deflationists, including Brandom, that there’s little reason to think (T) requires that there will be any features shared by all and only truths that explain their being true. In particular, there seems no reason to expect a connection between a predicate’s behaving according to (T) and its attributing the property of being correctly assertible according to

190  Lionel Shapiro certain socially instituted rules. There’s no reason to think the “logical property” of truth (Horwich 1998, 37) will turn out to be a socio-­ linguistic property.29 As for the predicate “is a material consequence of,” I’ve argued that its role can be completely understood in terms of how consequence talk allows expression of generalizations over conditionals. To understand how “is a consequence of” serves this function, it’s enough to know that for all sentences S and R in our language, freestanding or logically embedded, (C) “If S then R” can be replaced by “the claim that R is a material consequence of the claim that S,” or vice versa, with no effect on the game of giving and asking for reasons. Again, there seems no reason to expect any connection between a predicate’s behaving according to (C) and its attributing a socially instituted normative relation. Nothing about this account of how “is a material consequence of” serves its function suggests there will be interesting features shared by just the pairs of claims that stand in the relation of consequence beyond their standing in that relation. Material consequence appears to be a “merely logical relation” rather than a socio-linguistic one.30 Furthermore, though I can’t argue this here, I would suggest that the same holds for material incompatibility.

7. Conclusion As I hope to have shown, logical expressivism as advocated by Brandom and Peregrin combines two important lines of thought. The first is familiar from discussions of logic, the second from areas such as metaethics. (1) Logicians talk about which features of object language expressions, as specified by the theorist using a metalanguage, can be “expressed in the object language.” For example, it’s said that for many threevalued logics, the property of being untrue fails to be expressed by any operator. (2) “Expressivists” about normative and modal locutions stress “the practical role they play in our lives” (Price 2011a). For example, normative vocabulary may let us express our plans and epistemic modals let us express our leaving possibilities open in inquiry and action (Gibbard 2003; Yalcin 2011). As Brandom and Peregrin develop logical expressivism, it contributes to tradition (2) by exploiting tradition (1). Peregrin writes that “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 a ­language—that is within a metalanguage” (Peregrin 2008, 269).31

Logical Expressivism and Logical Relations  191 I have argued for an understanding of logical vocabulary that contributes to tradition (2) independently of (1). This is a logical expressivism on which logical operators don’t serve to internalize features of a discursive practice. To be logical expressivists, we shouldn’t say that logical operators serve to express in the object language the obtaining of logical relations. Instead, we should adopt the deflationist strategy of explaining talk of logical relations as a mere device of generalization, and focus attention on explaining the role of logical operators in terms of the discursive attitudes these let us express.32

Notes   1 See esp. Peregrin (2014, 215; 2000, 87–88) and Brandom (1994, 108; 2000, 19 ff).   2 As will be explained, the logical expressivism I’m proposing is in the tradition called “Humean expressivism” by Price (2011a).  3 The ambiguity sometimes leads to conflation. Thus Brandom (2002, 9) explains that on his “expressive view of the function of logic, the task characteristic of logical locutions as such is to let us say, in the form of explicit claims, what otherwise we could only do—namely endorse some material inferential relations and reject others.” Yet “endorse [. . .] inferential relations” isn’t something that we can “say” as well as “do.” Rather, we can come to do this by asserting something else, a claimable content.   4 Brandom characterizes “relations of material consequence and incompatibility” as “inferential relations” (Brandom 2011, 32), and Peregrin says that “to be correctly inferable from is nothing other than to be a consequence of ” (Peregrin 2014, 152–153). He explains that the “crucial role of rules with respect to our linguistic conduct is not prescriptive [. . .] but rather restrictive; rules tell us what not to do, what is prohibited” (Peregrin 2014, 72). In a sympathetic reconstruction of Hegel’s thought, Brandom too identifies material consequence with inferential propriety: “What it is for one proposition to stand in a relation of implying or entailing another just is for certain inferential moves and not others to be correct or appropriate.” These correctnesses “constrain what we should do without determining it” (Brandom 2002, 192, 194).   5 Brandom sometimes says conditionals state relations between claimable contents rather than content-bearers: “Conditionals assert explicitly that one thing that can be said follows from another thing that can be said, that the one is a consequence of the other” (Brandom 2008a, 46 n; also 1994, xix; 2011, 208 n).   6 Here, as in other contexts where the language being considered is a formally regimented one (containing, for example, arrows), italics serve as my device of quasi-quotation. Where the language is English, ordinary quotation marks will serve the same purpose.   7 If facts about material consequence are contingent, we should additionally require that the biconditional (*) would hold in any possible circumstance. Peregrin appears to deny that material consequence is contingent (Peregrin 2014, 187), but he may have in mind a relation between contents, not content-bearers (cf. Peregrin 2014, 249 n. 12).   8 Peregrin also writes that if A → B isn’t what “does the expressive work,” that work may instead be done by ⊢ A → B. Elsewhere, he defends this by saying

192  Lionel Shapiro that “the counterpart of necessary truth within the structure [on which ⊢ is defined] is clearly theoremhood” (Peregrin 2014, 187). Yet ⊢ A → B isn’t a sentence in the language of A and B; theoremhood of A → B would presumably be expressed in that language using (A → B). Anticipating logical expressivism, Došen (1989, 375; 1980, 284–285) gives a similar explanation of what it means for a conditional → to “serve to make explicit” a consequence relation that’s “implicit in the activity of making deductions.” He too argues that this is captured by the equivalence of ⊢ A → B with A ⊢ B. However, Došen’s explanation of how the equivalence yields an “analysis” of → in terms of ⊢ doesn’t help me understand what he means by making explicit.  9 Interestingly, such a ⇒ won’t count as what Peregrin calls a “deductor.” A deductor ⊳ is required to satisfy the condition that X, A ⊢ B if and only if X ⊢ A ⊳ B. Assuming reflexivity and weakening, as Peregrin does, this yields that B ⊢ A ⊳ B. Suppose B is true. If the consequence-expressing ⇒ is a deductor, then A ⇒ B is true, which by (*) implies that B is a consequence of A, for any A. But Peregrin wouldn’t concede this when B is a contingent truth. 10 See Weiss (2010, 249), who, however, assumes that such a predicate would have to belong to a metalanguage distinct from the object language the predicate is used to talk about. One ground for that conclusion might be the threat of a form of Curry’s paradox—for a discussion and response, see Shapiro (2011). Even if the consequence predicate did have to belong to a distinct metalanguage, however, the metalanguage could still contain the object language whose inferential relations it describes. 11 Quine’s target is the notion of analyticity. 12 Quine (1970). Brandom’s position on truth is deflationary as well (Brandom 1994, chap. 5). For critiques of Sellars’ definition of truth, see Williams (2016) and Shapiro (forthcoming). 13 I don’t mean to deny that there are normative facts about inference—no doubt there are several sorts of inferential propriety. Rather, I’m skeptical that there is any close connection between such goodnesses and a relation of material consequence that holds whenever a corresponding conditional is true. 14 What looks like implicit-content expressivism may sometimes be a notational variant of inferential-attitude expressivism. Consider the claim that in endorsing some inference, someone implicitly endorsed the claim that if p then q. Understood one way, this just means they did something that could also be done by asserting that if p then q. This may explain why Brandom, immediately following one of the above statements of inferential-attitude expressivism, adds this statement of implicit-content expressivism: “What the conditional says explicitly is what one endorsed implicitly by doing what one did” (Brandom 2008a, 46). 15 On semantic and pragmatic senses of “express,” see also Bar-On (2004). 16 Brandom has recently criticized Sellars’ accounts of ontological and modal discourse for “running together pragmatic issues, of what one is doing in saying something, with semantic issues of what is said thereby” (Brandom 2015, 267, 190). I am proposing that logical expressivism too benefits from the kind of separation Brandom urges. 17 Price applies this approach to negation (Price 2011b, 69–72) and conditionals (Price 2011b, 83). He argues that Humean expressivism is compatible with, indeed supports, Brandom’s account of discursive practices. The logical expressivism I will recommend here is a Humean expressivism that conflicts with Brandom’s views. See Field (2015) for a very different version of

Logical Expressivism and Logical Relations  193 Humean expressivism applied to an item of logical vocabulary, namely the predicate “logically valid.” 18 The asserter expresses these dispositions in the sense that the act of asserting the conditional has as a function to convey to hearers that the speaker is so disposed. 19 Here the assertion that p may be by the speaker herself or by someone else, though in the former case only when “p” is distinct from “q.” 20 Again, the assertion that p may be by the interlocutor or by some other speaker, though in the former case only when “p” is distinct from “q.” 21 Ryle, by contrast, writes: “I have said nothing about statements of the kind “ ‘p’ entails ‘q’ or ‘q’ does (or does not) follow from ‘p’.” Such locutions are used (roughly) not by the players in the field but by the spectators, critics and selectors in the grandstand. They belong to the talk of logicians, crossexaminers, and reviewers” (Ryle [1950] 2009, 259–260). If I am right, examining such talk is key to answering Ryle’s question, from the grandstand, about how an argument’s validity requires the truth of the corresponding conditional. 22 That paper concerns logical consequence, but the application to material consequence is immediate. 23 In Shapiro (2015), I argue that it’s in claims like these that consequence talk comes into its own as an expressive resource. 24 Peregrin (2014, 189–193, 201–203); see already Peregrin (2003; 2008). Brandom makes the same point: “Indeed, I would say that making it possible to make explicit multipremise inferences is the principal expressive role characteristic of conjunction” (Brandom 2010, 354). 25 Depending on the structural features of ⊢, a connective ∧am serving the expressive role underwritten by (Am) may exhibit a different logical behavior from a connective ∧sup serving the expressive role underwritten by (Sup). For example, if ⊢ is noncontractive, A ⊢ A ∧sup A but A ⊬ A ∧am A. Here ∧am is so-called “multiplicative” conjunction and ∧sup is “additive” conjunction. See Sambin et al. (2000). 26 (Am) only suffices to explain this for finite X. The expressive role of infinitepremise consequence locutions can then be understood in terms of a truth predicate: they allow us to generalize over conditionals whose antecedents say that all the members of a set are true. 27 This is the function pointed out by Quine (1970, 10–12). 28 I have argued elsewhere that this non-Quinean idea is suggested by Sellars’ discussions of the function of content ascriptions (Shapiro 2014). 29 Here I’ve been talking about the truth of claimable contents (or propositions). The truth of utterances, or sentences-in-context, won’t be a merely logical property: it will be the semantico-logical property of expressing a true content. 30 One might wonder in what sense, on the view I’ve criticized, material consequence between propositional contents (rather than linguistic content-bearers) is a socio-linguistic matter. An answer would be that constitutive of the identity of such contents are the inferential norms a practice would have to display in order to express those contents. This is compatible with holding that the material consequence relation between the contents obtained prior to the existence of any such practice. 31 Another position of this sort is Thomasson’s explanation of the expressive function of modals like “necessarily” (Thomasson 2013). She holds that modals “convey semantic rules in the object language, under conditions of

194  Lionel Shapiro semantic descent, rather than stating them in a metalanguage” (Thomasson 2013, 148). And the modal sentence that conveys such a rule is said to be correctly asserted just in case the rule in fact holds of the language. 32 I am very grateful to Jaroslav Peregrin for discussion and criticism over the years. For helpful feedback, I thank the participants of the conference Why Rules Matter, especially Pavel Arazim and Matej Drobňák. Part of this work was done while I was supported by a fellowship from the Alexander von Humboldt Foundation.

References Bar-On, Dorit. 2004. Speaking My Mind: Expression and Self-Knowledge. Oxford: Oxford University Press. Brandom, Robert. 1994. Making It Explicit: Reasoning, Representing, and Discursive Commitment. Cambridge, MA: Harvard University Press. Brandom, Robert. 2000. Articulating Reasons: An Introduction to Inferentialism. Cambridge, MA: Harvard University Press. Brandom, Robert. 2002. Tales of the Mighty Dead: Historical Essays in the Metaphysics of Intentionality. Cambridge, MA: Harvard University Press. Brandom, Robert. 2008a. Between Saying and Doing: Towards an Analytic Pragmatism. Oxford: Oxford University Press. Brandom, Robert. 2008b. “Responses.” Philosophical Topics 36 (2): 135–155. Brandom, Robert. 2009. Reason in Philosophy: Animating Ideas. Cambridge, MA: Harvard University Press. Brandom, Robert. 2010. “Reply to Bernhard Weiss’s ‘What Is Logic?’.” In Reading Brandom, edited by Bernard Weiss and Jeremy Wanderer, 353–356. Abingdon: Routledge. Brandom, Robert. 2011. Perspectives on Pragmatism: Classical, Recent, and Contemporary. Cambridge, MA: Harvard University Press. Brandom, Robert. 2015. From Empiricism to Expressivism: Brandom Reads Sellars. Cambridge, MA: Harvard University Press. Carnap, Rudolf. 1934. Logische Syntax der Sprache. Berlin: Springer. Došen, Kosta. 1980. “Logical Constants: An Essay in Proof Theory.” PhD diss., University of Oxford. Došen, Kosta. 1989. “Logical Constants as Punctuation Marks.” Notre Dame Journal of Formal Logic 30 (3): 362–381. Field, Hartry. 2015. “What Is Logical Validity?” In Foundations of Logical Consequence, edited by Colin Caret and Ole Hjortland, 33–70. Oxford: Oxford University Press. Gibbard, Allan. 2003. Thinking How to Live. Cambridge, MA: Harvard University Press. Horwich, Paul. 1998. Truth. 2nd ed. Oxford: Oxford University Press. Peregrin, Jaroslav. 2000. “The ‘Natural’ and the ‘Formal’.” Journal of Philosophical Logic 29 (1): 75–101. Peregrin, Jaroslav. 2003. “Logic as ‘Making It Explicit’.” In Logica Yearbook 2003, edited by Libor Běhounek, 209–226. Prague: Filosofia. Peregrin, Jaroslav. 2008. “What Is the Logic of Inference?” Studia Logica 88 (2): 263–294. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan.

Logical Expressivism and Logical Relations  195 Price, Huw. 2011a. “Expressivism for Two Voices.” In Pragmatism, Science and Naturalism, edited by Jonathan Knowles and Henrik Rydenfelt, 87–113. Frankfurt a.M.: Peter Lang. Price, Huw. 2011b. Naturalism without Mirrors. Oxford: Oxford University Press. Quine, Willard Van Orman. 1953. “Mr. Strawson on Logical Theory.” Mind 62 (248): 433–451. Quine, Willard Van Orman. 1970. Philosophy of Logic. Cambridge, MA: Harvard University Press. Ryle, Gilbert. 2009. “ ‘If,’ ‘So,’ and ‘Because’.” In Collected Essays 1929–1968, 244–260. Abingdon: Routledge. Original edition, 1950. Sambin, Giovanni, Giulia Battilotti, and Claudia Faggian. 2000. “Basic Logic: Reflection, Symmetry, Visibility.” Journal of Symbolic Logic 65 (3): 979–1013. Sellars, Wilfrid. 1967. Science and Metaphysics: Variations on Kantian Themes. London: Routledge and Kegan Paul. Sellars, Wilfrid. 1969. “Language as Thought and as Communication.” Philosophy and Phenomenological Research 29 (4): 506–527. Shapiro, Lionel. 2011. “Deflating Logical Consequence.” Philosophical Quarterly 61 (243): 320–342. Shapiro, Lionel. 2014. “Sellars on the Function of Semantic Vocabulary.” British Journal for the History of Philosophy 22 (4): 792–811. Shapiro, Lionel. 2015. “Naive Structure, Contraction and Paradox.” Topoi 34 (1): 75–87. Shapiro, Lionel. Forthcoming. “Sellars, Truth Pluralism, and Truth Relativism.” In Sellars and Twentieth-Century Philosophy, edited by Stefan Brandt and Anke Breunig. London: Routledge. Thomasson, Amie. 2013. “Norms and Necessity.” Southern Journal of Philosophy 51 (2): 143–160. Weiss, Bernhard. 2010. “What is Logic?” In Reading Brandom: On Making It Explicit, edited by Bernhard Weiss and Jeremy Wanderer, 247–261. Abingdon: Routledge. Williams, Michael. 2016. “Pragmatism, Sellars, and Truth.” In Sellars and his Legacy, edited by James O’Shea, 223–260. Oxford: Oxford University Press. Yalcin, Seth. 2011. “Nonfactualism about Epistemic Modality.” In Epistemic Modality, edited by Andy Egan and Brian Weatherson, 295–332. Oxford: Oxford University Press.

9 Propositional Contents and the Logical Space Ladislav Koreň

1. Introduction Robert Brandom’s formulation of the inferentialist doctrine advances a number of bold claims. One of them is that logical vocabulary has a distinctive expressive role to play in linguistic practice (see Brandom 1994, chap. 2, and 2000, chap. 1). It serves to make explicit, in the content of claims, material-inferential proprieties implicitly governing use of nonlogical expressions within discursive practices of making, challenging, and justifying claims. Such proprieties confer conceptual contents on performances and expressions playing suitable roles in those practices. Consequently, rather than contributing to the inferential articulation of the contents of nonlogical expressions, logical devices elaborated from a basic prelogical layer of language presuppose and explicate them. In this chapter, I elaborate a challenge to this account of logic and its relation to prelogical discourse. I start by situating it in a wider context of Brandom’s inferentialism. Next I turn to Jaroslav Peregrin’s (2014) development of the inferentialist approach, which contains a line of reasoning that flirts with an alternative conception of logic. According to it, logical devices contribute to constituting the very space of reasons relative to which full-fledged propositional contents are articulated. This conflicts with Peregrin’s “official” endorsement of the expressive conception of logic. My dialectical goal is to show that this specific tension in Peregrin’s view of logic points to a deeper problem in the inferentialist approach. I presume that Brandom and Peregrin are committed to the view that fullfledged conceptual contents materialize in discursive practices of giving and asking for reasons governed by socially articulated inferential norms instituting a dimension of correctness. To establish such norm-governed practices, I submit, practitioners must be able to make it sufficiently manifest to one another what inferentially articulated commitments they undertake and attribute, and hence what utterances and inferential moves they endorse or reject. Approaching this issue in the spirit of a conjectural genealogy, I argue the following: without some expressive tools for bringing it into the open that something is endorsed (or rejected) as a reason for (or against) something else, prelogical communicative practices could be

Propositional Contents and the Logical Space  197 in key pragmatic respects too ambiguous across practitioners-­interpreters to provide for intersubjective norms governing shared practices of giving and asking for reasons, hence constituting propositional contents. Having these conjectural considerations and conclusion in place, I finally discuss its ramifications for the explicitating role of logic.

2. Discursive-Inferential Articulation of Conceptual Contents Sapient creatures think and reason in a propositional mode. For inferentialists, sapience is primarily exemplified in a language-mediated social practice of communication and mutual interpretation (cf. Brandom 1994, 2000, 2008a, 2010a; and Peregrin 2014). To understand sapience, we are thus well advised to ask what structure a social practice must have for it to be linguistic. At a minimum, Brandom says, the practice must incorporate discursive performances with the pragmatic significance of claims. For this to be the case, some performances must come to play a specific normative-functional role in the economy of the practice: being treated by practitioners (a) as potential premises that, together with other claims, make it appropriate to make some further claims (and inappropriate to make other claims) and (b) as something for which justificatory demand might be in order to be discharged in a like manner. To be a claim is essentially to be something that can provide reasons for other claims (or actions) and for which reasons can be provided in turn, since its justification is “always potentially at issue” (Brandom 2000, 193). Declarative sentences serve as vehicles for such discursive moves apt to play the role of a premise or conclusion in inferences. And propositional contents are essentially claimable contents expressible by (uses of) such sentences. Based on such considerations, inferentialists allege that practices of giving and asking for reasons (PGAR) form the core of any linguistic practice. Accordingly, their semantics approaches language primarily in its role of a vehicle of PGAR. At the most basic level, it is viewed as a system of declarative sentences whose contents can be reconstructed in terms of relations of inferability and incompatibility, provided these incorporate material relations of inferability and incompatibility, as well as proprieties governing non-inferential language-entry transitions and practical language-exit transitions issuing into action. Inferential relations, understood in this liberal sense, determine the inferential potential of sentences. And contents of expressions in general can then be accounted for as their specific contributions to inferential potentials of sentences in which they occur as ­components—that is, their inferential roles.1 Brandom’s main theoretical undertaking is to describe the “normativefine structure” of a rational practice, which would warrant its interpretation as a linguistic practice apt to be semantically reconstructed in terms of inferential relations. To this end, he deploys a deontic scorekeeping model (see Brandom 1994, chap. 3). It purports to characterize the normative

198  Ladislav Koreň structure of a minimal linguistic practice in terms of the undertaking and attributing of discursive commitments to which performers might or might not (be taken to) be entitled. Commitments and entitlements are basic normative statuses. They serve to explicate—in a normative meta-language— what it takes for someone’s performance to be correct or appropriate (it is correct or appropriate for one to do what one is committed or entitled to do). Their undertaking and attributing are practical attitudes adopted by practitioners toward performances of themselves and others. They serve to explicate what it takes to treat someone’s performance as correct (something implicit in what one does, as opposed to being expressed in what one claims). By adopting practical attitudes of undertaking and attributing normative statuses, agents mutually keep score on commitments, entitlements, and on changes in their normative standings (deontic scores) effected in the course of a social exchange. Utterances purporting to have the force of claims are modeled precisely in terms of what difference to the deontic score scorekeepers take them to effect. Basically, they treat them as undertakings of discursive commitments. What this amounts to is further unpacked by explaining that their authors are practically treated by scorekeepers as undertaking responsibility to back them up by reasons (to thereby vindicate their entitlement to corresponding commitments) if properly challenged (until such a challenge arises, authors are treated as enjoying a default entitlement). Furthermore, authors are practically treated by scorekeepers as being precluded from making other utterances with that force, and also as licensing others to retoken original utterances as it were on their authority. This sketchy account of the scorekeeping model is oversimplified, but let us suppose we can recognize in it performances with the pragmatic significance of claims. Then contents of claims can be modeled in terms of their inferential articulation: that is, their position in the space of reasons implicitly established by scorekeeping activities. To cut a long story short, the scorekeeping model distinguishes three kinds of consequential relations linking normative statuses that practitioners can keep track of. First, in keeping track of commitment-preserving relations, they treat those whom they take to be committed to a claim as being thereby committed to some other claims (commissive consequences). Second, in keeping track of entitlement-preserving relations, they treat those whom they take to be entitled to a claim as being thereby entitled to some other claims (permissive consequences). Finally, in keeping track of incompatibility relations they treat those whom they take to be committed to a claim as being thereby precluded from being entitled to some other claims.2 When the practice reaches a threshold point when practitioners can be described as mutually keeping score on such relations, it is plausible to interpret them as engaging in a linguistic practice.3 That is, we are then warranted to interpret their performances as having the significance of claims cashed out in inferentially articulated (propositionally contentful) sentences. This justifies a semantic account of sentences in terms of

Propositional Contents and the Logical Space  199 inferential roles such that a practitioner is able to determine a pragmatic significance of a given performance (that is, how it changes the score) based on attaching a certain inferential role to a corresponding sentence and bringing it to bear on the context at hand (as determined by the current score—from her perspective).4 However, because practitioners “update” the score in a holistic-­ perspectival manner—factoring in possibly different sets of collateral commitments—there is no guarantee that they will converge on the same interpretation of the significance of a given performance. So rather than construing communication on the model of a sender conveying a shared meaning to a recipient, we should think of it as based on a shared practice of normative interpretation and practical abilities for navigating between various perspectives. Importantly, scorekeepers are practically sensitive to the difference between commitments (entitlements) acknowledged by gameplayers and commitments (entitlements) undertaken by them. They attribute to gameplayers the latter based on what they take to be the inferential consequences of the former. Scorekeepers might thus attribute statuses that outrun those avowed by gameplayers, thereby developing a basic sense that what is appropriate to do or say (what one is committed or entitled to) does not coincide with what (any) one takes one to be appropriate to say or do.5 To understand a given performance is thus to understand how it can acquire different significances from different individual perspectives and be able to traverse between them in communicative ventures. At the same time, this is supposed to ground the very process of instituting intersubjective inferential norms governing practices of giving and asking for reasons. These are not independent of the practice. They are contestable and “constantly in the making.” Still, they are supposed to establish some objective dimension of correctness—and a sense thereof on the part of practitioners—that does not collapse what is correct into what seems correct from a particular perspective. Moreover, to the extent that practitioners come to treat (if only implicitly) one another’s performances as subject to such norms, they come to establish an intersubjective basis governing use of expressions ensuring a reasonable amount of successful communication. Being caught up in practices governed by such implicit norms, performances come to possess genuine conceptual and rational significance.

3. Expressive Role of Logic and the Layer-Cake Picture of Language I intimated at the outset that a particularly attractive ingredient of the inferentialist approach is encapsulated in the following claim: Expressive role of logical vocabulary (ERL): logical vocabulary is elaborated from the basic prelogical linguistic practice, serving the expressive (explicitating) function of making explicit

200  Ladislav Koreň material-­inferential proprieties implicit in that practice that suffice to confer propositional contents on nonlogical sentences (and sub-­ propositional contents on their subsentential components, if any) in which its performances are cashed out. The flagship of ERL is the conditional “If P, then Q.”6 We are told that this device makes it possible for practitioners to explicitly endorse something (in what they say) that before they could endorse only in what they do with nonlogical sentences “P” and “Q”: namely that it is correct to infer “Q” from “P.”7 It codifies an implicit propriety of the material-inferential practice to the effect that gameplayers who play “P” are treated (by scorekeepers) as incurring a certain normative status (entitlement or commitment) that makes it appropriate for them to play “Q” (being entitled or committed to “Q”), if suitably prompted. Negation is another basic logico-expressive device—one that allows practitioners to explicitly endorse, as the content of claims, implicit incompatibility relations between prelogical claims.8 ERL presupposes the intelligibility of a discursive practice having the pragmatic structure of PGAR whose participants are capable of expressing and endorsing inferentially articulated contents (commitments) in claims made by means of nonlogical sentences.9 There is, Brandom says: [. . .] nothing incoherent about a language or stage in the development of a language in which the only vocabulary in play is nonlogical. (Brandom 1994, 383) This presupposes that practitioners are somehow able to identify and keep track of material-inferential moves to eventually treat and endorse them as good or reject them as bad. The important point is that before the elaboration of logical devices, practitioners can manage this only implicitly, by adopting practical attitudes and conducting scorekeeping (for example, practically treating those who undertake a discursive commitment with respect to “P” as thereby undertaking a commitment with respect to “Q”). But they cannot yet express and explicitly endorse material-inferential proprieties, making them the topic of the game of giving and asking for reasons. To make it possible to express them in the content of claims—and to endorse (or challenge) them in that explicit form—is the singular raison d’etre of logical expressions. In Brandom’s dialectical setting, we can interpret prelogical practitioners as rational creatures who are semantically conscious. Pragmatic elaboration of explicitating logical devices—making it possible to turn the rules governing their practices into the topic of PGAR—transforms them into logical creatures who are semantically self-conscious.

Propositional Contents and the Logical Space  201 ERL implies a layer-cake picture of language (as Brandom 1997b, 206, 209, 210 labeled it). It is so called, since it portrays linguistic practice as divided into layers deploying vocabularies of increasing complexity and expressive power. The ground-level layer is a material-inferential practice operating with nonlogical expressions. Once such a communicative practice reaches a certain threshold of score-keeping complexity, it becomes an autonomous discursive practice:10 [. . .] language game one could play though one played no other. (Brandom 2008a, 27) Linguistic practices operating with logical expressions are then accounted for as late-coming elaborations that cannot exist on their own. In other words, one cannot play a logical language game though one plays no other language game, specifically no prelogical language game.11 The layer-cake picture of language is far from uncontroversial. It is one thing to claim that an autonomous language game cannot be played solely with logical vocabulary. Hardly anybody would dispute that. It is another thing to claim that the prelogical practice, as described by inferentialists, constitutes a genuine language game whose players manage to express full-fledged propositional contents in their performances. We shall have an occasion to see that it is possible to argue that propositional contents are inferentially articulated, while rejecting the layer-cake picture on the ground that logical expressions shape—in some sense—the inferential articulation of propositional contents, including the contents of nonlogical sentences. Brandom himself is acutely aware of this dialectical possibility, though he consistently defends his position. Interestingly, some fellow travelers appear to hold views that are less consistent in this respect. In the next part, I focus on Jaroslav Peregrin’s (2014) elaboration of inferentialism, since it contains a line of reasoning that gestures toward an alternative view of logic as (co-) constitutive rather than merely explicitative of the space of reasons. This sets the stage for the reminder of the chapter, in which I provide considerations in support of the view that logic—in a suitably broad expressive sense—might indeed play such a role.

4.  An Alternative Perspective on Logic Peregrin officially subscribes to ERL when he alleges that nonlogical vocabulary and the rules governing it constitute the basis of language while the single role of the logical vocabulary is allowing us to make the material inferential links explicit. (Peregrin 2014, 26–27)

202  Ladislav Koreň And he concurs with Brandom that this “basis of language” is autonomous in the following sense: [. . .] inferentially structured nonlogical sentences, but a language (protolanguage?) consisting of only empirical sentences can exist as a matter of principle without this explicitating superstructure. (Peregrin 2014, 113) However, in other places of his book, Peregrin flirts with a different view of the function of logical devices. He illustrates the inferentialist approach by considering properties of a “Toy Language” (TL)—a simple model of a material-inferential fragment of language operating with nonlogical expressions (Peregrin 2014, chap. 3). TL consists of: (a) a stock of terms and predicates (one-place and two-place), (b) implicit syntax for generating complex (sentential) expressions from those terms and predicates, (c) 18 generalized inferential (including metainferential) rules generating their inferential proto-semantics (including rules for appropriately making language-entry and language-exit moves). For example, a sentence of TL that has a term-predicate structure would have an inferential (or toy-inferential) role specified by rules determining in what circumstances it could be correctly uttered (in assertoric mode), from what (sets of) other sentences it is inferable, and what (sets of) other sentences are inferable from it. The details need not detain us here. What matters is that Peregrin does not stop here but asks: what would have to be added to TL’s repertoire to make toy-sentences into genuine sentences expressing propositional contents? His answer is as follows: In fact we would need resources that are not available in our toy language, resources that would structure the sentences of the language into a “logical space.” In particular, for every sentence of the language we would need something as a complement (contradictory sentence); for every two sentences we would need something as their meet (disjunction) and join (conjunction) and so forth. As this is not the case, the sentences of our toy language do not really express propositions, do not have genuine meanings. (Peregrin 2014, 56) Unpacking this, what Peregrin suggests is that propositional contents are individuated by their positions in “the space of reasons,” in which they can be contradicted (have a complement), disjoined (meet), conjoined (join), and so on. Peregrin further expands on this point by saying that this is to view genuine sentences as forming something like a Boolean algebra. So a language capable of expressing propositional contents must contain some basic (he calls them “native”) logical operations. Prima facie at least, it

Propositional Contents and the Logical Space  203 is logical vocabulary that provides for such operations: “resources that would structure the sentences of the language into a ‘logical space’.” I hasten to add that Peregrin is not unambiguous on the last point. On some occasions he clearly sticks to ERL, saying that the prelogical practice might already be complex enough to institute the space (or web) of reasons linking expressions by material implications and incompatibilities, owing to which links they come to stand in implicit relations of contradictoriness, meet, join, and so on. Thus an algebraic structure can be discerned in a prelogical language such that its “vertices” can be made explicit by means of “native” logical operators, including negation, disjunction, conjunction, or conditional. Such comments may lead us to cancel the “prima facie” suggestion that logical operators are required to establish the logical space. The space, though implicit, is already there. The function of logical operators is to make it (its vertices) explicit. On other occasions, however, Peregrin again suggests that such expressions contribute to the establishment of the logical space relative to which sentences acquire their contents. He implies this when talking of logical rules in the following spirit: Logic, therefore, is primarily a matter of rules, rules that form our “space of meaningfulness.” Logical words, as a species of the “cognitive tools” that our sounds/scrawls are transformed into when they become meaningful, constitute the fundamental pillars of the whole “space of meaningfulness.” (Peregrin 2014, 238–239) It is clear from the context of his discussion that Peregrin has in mind rules of inference such as modus ponens, which involve logical vocabulary. Indeed, such rules are determinants of inferential roles of specifically logical expressions. So it seems as if the space of reasons comes into being with basic logical operators governed by such rules. This supports the “prima facie” suggestion that such operators provide resources required to establish such a structure. I conclude that Peregrin oscillates between ERL and an alternative conception of logic whose gist we can summarize thusly: Constitutive role of logical vocabulary (CRL): full-fledged propositional contents are constituted only relative to a finely structured “logical space” (of reasons), which comes into being only with the introduction of basic logical vocabulary. Isn’t this like wishing to have one’s cake while eating it too? Clearly, CRL and ERL appear to be commitments to which one cannot be entitled at the

204  Ladislav Koreň same time. ERL implies that logic merely makes explicit content-conferring material-inferential proprieties implicitly structuring the prelogical practice, and hence does not constitute propositional contents expressible by nonlogical sentences. Whereas CRL implies that logic contributes to the constitution of the very space of reasons relative to which propositional contents—including those expressible in nonlogical sentences—are identified and individuated in the first place. But if so, can the prelogical game be autonomous and logic expressive in the way they are officially stated to be (in ERL)?

5. Semantic Self-Consciousness and Rationality: Two Views It seems that something has to give. The orthodox inferentialist line is to stick to ERL, while rejecting (or ceasing to flirt with) CRL. This line is consistently pursued by Brandom. A version of it is pursued by Peregrin when he talks about sentences being localized in the implicit space of reasons whose vertices are made explicit by means of logical expressions. Brandom defends the orthodox line in response to critics who have challenged the layer-cake picture of language. McDowell, in particular, has voiced the worry that “nothing can be made explicit” (not even assertional commitment) without a command of basic logical vocabulary (McDowell 1997, 162). Brandom recapitulates the objection as follows: It can sensibly be argued [. . .] that we must be able to argue about whatever it is that entitles us to a commitment, if the whole game is to count as rational, hence as semantogenic. McDowell, for instance, argues along these lines that the idea of a language without logical vocabulary is unintelligible. In such a putatively rational but not yet logical practice, one could challenge claims, but not inferences. For one has no way to say that one does or does not endorse the inference from p to q, unless one has the expressive resources provided by conditionals. (Brandom 2010b, 319) As McDowell puts it himself: Semantic self-consciousness is required, and hence a command of logical vocabulary is required, if one is to be able to make anything explicit—including explicitly undertaking assertional commitment. (McDowell 1997, 162) explaining that self-consciousness requires the capacity to make the goodness of materially good inferences explicit, and hence command of logical vocabulary. (McDowell 1997, 162, footnote n. 4)

Propositional Contents and the Logical Space  205 What McDowell means is that there can be no game of giving and asking for reasons worth that name that is not also a logical game, so no gameplayers sensitive to “the force of a better reason” who are not also logical creatures capable of semantic self-consciousness. This is one way in which CRL can be motivated. If logical vocabulary is required for the constitution of genuine PGAR, and such practices are required for the constitution of full-fledged propositional contents, then logical vocabulary is required for the constitution of full-fledged propositional contents.12 In reply, Brandom acknowledges that discursive practices require, on the part of concept-mongering creatures, abilities for the “critical assessment of the credential of claims and reasons for them” (Brandom 1997a, 193). Yet he thinks that a ground-level discursive practice is possible in which practitioners practically treat claims as materially incompatible (for example, by making materially incompatible counterclaims) and inferences as materially good or bad. Participants in a discursive practice that is rational but not yet logical would have no way to reason or resolve disputes about their inferential practices. They would not be semantically self-conscious. They would not be very much like us. But could they still claim that things are thus-and-so, even though they were deprived of this dimension of critical self-consciousness. (Brandom 2010b, 319) Elsewhere, he expands on this point as follows: Just as even in the absence of logical vocabulary, scorekeepers can treat the contents of claims as materially incompatible [. . .] so they can treat inferences [. . .] as materially good or bad. [. . .] inferential articulation and the critical assessment of doxastic and inferential commitments, and so genuinely conceptual contents, are intelligible even in advance of the capacity logic gives us to say explicitly what in the more primitive practices remains implicit in what is done by scorekeepers. (Brandom 1997a, 193) To further clarify what is at issue between the disputants, it is useful to distinguish a strong and weak notion of semantic self-consciousness. On the strong notion, semantically self-conscious beings must be able to critically discuss or argue about their inferential practices. If semantic self-consciousness amounts to this kind of intellectualist capacity, it is easier to sympathize with Brandom when he says that it is not a necessary component of discursiveness (sapience). On the weak notion, semantically self-conscious beings must be able to make an aspect of inferential practice explicit in the first place. This is a prerequisite for arguing about it. This more basic kind of self-consciousness concerns making explicit

206  Ladislav Koreň “goodness of materially good inferences” (and let us add, incompatibility relations). Both thinkers assume that linguistic devices implementing it are logical expressions such as the conditional and negation. The basic issue is: can we make sense of practitioners who interact in an up-andrunning PGAR while having at their disposal no logical devices making explicit what claims they take to be inferable from what claims or what claims they take to conflict? For McDowell, the answer has to be negative, whereas Brandom replies that he “does not see why.” What one claims to be unintelligible (in principle), the other claims to be intelligible (in principle).

6.  An Argument from a Genealogical Perspective Brandom might be right that McDowell adduced less than compelling considerations to support his claim that there can be no genuine language game without logical expressions, and so no rational creatures who are not also semantically self-conscious. I am less sure, though, that he won the war, since it is open to debate whether no pertinent considerations exist. Part of the problem is that their arguments revolve around the issue of intelligibility of a prelogical discursive practice. Since they have different intuitions about what the game of giving and asking for reasons (or sensitivity to reasons characteristic of sapience) involves, they reach opposite conclusions. McDowell thinks that some critical-reflexive perspective on inferential practices is required that cannot be had without logical devices. For Brandom, prelogical practice with a critical dimension is conceivable without logical devices, although it is not yet selfconscious in that critical assessment of performances is implicit in doings and practical attitudes. I propose to transpose the issue into another key. It might be productive to look at it from a perspective of conjectural genealogy. Imagine that our prelogical ancestors evolved a practice of communication— including linguistic devices required for its implementation—of the kind that the inferentialists’ description of the minimal prelogical discursive practice presupposes. Brandom’s description of it is rather austere on the face of it. Basically, it is characterized as an exchange of nonlogical utterances with a declarative force, including those utterances supposed to play the pragmatic role of challenges and justifications. Some utterances are prompted by and prompt other utterances. Other utterances are elicited by environing stimuli or issue into actions.13 True, Brandom talks about practices of giving and asking for reasons. This suggests a dialectical structure realized by performances with complementary discursive functions (claims, challenges, and queries). Yet the idealized description has us imagine that a suitable challenge to a claim-making utterance discharges also the role of requests for reasons, the challenge

Propositional Contents and the Logical Space  207 being realized by another declarative utterance taken to be incompatible with the target utterance.14 Crucially, practitioners have no expressive devices for making explicit which utterances they take to provide reasons for or against which other utterances. Given this description, we might consider how plausible or likely it is that so modestly equipped creatures come to coordinate their communicative and interpretive activities so as to establish shared PGAR governed by intersubjective inferential norms. Endorsing Wittgenstein’s rule-following lesson to the effect that conceptual content is determined by socially articulated norms of correct application (inferential proprieties), I presume that inferentialists accept that norms governing practices be intersubjective.15 That is to say, I presume that inferential articulation of full-fledged contents requires not only that practitioners are individually able to classify claims and inferences as good or bad by their lights, but that they can coordinate and calibrate their normative attitudes so as to institute norms of assessment (however provisional) making it possible to distinguish correct from incorrect performances. To establish such a common ground, I submit, they must be able to make it sufficiently manifest to one another what inferentially articulated commitments they undertake and attribute, hence what inferential moves they endorse as good or reject as bad. I shall now argue the following: without some expressive devices indicating that something is endorsed (rejected) as a reason for (against) something else, prelogical communicative practices could be in key pragmatic respects too ambiguous among practitioners to provide for intersubjective norms governing practices of giving and asking for reasons, hence constituting full-fledged propositional contents. To begin with, declarative utterances of nonlogical sentences do not wear marks of playing the role of a premise or conclusion on their sleeves. So practitioners won’t have readily available for practical assessment reason-giving sequences consisting of a premise and conclusion. This complicates their task, because in order to manifestly endorse (as good) or reject (as bad) inferences, they must identify relevant sequences. Moreover, even if they register such sequences, it remains to be seen how they could unambiguously indicate to one another (hence register) that they endorse as correct a material inference from, say, “P” to “Q.” If A acknowledgingly utters “Q” (or otherwise practically endorses it) after A has acknowledgingly uttered (or otherwise endorsed) “P” (or after his or her interlocutor B has uttered or otherwise endorsed “P”), this might be taken in several ways by scorekeepers (B included). For instance, they might read it as A’s undertaking of a commitment with respect to “Q,” that is, independent of “P.” Here, I submit, one aspect of the difficulty lurks. With that much leeway for alternative readings of communicative exchanges, it is unclear how practitioners could coordinate their

208  Ladislav Koreň score-keeping activities so as to establish a common ground of inferential proprieties grounding conceptual norms. It being so ambiguous as to what is to be taken as giving reason for what, we should wonder whether the game deserves to be described as the game of giving and asking for reasons, hence as an autonomous linguistic practice. In reply, it could be said that reason-giving performances must be considered in the proper dialectical context of challenging performances. After all, to claim something is to undertake a corresponding discursive commitment such that the author of the claim might or might not be entitled to it (might be so treated by scorekeepers). Given the defaultchallenge structure of entitlement, the author is treated as undertaking a conditional task-responsibility to justify one’s claim (to vindicate one’s entitlement to the commitment undertaken in making the claim) if appropriately challenged (otherwise he or she is treated as enjoying a default entitlement to the commitment).16 Accordingly, for one to be called on to the task of giving reasons for a claim, one must be appropriately challenged in the first place. Thus, if A utters “Q” (or otherwise endorses it), B might challenge A by uttering some “R” that B takes to be incompatible with “Q.” If A responds by uttering “P,” B might take it that A treats “P” as a reason for “Q.” This rebuttal presupposes that prelogical gameplayers can make challenges manifest based on registering some incompatibility (in the sense that a commitment to one claim precludes an entitlement to some other claim). But consider that what declarative utterances are taken to be incompatible by individual scorekeepers depends on what other collateral information (commitments) they also have. Since scorekeepers differ in this respect, establishment of the shared space of material incompatibilities is liable to the problem of indeterminacy. What B takes to be incompatible with “P” might be compatible with “P” for A, if A has the right constellation of collateral commitments. Or A may fail to consistently track his or her commitments and consequently fail to register some incompatibility registered by B. But again, nonlogical declarative utterances do not wear a mark of incompatibility on their sleeves. So, if A does not register incompatibility between “P” and “Q” that B registers, A might fail to register that B is challenging his or her utterance of P by uttering “Q.” To drive the point home, consider the following exchange adapted from Huw Price:17 A: B: A: B: A:

“Fred is in the kitchen.” (Sets off for kitchen.) “Wait! Fred is in the garden.” “I see. But he is in the kitchen, so I’ll go there.” (Sets off.) “You lack understanding. The kitchen is Fred-free.” “Is it really? But Fred’s in it, and that’s the important thing.” (Leaves for kitchen.)

Propositional Contents and the Logical Space  209 Here A reacts as if not appreciating that B’s utterances are incompatible with his or her own (B intending them as challenges to A’s utterance). This is something that can happen.18 The problem, I submit, would likely be more daunting for exchanges of prelogical creatures with different collateral commitments, who produce and consume declarative utterances only. Given the conditional-task responsibility to justify one’s claims (or commitments) via-à-vis appropriate challenges (to be recognized as such), these considerations bring back the initial problem. One cannot hope to circumvent this difficulty by asserting that A and B might have arrived at a shared sense of material incompatibilities via a shared sense of some material-inferential proprieties or improprieties. For this is the problem we have started with in the first place. Incidentally, this gestures toward a related difficulty for prelogical creatures: how are they to make it sufficiently manifest—out in the open— that they reject an inference from “P” to “Q” as bad? Clearly, even if B rejects (challenges) “Q” (for example, by uttering some expression “R” that B takes to be incompatible with “Q”) after B (or A) has uttered (or otherwise endorsed) “P,” this might still be taken in a number of ways. Again, for instance, B might reject (challenge) “Q” independently of “P.” And if, for whatever reason, B already happens to have among his or her collateral information (commitments) “Q,” rejecting “Q” would not be a particularly happy way of rejecting the inference from “P” to “Q” as bad. This consideration, I take it, further reinforces the initial worry that prelogical creatures could have a hard time to establish a common ground of inferential norms required for full-fledged propositional contents. Any attempt to disambiguate the practice in this respect by invoking challenges will likely suffer from the same kind of problem I have highlighted above. In all, if creatures have just the recourses that the austere description of the prelogical practice gives them, a problem looms large of how they are to make it sufficiently manifest—so how they are to coordinate and calibrate—what they treat as giving a reason for what or, for that matter, of what to treat as challenging (asking reasons) for what. This makes one wonder if what they practice does not fall short of a norm-governed game of giving and asking for reasons. It suggests itself to say that what practitioners need are some expressive devices that would enable them to indicate and register that they reject (challenge) some claims and that they endorse or reject inferences from claims to claims. At first blush at least, logical devices—in particular, conditional and negation—appear tailor-made for this task. Having at their disposal an idiom with the significance of “If P, then Q,” scorekeepers could make it clear to one another that they endorse the inference from “P” to “Q” (the conditional functioning somewhat as an inference-license in Ryle’s sense).19 And an idiom having the significance

210  Ladislav Koreň of “Not:..” would provide them with a means of making more manifest incompatibilities between claims (commitments). Eventually, such devices would help them to make it more manifest that they reject an inference from “P” to “Q” as bad, giving them something with the significance of a negated conditional “Not: if P, then Q.”20 In all, by elaborating such tools they could more efficiently monitor, control, and coordinate their inferential and interpretational activities so as to arrive at a shared sense of what counts as a reason for what and what counts as a reason against what. With them in place, it is easier to see how the shared normative space of reasons could be socially instituted possessing those features that Peregrin intimates are required for genuine sentences expressing propositional contents (having the contradictory, meet, join, etc.). But of course, the proposal that logical devices contribute in this way to constituting the pragmatic structure typified by PGAR is not consistent with the core inferentialist idea that a prelogical practice is a basic-autonomous linguistic practice that does not require any semantic self-consciousness at all. This is not the end of the matter, though. One might voice the following reservation: “Your considerations show, at most, that the culprit is the austere description of the prelogical practice (which is an optional element of the inferentialist doctrine). But for all you have said, there might be a way of equipping prelogical beings with linguistic devices that, albeit not genuinely logical, would enable them to openly endorse, reject, or challenge inferences and claims. Hence, your considerations do not undermine the idea that a minimal discursive practice is prelogical and that logical devices are pragmatically elaborated from such a practice so as to play a distinctive explicitating role (a core tenet of the inferentialist doctrine).” The suggestion is that we should go beyond the austere description of the prelogical practice. So we should consider whether our imaginary prelogical ancestors could make progress on this front without encountering the need to elaborate tools enabling them to make reasons explicit. Let’s return to the problem of making manifest reason-giving moves and their endorsement. It could be a significant boost if prelogical gameplayers had at their disposal some inference markers (playing the role of “So,” “Hence,” “Thus,” and the like) if not operators connecting sentences in conditional compounds (embeddable in other sentences of increasing complexity). By means of inference markers, they could unambiguously indicate to each other (hence register) that an inference from “P” to “Q” is underway. Now, inference markers do not behave quite like sentence-forming logical operators (such as conditional). A piece of discourse embodying an inference is not a claim assessable as true or false (though consisting of a premise-claim and a conclusion-claim that are so assessable). Relatedly, inference markers do not embed and inferences

Propositional Contents and the Logical Space  211 marked by them are not fit to play the role of premises or conclusions. Hence the suggestion: give prelogical game-players access to inference markers, enabling them to indicate material-inferential transitions. A prima facie problem with this proposal is that the introduction of inference markers into the prelogical practice is dangerously close to transforming it into a rudimentary logical practice already displaying elements of semantic self-consciousness. My reason for this claim is simple: in discursive exchanges of the sort “P.” “So Q.” one does not just make manifest that one draws an inference; one also openly endorses (goodness of) the inference. In this specific respect, inference markers are akin to expressions (paradigmatically conditionals) that, according to inferentialists, make explicit inferential relations previously implicit in their practices with nonlogical expressions and sentences. So unless one comes up with a further argument to the effect that the elaboration of dialectical devices typified by inference markers does not introduce an element of semantic self-consciousness into PGAR (making explicit reason-giving links), this proposal does not mitigate my critique of ERL and the layercake picture of language. I have yet to see how such an argument would proceed, given the apparent analogy between the role of inference markers and explicit conditional pointed out above.21 Let’s continue our exploration of how a prelogical practice could be enriched whilst dispensing with logical operators. A promising suggestion on behalf of inferentialists is to appreciate the need for a variety of speech acts alongside claim-making performances. In particular, if A and B could address one another with a certain kind of pointed queries, it should be easier for them to establish a mutual understanding as to what (inference or claim) is at issue.22 After all, raising questions is a fairly straightforward way of “asking for reasons,” while making claims is a straightforward way of “giving reasons” for (challenged) claims (subject, let us assume, to the default-challenge structure of PGAR). For instance, if A utters “Q” and then B asks A something with the significance of “Why (Q)?,” A might go on to reply “P,” thereby bringing it into the open that he or she endorses “P” as a reason for “Q” (rather than treating the two as expressing independent commitments). Although asking-for-reasons would involve constructions having the significance of “why,” it is not obvious that such devices must be conceived of on the model of expressing, in the content of claims, preexistent inferential relations. Instead, they might be construed as belonging to a toolkit for coordinating communicative practices so as to acquire the public structure that makes it possible to establish intersubjective norms of discourse. This proposal might point in the right direction. And Brandom can admit that without giving up the layer-cake picture. He just needs to reconsider his treatment of queries as auxiliary speech acts that facilitate scorekeeping-communicative practices but are dispensable in principle.

212  Ladislav Koreň However, the problem of making manifest that one treats some utterances (commitments) as incompatible might compel us to look after additional resources. Recall that the minimal discursive practice involves challenges performing the role of demands for justification of claims, realized by affirming sentences treated as making incompatible claims. This proved problematic, for the reasons spelled out before. On the other hand, reason-seeking questions, though fit to discharge the role of requesting reasons, do not by themselves capture an element of conflict present in the original conception of challenge. As Brandom puts it: Tracing the provenance of the entitlement of a claim through chains of justification and communication is appropriate only where an actual conflict has arisen, where two prima facie entitlements conflict. (Brandom 1994, 178) To raise a query is not yet to disclose anything about what one takes to be incompatible with what. It suggests itself to say that our prelogical ancestors would have been better off if they could explicitly reject (or disavow) commitments in acts of denial as well as explicitly accept (or reaffirm) them in acts of assertion. Suppose A makes a claim that p. Then B could openly reject it (signaling its incompatibility with some commitment of her) by uttering something with the pragmatic significance of “No” (with a conventional gesture possibly accompanying it). If, in addition, A and B could address each other with queries, we can appreciate the point and benefit of communicative exchanges of the following type (given that challenges, too, are always potentially at issue): A: B: A: B:

“Food (over there).” (Pointing to his/her cave.) “No.” (Shaking his/her head.) “Why (no)?” (Or, perhaps, “How (so)?”) “Eaten.” (Pointing to his/her belly.)

The idea that denial might be considered a basic speech act on all fours with assertion has been elaborated in a number of recent approaches that reject the view that a denial of p is to be explained in terms of conceptually prior notions of negation and assertion: that is, as an assertion of not-p. (Cf. Price 1983; Price 1990; Smiley 1996; Rumfitt 2000; Ripley 2011). Rather, negation is to be explained in terms of the speech act of denial. Particularly intriguing is Huw Price’s proposal: a device with the pragmatic significance of denial is needed for dialectical reasons. It provides a “perfectly general means of registering and pointing out the incompatibility” (Price 1990, 224). This applies to Price’s example of an exchange in which A does not register incompatibility that B aims to convey and exploit in challenging A’s claim. The example

Propositional Contents and the Logical Space  213 shows that discursive creatures could greatly benefit from elaborating a device that unambiguously indicates to communicating parties that “an incompatible claim was being made” (Price 1990, 224). According to Price, negation-based denial will do. However, denial can be performed by means of a device having the pragmatic significance of “No.” that applies to utterances of negation-free sentences. In this sense, the speech act of denial could be a basic dialectical device for making the incompatibility of commitments manifest. It could thus sub-serve the practice of making dialectical challenges to attributed commitments by conventionally marking “points of conflict or disagreement” (possibly followed by a specification of the source of incompatibility). It is not that farfetched to speculate that a rudimentary denial could have paved the way for a subsequent elaboration of the sign of negation functioning as a sentential operator.23 I sympathize with this proposal. Again, however, I read it as the grist on my mill. Denying (rejecting) a claim is akin to the use of expressions making explicit inferential relations, including incompatibility. By explicitly marking and registering incompatibilities in a piece of discourse, denial serves to coordinate scorekeeping practices and normative attitudes toward intersubjective discursive norms required for a shared discursive practice. I do not mean to imply that Price himself would endorse my diagnosis. He assumes some sense of material incompatibilities on the part of speakers and explains the sign of denial as a means of making interpersonal disagreements sufficiently manifest. He offers an account of how rational creatures could have developed such a sense. First, by having to make practical choices between performing and not performing a certain course of action, they could have acquired a basic awareness of mutually excluding options. Furthermore, they could have started to appreciate that a communicative signal (for example, “Berry—over there”) is appropriate in the presence of a certain condition (if there are berries in the direction of pointing) and inappropriate in its absence (if there are no berries in the direction of pointing). Price’s account is interesting in its own right. That said, it seems to me that inferentialists are committed to explaining how intersubjective norms—responsible for creating the rational space of incompatibilities and inferential relations—can be socially instituted in the first place. Then my point can be reformulated as follows: even if we grant that agents have their private tastes of (say, Price’s practical) incompatibilities, they still need to coordinate and calibrate them in the public arena via suitable pragmatic devices that ensure that what they practice are shared PGAR subject to intersubjective proprieties. My challenge is that it is difficult to see how they could manage this without elaborating some dialectical device with the significance of denial, which brings into play an element of semantic self-consciousness.24

214  Ladislav Koreň

7. Conclusion It is possible to retort that, for all that has been said, the prelogical practice might come to contain performances and expressions linked by material inferential relations, owing to which links they acquire full-fledged contents. In principle, inferentialists can persist in holding that logical devices presuppose and explicitate implicit content-conferring relations. This is fair enough. I have not excluded this possibility. Rather, by hypothetically reconstructing the predicament of our prelogical ancestors equipped with the abilities and devices supposedly sufficient for PGAR, I have argued that it is far from clear how this possibility could plausibly have been realized. Such ancestors would have a problem to establish PGAR governed by intersubjective norms in the first place. Specifically, I have argued that some ascent to the level of semantic self-consciousness would seem to be more than vital. This leaves open the possibility that our prelogical ancestors could have made a significant progress by first elaborating rudimentary dialectical devices, such as inference markers or denial, together with declarative (likely also interrogative) utterances composed of nonlogical expressions. Logical operators could have been latecomers enabling increasingly controlled (self-conscious) inferential practice, thus making the space of reasons ever more articulated.25 On this picture, semantic self-consciousness is not an all-or-nothing matter. It comes in grades. This picture provides a different perspective on what logic is by reconstructing a different story of why and for what purposes it could have been elaborated. This, I take it, is in the spirit of the inferentialist enterprise. But the conjectural conclusion eventually reached on this basis challenges some of its core ingredients. For note that by enriching the prelogical practice with dialectical devices we have come quite close to making it a rudimentary logical practice—at least in the sense of introducing an element of (weaker) semantic self-consciousness. Does this imply that the expressive conception of logic is to be given up? Not really. ERL is just one way of elaborating what it might take for logic to be expressive. If we include in logic also dialectical expressions (on account of their expressive role), the expressive role of logic can be redefined. Rather than conceiving of expressing on the model of making explicit ready-made proprieties structuring the prelogical practice, let’s think of it in terms of making more coordinate, controlled, hence shared that which has been less so, precisely because it has been left on the implicit level that is liable to ambiguities of interpretation that I have attempted to highlight. On this view, logic does not merely recapitulate preexisting inferential relations in a perspicuous idiom. Rather, by helping to establish normgoverned PGAR, it both shapes the very space of reasons and makes it increasingly articulate. This is consistent with it being the case that prelogical practices involve rudimentary intentionality and proto-language

Propositional Contents and the Logical Space  215 games. Hence, it does not follow that logic forges completely new links between utterances and expressions where there have been none before, conferring contents upon them from scratch. What elaboration of logical devices makes possible is individuation of full-fledged propositional contents relative to a space of reasons held in a common ground. Once the space is established, we can isolate a material fragment of a language and interpret its sentences (utterances) as expressing finely articulated propositional contents. Indeed, we can give material inferences (incompatibilities) their due: that logic has this kind of role by no means implies that all genuine inferential relations must be formal. At the same time, we should be wary about projecting those emergent features of our developed practice into ancestral prelogical practice.26

Notes   1 This is to give pride of place to inference, rather than reference, as a central theoretical notion of semantics. Part of the inferentialist plan is to reconstruct referential idioms in terms of their inferential roles. See Brandom (1994, chap. 5–8).   2 This grounds what Brandom calls incompatibility entailments: “P” (its claimable content) entailing in this sense “Q” (its content) if everything materially incompatible with “Q” (its content) is materially incompatible with “P” (its content).  3 More precisely, a social practice worth interpreting as linguistic must also involve proprieties of reliability inferences (language-entry transitions), practical inferences (language-exit transitions), and socially articulated inferences (constituting performances with the significance of claims). Cf. Brandom (1994, chap. 3–4), Brandom (2010a).   4 Cf. Brandom (1994, 190).  5 Idioms for ascribing commitments (beliefs) in de re/de dicto style are late comers elaborated to make this explicit. For the purposes of the present chapter there is no need to go into these subtleties.   6 Cf. Brandom (1994, 2000).  7 According to Brandom (2008a), different conditionals can be elaborated from and explicitate different kinds of inferential proprieties (and formally modelled by alternative logical systems). Thus a conditional may codify commitment-preserving or entitlement-preserving material-inferential relations (corresponding, respectively, to generalizations of deductive and inductive inferences). Whether this allows a plausible account of conditional sentences in everyday use is quite controversial. See also Shapiro (this volume, chap. 8) for a brief recapitulation of the doctrine and criticism to the effect that inferentialists had better construe explicit conditionals as making explicit (endorsement of) implicit conditionals (instituted by social practices) rather than inferential relations.   8 Brandom (1994, 115) says that a formal negation of a claim is “its minimal incompatible, the claim that is entailed by each one of the claims incompatible with the claim of which it is the negation.”   9 We can imagine that some of the sentences they use are simple, while others have a term-predicate structure of a sort. 10 Brandom (2008a) explains that such a practice is one that deploys an autonomous vocabulary: that is, such that one must be able to deploy it in order to be able to make any claim whatsoever.

216  Ladislav Koreň 11 Brandom (2008a) develops a theory of algorithmic elaboration of linguistic practices (practical abilities) from more elementary linguistic practices ­(practical abilities). 12 See McDowell (2008) for further elaboration. 13 Of course, there are scorekeeping (deontic) attitudes as well. But it is maintained that scorekeeping is implicit in discursive exchanges—prelogical beings cannot yet ascribe scorekeeping attitudes to each other. 14 Brandom (1994, chap. 3, 191–193) discusses challenges (as well as queries, deferrals, and disavowals) under the rubric of “auxiliary speech acts.” 15 See Wittgenstein (1953). This worry applies even if we acknowledge inevitable indeterminacy in interpreting the pragmatic significance of particular utterances owing to individual differences in how scorekeepers view the context and the current normative score. Still, existence of intersubjective norms governing use of expressions appears to be required to ensure a reasonable amount of smooth communication between practitioners and to supply shared criteria of correctness. 16 Scorekeepers treat A as possessing a default entitlement to the commitment if they take it that no appropriate challenge has been made and that A has not undertaken incompatible commitments. Appropriately challenged, A can discharge the conditional task-responsibility either by making other claims from which the commitment is inferable, or by deferring the justificatory burden to some peer who has previously authorized A to undertake the commitment. Should A not be willing or able to defend the commitment appropriately, scorekeepers would treat him/her as no longer entitled to it. 17 Price (1990, 224). Of course, this is not to be taken seriously as exemplifying exchanges of our prelogical ancestors. 18 Price uses this example to argue for a pragmatic role of denial with the significance of negation. More on this issue later. 19 Ryle (1950). To encapsulate one’s endorsement of (goodness of) an inference in a conditional claim is not the same thing as drawing one, since one need not be in a position to claim (endorse) its antecedent or consequent (whereas in drawing an inference one claims [endorses] both the premise and the conclusion—at least on the account of material inference that Brandom and Peregrin work with). 20 There are reasons to think that the two expressive devices would require each other: for example, to make it manifest that one rejects an inference from “P” to “Q.” 21 It seems to me that if one can be said to explicitly endorse (goodness of) inference by means of uttering the conditional “If P, then Q,” one can also be said to explicitly endorse it in producing a piece of discourse: “P.” “So Q.” After all, the difference cannot be that the former, unlike the latter, presupposes a normative vocabulary on the part of speakers (or that it is a disguised meta-linguistic claim). Admittedly, there are differences. But the crucial consideration is that, one way or another, inferential commitments are rendered manifest in a piece of discourse and as such can be registered, tracked, and eventually endorsed (or rejected) by other scorekeepers. Since inference markers display a less complex syntactic behavior than sentential operators (in particular, they do not embed), one might speculate that, owing to their expressive role, they could have been precursors of the latter. 22 I am indebted to Ulf Hlobil and Preston Stovall, who urged me to give a hearing to this proposal. A number of thinkers have already explored the theme. Millson (2014) argues that Brandom’s parsimonious conception of challenges as claims with incompatible contents is incoherent. He suggests that reason-seeking questions (why- or how-questions) should be added into the arsenal of prelogical creatures (minimal discursive practices).

Propositional Contents and the Logical Space  217 Kukla and Lance (2009) also stress the basic role of interrogative practices, as well as what they call recognitives, vocatives, etc. Belnap’s (1990) incisive critique of the “declarative fallacy” is an important source of influence here. 23 In addition, a dialectical toolkit consisting of denial and reason-seeking questions would seem to also be vital for making manifest one’s rejection of inferences. Plus, the notion of denial provides a rather straightforward way of capturing what it is for one to take an inference from “P” to “Q” to be correct: namely, to take it that one should not claim “P” while denying “Q.” This matters, because inferentialists maintain that a propriety of inferring “Q” from “P” does not mean that one ought to claim “Q” after one has claimed “P.” Rather, it means that one ought not to claim “P” while making “Q” incompatible claims. As Peregrin puts it (emphasis is mine): “If you assert that Fido is a dog, you are not obliged to assert that Fido is an animal, but you are obliged not to deny it; if you do deny it, you are a legitimate target of criticism” (Peregrin 2014, 72). 24 One may wonder why an expression of denial should be linguistic. Granted, verbal forms of assent and dissent—such as yes and no—could facilitate communication and scorekeeping (interpretation). But won’t some preverbal forms suffice for the purposes of prelogical ancestors? Furthermore, one may ask whether the problem of misaligned incompatibility-tastes (owing to differences in collateral commitments) is as daunting as I have intimated. Shared bio-social interests and an obligate cooperative lifestyle—requiring, early on, a signaling practice of a kind—could have pressed our ancestors to develop quite a robust shared sense of what excludes (hence is a reason against) what. No doubt a sanctioning practice could significantly contribute to its formation. If so, a shared sense of what is a reason for what could have been developed as well. Then it can be more plausible to claim that prelogical communicative practices could have exploited and further refined such a common ground of rudimentary inferences and incompatibilities so as to eventually establish full-fledged material implications and incompatibilities. These are interesting issues that deserve closer scrutiny than I can attempt here. But let me point out one thing. The further one pushes this strategy, the greater the risk that one would have no need to invoke PGAR as the ultimate setting in which rational performances (hence conceptual contents) materialize. If we grant that so much is shared in a common ground, why not locate rationality and contentfulness well before anything like PGAR enters the scene? 25 For example, making explicit multipremise and multiconclusion inferential relations. 26 Work on this chapter was supported by the joint Lead-Agency research grant between the Austrian Science Foundation (FWF) and the Czech Science Foundation (GAČR), Inferentialism and Collective Intentionality, No. I 3068-G24.

References Belnap, Nuel. 1990. “Declaratives Are Not Enough.” Philosophical Studies 59 (1): 1–30. Brandom, Robert. 1994. Making It Explicit: Reasoning, Representing, and Discursive Commitment. Cambridge, MA: Harvard University Press. Brandom, Robert. 1997a. “Replies.” Philosophy and Phenomenological Research 57 (1): 189–204. Brandom, Robert. 1997b. “Reply to Commentators.” Philosophical Issues 8 (Truth): 199–214.

218  Ladislav Koreň Brandom, Robert. 2000. Articulating Reasons: An Introduction to Inferentialism. Cambridge, MA: Harvard University Press. Brandom, Robert. 2008a. Between Saying and Doing: Towards an Analytic Pragmatism. Oxford: Oxford University Press. Brandom, Robert. 2008b. “Responses.” Philosophical Topics 36 (2): 135–155. Brandom, Robert. 2008c. “Responses.” In The Pragmatics of Making It Explicit, edited by Pirmin Stekeler-Weithofer, 209–229. Amsterdam: John Benjamins. Brandom, Robert. 2010a. “Conceptual Content and Discursive Practice.” Grazer Philosophische Studien 81 (1): 13–35. Brandom, Robert. 2010b. “Reply to Mark Lance and Rebecca Kukla’s ‘Perception, Language, and the First Person’.” In Reading Brandom: On Making It Explicit, edited by Jeremy Wanderer and Bernhard Weiss, 316–319. New York: Routledge. Kukla, Rebecca, and Mark Lance. 2009. “Yo!” and “Lo!”: The Pragmatic Topography of the Space of Reasons. Cambridge, MA: Harvard University Press. McDowell, John. 1997. “Brandom on Representation and Inference.” Philosophy and Phenomenological Research 57 (1): 157–162. McDowell, John. 2008. “Motivating Inferentialism: Comments on Making It Explicit (Ch. 2).” In The Pragmatics of Making It Explicit, edited by Pirmin Stekeler-Weithofer, 209–229. Amsterdam: John Benjamins. Millson, Jared. 2014. “Queries and Assertions in Minimally Discursive Practices.” In Questions, Discourse, and Dialogue: 20 Years After Making It Explicit—Proceedings of AISB50. http://doc.gold.ac.uk/aisb50/. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan. Price, Huw. 1983. “Sense, Assertion, Dummett, and Denial.” Mind 92 (366): 161–173. Price, Huw, 1990. “Why ‘Not’?” Mind 99 (394): 221–238. Ripley, David. 2011. “Negation, Denial, and Rejection.” Philosophy Compass 6 (9): 622–629. Rumfitt, Ian. 2000. “ ‘Yes’ and ‘No’.” Mind 109 (436): 781–823. Ryle, Gilbert. 1950. “ ‘If,’ ‘So,’ and ‘Because’.” In Philosophical Analysis, edited by Max Black, 323–340. Ithaca: Cornell University Press. Smiley, Timothy. 1996. “Rejection.” Analysis 56 (1): 1–9. Wittgenstein, Ludwig. 1953. Philosophical Investigations. Oxford: Blackwell.

10 Assertion, Inference, and the Conditional Peter Milne

In this chapter, I pull together some ideas on which I have written previously (Milne 2009, 2012a, 2012b) but that I have not previously brought together. The topics arise in the order given in my title. Assertion is normatively constrained by logical relations, in particular by consistency and by logical consequence. This gives inference a role in the critical evaluation of others’ (and our own) assertions, which, I suggest, allows us to escape Harman’s challenge that all reasoning is a matter of reasoned change in view. However, Harman’s distinction between reasoned change in view and logical consequence is crucial to the evaluation of certain patterns of discourse involving indicative conditionals, patterns that are significant for the determination of the semantics of the indicative conditional of natural languages.

1. Assertion 1.1.  Assertion: Some Reminders One central use of language is to tell each other things—things about the way the world is, things about our own mental states (including ways we would like the world to be). My Stirling colleague Alan Millar puts it like this (where p is any declarative sentence): Telling is a distinctive communicative act. My act of telling you that p is an act of saying to you that p by which I give you to understand that I am informing you that p. Informing you that p is a matter of saying to you that p, speaking from knowledge, with the aim of bringing it about that you come to know that p from my saying that p. (Millar 2010, 177) What Alan calls telling, I pretty much think of as assertion. Of course, we don’t always say things with quite such emphasis on imparting

220  Peter Milne knowledge; we do have our lighter moments. Telling is really serious, full-on ­assertion—what Tim Williamson calls flat-out assertion (Williamson 1996, 498). And one still asserts when, whether knowingly or unwittingly, one asserts a falsehood—we do, after all, speak of telling a lie. The important thing is that assertion is never mere expression of opinion—a good bit more is going on. One can see that a good bit more is going on in various ways. From the literature, here are a few: Adding “almost certainly” at the beginning or “I believe” at the end of an assertion are devices used to weaken it. (Cf. Wolgast 1977, 114; Unger 1975, 261; Dudman 1992, 206) In telling others, in asserting a sentence, “one both commits oneself to it and endorses it; [. . .] in asserting a sentence, one not only licenses further assertions on the part of others, but commits oneself to justifying the original claim.” (Brandom 1983, 640–641) In making an assertion, one lends to the asserted content one’s authority, licensing others to undertake a corresponding commitment to use as a premise in their reasoning. (Brandom 2000, 165, emphasis in the original) Non-accidentally, assertions tend to meet standards of reliability and trustworthiness: Most chess moves are valid, most intentions are carried out, most statements are veracious; none of these statements is just a rough generalization, for if we tried to describe how it would be for most chess moves to be invalid, most intentions not to be carried out, most statements to be lies, we should soon find ourselves talking nonsense. (Geach 1956, 39) Assertions take place against the background of a custom of uttering them with the intention of saying something true. (Dummett 1981, 302) This highly structured information-propagation procedure [of secondhand knowledge] works on the assumption that when an utterer makes an assertion, others can rely on it as more than a random guess. The usefulness of the whole system would wither if members did not generally attempt to meet, and could not expect others to meet, standards of trustworthiness in making assertions. (Cherniak 1986, 105)

Assertion, Inference, and the Conditional  221 We withdraw or retract assertions—“I take that back”—upon finding them to be incorrect and sometimes apologize for having made them—“I’m sorry, I take that back.” (Cf. Kvanvig 2011, 248) These are just a few pointers or reminders about the nature of assertion. They do not all apply all the time. The second Brandom quotation is obviously compatible with deliberately misleading the audience addressed in one’s act of assertion; the first is much less obviously so. One might think that the first needs a sincerity qualification: in sincerely telling others, in sincerely asserting a sentence, one both commits oneself to it and endorses it. I’m not sure that it’s right that a sincerity condition is needed for, as we shall see, the mere making of an assertion leads to the maker incurring commitments. 1.2.  Assertion and Probability Although our reminders do not obviously lend much in the way of encouragement to this idea, it used to be said—by David Lewis and Frank Jackson, for example—that a proposition is assertible (or assertable) for an individual only if she has a high enough degree of belief in it. (Jackson added a wrinkle to deal with conditionals that we’ll come back to.) Now, although Lewis may cautiously have stated this, as I just have, as a necessary condition—“the truthful speaker wants not to assert falsehoods, wherefore he is willing to assert only what he takes to be very probably true” (Lewis 1976), Jackson was not alone in taking it to be also sufficient. Vic Dudman reported: It is a conjecture popular with philosophers today that just those things are assertible which seem highly probable, or that things are assertible to just the degree that they seem probable. (Dudman 1992, 204) The second disjunct closely parallels Jackson: As a rule, our intuitive judgments of assertability match up with our intuitive judgments of probability, that is, S is assertable to the extent that it has high subjective probability for its assertor. (Jackson 1979, 565) Jackson makes assertibility a matter of degree that sits oddly with the all-or-nothing nature of assertion—one either performs the speech-act or one does not. (The Wolgast-Dudman point about adding “almost certainly” and “I believe” concerns weakening of the content asserted, the claim made, not gradations of assertion.)

222  Peter Milne Be that as it may, Dudman himself pointed out, “lotteries prove it is not probability that governs assertion” (Dudman 1992, 207, Dudman’s emphasis). How do lotteries do this? Dudman offers a line of attack that has become familiar in the hands of others: I can withhold assent even when the subjective probability is enormous. Full knowing that the chance of my ticket’s winning is extremely small, I nevertheless vigorously dissent from “My ticket won’t win.” I would not have bought it unless I had thought it might win, and I still maintain that it may. I do not expect it to win, and agree that it probably won’t, but I disagree that it won’t win simpliciter. Someone has to win: why not me? And similarly when apprised that the lottery has already been drawn. Conceding that the chance of my ticket’s having won is extremely small, and agreeing that it probably didn’t win, I decline to assent to either “My ticket didn’t win” or “My ticket won’t have won,” preferring “My ticket may/ might have won.” It is not just that the probability is never high enough to trigger assertion. An exacter appreciation is that even the smallest uncertainty is enough to cohibit it. (Dudman 1992, 205) Sufficient as this is for showing high probability not sufficient for assertion, it’s a second line of attack which we can extract from Dudman’s (1991) that is more significant for where I want to go here. There Dudman says: I deprecate the idea of explaining discourse in terms of belief, preferring C. L. Hamblin’s notion of individual speakers’ commitments. To these belief is strictly irrelevant: “We do not believe everything we say; but our saying it commits us whether we believe it or not” (Fallacies (London, 1970): 264). When a speaker affirms a proposition, for example, I construe that as her incurring public commitments to its truth, not as her confiding private belief in its truth. Commitment has desirable properties denied to belief, e.g., it is sheer romancing to suppose that a speaker’s current beliefs might be consistent and closed under deduction, but it is a fundamental dialectical requirement that each speaker keep her cumulative commitments consistent, and treat entailments of commitments as commitments. (Dudman 1991, 228, n. 14) The dialectical and public nature of the requirement means that a speaker lays herself open to criticism—which doesn’t mean that she will be criticized, just that she is open to criticism—if

Assertion, Inference, and the Conditional  223 she makes inconsistent assertions; she asserts some propositions and denies, or otherwise indicates overt reluctance to accept, a logical consequence of them. Now consider a lottery which an individual takes—perhaps even knows— to be eminently fair: every ticket has the same chance of winning, and one ticket will win. With enough tickets—say, 10,000—all of the following are at least highly probable for that individual: Ticket 1 won’t win. Ticket 2 won’t win. Ticket 3 won’t win. . . . Ticket 10,000 won’t win. One of tickets 1 to 10,000 will win. These propositions being jointly inconsistent, thus (classically) entailing a contradiction of the form “p ∧ not-p,” from this we see: highly probable propositions need not be jointly consistent; the logical consequences of highly probable propositions need not be highly probable. This is Kyburg’s Lottery Paradox (Kyburg 1961, 197).1 Given Dudman’s dialectical requirements on assertion, the first of these shows, as we have seen already, that high probability is not sufficient for assertion, the second strongly suggests that it is not necessary.2 Gilbert Harman has noted how odd it would be to engage in dialogue with someone who is guided solely by degree of belief (subjective probability). He goes so far as to state that it would be “contrary to the way we normally think.” He says, Imagine arguing with such a person. You might get him to believe certain premises and to appreciate that they imply your conclusion, but he is not persuaded to believe this conclusion, saying that, although you have persuaded him to assign a high probability to each of your premises, that is not enough to show he should assign a high probability to the conclusion! This is not the way people usually respond to arguments. Or consider the following attitude toward contradiction. As Jack asserts several things, you observe that he has contradicted himself. His response is that he sees nothing wrong, since all the things he has asserted are highly probable. This is comprehensible, but it is again different from the normal way of doing things. (Harman 1986, 23)

224  Peter Milne Indeed it is. The norms, the dialectical requirements, governing assertion require that one stand by the conclusion or withdraw one or more of the premises and that one not assert jointly contradictory propositions. Supposing there is no good reason to withdraw any of the premises, we find ourselves in a situation that may seem problematic. If we ever assert propositions which are highly probable but not certain (and we do!), in all likelihood the norms governing assertion require us to incur commitments to highly improbable propositions—but that is just how it goes. (And if proof transmits warrant for assertion from premises to conclusion, in all likelihood the norms governing assertion give us warrant to assert highly improbable propositions—but that’s not a topic I shall follow up here.) Especially since Tim Williamson’s (1996) “Knowing and Asserting,” a lot has been written on norms of assertion. Candidates include a norm of truth—Assert only what is true! a norm of belief or sincerity—Assert only what you believe! a norm of knowledge—Assert only what you know! a knowledge norm for belief—Believe only what you know!—and a belief or sincerity norm for assertion—Assert only what you believe! For present purposes, it does not matter whether any of these is correct or even whether there is a norm of assertion in this sense.3 What matters here is that assertion is governed by norms invoking consistency and logical consequence in the way indicated above. What is expected of a participant trained—as Wittgenstein would put it—in the public practice of assertion is that she stands by the logical consequences of her unwithdrawn assertions and that these be jointly consistent—she is open to criticism if she fails to meet these expectations. To Dudman’s two “fundamental dialectical requirements” a third could be added: a speaker lays herself open to criticism if she denies, or otherwise indicates overt reluctance to accept, a logical truth, or more broadly, if she denies, or otherwise indicates overt rejection of, all of a finite set of propositions not all of which can be false.4

2. Inference 2.1.  Meaning and Use “Meaning is use” is a slogan often associated with the later Wittgenstein. What Wittgenstein actually said was, “for a large class of cases of employment of the word ‘meaning’—though not all—this word can be explained in this way: the meaning of a word is its use in the language” (Wittgenstein 1953, § 43). But even a stronger, unqualified, reading tells

Assertion, Inference, and the Conditional  225 us little. It tells us only that there are no facts beyond those that concern the general practice of use in the community of language users to which appeal can be made in determining meaning. It tells us little about the form a theory of meaning can or should take. It tells us only where we should look to find whatever it is that constrains meaning, however meaning is characterized.5 Explaining what we nowadays call the inferentialist position in the philosophy of logic, Nuel Belnap characterized various philosophers as treating the meaning of connectives as arising from the role they play in the context of formal inference. It is equally well illustrated, I think, by aspects of Wittgenstein and those who learned from him to treat the meanings of words as arising from the role they play in the context of discourse. (Belnap 1962, 130–131) (Belnap’s “arising” is subtle, perhaps even a little evasive. Wittgenstein’s word is “erklären.” Anscombe had “be defined;” Hacker and Schulte ­substitute “be explained” and note, “Wittgenstein’s use of Erklärung (‘explanation’) and Definition (‘definition’) was not always respected in Anscombe’s translation but we have kept to Wittgenstein’s choice of words” (see Wittgenstein [1953] 2009, xiii). The very same lack of respect, if I may put it that way, in translations of Frege is noted by Philip Ebert and Marcus Rossberg (see Frege [1893/1903] 2013, xvi) who likewise cleave to the author’s choice of German words. The fly in the ointment is that in ordinary German “Erklärung” can be used with the sense of “definition” although perhaps this usage is not frequent.) 2.2. Inferentialism Inferentialism can be held generally, as Peregrin (2014) holds it. Inferentialism says that the meaning of an expression in a language or the content of a concept is determined by some among its inferential relations to other expressions/concepts. As Robert Brandom says, inferentialism privileges inference over reference in the order of semantic explanation (Brandom 2000, 1). Unsurprisingly, perhaps, logic is where the inferentialist project has been most fully investigated, in the project nowadays called “proof-theoretic semantics.” Logic is where Peregrin spends a good bit of his book (Peregrin 2014) spelling out details of why rules matter. That logic ought to be a congenial domain for the inferentialist is suggested—no more than suggested—by Wittgenstein’s Tractarian Grundgedanke: Mein Grundgedanke ist, daß die “logischen Konstanten” nicht vertreten. (Wittgenstein [1921] 1961, § 4.0312)

226  Peter Milne The most commonly used framework for spelling out inferentialism for logic is natural deduction, the format for laying out inferences developed by Gerhard Gentzen (1935). That this is so is, I think, to some extent a matter of historical accident. It’s not, I want to say, that you couldn’t spell out inferentialism in, say, tableaux format; it’s just it hasn’t been done yet. (Increasingly the tableaux format is what is taught to undergraduates in their first logic course. Giving an inferentialist gloss to that format would seem to be necessary, if future, work.) This is an important point. The critical/normative role of logic extends readily to multiple-conclusion conceptions of logical consequence as in sequent calculus: if, where Γ and Δ are finite sets of propositions, Γ ⊢ Δ, a speaker lays herself open to criticism (and possibly sanction) when she asserts all members of Γ and denies, or otherwise indicates rejection of, all members of Δ. In his Notre Dame Philosophical Reviews review of Peregrin’s book, Chauncey Maher says, [Peregrin] holds that ∨ cannot be captured [by an inferential pattern]. In brief, his argument is that the introduction rules for ∨ (A ⊢ A ∨ B; B ⊢ A ∨ B) do not forbid a circumstance in which A ∨ B is true, but neither A nor B is true. So, there is “no straightforward inferentialist way to classical logic” (184). This need not be a problem for the inferentialist because she could [. . .] allow for “multiple conclusion” rules of inference, which permit one to draw multiple conclusions from a single set of premises (e.g., A ∨ B ⊢ A, B). Or she could admit that from an inferentialist point of view, intuitionistic logic is more “natural” than classical logic. (Maher 2015) Ian Hacking once reported that William Tait suggested to him that “the sequent calculus is right for classical logic, whereas natural deduction best fits a constructive approach” (Hacking 1979, 292). Whatever the truth of that, we should be open to the thought that, for an inferentialist, standard, single-consequence natural deduction may not be the only format in which the rules that matter for logic can be presented.6 And, contrary to what may be suggested by the passage from Maher that I have quoted, Jarda Peregrin is open to this thought—see Peregrin (2014, § 9.3).

3.  Harman on Reasoning and Inference In his Change in View (Harman 1986), Gilbert Harman mounts what is, on the face of it, a head-on challenge to the inferentialist position. Harman claims that inference has no special relationship with reasoning. It’s a challenge Jarda addresses in Chapter 11 of Peregrin (2014). He agrees with Harman that rules of inference are not tactical rules of belief management (reasoning); rather they are rules constitutive of that with which

Assertion, Inference, and the Conditional  227 or in terms of which we reason, “constitutive of the very space of argumentation and consequently of beliefs as inner correlates of assertions” (Peregrin 2014, 230).7 According to Harman, there is “no clearly significant way in which logic is specially relevant to reasoning.” There is, he maintains, inductive reasoning (belief revision) but not inductive argument, and there is deductive argument but not deductive reasoning. Logic deals with logical consequence, what follow from what. As it is put in a more recent work: Following tradition, we have been writing as if there were two kinds of reasoning, deductive and inductive, with two kinds of arguments, deductive and inductive. That traditional idea is confused, and correcting the confusion complicates the way the issue of inductive reliability is to be formulated. [. . .] The trouble is that this traditional picture of the relation between induction and deduction conflates two quite different things, namely, a theory of reasoning and a theory of what follows from what. [. . .] Sometimes in reasoning, we do construct a more or less formal proof or argument. But we do not normally construct the argument by first thinking of the premises, then the intermediate steps, and finally the conclusion. We do not generally construct the argument from premises to conclusion. Often we work backward from the desired conclusion. Or we start in the middle and work forward toward the conclusion of the argument and backward toward the premises. [. . .] It is a category mistake to treat deduction and induction as belonging to the same category. Deductive arguments are abstract structures of propositions, whereas inductive reasoning is a process of change in view. There are deductive arguments, but it is a category mistake to speak of deductive reasoning except in the sense of reasoning about deductions. There is inductive reasoning, but it is a category mistake to speak of inductive arguments. There is deductive logic, but it is a category mistake to speak of inductive logic. [. . .] [T]o call deductive rules “rules of inference” is a real fallacy, not just a terminological matter. It lies behind attempts to develop relevance logics and inductive logics that are thought better at capturing ordinary reasoning than classical deductive logic, as if deductive logic offers a partial theory of ordinary reasoning. It makes logic courses difficult for students who do not see how the deductive rules are rules of inference in any ordinary sense. It is just wrong for philosophers and logicians carelessly to continue to use this “terminology,” given the disastrous effects it has had and continues to have on education and logical research. We are not arguing that there is no relation between deductive logic and reasoning. Our limited point here is that deductive rules are rules about what follows from what, not rules about what can

228  Peter Milne be inferred from what. Maybe, as has often been suggested, it is an important principle of reasoning that, roughly speaking, one should avoid believing inconsistent things, where logic provides an account of one sort of consistency. But whether or not there is such a principle and how to make it more precise and accurate is an interesting question that is not to be settled within deductive logic. (Harman and Kulkarni 2007, 5–9) William Knorpp helpfully summarizes Harman’s view thus: Harman argues that (i) all genuine reasoning is a matter of belief revision, and that, since (ii) logic is not “specially relevant” to belief revision, (iii) logic is not specially relevant to reasoning, either. In commentary, Knorpp says, Harman’s argument begins with the claim that reasoning is a matter of reasoned change in view. But he is wrong about this. While many cases of reasoning do involve, or, rather, result in, changes in view, there are many examples of reasoning which obviously do not. I can reason unsuccessfully (that is, without arriving at a conclusion, thus having no reason for changing my view); I can reason about a problem that I have thought through previously, arriving at the same conclusion, or I can reason through a purely hypothetical problem, perhaps merely for amusement, with the results of this recreational reasoning having no significant effect on my “view” whatsoever. (Knorpp 1997, 81) This seems to me to be exactly right. But it misses something. To see what, let’s go back to the normative role of logic vis-à-vis assertion. We can criticize others’ assertions on the basis of (a) their inconsistency, (b) their failure to respect logical consequence, and (c) their failure to respect logical truth. And if we are going to do that effectively, we have to figure out logical ­relationships—maybe not in great detail, but we’ve got to make small steps, at least, steps of the sort encoded in the introduction and elimination rules of natural deduction or in the positive and negative rules for tableaux or in some such. Logic may not be “specially relevant” to belief revision, but it is relevant to our policing of ourselves and others in the practice of assertion.

4.  The Conditional 4.1.  Indicative Conditionals and Logic Harman’s distinction between belief revision and inference is important. It’s vitally important to what we do in conditional reasoning, reasoning involving “if.”

Assertion, Inference, and the Conditional  229 A long tradition in logic, going back to some among the ancient Greeks, has maintained that a proposition such as “If Anna is writing an essay, she’ll be in the library” is true if Anna is in the library, true if Anna is not writing an essay, false if Anna is writing an essay but is not in the library, these conditions being exhaustive. Two things need to be said. (i) However odd it may seem, this account gets right that a statement of the form “If not-p then q” follows from the correlated statement “p or q,” a step we very often take “without thinking.”8 (ii) It forces us to count as true an awful lot of very odd claims: If Stirling is in Scotland, Hradec Králové is in the Czech Republic. If Stirling is in Finland, Hradec Králové is in the Czech Republic. If Stirling is in Finland, Hradec Králové is in Slovakia. We must also accept as valid a whole lot of inferences suspect to the naïve ear. Here are ten examples taken from Cooper (1968): If John is in Paris, then he is in France. If he is in Istanbul, then he is in Turkey. Therefore, if John is in Paris he is in Turkey, or, if he is in Istanbul he is in France. It is not true that if she is over forty she is still young. Therefore, if she is still young she is over forty. If the temperature drops, it will snow. Therefore it will snow, or, if the temperature drops it will rain. It is not the case that if the peace treaty is signed, war will be avoided. Therefore, the peace treaty will be signed. If both the main switch and auxiliary switch are on, then the motor is on. Therefore, if the main switch is on the motor is on, or, if the auxiliary switch is on the motor is on. If Jones comes from Georgia, then he is a southerner. Therefore, if Jones rides a bicycle to work he is a southerner, or, if he comes from Georgia he owns a station wagon. It is not the case that if we follow that road we will reach the city. Therefore we will not reach the city. If it rains, then it will not snow. Therefore, if it rains the game will continue, or if it snows, the game will continue. If Albert’s age is greater than twenty and less than twenty-three, then Albert is either twenty-one or twenty-two. Therefore, if Albert’s age is greater than twenty then Albert is twenty-two, or if his age is less than twenty-three then he is twenty-one.

230  Peter Milne If Goldbach’s conjecture is correct, then it is false that if the mayor’s telephone number is an even number, it cannot be represented as the sum of two primes. Therefore, if the mayor’s telephone number is not an even number, Goldbach’s conjecture is not correct. 4.2.  Indicative Conditionals and Probability The logic tradition’s account of when indicative conditionals are true is completely at odds with what psychologists of reasoning tell us about how probable, how likely (to be true), we think conditional statements are. (See Milne 2012b for references to the extensive literature in the psychology of reasoning.) Consider an ordinary, well-shuffled deck of cards. Draw one “at random.” First, how likely is it that the drawn card is the queen of hearts? Second, how likely is it that the drawn card is the queen of hearts, if it is a red card (that is, heart or diamond)? I expect, and certainly the psychologists of reasoning expect, that you answered “1/52” to the first question and “1/26” to the second. On what I am calling the logicians’ account of the conditional, the answer to the second question is “27/52”! On the other hand, according to a great many psychologists, too many to list here, we quite systematically take Prob(if ϕ, ψ), equivalently, Prob(ψ, if ϕ) to be Prob(ψ | ϕ), the conditional probability of ψ given ϕ. Consider these short, banal discourses: Alice: If you get the wine from the fridge and I get the beer from the garage, everything will be ready for the party. Bob: I’ve already got the wine out. Alice: Okay, so we’re ready if I get the beer. Alice (to Bob and Cath): I f you go left at the Post Office and left again at the church you’ll be on North Street. We went left at the Post Office . . . can you see Bob to Cath (later): the church? Cath: Yes, there it is up ahead. Left there and we’ll be on North Street. Alice: 3  8,985 is divisible by fifteen if it’s divisible by three and divisible by five. Bob: 38,985 is divisible by three. Alice: S o if it’s divisible by five—which it obviously is—it’s divisible by fifteen. Do they involve reasoning, in more or less Harman’s sense, or do they represent cases of logical consequence? The question is vital because if

Assertion, Inference, and the Conditional  231 they are cases of logical consequence, the general pattern at work, taken along with other bits of logic that are unexceptionable or at least rather less contentious, make the logicians’ account of the indicative conditional inescapable. Here’s how. The pattern involved is If (ϕ ∧ ψ) then χ. ϕ. Therefore, if ψ then χ. Now we go (∧-elim). ϕ∧ψ⊢ϕ So ⊢ if (ϕ ∧ ψ) then ϕ (weak Conditional Proof). So ϕ ⊢ if ψ then ϕ (the pattern).

—and we have the positive paradox of material implication. not-ϕ ∧ ϕ ⊢ ψ (∧-elim and not-elim or ex contradictione quodlibet). So ⊢ if (not-ϕ ∧ ϕ) then ψ (weak Conditional Proof). So not-ϕ ⊢ if ϕ then ψ (the pattern).

—and we have the negative paradox of material implication.9 But the discourses can be explained using probabilities (degrees of belief) if reasoning, changing degrees of belief, is modelled like this:10 On learning that ϕ your probability for/degree of belief in ψ shifts like this: Probnew(ψ) = Probold(ψ | ϕ) (Bayesian conditionalization). We have Probold(if (ϕ ∧ ψ) then χ) = Probold(χ | ϕ ∧ ψ). On learning that ϕ and changing degrees of belief, we have that Probnew (if ψ then χ ) = Probnew (χ | ψ ) = =

Probnew (ψ ∧ χ Probnew (ψ )

)

Probold (ψ ∧ χ |ϕ ) = Probold (χ | ϕ ∧ ψ ) = Probold (if (ϕ ∧ ψ ) then χ ). Probold (ψ |ϕ )

We also have that Probnew(ϕ) = Probold(ϕ | ϕ) = 1 and so Probnew(χ | ψ) = Probnew(χ | ϕ ∧ ψ).

232  Peter Milne Hence learning that ϕ is the case leads to assigning the same degree of belief to “if ψ then χ” as to “if (ϕ ∧ ψ) then χ” in two senses: Probnew(if ψ then χ) = Probnew(if (ϕ ∧ ψ) then χ) = Probold(if (ϕ ∧ ψ) then χ). In principle we now have a straightforward way to tell whether If (ϕ ∧ ψ) then χ. ϕ. Therefore, if ψ then χ. is counted as logically valid. Do we criticize—or at least consider open to criticism—people who assert propositions of the form of the premises and deny, or otherwise indicate overt reluctance to accept, the cognate conclusion?—Or not? But if belief usually accompanies assertion (and nothing we have said suggests that this is not the case), such lapses should prove rare. Moreover, are we criticizing lapses of logic, failures to recognize what follows from what, or failures to conform to Bayesian conditionalization/change in view? It will, I think, prove difficult to contrive experiments that show up the difference. Perhaps the approach needs to be a little indirect. For example, Tibor Palfai and Peter Salovey found that: Elated and depressed moods had differential effects on two tasks that emphasized distinct components of the reasoning process. Elated mood had a debilitating effect on the solving of deductive reasoning problems, which are challenging because of the selective combination process required. Depressed mood, on the other hand, slowed performance only on analogies, which derive their difficulty from the nature of the selective comparison process. These findings are consistent with the notion of a mood specific cognitive style. Subjects in an elated mood had particular difficulty with a task that emphasized a style of processing inconsonant with their divergent mode of knowing. Similarly, those in a depressed mood were particularly slow in solving problems that required a mode of processing inconsonant with a logical, analytical cognitive style. (Palfai and Salovey 1993, 65–67) Well, there’s a hint there of evidence which may help determine what kind of reasoning lies behind our conversational snippets. Even if we do resolve that question and resolve it in favor of the soundness of the inference pattern, another problem looms. By appeal to the notion of robustness, Jackson could offer an explanation of why assertibility of the material conditional, the logicians’ conditional, as I have called it, “ϕ → ψ,” requires, as he thought, not just that Prob(ϕ → ψ) be high but also that Prob(ψ | ϕ) be high too: one thereby indicates that one is not asserting

Assertion, Inference, and the Conditional  233 “ϕ ⊃ ψ” largely on the basis of assigning a low probability to ϕ; one’s assertion of “ϕ → ψ” is robust in that on learning that ϕ one will continue to assert the conditional. On the face of it, however, robustness does not help in the slightest in explaining why you answered, as I take it you did, “1/26” when I asked, “How likely is it that the drawn card is the queen of hearts, if it is a red card?”11

Notes  1 Distinguishing knowledge and rationality versions of the paradox, Dana Nelkin (2000) notes that responses may differ: “it is tempting to many to assume” that one cannot know that ticket i won’t win but some, such as Kyburg himself, have thought that it can be rational to believe inconsistent things that one recognizes are inconsistent. (An historical aside: “In his lecture on probability at Cornell University, 1954 and 1958, G. H. von Wright discussed a paradox in connection with probability and practical certainty which is, from the logical point of view, identical with Kyburg’s lottery paradox,” Hilpinen 1968, 41.)   2 Of course, Dudman’s fundamental dialectical requirements are both complicated by the fact that one can, quite reasonably, change one’s mind. So maybe they should be stated more like this: a speaker lays herself open to criticism if • she makes inconsistent assertions over time and there are no factors, such as her overtly saying so, that indicate that she has changed her mind about some of them; • she asserts some propositions and she denies, or otherwise indicates overt reluctance to accept, a logical consequence of them and there are no factors, such as her overtly saying so, that indicate that she has changed her mind about some of them. Should enough time have passed, we might charitably take its mere passage to be such a factor.   3 I have written the norms as directives. I use this means only as shorthand. I am aware that care needs to be exercised and that perhaps the norms above would be better stated on the model of Judith Jarvis Thomson’s “An act of asserting that p is a correct asserting that p only if the asserter knows that p” (Thomson 2008, 90).   4 Notice that in the latter case overt reluctance to accept is not enough. Having not a clue as to which of p and not-p is the case, she will rightly indicate overt reluctance to accept either; she would, though, be open to criticism were she overtly to indicate rejection of both.   5 I have found Barry Stroud’s work helpful in understanding the later Wittgenstein on meaning. For the present points, see Stroud (1990a, 1990b, 1996).   6 Smullyan (1968, chap. 11) shows how closely tableaux rules are related to cut-free sequent calculi.   7 I would look to Stroud (1979) and to Cherniak (1986) for an elaboration of the constitutive role here. See Milne (2009, 273–275).   8 Some relevantists, for example, Stephen Read (1988), discern an ambiguity in our use of “or”: one sense, an extensional sense, of “or” allows that “ϕ or ψ” follows from “ϕ”; a different sense, an intensional sense, of “or” allows that “If not-ϕ then ψ” follows from “ϕ or ψ.” C. I. Lewis’s well known proof of ex contradictione quodlibet then trades on a fallacy of equivocation.

234  Peter Milne   9 The first argument goes through in Cooper’s (1968) OL, “ordinary logic,” supposedly the propositional logic of ordinary discourse; the second does not as OL does not admit its starting point. 10 It should be noted that Harman rejects this sort of modeling: “[I]t is too complicated for mere finite beings to make extensive use of probabilities” and updating by conditionalization, in particular, “leads to a combinatorial explosion” (Harman 1986, 25, 27). Nonetheless, this sort of modeling is already widely, and increasingly commonly, employed in the psychology of reasoning. 11 Jackson “now [that is, in 1998] think[s] that we should simply observe that indicative conditionals seem to have a probability of truth given by the probability of their consequents given their antecedents—call this their intuitive ­probability—and that this intuitive probability plays for indicative conditionals the role that (subjective) probability plays elsewhere in governing assertion” (Jackson 1998, 53–54). This recognizes that indicative conditionals behave differently from other assertible contents but does not tell us why.

References Belnap, Nuel. 1962. “Tonk, Plonk and Plink.” Analysis 22 (6): 130–134. Brandom, Robert. 1983. “Asserting.” Noûs 17 (4): 637–650. Brandom, Robert. 2000. Articulating Reasons: An Introduction to Inferentialism. Cambridge, MA: Harvard University Press. Cherniak, Christopher. 1986. Minimal Rationality. Cambridge, MA: MIT Press. Cooper, William S. 1968. “The Propositional Logic of Ordinary Discourse.” Inquiry 11 (1–4): 295–320. Dudman, Victor Howard. 1991. “Interpretations of ‘If’-Sentences.” In Conditionals, edited by Frank Jackson, 202–232. Oxford: Oxford University Press. Dudman, Victor Howard. 1992. “Probability and Assertion.” Analysis 52 (4): 204–211. Dummett, Michael. 1981. Frege: Philosophy of Language. 2nd ed. London: Duckworth. Frege, Gottlob. 2013. Basic Laws of Arithmetic: Derived Using Concept Script. Volumes I–II. Translated and edited by Philip A. Ebert and Marcus Rossberg with Crispin Wright. Oxford: Oxford University Press. Original edition, 1893/1903. Geach, Peter T. 1956. “Good and Evil.” Analysis 17 (2): 33–42. Gentzen, Gerhard. 1935. “Untersuchungen über das logische Schließen I, II.” Mathematische Zeitschrift 39 (2–3): 176–210, 405–431. Hacking, Ian. 1979. “What Is Logic?” Journal of Philosophy 76 (6): 285–319. Harman, Gilbert. 1986. Change in View: Principles of Reasoning. Cambridge, MA: MIT Press. Harman, Gilbert, and Sanjeev Kulkarni. 2007. Reliable Reasoning: Induction and Statistical Learning Theory (The Jean Nicod Lectures). Cambridge, MA: MIT Press. Hilpinen, Risto. 1968. Rules of Acceptance and Inductive Logic. Amsterdam: North-Holland. Jackson, Frank. 1979. “On Assertion and Indicative Conditionals.” Philosophical Review 88 (4): 565–589. Jackson, Frank. 1998. Mind, Method and Conditionals: Selected Papers. Abingdon: Routledge.

Assertion, Inference, and the Conditional  235 Knorpp, William Max. 1997. “The Relevance of Logic to Reasoning and Belief Revision: Harman on ‘Change in View’.” Pacific Philosophical Quarterly 78 (1): 78–92. Kvanvig, Jonathan. 2011. “Norms of Assertion.” In Assertion: New Philosophical Essays, edited by Jessica Brown and Herman Cappelen, 233–250. Oxford: Oxford University Press. Kyburg, Henry E., 1961. Probability and the Logic of Rational Belief. Middletown, CT: Wesleyan University Press. Lewis, David. 1976. “Probabilities of Conditionals and Conditional Probabilities.” Philosophical Review 85 (3): 297–315. Maher, Chauncey. 2015. “Jaroslav Peregrin, Inferentialism: Why Rules Matter.” Notre Dame Philosophical Reviews 2015.04.01. http://ndpr.nd.edu/ news/56764-inferentialism-why-rules-matter/. Millar, Alan. 2010. “Knowledge and Recognition.” In The Nature and Value of Knowledge: Three Investigations, edited by Duncan Pritchard, Alan Millar and Adrian Haddock, 91–190. Oxford: Oxford University Press. Milne, Peter. 2009. “What Is the Normative Role of Logic?” Proceedings of the Aristotelian Society, Supplementary Volume 83 (1): 269–298. Milne, Peter. 2012a. “Belief, Degrees of Belief, and Assertion.” Dialectica 66 (3): 331–349. Milne, Peter. 2012b. “Indicative Conditionals, Conditional Probabilities, and the ‘Defective Truth-Table’: A Request for More Experiments.” Thinking & Reasoning 18 (2): 196–224. Nelkin, Dana K. 2000. “The Lottery Paradox, Knowledge, and Rationality.” Philosophical Review 109 (3): 373–409. Palfai, Tibor P., and Peter Salovey. 1993. “The Influence of Depressed and Elated Mood on Deductive and Inductive Reasoning.” Imagination, Cognition and Personality 13 (1): 57–71. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan. Read, Stephen. 1988. Relevant Logic: A Philosophical Examination of Inference. Oxford: Basil Blackwell. Smullyan, Raymond M. 1968. First-Order Logic. Berlin: Springer. Stroud, Barry. 1979. “Inference, Belief, and Understanding.” Mind 88 (350): 179–196. Stroud, Barry. 1990a. “Meaning, Understanding, and Translation.” Canadian Journal of Philosophy, Supplementary Volume 16: 343–362. Stroud, Barry. 1990b. “Wittgenstein on Meaning, Understanding, and Community.” In Wittgenstein—Towards a Reevaluation: Proceedings of the Fourteenth International Wittgenstein Symposium, edited by Rudolf Haller and Johannes Brandl, 27–36. Vienna: Holder—Pichler—Tempsky. Stroud, Barry. 1996. “Mind, Meaning, and Practice.” In The Cambridge Companion to Wittgenstein, edited by Hans Sluga and David Stern, 296–319. Cambridge: Cambridge University Press. Thomson, Judith Jarvis. 2008. Normativity. La Salle, IL: Open Court. Unger, Peter. 1975. Ignorance: A Case for Scepticism. Oxford: Clarendon Press. Williamson, Timothy. 1996. “Knowing and Asserting.” Philosophical Review 105 (4): 489–523. Wittgenstein, Ludwig. 1953. Philosophical Investigations. Oxford: Blackwell.

236  Peter Milne Wittgenstein, Ludwig. 1961. Tractatus Logico-Philosophicus. Translated by David F. Pears and Brian F. McGuinness. London: Routledge and Kegan Paul. Original edition, 1921. Wittgenstein, Ludwig. 2009. Philosophical Investigations. Revised 4th ed. Translated by Gertrude Elizabeth Margaret Anscombe, Peter Michael Stephan Hacker, and Joachim Schulte. Oxford: Blackwell. Original edition, 1953. Wolgast, Elizabeth. 1977. Paradoxes of Knowledge. Ithaca, NY: Cornell University Press.

Part III

Rules, Agency, and Explanation

11 Naturecultural Inferentialism Joseph Rouse

1. Introduction Normative inferentialists from Sellars (2007) to Brandom (1994, 2000) and Peregrin (2014) develop a sophisticated logical and semantic apparatus to serve a broader social-rationalist vision. They treat the human world of meaning and understanding as a social space of mutual recognition among concept-users. Speakers are rational agents who track and respond to interactively instituted commitments and entitlements. The resulting “space of reasons” is the net outcome of many local discursive performances and assessments. That space is first and foremost a social space. It is also world-involving, through the discursive significance of reliable perception and action. The motivating telos of their versions of inferentialism is a maximally inclusive community of rational speakers and agents, whose performances are accountable to a common world in being rationally answerable to one another. In How Scientific Practices Matter (Rouse 2002) and Articulating the World (Rouse 2015), I endorse the impressive technical achievements of the normative inferentialist tradition, but appropriate them within a different philosophical vision. This revision turns Brandom’s or Peregrin’s social rationalism inside out. They start from the linguistic abilities and performances of rational agents. They then consider how intra-­linguistic performances incorporate and answer to perception and action, as causally reliable. I begin instead with our lives and lineage as organisms, perceptually and practically responsive to a partially shared biological environment. Our responsive capacities were shaped and utterly transformed by coevolution with language and other conceptual repertoires, through iterated cycles of niche construction. The result is a revisionist evolutionary naturalism. Discursive intelligibility and rationality are natural, scientifically intelligible phenomena, part of the world-transformative natural history of a very strange organism, homo sapiens. The political significance of inferentialism also shifts. Liberal rationalism aiming for a maximally inclusive discursive community is no longer understood as a quasi-transcendental commitment of rational discourse, but is instead one contestable and contested position within an evolving way of life.

240  Joseph Rouse I present this philosophical appropriation of inferentialist semantics in two parts. The first part reviews three central themes of the critical response to inferentialists’ broader philosophical vision that was developed in How Scientific Practices Matter and Articulating the World. I then sketch my alternative account of conceptual normativity and some of its consequences.

2.  Challenges to “Classical” Inferentialism Normative inferentialists begin their analysis with norms governing intralinguistic inferences. The semantic significance of an assertion is a functional relation from good reasons for that assertion to the entitlements bestowed by warranted commitment to it. Since collateral commitments affect that inferential significance in both directions, each inferential role incorporates contributions to a more extensive inferential network. The semantic significance of subsentential expressions is analyzed in turn using substitution and anaphoric dependences upon token expressions. With the semantics in place, the analysis then extends to the inferential significance of perception and action. Perception and action are causal processes. On Brandom’s or Peregrin’s accounts, they only enter the space of reasons indirectly, through defeasible judgments of practical and perceptual reliability. To be sure, this indirect extension is crucial to empirical conceptual content. Without connection to perceivable circumstances or practical activity, inferential relations among linguistic expressions would be empty, a “frictionless spinning in a void” in McDowell’s (1994) picturesque phrase. On this analysis, however, perception and action only contribute to intralinguistic proprieties via the rational recognition of causal capacities and constraints. One reason to reconsider this order of analysis turns on the public accessibility of discursive practices. On Brandom’s model, speakers are discursive scorekeepers who track one another’s changing commitments and entitlements in light of further performances. One cannot be a discursive scorekeeper without reliably recognizing token assertions, and reliably producing recognizable tokens in turn. Whether those tokens are spoken, written, signed, or drawn, their practical production and perceptual uptake is necessary to constitute those performances as intralinguistic moves within a discursive space of reasons. The game of giving and asking for reasons is a practical-perceptual activity. Brandom did claim that propositional content does not depend upon its “enrichment” by accountability to perception and action (Brandom 1994, 234), such that there might be an exclusively mathematical language whose objects are not empirically manifest, and Peregrin suggests that chess “can be seen as existing wholly independent of the causal realm, and chess as such can be seen as purely a matter of an ideal realm” (Peregrin 2014, 38). A moment’s reflection dissolves such fantasies of an acausal normative

Naturecultural Inferentialism  241 domain. The practical and perceptual reliability of public performances and their uptake is constitutive of a normative discursive practice even in formalizable domains such as mathematics or chess. We cannot separate the practical-perceptual and the conceptual-­ discursive aspects of linguistic understanding, even analytically. Davidson attempts that separation in his account of radical interpretation: interpreters differentiate linguistic expressions perceptually, and only then assign them semantic significance by holistic correlation to partially shared circumstances. The difficulty is that perceptual discrimination of semantically significant units and semantic grasp of how they fit together are entangled (Ebbs 2009, chap. 4–5; Rouse 2015, 121–126). This entanglement is familiar to anyone who has encountered conversations in a language she does not understand; discriminating the semantically significant units perceptually and imitating them vocally are integral to semantic interpretation. Reintegration of discursive practice into the practical-perceptual domain is reinforced by recognizing that classic inferentialist analyses mischaracterize the relations among perception, action, and intra-­ linguistic moves. Intralinguistic moves supposedly mediate between perceptual uptake and practical response. Perception is not just receptive uptake, however, but is itself active and exploratory; as Noë (2003) put it, there is always “action in perception.” Action is also always perceptual; embodied agents are responsive to the circumstances of action, in ways constitutive of action. In acting, we maintain balance, track our movements, and adjust to their proximate effects. John Haugeland criticized cognitivist accounts of intentionality because the very distinction between perception and action is itself artificially emphasized and sharpened by the image of a central processor or mind working between them, receiving “input” from the one and then (later) sending “output” to the other. The primary instance is instead interaction, which is simultaneously perceptive and active. (Haugeland 1998, 221) Social-rational inferentialism is neo-Cartesian in this way, substituting an ethereal realm of inferential assessments for a central processor of representations. Inferentialists treat intra-linguistic moves as ethereal in abstracting not only from the perceptual and skillful aspects of their performance and uptake, but also from how those moves are themselves worldly actions. Asserting is a practical performance with causal consequences as well as undertaking an inferential commitment in the space of reasons. In asserting, I also perform actions such as supporting the opposition party, recognizing a colleague’s professional standing, disrupting an economic transaction, or bringing an experiment to an end.

242  Joseph Rouse Recognizing the seamless integration of perception and action and the practical-perceptual character of language reorganizes our philosophical target. We should not begin with intra-linguistic moves—inferences— and only then ask how their proprieties confer conceptual significance on perception and action. We must instead begin with perceptual and practical interaction with an environment. We can then ask how some performances and recognitions accrue semantic significance through systematic, iterable relations to other performances. Classical inferentialists have resisted assimilating conceptual normativity to practical/perceptual interaction, because perception and action are causal processes within scientifically explicable nature. Inferentialists worry that naturalizing our conceptual capacities undermines the normativity of meaning and justification. My second consideration shifts the threat to conceptual normativity onto Brandom’s and Peregrin’s own efforts to maintain the rational autonomy of discursive practices. Understanding how discursive commitments and entitlements have normative force thus provides a second, related reason to invert the social-rationalist order of explication of classic inferentialism. Brandom and Peregrin approach this issue with an expressivist strategy that makes explicit the normative attitudes already at work in discursive practice. Only Brandom actually discusses the normative force of those attitudes, albeit briefly. He appeals to “differences in bodies and desires” to account for both the normative force of our commitments and entitlements and the differences in conceptual perspectives. A close, careful reading of his account, worked out in Chapter 7 of How Scientific Practices Matter (Rouse 2002), shows how Brandom relies here on another version of the Myth of the Given. On one hand, he identifies desires with Davidsonian de facto “pro-attitudes,” and treats bodies as causally interactive objects. On the other hand, desires must have irreducibly normative significance to express how discursive commitments are bindingly authoritative. Embodied agency likewise places us in a normative space of different conceptual perspectives. The underlying problem is a dualistic distinction of natural causality or law from the normative social space of reasons. In that context, bodies and desires are the inferentialist analogue to the role Descartes assigned to the pineal gland, as a locus for the magical reconciliation of irreconcilably conceived domains. My third consideration shows how recent developments in evolutionary biology allow us to circumvent the dualism. Orthodox neo-Darwinism also accepted a debilitating dualism of nature and normativity. Evolutionary programs for psychology and semantics developed in its terms were self-destructive: if correct, their own scientific explanations would be causally determined noise rather than meaningful, justified, or explanatory claims.1 Ecological-developmental biology and niche construction instead enable a non-dualistically naturecultural inferentialism. This revision

Naturecultural Inferentialism  243 has three primary components. First, ecological-­developmental biology shows organismic embodiment to be irreducibly normative.2 Organisms are not physical objects, but goal-directed processes of environmental interaction.3 Their biological environment is not the entirety of their physical surroundings, but a pattern of affordances for and obstacles to that life-process. Their goal is to maintain and reproduce that very process in changing circumstances, and they can fail to do so. Neither organisms nor their selective and developmental environments are determinate apart from these normative patterns of mutual interaction, for each can only be specified in relation to the other. Niche construction theory (Odling-Smee et al., 2003) then shows how organism and environment are entangled in a second way. Organismic life processes change their environments in ways that affect their subsequent development and natural selection. The most widely recognized forms of niche construction are abiotic: beaver ponds, soil breakup by worms, atmospheric oxygen produced by cyanobacteria, or the material infrastructure of human life. Behavioral patterns are also niche constructive, however, if they affect the selection pressures encountered by subsequent generations in ways that help reproduce that pattern. Language and other conceptual practices are preeminent forms of behavioral niche construction in the hominid lineage. Human beings normally develop as organisms in the midst of a multitude of discursive performances, which are usually heavily scaffolded to enhance acquisition of language, image-recognition, and equipmental skills. These capacities for acquisition evolved in concert with the gradual articulation of languages and other forms of conceptual practice, such that human brains were shaped by adaptation to language as much as the reverse. The third component of this reconception of discursive practices as naturecultural incorporates semantic inferentialism. Language and other conceptual practices have a partial autonomy. Utterances and other performances of a conceptually articulated practice are proximally assessed in relation to other such performances. Sentences in a language belong to a conversational or textual context, and iterate and recombine expressions from other contexts. They are assessed as meaningful and grammatically or semantically appropriate through those proximal relations to other linguistic performances. Such patterns of performance are nevertheless also open to assessment in another dimension: are they justified or true? The interplay of these two dimensions of language is nicely captured as a more inclusive semantic inferentialism and a prosentential conception of truth. A similar two-dimensionality also characterizes uses of equipment: one can ask both whether its use was appropriate (as a tool of that type in that role), and whether its use successfully fulfilled its practical aims. Actions in turn allow distinctions between what an agent was trying to do and whether the action succeeds.4 One-dimensional behavior, by contrast, cannot distinguish what an organism is trying to do from

244  Joseph Rouse how its behavior fits into a holistic pattern of life-relevant, goal-directed interaction. Such one-dimensionality nevertheless enables other organisms to respond in flexible, appropriate, and often highly sophisticated ways to changing circumstances, without needing a capacity for twodimensional normativity.5 Language, equipmental complexes, images, and other expressive practices are publicly accessible elements of normal human developmental environments. Our species has coevolved with these practices to enable their partial genetic assimilation, for ease, fidelity, and complexity of acquisition. These practices nevertheless only exist in their ongoing differential reproduction, and can disappear, in an extended form of biological extinction. Unlike other organisms, human evolution has itself become two dimensionally normative: what is at issue in how we go on is not only whether the lineage continues, but how we live, with tradeoffs between them. The normative force of our practices comes from our interdependence: we can only live a human life with the right supports from others as well as other environmental conditions. We must therefore adjust our performances to align with what others do in partially shared circumstances. Understanding these evolutionary and functional patterns provides a thoroughly naturalistic, biological conception of human life, which nevertheless encompasses the social-inferential articulation of semantic and practical normativity.

3. Why Niche Constructive Naturecultural Inferentialism Matters The central challenge for naturalistic accounts of meaning and knowledge is to understand the normative authority and force of conceptually articulated performances. That challenge also arises for Brandom’s or Peregrin’s minimalist naturalisms, which only demand the consistency of their philosophical account with a scientific conception of the world. Their response to this challenge is to show how discursive practices are objectively accountable. For example, Brandom argues that speakers’ differing conceptual perspectives within discursive practice must be triangulated with the objects to which they undertake de re commitments. Such commitments extend beyond those actually acknowledged, to incorporate whatever inferential significance accrues to claims one ought to undertake concerning those objects. The possible incompatibility of multiple claims about one object supposedly confers an independent check upon our discursive commitments. I argued in How Scientific Practices Matter (Rouse 2002, chap. 6–7) that this strategy is irreparably brokenbacked. I will not recapitulate that line of argument here, but will instead sketch the naturecultural inferentialist alternative developed in Articulating the World (Rouse 2015).

Naturecultural Inferentialism  245 A naturecultural inferentialist strategy circumvents the problem of rendering a network of inferential commitments accountable to independent objects. It does not begin with ethereal inferential relations that must then be held accountable to the world. It begins with our lives as organisms, whose life processes are entangled with and dependent upon a biological environment. Discursive performances and their uptake are part of that environment. We only develop normally as humans amid discursively and practically articulated patterns. We are social organisms, whose survival and way of life depend upon what others do in partially shared circumstances. What we can do, and what lives we can lead, depend upon how our performances align with what others say and do in response to these circumstances. We are always already amid a discursive way of life. The extant patterns of that way of life open intelligible possibilities for how to live within them. How that way of life continues, however, depends upon how later performances unfold and interact with one another in partially shared circumstances. Facing resistance from others or circumstantial obstacles to our performances and their intended significance, we adjust what we do. Issues arise wherever our interdependent performances fail to align effectively. What is at issue in those misalignments is how those patterns of practice will then go on. What is at stake in the resolution of those issues is whether and how those patterns can continue as part of an ongoing way of life. On one hand, discursive practices only exist if people continue to take them up and act in response to patterns of past practice. On the other hand, what those practices become depends upon how they are taken up. The result is a constitutively temporal conceptual normativity. The norms that govern discursive practices are not already determinate but instead are at issue in ongoing practice. What is at stake in resolving those issues is whether and how those practices and their encompassing way of life go on. “Issues” and “stakes” are only anaphorically specifiable, as responsive to patterns of past practice and projected continuations in more or less compatible ways. We can and do try to say explicitly what is at issue and at stake in our practices and our way of life. These utterances, however, themselves belong to the ongoing development of the practices they characterize. In the end, discursive performances are mutually accountable to one another and the other circumstances upon which they depend for their intelligibility and outcome. What differentiates our conceptually articulated way of life from the ways of life of other organisms is its two-dimensionality. One-­ dimensionally normative ways of life do not pick out what they are responding to or trying to do except as an overall pattern of environmental responsiveness. Conceptually articulated repertoires introduce a second dimension of accountability. Their performances—in language,

246  Joseph Rouse equipmental complexes, images, expressive musical performance, gesture, dance, or games—are proximally evaluated for appropriateness within the repertoire. Grammatically, semantically, and pragmatically appropriate utterances; properly performed skills and occupational roles; or competent, skillful performances exemplify one dimension of accountability. Such performances, and the standards to which they are held, are also assessed on a second dimension. Is what you said true, justified, or insightful? Did your skilled performance succeed in its broader aims within an ongoing practice? The norms to which performances are accountable are always at issue in the continuation of the practice, and part of what is at issue is the mutual alignment of the two dimensions. For linguistic practices, these two dimensions are expressed by pragmatic and semantic inferentialism and a prosententialist conception of truth. In the broadest evolutionary context, the two dimensions concern whether our way of life continues and what it becomes. In both cases, assessment on these two dimensions can play off one another. By contrast, onedimensional organisms evolve and change their behavioral patterns, but those changes and the character of the resulting transformations to their way of life are not themselves at issue for the organism or its lineage. What is at stake in their ways of life is only whether individual organisms stay alive and lineages reproduce themselves in the next generation, however that happens. I conclude by briefly noting two constructive consequences of this inversion and naturalization of inferentialism. First, this conception allows for a normative conception of power as distinct from coercive force. Inferentialists sharply distinguish causal relations from rational normativity, and typically treat causal interventions into discursive practice as arational. Naturecultural inferentialism instead recognizes that discursive performances are materially and practically situated, in ways integral to how we think and act. Paralleling Brandom’s and Peregrin’s accounts of the role of logical vocabulary, “power” is an expressive concept. It allows us to make explicit and reason about the normative significance of causal relations, including the causal efficacy of discursive performances. It lets us ask how one action aligns with others in shared circumstances to change the normative significance of other agents’ performances. What others do shapes my field of meaning and action, in ways I can resist, but not without consequences; my resistance or accommodation, and its alignment with other subsequent performances, in turn reshapes the field of action of those around me. Discursive practices and conceptually significant actions are always power-laden, without thereby becoming alien to discursive normativity. A second constructive consequence revises how we should think about scientific understanding. Representationalists and inferentialists each attribute to the sciences a telos of a comprehensive articulation of natural

Naturecultural Inferentialism  247 causes or laws. That conception generates Sellars’ (2007, chap. 14) classic problem of reconciling the manifest and scientific images. In Articulating the World, I show why this conception of scientific understanding is philosophically misguided (Rouse 2015, chap. 6–10). The sciences are research practices, whose conceptual articulation is always partial and future-directed. Scientific understanding is open to and directed toward further intensive and extensive articulation. Such developments are twodimensionally normative, just like any other conceptual practice or performance. The sciences aim not for truth alone, but for significant truths, insightful models, applicable capabilities, and partial connections among modally autonomous domains. We can thereby understand how the sciences both respond to and reconfigure what matters in our ongoing way of life. Scientific understanding of nature is neither an alien appendage to human life nor a “mere” social or cultural construction. It enables understanding ourselves as belonging to and dependent upon the natural world, even in our capacities to understand that world scientifically. Our evolved, niche constructive, two-dimensionally normative biological way of life articulates the natural world from within, as conceptually intelligible.

Notes 1 Millikan (1984) is a more complicated case of an explicitly Darwinian program in semantics. The difficulties with her account are not the straightforward problems introduced by efforts to account for semantic content and rational normativity in causal-functional terms, but instead turn on the subtler difficulties confronting representational semantics. 2 For more extensive discussion of ecological-developmental biology, see Gilbert (2001), Sultan (2015), and Lewontin (2000). 3 For discussion of why biological teleology should be understood in terms of goals rather than functions, see Okrent (2007). 4 Recognizing the diversity of two-dimensional conceptual repertoires does not require any close parallelism between the ways the two dimensions are divided in different conceptual repertoires, such as language, iconic representations, musical performances, equipment use, or various kinds of action. Indeed, performances in a single repertoire can be assessed in different ways in the same dimension, as for example when we are concerned with either the justification or the truth of an utterance. Thanks to Bob Brandom for calling attention to the need to address this question. 5 Rouse (2015, chap. 3–4) shows that it is a serious mistake to treat two-dimensional, conceptual normativity as a “higher” capacity that other organisms lack. On the contrary, the challenge for how to understand the evolution of human capacities for two-dimensionally normative performances and responses is to recognize the selective barriers to such capacities that had to be overcome within the hominid lineage and that persist in other organisms’ ways of life. Capacities for conceptual normativity would interfere with the flexible, close attunement to conflicting environmental signals that enables more complex patterns of behavior in many nonhuman animals.

248  Joseph Rouse

References Brandom, Robert. 1994. Making It Explicit: Reasoning, Representing, and Discursive Commitment. Cambridge, MA: Harvard University Press. Brandom, Robert. 2000. Articulating Reasons: An Introduction to Inferentialism. Cambridge, MA: Harvard University Press. Ebbs, Gary. 2009. Truth and Words. Oxford: Oxford University Press. Gilbert, Scott. 2001. “Ecological Developmental Biology: Developmental Biology Meets the Real World.” Developmental Biology 233 (1): 1–12. Haugeland, John. 1998. Having Thought: Essays in the Metaphysics of Mind. Cambridge, MA: Harvard University Press. Lewontin, Richard. 2000. The Triple Helix: Gene, Organism, and Environment. Cambridge, MA: Harvard University Press. McDowell, John. 1994. Mind and World. Cambridge, MA: Harvard University Press. Millikan, Ruth. 1984. Language, Thought, and Other Biological Categories. Cambridge, MA: MIT Press. Noë, Alva. 2003. Action in Perception. Cambridge, MA: MIT Press. Odling-Smee, John, Kevin Laland, and Marcus Feldman. 2003. Niche Construction: The Neglected Process in Evolution. Princeton, NJ: Princeton University Press. Okrent, Mark. 2007. Rational Animals: The Teleological Roots of Intentionality. Athens, OH: Ohio University Press. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan. Rouse, Joseph. 2002. How Scientific Practices Matter: Reclaiming Philosophical Naturalism. Chicago: University of Chicago Press. Rouse, Joseph. 2015. Articulating the World: Conceptual Understanding and the Scientific Image. Chicago: University of Chicago Press. Sellars, Wilfrid. 2007. In the Space of Reasons: Selected Essays of Wilfrid Sellars. Edited by Kevin Scharp and Robert Brandom. Cambridge, MA: Harvard University Press. Sultan, Sonia E. 2015. Organism and Environment: Ecological Development, Niche Construction and Adaptation. Oxford: Oxford University Press.

12 Inferentialism Where Do We Go from Here? Jaroslav Peregrin

“Because the rules are the only thing we’ve got!” William Golding, Lord of the Flies

1.  Where We Can Go from Here and Where I Want to Go In Brandom’s (1994) Making It Explicit, inferentialism was founded and developed as a relatively clear-cut philosophical edifice; and Brandom’s subsequent writings, despite adding some new stocks, have not changed its layout significantly. However, the edifice is surrounded by several burgeoning neighborhoods that threaten—or promise, depending on one’s view—to mesh with it and to change its nature significantly. One of these neighborhoods is constituted by a development within logic, where the term inferentialism has emerged independently of Brandom’s teaching and is now flourishing, somewhat overlapping with the Brandomian variety. Another neighborhood is emerging in connection with the current naturalistic trends of philosophy, which are closely interweaved with natural science; it brings about questions of the feasibility of the Brandomian picture of language and of human society from the viewpoint of scientific findings. A further neighborhood concerns the intricate relationship of inferentialism with the philosophical tradition, especially German idealism. And there are still other, smaller neighborhoods to consider. Personally, I see them as welcome challenges, engagement with which will ultimately strengthen the inferentialistic case (in the sense of the Nietzschean “what does not kill us makes us stronger”). I have already done some work on the interface between Brandomian inferentialism and the logical variety (see especially Peregrin 2008, 2010 and the second part of Peregrin 2014a); and in this chapter I would like to elaborate on certain ideas concerning its interface with natural sciences, previously introduced in chapter 6 of Peregrin (2014a) and in Peregrin (2014b). My overall aim is to summarize the current state of the art of such potential extensions of inferentialism, to address some objections, and to offer a (highly idiosyncratic, needless to say) view of its future.

250  Jaroslav Peregrin

2.  Philosophy and Science According to Brandom (2009, 149–150), what philosophers do is produce new vocabularies in which we can understand ourselves and each other, and they do that by thinking about the kinds of being we are, and about the role of such vocabularies in instituting and constituting the conceptual normativity that is the medium in which beings like us live our lives. Thus, the role of philosophy is distinct from that of science—philosophers neither tell us how the world around us is, nor explain why it is so. They rather equip us with certain expressive tools. I have my doubts about this: though agreeing that the task of a philosopher has some specific aspects, I would say that it is continuous with that of a scientist to the extent that the two cannot be disentangled. Take language and meaning, with which inferentialism deals intimately. True, we inferentialists offer new ways of looking at what people do when using language and expressing meanings, and we provide new conceptual resources to help us make this explicit. On the other hand, to be able to do this we first need to know what it is that people really do when using language, and to map this is an empirical enterprise. In this sense, I agree with Quine that “philosophy [. . .], as an effort to get clearer on things, is not to be distinguished in essential points of purpose and method from good and bad science” (Quine 1960, 3). Thus I think that even if we believe that philosophy is not necessarily the very same descriptive and explicative kind of enterprise as science, we philosophers should not shun learning what scientists have to tell us about the subject matters of our considerations, and we should pay attention to whether what they tell us is compatible with what we want to say. What I consider to be crucial for the inferentialist construal of the position of us humans within our world, is that the world is interwoven by rules. Our human sociality consists in redistributing the impact of our natural, physical environment on us in such a way that the limits of the world of an individual are no longer solely its natural limits: rather, they are normative, and are posed by all kinds of social rules. (But it is important not to overburden the opposition “social” vs. “natural” here—for social rules are not severed from nature, and often incorporate natural facts.) This crucial feature of our position in the world has been dramatically neglected, but I am convinced that it cannot fail to influence the interface of philosophy and the sciences. Arguably, we can identify three general areas of questions implied by a broadly conceived inferentialism (or should we better speak about normativism?) where the results of empirical research may be of intrinsic relevance:

Inferentialism: Where Do We Go from Here?  251 (1) The ontogeny of rules: how do rules become ubiquitous in the life of an individual, how does one learn to follow rules, and what does an individual life look like within the network of rules that constitute a human society? (2) Language and its rules: what is the role of rules, and especially inferential rules, with regard to natural language; which of these rules are de facto in force and how do they exist? (3) The phylogeny of rules: why have we, and how do we humans become the normative creatures we are; what might be the point of normativity from the viewpoint of evolution? It seems to me that over the last ten or twenty years, the first area of questions has been gravitating toward the full attention of empirical scientists; however, the other two areas have remained relatively unexplored. In what follows I would like to map the situation in greater detail.

3.  Normativity and Naturalism Inferentialism maintains that there is a sense in which the normative is not reducible to the non-normative—indeed, this was the point of quarrel between the so-called “right-wing Sellarsians,” who subscribed to its reducibility, and their “left-wing” opponents, who voted for its irreducibility. Brandom, and hence his inferentialism, belongs to the latter camp. It is, however, crucial to explain what the avowed irreducibility amounts to. I have tried to sort this out elsewhere (Peregrin 2016). I argued that the said irreducibility amounts to normative claims not being translatable into declarative ones; but that nevertheless this does not preclude there being a naturalistic story telling us how normative claims, as a specific kind of speech act, came into being and how normative discourse functions. My explanation of the irreducibility is thus utterly naturalistic: I claim that it is the consequence of the fact that “normatives” (statements to the effect that something is correct or that it ought to be) and declaratives are simply two different kinds of speech act, and hence that the intranslatability of the former into the latter is no more esoteric than the intranslatability of, say, interrogatives into declaratives. (I am unsure what Bob Brandom thinks about this, but I suspect he disagrees. In Brandom (2008) he talks about the idea that “although normative vocabulary is not reducible to naturalistic vocabulary, it might still be possible to say in wholly naturalistic vocabulary what one must do in order to be using normative vocabulary” and he ascribes it to Huw Price (Brandom 2008, 12). This is interesting in two respects. First, I am convinced that this very idea is explicit in the work of Bob’s mentor Wilfrid Sellars,1 whom Bob does not mention at all. Second, though Bob does not reject the idea, neither does he subscribe to it explicitly, which would seem to

252  Jaroslav Peregrin indicate that he wants to distance himself from it.)2 My hunch, then, is that we can have a fully naturalistic story about our normative capacities. And this chapter is a sketch of a travel plan according to which we can, I hope, arrive at it.

4.  The Ontogeny of Rules The fact that, as Sellars (1949, 298) puts it, “man is a creature not of habits, but of rules” must manifest itself in the way in which one is initiated into the community of others, given that a newborn child certainly is not yet “a creature of rules.” So it would seem that a child must be turned into such a creature during the process of its enculturation; and indeed forging it thus must be one of the most basic points of enculturation. And it would be strange if scientists who inquire into this process did not notice this. And indeed, recently there have appeared a number of papers indicating that one of the most basic skills an adept of a human society must inevitably master is the skill of assessing human doings as correct or incorrect (in more than one dimension) and of weaving her or his way through the maze of rules that comprise human society. I have discussed some papers of this kind elsewhere (Peregrin 2014b), so here I give only a digest. Some ten years ago, there started to appear papers considering the sensitivity of young children to norms. Probably the most popular (the results of which even found their way into popular media) was Hamlin and Bloom (2007). However, a lot of papers were produced especially by the Leipzig school of Michael Tomasello (Rakoczy and Tomasello 2008; Tomasello et al. 2012; Schmidt and Tomasello 2012; Rakoczy and Schmidt 2013; etc.). Schmidt and Tomasello write: Beginning at around 3 years of age, young children do not just follow social norms but actively enforce them on others—even from a thirdparty stance, in situations in which they themselves are not directly involved or affected. [. . .] Although there are many prudential reasons for following social norms, it is not immediately clear why a 3-year-old child should feel compelled to actually enforce them on others. Such group-oriented behavior opens the possibility that young children are not merely driven by individualistic motives but that, from early on, they start to identify with their cultural group, which leads to prosocial motives for preserving the group’s ways of doing things. (Schmidt and Tomasello 2012, 233) Thus, it seems that we humans are disposed to consider the doings of others not only from a narrowly egocentric perspective, but also from the perspective that classifies some forms of behavior as attractive or

Inferentialism: Where Do We Go from Here?  253 repulsive independently of who is its source and its target; that is, not only when these behaviors target me, but equally when they target somebody else, including, at least sometimes, even when it is me who is the source of the behavior in question. This tendency to assume an “impartial standpoint,” we can speculate, is a specifically human innovation in evolution; and I would go as far as to speculate that it is this single innovation that makes us creatures so different (discoursive, cultural, ultra­ social, . . .) from all other creatures of our world. In addition to this, in a recent book, Henrich, one of the current stalwarts of the burgeoning evolutionary studies of human culture, puts forward a picture that is a rudimentary synthesis concerning the role of rules within human societies and in the process of socialization (Henrich 2015). It is amazing to see how this thoroughly naturalistic picture resonates with the basically speculative picture drawn by Sellars and his followers. I think that Henrich is completely right when he talks about “norm psychology”: Over our evolutionary history, the sanctions for norm violations and the rewards for norm compliance have driven a process of self domestication that has endowed our species with a norm psychology that has several components. First, to more effectively acquire the local norms, humans intuitively assume that the social world is rule governed, even if they don’t yet know the rules. [. . .] Second, when we learn norms we, at least partially, internalize them as goals in themselves. This internalization helps us navigate the social world more effectively and avoid temptations to break the rules to obtain immediate benefits. (Henrich 2015, 188) In fact, my view is that the “norm psychology” is precisely the tendency to assume the “impartial standpoint” I talk about above (though I prefer to see it as a behavior pattern rather than as a matter of a psyche, which might misleadingly suggest that is it something sealed within the human mind). Henrich, of course, pays attention also to the ontogenetic aspects of “norm psychology”: By observing others, young children spontaneously infer contextspecific rules for social life and assume these rules are norms—rules that others should obey. Deviations and deviants make children angry and motivate them to instill proper behavior in others. What’s striking about these findings is that children can and will do all this without any direct teaching or pedagogical cues (like pointing or eye contact) from adults—though no doubt these must help convey the rules in many circumstances. (Henrich 2015, 186)

254  Jaroslav Peregrin All in all, the ubiquity of norms within human life is summarized as follows: It’s clear that when people encounter a new situation, they try to figure out which norms, among those they’ve already acquired, might apply to the situation and are also prepared to acquire new norms specific to this unfamiliar context (Henrich 2015, 190) It is interesting how similar this is to the well-known colorful depiction of human predicament given by Sellars: When God created Adam, he whispered in his ear, “In all contexts of action you will recognize rules, if only the rule to grope for rules to recognize. When you cease to recognize rules, you will walk on four feet.” (Sellars 1949, 298)

5.  Language and Rules That language is a matter of rules is generally accepted as a matter of course, but surprisingly, this feature is rarely pursued to its important consequences. Everybody knows that rules of grammar (and perhaps some other kinds of rules, like rules of orthography) are crucial for language. It is less clear, at least outside philosophical circles, that there are other, more important rules that do not determine how to produce wellformed expressions, but rather what to do with them. The usual view seems to be that although which linguistic vehicles are available for our perusal is a matter of (the grammatical) rules, how we peruse them is a matter that has nothing to do with rules, for we are completely free to juggle with the contents the vehicles are engaged to display. This, I think, betrays two misconceptions concerning rules and meanings. The first is the belief that an act that is rule-governed cannot be free, and the second is the misconception that the meanings of our expressions exist before the given expressions, and the given expressions are invented only to make these meanings public. That these are essential misunderstandings is quite clear to any adept of inferentialism (and possibly to some wider range of philosophers), but I do not think it is clear to those who are doing empirical research concerning language and its semantics. Empirical semantic theories are usually guided, implicitly, by uncritically accepted representational theories of human cognition and of language. (I do not want to say that representations cannot play an important role in the human mind and in its coping with the world, but I would stress that we should not simply assume that meanings are therefore a matter of representations.) And of course, we inferentialists, because we are pragmatists, insist that meaning is a matter of interaction, of interactions among individuals and interactions

Inferentialism: Where Do We Go from Here?  255 between individuals and the world, and that seeing it in terms of representations is utterly misguided. The rules that determine the semantic component of language are not as obvious as those of grammar, and in some cases, they are not even explicit. However, this makes them no less important than grammatical rules. Take the sentence “This is a dog.” One of the most basic skills which one who learns to handle it—and thus comes to count as understanding it—is that it is correct to display it in certain situations and incorrect in others (there will probably be a gray zone between these). This rule, however, is difficult to make explicit—for this would yield something as “One can use ‘This is a dog’ correctly if she points at a dog,” which is not very informative. Some of the other rules that must be mastered by anybody learning to use “This is a dog” are better in this respect. One must learn that whenever it is correct to display “This is a dog” it is also correct to display “This is an animal,” while it is incorrect to display “This is a cat”— namely, the inferential rule taking us from “This is a dog” to “This is an animal” and the rules that the former is incompatible with “This is a cat.” These rules can be made explicit without problems; however, they are usually taken, by linguists, as irrelevant for meaning, for they have learned, from logicians, to call inference “syntax,” and they have learned from Searle that “syntax is not enough for semantics.”3 What I find especially striking is the fact we do not know, by and large, which particular inferential rules hold for a natural language like E ­ nglish. I think that the only justified way to get clear about this is to find out which inferential patterns are endorsed by (the great majority of) the speakers of the language. Take the logical vocabulary. Since Gentzen, we know which basic inferential patterns are needed to characterize the most basic logical constants (and by now we know lots and lots about how to characterize all kinds of operators, including very weird ones); but what about their counterparts in natural language? Is, for example, the English “or” governed by the rules governing the classical “∨”? It might seem that this is the case, but would speakers of English accept “It is raining; hence it is raining or it is sunny” as an acceptable inference? Do we, in English, reason from “The streets are wet” to “If it is sunny, the streets are wet”? And to move from logical words to more mundane parts of English vocabulary, which basic inferential rules, featuring a word such as “dog” are the speakers willing to endorse? A large unexplored field of research activity is looming here!

6.  The Phylogeny of Rules An extremely interesting question, for me, is then the question of how and why rules and rule-abiding creatures emerged from the ferment of evolution. My idea is that it was selected as a tool of the peculiar form of sociality that we humans have developed.

256  Jaroslav Peregrin There are many kinds of social animals, but none of them has developed such a spectacular correlate of their social bonds as our human culture. I do not mean to say that it is culture that holds us together. I think that culture is better seen as an extravagant by-product of that which does; namely, rules. We humans build fantastic virtual worlds in which we are able to live: states, churches, universities, orders of knighthood, criminal gangs, gardening clubs, . . . All such virtual worlds are largely a matter of make-believe, they stand and fall with people taking them to stand or fall. They are, to use the notorious and treacherous word, conventional. A paradigmatic convention, like the Geneva convention, takes the form of explicit agreement among people, usually written down and ratified by the parties involved. But certainly not all human institutions can result from such explicit convention—language, for example, the institutional mother of all institutions, cannot itself be a matter of explicit conventions. Hence if we want to see it (and many other institutions) as based on convention, it would have to be convention of a special sort, it would have to be, as it were, implicit convention. And what I think is an ability piggybacking on our “norm psychology” is precisely the ability to establish implicit conventions. The first philosopher to grip this problem by the horns was David Lewis (2002), who showed how the kind of implicit convention that is capable of sustaining language could have come into being. His idea was that the convention can be established as an equilibrium of certain coordination “games”—“games” that characterize our human kind of interaction and that we thus come to play, inevitably and involuntarily. This is an important idea, but I am afraid that the kind of coordination considered by Lewis is not enough to explain what is really going on when we humans interact. For me what is crucial, and what ultimately differentiates our kind of sociality from the kinds of other animals, is precisely our tendency to abide by rules—I think it is precisely this that enables us to play games far more complex than were they solely ones of coordination, and that sets us up for erecting the awesome institutional edifice that is our culture. Coordination, in the straightforward sense of the word, clearly is something that is important for any social animal—in fact it represents, on the most fundamental level, what it takes to be social. But alone it brings us nowhere near to our human sophisticated kind of ultrasociality yielding our institutions and our culture. What I think is needed at the next level is the coordination of our normative attitudes. And this requires us to have normative attitudes, to be equipped with the Henrichean “norm psychology.” At the most fundamental level, I do not care about anything but my own business. The fundamental-level coordination is achieved because it

Inferentialism: Where Do We Go from Here?  257 results from everybody following their own interests. At the next level, however, I do care what others do. I care that everybody does what she or he should do—and consequently, I care whether I do what, according to others, I should do. This, needless to say, opens up a wholly new range of possibilities of coordination, or better something that is no longer so aptly called merely coordination, for there is an entirely new level of complexity of cooperation in play. Hints at this interconnection between norms and our specific human kind of sociality can be found scattered in the writings of Sellars. Recently, this has been picked up by Michael Tomasello (2014), who elaborated his earlier view, according to which it was shared intentionality that was behind our human specificity, in the Sellarsian direction, ending up with the view that it was social norms that were at bottom. He writes: Social self-monitoring is thus the first step in humans’ tendency to regulate their behavior not just by its instrumental success, as apes do in their goal-directed activities, but also by the anticipated social evaluations of important others. Because these concerns are about the evaluations of specific other individuals, we may think of them as second-personal phenomena. They thus represent an initial sense of social normativity—a concern for what others think I should and should not be doing and thinking—and so a first step toward the kind of normative self-governance, so as to fit in with group expectations, that will characterize modern humans in the next step of our story. (Tomasello 2014, 47) This, according to Tomasello, led to the following result: Modern humans thus operate with the social norms of the group as internalized guides to both action and thinking. This means that in their collaborative interactions modern humans conform to the collectively accepted ways of doing things, based on norms of cooperation, and in their communicative interactions they conform to the collectively accepted ways of using language and also linguistically formulated arguments, based on the group’s norms of reason. (Tomasello 2014, 120) I think that this view duly appreciates the role of norms within the development of our species, not only as a catalyst of our specific kind of social cohesion, but especially as the mold in which our specifically human thinking is cast. In this way, it seems to me that it is our “norm psychology,” our ability to assume the normative attitudes and thus to institute, maintain and

258  Jaroslav Peregrin abide to rules, which is the root of the diversion of the evolutionary trajectory of our human species from those of other species, including our cousins—apes. This principled innovation is, I think, the root of our culture, of our language, and of our distinguishing between appearance and reality, which launched our chase of the “objective truth” and led us to our science. This allows us to say that we humans, indeed, are creatures of norms.

7. Conclusion I am convinced that Brandomian inferentialism should not only be compatible with the results of relevant empirical research, but that it is virtually impossible to separate its philosophical from its empirical part. Thus, I think that inferentialism not only gives us new tools for explicitating ourselves and thereby making ourselves duly self-conscious (as stressed by Bob Brandom), but that it also indicates how certain things in our world (such as our languages, our societies and our minds) function. Of course it should not be taken as an armchair replacement of empirical research; however, I am convinced it can indicate helpful directions for empirical research, and that it can interpret the results of the research in a fruitful way. The crucial role of normativity for our human predicament, and the ubiquity of norms and rules in human lives, is not merely something that we philosophers have fancied as our way of embellishing reality; I am convinced that it is a tangible part of how we humans exist, and hence it is available for empirical sciences to find and anatomize. I think that until recently, this dimension of human existence has scarcely been reflected upon by scientists; however, it seems to me that recently the situation has been changing. I find it fascinating, and I believe that this amazing handshaking between us philosophers and scientists is something to cultivate.4

Notes 1 This is most explicit in Sellars (1953); see Christias (2015) for an exposition. 2 In a recent lecture I suggested, half-jokingly, that as Bob Brandom, as a trueblue left-wing Sellarsian, subscribes to the irreducibility of the normative to the natural, his followers might be divided into left-wing and right-wing Brandomians, according to whether they accept that this irreducibility is explainable, without a residuum, in naturalistic terms. Given this division, I am a devoted right-wing Brandomian. 3 A very specific role here is played by Chomsky and his school. According to them, language is rules all the way down. Aside of the rules of grammar, which are responsible for the “surface structure” of an expression, there are similar rules responsible for a “deep structure” or “logical form” that, as a matter of fact, amounts to meaning. Thus, in this sense, even the semantics of language is governed by rules, nota bene (pseudo?) grammatical rules. This, needless to say, is a notion of rules very different from that employed

Inferentialism: Where Do We Go from Here?  259 here (rules in our sense are characterized by the fact that they, as a matter of principle, can be violated). And it leads to the conclusion that it is not only rules all the way down, but in effect, syntax all the way down (and not syntax in the extended Carnapian sense of “logical” syntax that includes inference, but syntax in the narrowest sense of the word, which is a matter of merely well-formedness). 4 Work on this chapter was supported by grant no. 13-20785S of the Czech Science Foundation (GAČR).

References Brandom, Robert. 1994. Making It Explicit: Reasoning, Representing, and Discursive Commitment. Cambridge, MA: Harvard University Press. Brandom, Robert. 2008. Between Saying and Doing: Towards Analytical Pragmatism. Oxford: Oxford University Press. Brandom, Robert. 2009. Reason in Philosophy: Animating Ideas. Cambridge, MA: Harvard University Press. Christias, Dionysis. 2015. “A Sellarsian Approach to the Normativism-Antinormativism Controversy.” Philosophy of the Social Sciences 45 (2): 143–175. Hamlin, J. Kiley, Karen Wynn, and Paul Bloom. 2007. “Social Evaluation by Preverbal Infants.” Nature 450 (7169): 557–560. Henrich, Joseph. 2015. The Secret of Our Success: How Culture Is Driving Human Evolution, Domesticating Our Species, and Making Us Smarter. Princeton: Princeton University Press. Lewis, David. 2002. Convention. Oxford: Blackwell. Peregrin, Jaroslav. 2008. “What Is the Logic of Inference?” Studia Logica 88 (2): 263–294. Peregrin, Jaroslav. 2010. “Brandom’s Incompatibility Semantics.” Philosophical Topics 36 (2): 99–122. Peregrin, Jaroslav. 2014a. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan. Peregrin, Jaroslav. 2014b. “Rules as the Impetus of Cultural Evolution.” Topoi 33 (2): 531–545. Peregrin, Jaroslav. 2016. “Should One Be a Left or Right Sellarsian? (And Is There Really Such a Choice?).” Metaphilosophy 47 (2): 251–263. Quine, Willard Van Orman. 1960. Word and Object. Cambridge, MA: MIT Press. Rakoczy, Hannes, and Marco F. H. Schmidt. 2013. “The Early Ontogeny of Social Norms.” Child Development Perspectives 7 (1): 17–21. Rakoczy, Hannes, Felix Warneken, and Michael Tomasello. 2008. “The Sources of Normativity: Young Children.” Developmental Psychology 44 (3): 875–881. Schmidt, Marco F. H., and Michael Tomasello. 2012. “Young Children Enforce Social Norms.” Current Directions in Psychological Science 21 (4): 232–236. Sellars, Wilfrid. 1949. “Language, Rules and Behavior.” In John Dewey: Philosopher of Science and Freedom, edited by Sidney Hook, 289–315. New York: The Dial Press. Sellars, Wilfrid. 1953. “A Semantical Solution of the Mind-Body Problem.” Methodos 17 (5): 45–82.

260  Jaroslav Peregrin Tomasello, Michael. 2014. A Natural History of Human Thinking. Cambridge, MA: Harvard University Press. Tomasello, Michael, Alicia P. Melis, Claudio Tennie, Emily Wyman, and Esther Herrmann. 2012. “Two Key Steps in the Evolution of Human Cooperation.” Current Anthropology 53 (6): 673–692.

13 The Nature and Diversity of Rules Vladimír Svoboda

1. Introduction In philosophy, as in other disciplines of human inquiry, we witness a kind of terminological flux—some terms/concepts are fading away while others are becoming trendy. Among those terms whose frequency in philosophical debates has grown significantly over the last decades are surely “rule” and “norm” (in their various versions). Of course, debates about rules and norms have traditionally occupied an important place in areas like ethics or philosophy of law, but recently these concepts have also moved to center stage in areas such as the philosophy of language or the philosophy of mind. If we were to name one philosopher whose work gave the strongest impetus to this process, Ludwig Wittgenstein would be the obvious candidate. His sketchy yet deep meditations concerning rules and rule following (especially from Philosophical Investigations— Wittgenstein 1953) have directly or indirectly inspired many prominent philosophers of the analytical bent. Although numerous scholars follow Wittgenstein in recognizing the key role of rules in the formation of the human world and its various zones,1 attempts to pin down the meaning(s) associated with the term “rule” in a systematic and comprehensive fashion are scarce. Of course, all competent English speakers understand the word, but they are likely to be in trouble when asked to explain its exact meaning. This is u ­ nsurprising—in this respect the word “rule” is not different from words like “bed” or “penalty.” But it is obvious that though our ordinary grasp of the meaning of these words is sufficient for everyday conversation, it may let us down when we face the task of preparing a carpentry catalogue or substantiating a reform of the civil code. In philosophical debates, the question as to whether we understand each other when using certain words is of specific importance, as philosophers include concepts—meanings associated with the words—among the principal objects of their inquiry. Though reaching a wide consensus concerning the adequate explicating of the meanings of pivotal philosophical terms is close to impossible, investigations that may move us nearer to such a consensus (or at least to a better mutual understanding)

262  Vladimír Svoboda are surely worthwhile. This study is an attempt to proceed a few steps in this direction. The observation that the words “rule” and “norm” bear varied and rather indefinite meanings in English is close to trivial,2 and hence it is also not surprising that the mutual relationship of the two related concepts is far from clearly established. In the literature which addresses the relevant issues, one of these concepts is usually understood as superordinate. For example, G. H. von Wright in Norm and Action (von Wright 1963) conceives the concept of norm as more general.3 Others, like F. A. Hayek (1973), J. Raz (1990), or C. Bicchieri (2005), tend to take the concept of rule as more general and they treat norms as specific types of rules. Obviously, there is no point in trying to decide which terminology is the right one. In this study, I will adhere to the latter convention. I will try to develop conceptual tools that might help put discussions that focus on rules and norms on a firmer ground and underpin a comprehensive general account of the nature of rules. My intention is to complement (and to some extent rectify) the core analysis of normative concepts proposed by von Wright and point toward a solution to the so called ontological problem of norms mentioned in his Norm and Action. It is somewhat surprising that attempts in philosophical literature at a systematic general elucidation of the concept of rule are in short supply.4 The concept of rule is often (I am tempted to say “too often”) treated as primitive. At the same time, the term “rule” is associated with a surprising number of different characteristics/specifications.5 Are there, for example, rules that do not exist or that are not binding for anybody? Are moral rules, legal rules, rules of grammar, rules of logic, rules of games, prudential rules, or rules of a wolf pack substantially akin to each other in some respect, or are they connected just by a family resemblance, or indeed, are we simply encountering a terminological mismatch? I believe that such questions are worthy of attention. My account is to a large extent inspired by the analytical approach characteristic of von Wright’s foundational book Norm and Action. Though the present study is much more limited and less comprehensive than von Wright’s classical work, its main goal is similar—to contribute to a fundamental explication of the concepts of rule and norm that isn’t bound to any particular discourse (ethical, legal, sociological, linguistic, ethological, etc.) but might serve as a kind of reference point for philosophical debates on rules (in particular, for debates within the inferentialist “environment”).

2.  Social Norms and the Concept of Rule As I have suggested, my aspirations concerning the elucidation of the concepts of rule and norm are limited to the framework of general studies within analytically oriented philosophy. I will thus disregard

The Nature and Diversity of Rules  263 sociologico-psychological accounts of norms that conceive of them as specific beliefs/perceptions regarding what is expected in a social context6 or critical accounts proposing that norms are essentially concepts that are constantly used to control us and to exclude those who are not “normal” enough (cf. Foucault [1975] 1977). I will just frame the discussion by briefly mentioning two philosophical accounts of social norms that, in my view, illustrate the need for a fundamental elucidation of the concept of a rule. The first of them is the delineation of the concept of a social norm from an influential book by Cristina Bicchieri, The Grammar of S­ ociety (Bicchieri 2005). Social norms in Bicchieri’s account are informal ­ ­(uncodified) norms. Necessary and sufficient conditions for a social norm to exist are articulated in the following definition (Bicchieri 2005, 11):7 Let R be a behavioral rule for situations of type S. We say that R is a social norm in a population P if there exists a sufficiently large subset of the population such that, for each individual i from the subset: (i) i knows that a rule R exists and applies to situations of type S; (ii) i prefers to conform to R in situations of type S on the condition that: (iii) i believes that a sufficiently large subset of P conforms to R in situations of type S; (iv) i believes that a sufficiently large subset of P expects i to conform to R in situations of type S. I don’t want to analyze this definition here.8 I just want turn attention to a point that is easy to overlook, namely that the concept of rule (behavioral rule) is taken for granted in it. Bicchieri expects her readers to understand what it means that somebody “knows that a rule R exists and applies to situations of type S.” Though the concept of rule assumes this pivotal role, we don’t learn much about the nature of (behavioral) rules in Bicchieri’s book. She says, in passing, that rules prescribe a particular course of action for a certain situation or a class of similar situations, and that “once one adopts a behavioral rule, one follows it without the conscious and systematic assessment of the situation performed in deliberation” (Bicchieri 2005, 4) before stating that behavior tends to be “guided by default rules stored in memory that are cued by contextual stimuli” (Bicchieri 2005, 5). All this sounds prima facie plausible but without a clear clue as to the nature of the special entities called (behavioral) rules, the definition seems to lack firm grounding. I suggest that the strategy that invites the reader to adopt the concept of a (behavioral) rule as an “unexplained explainer” is too optimistic and that the concept is worth more careful attention.

264  Vladimír Svoboda In Jaroslav Peregrin’s Inferentialism: Why Rules Matter (Peregrin 2014) the concept of rule plays the central role. Peregrin focuses his attention on rules which shape our social world and our linguistic practices in particular. This specific concern influences the way in which he delineates the concept of rule. “Let us say, as a first approximation,” Peregrin proposes, “that a rule is a matter of a certain cluster of interlocking behavioral patterns” ­(Peregrin 2014, 70). In another place he claims: Rules are not a matter of merely resonating attitudes, but rather they tend to invoke a superstructure of customized and institutionalized reactions to improper behavior (“punishments”) as also to proper ones (“rewards”) that are often wielded in a cooperative manner. [. . .] The existence of a rule is thus a matter of the interlocking patterns of attitudes, actions, and reactions of many people. (Peregrin 2014, 10) Peregrin’s characterization of rules offers, in my view, a quite plausible account of the most substantial kind of social rules (or, in an alternative terminology, social norms).9 He convincingly shows that rules of this kind are fundamental in the sense that their existence is a precondition of existence of other kinds of rules, for example, of the explicit rules we encounter in systems of law, rules of games, or regulations issued by different authorities. It is, however, in my view not acceptable as a general delineation of the concept of a rule. I suggest that if we want to get a grasp of the nature of rules, we have to take into account rules of different sorts. In particular, I want to argue that it is useful to turn attention to the often-neglected rules we encounter at the social micro-level.

3.  L-Rules and F-Rules Let us imagine a situation when a mother named Martha tells her son, named Philip: “Philip, never climb up trees if you are wearing your dress uniform!” By her utterance, Martha articulated a rule and—if she succeeded in addressing her son properly and some other conditions have been ­satisfied—a certain rule has been established by her speech act. In this case, we don’t come across the interlocking patterns of attitudes and the behavioral patterns of many people—only two people are involved—but it is still hard to deny that in this situation a certain rule came into existence: the mother imposed a regulation on her son’s behavior.10 The mechanism for establishing simple rules of this kind is intuitively transparent. We are ready to say that the rule exists in the situation because we assume that a combination of two things occurred: (1) the mother successfully presented a certain general requirement concerning the behavior of her son, and (2) the son recognized that his mother imposed a restriction on his behavior. We can thus say that the mother and

The Nature and Diversity of Rules  265 the son have been bound by a new relationship—a n ­ ormative/­regulative relationship of a specific kind.11 Of course, in concrete, real-life situations it is often difficult to decide whether a certain rule has been set down.12 I am not here going to address problems associated with this elusiveness (which is, after all, characteristic of most social phenomena). I will instead open up my discussion of the nature of rules by exposing a fundamental ambiguity inherent to the common usage of the word “rule.” The ambiguity almost imperceptibly infiltrates philosophical texts and can also be identified in the brief presentation of our model example. When I first described the model situation, I said: “By her utterance, the mother articulated a rule and—if she succeeded in addressing her son properly and some other conditions have been satisfied—a certain rule has been established by her speech act.” If we read the sentence carefully, we notice that, in its latter occurrence, the term “rule” must bear a different meaning than in the former. First the word is used to refer to a certain general guideline of action that is linguistically articulated and then, in the second occurrence, the word “rule” is used to refer to a certain social fact. I suggest that the two kinds of uses of the word “rule” should be clearly distinguished. Let us begin by focusing on the first one. We talk about rules in this sense when we talk about linguistically articulated regulations of action/behavior. When we, for example, say that the European Council discussed a new rule that should guide the distribution of money from European Solidarity Funds or that some rule is mentioned in an etiquette handbook, we clearly speak about rules of this type. We mean various articulated regulations that can be found in written codes and assessed as concerns their clarity, coherency, or potential efficiency with respect to achieving goals that the codes are meant to achieve. To make clear that the term “rule” is used in this sense, I propose to speak about L-rules. The letter L indicates that we are dealing with linguistic objects. L-rules can be also identified as meanings of sentences that are suited for articulation of general regulations of behavior.13 Such sentences can be called rule sentences. Since quite diverse types of sentences are employed for the issuing of different kinds of regulations, it is advisable to distinguish a narrower delineation of rule sentences from a broader one. I propose to speak about proper rule sentences when we speak about sentences whose literal meaning is straightforwardly action guiding. Imperative sentences like “Do not smoke” or “Come to visit your grandmother every Sunday” can serve as examples. It might seem tempting to identify proper rule sentences with sentences in the imperative mood, but we shouldn’t forget that not all imperative sentences are straightforwardly action guiding. Sentences like “Do whatever you want,” “Eat the cake if you like it,” or “If you wish to make the soup thicker, add some roux” can serve as examples. It will hence be more adequate to use the denomination proper

266  Vladimír Svoboda rule sentences only for those imperative sentences that in their standard use are suitable for imposing a general limitation on the behavior of the addressee. Often it may be useful to adopt a broader concept of rule sentences and suppose that the term “rule sentences” also covers other types of expressions commonly used in speech acts whose purpose is to regulate someone’s behavior—especially should/ought sentences.14 In practice, of course, rules are established by utterances of various grammatical forms. We often use sentences in the future indicative (“You will visit the doctor every Thursday”), present indicative (“Patients visit the doctor every Thursday”), or even interrogative sentences (“Would you be so kind as to visit the doctor every Thursday?”), but it seems inappropriate to broaden the concept of the rule sentence so that it covers any sentence that can, in some circumstances, be used as a means of establishing a rule.15 Besides the cases when the word “rule” is used for talking about L-rules, the word is often used for talking about certain social facts. When we say that somebody breached the rules of good manners, showed his respect for the rules of fair play or that Sicilian Mafiosos respect certain unwritten rules, we manifestly use the word in this way. I suggest using the term F-rule whenever we want to make clear that we use the term “rule” in this sense. F-rules that give shape to our social environment—rules of morals, legal rules, or rules enabling linguistic communication, that is, rules that tend to form complex systems are naturally the focus of attention of philosophers. But we can, as I have suggested, profit from turning attention to F-rules that are less complex. As we have seen in our example with Martha and Philip, F-rules often come to existence through utterances by which one person addresses another.16 This is not, however, necessarily the case. F-rules can be established by means of non-linguistic actions such as gestures, physical manipulations, or by exhibiting a behavior that is presented as a pattern to be followed. F-rules are important constituents of social reality. What is the nature of these specific entities? Social reality is, I suggest, shaped primarily by different kinds of relations. In this case, we deal with relationships which can be called regulative. In our model example, one person—the mother—tries to affect the behavior of another person—her son—by a speech act that is most straightforwardly suited for this purpose, and she is, according to our assumption, successful. The success does not consist in the fact that she managed to regulate Philip’s behavior (this kind of success can only be assessed in the long run) but in the fact that she has managed to put a regulative pressure on her son which is to discourage him from climbing trees while wearing a dress uniform. We can generally say that a regulative relationship between two social subjects S1 and S2 is established when S1 has successfully manifested its

The Nature and Diversity of Rules  267 effort to regulate the behavior of S2—making S2 abstain from a certain kind of action or to act in a certain way (in a given situation). The subject who is in the position of being the authority of the regulative relationship plays, in the context, the role of the Prescriber while the subject whose behavior is (to be) “shaped” by the demand of the Prescriber plays the role of the Doer.17 We can generally say that the relationship tends to be robust if the Prescriber is capable of efficiently sanctioning the breaching of the rule while, in other cases, it is easily canceled. Normally, adoption of the role of the Prescriber is connected with accepting a certain measure of responsibility for the “rule-following behavior” of the Doer (even though the responsibility may be hard to circumscribe). Let us now return to L-rules for a moment. It is obvious that the same L-rule can be expressed by different rule sentences and the sentences can vary in their form or/and use of vocabulary. I suggest calling the rule sentences, whose communicatively successful articulation in common (nonspecific) circumstances would lead to the establishing of the same F-rule functionally equivalent. Adopting the opposite perspective, we can say that different functionally equivalent rule sentences represent alternative formulations of the same L-rule. L-rules can thus be understood as prescriptive versions/counterparts of propositions.18 Unlike propositions, which are typically seen as truth value apt by definition, L-rules cannot be reasonably considered as true or false. The picture I have outlined while building up the terminology can be presented in the form of the scheme captured by the figure 13.1: rule sentence

L-rule

(Prescriber-Doer) L-rule operative(Prescriber-Doer) (F-rule)

L-rule not operative(Prescriber-Doer)

circumstances C

F-rule non-applicable in C

F-rule applicable in C

F-rule followed by the Doer

F-rule not followed by the Doer

Figure 13.1 

268  Vladimír Svoboda According to this scheme any L-rule (expressed by a rule sentence) can be confronted with any social framework formed by an ordered pair consisting of two agents. We can then decide—providing that we have the relevant knowledge—whether the L-rule is operative within the framework. The L-rule is operative if and only if the agents are bound by the relevant regulative relationship (the relevant F-rule exists).19 Any F-rule (L-rule operative within a Prescriber-Doer framework) then can be, depending on circumstances, applicable or not. If it is applicable then we can say—providing that we have the relevant knowledge—whether it is followed or not followed by the Doer.20 I believe that this schematic picture appears quite plausible if we limit attention on the relatively simple case of micro-level rules, but is it sustainable as a general prism through which we may view rules of different kinds? I want to suggest that it is, though with some provisos. In modern societies diverse kinds of social subjects are able to get bound by regulative relationships—to occupy the positions of a Prescriber or a Doer. A substantial feature of each subject (social body) that can occupy such a position is the ability to function as an agent. Ascribing the status of an agent to a person or a social body can, unsurprisingly, be quite a controversial issue. The status is sometimes not hard-set, but rather ascribed to different individuals and social bodies in different degrees and relative to circumstances. For example, children only gradually gain the ability to “operate” as fully-fledged agents—Prescribers or Doers. The states, as well as the different social institutions existing within states, assume the role of Prescribers, establishing many important F-rules which are crucial for the functioning of modern societies. Such institutional social subjects typically establish F-rules that are not aimed at a particular individual (or a super-individual social body) but that are general—any agent that satisfies a certain condition (is, for example a citizen, a student of a school, a visitor to a gallery) is supposed to occupy the role of the Doer. Thus, we often have an institutional Prescriber on the one hand and individual Doers on the other. We thus can say that a number of parallel regulative relations (F-rules) are established by the utterance which brought such F-rules to existence. Alternatively, it can be convenient to talk about one F-rule with a single Prescriber and a collective Doer (the citizens, the pupils, the visitors, etc.). It is, however, important to keep in mind that members of the collective typically act as autonomous agents.21 Actions of institutional or collective subjects have their peculiar features I am not going to discuss here.22 Generally, I suggest employing the term “norm” to designate social F-rules that regulate certain activities in the whole (sub)society. Norms of this kind typically have a “super-individual” Prescriber and usually form precisely or less precisely delineated systems. As the distinguishing of interwoven norms can be very difficult, it may sometimes be more natural to view the whole normative system as a single, very complex

The Nature and Diversity of Rules  269 F-rule. The existence of this F-rule then substantiates claims to the effect that different L-rules are operative (in the given context). This allows for alternative (partial) articulations of such complex normative systems.

4.  Normative Spaces and Relative Validity of L-Rules Let us now turn to one more example which should help us get a grasp on another aspect of the common (and professional) talk of rules. Suppose that Martha invented a new card game. The invention consists in setting down a certain collection of L-rules that are formulated by a set of natural language sentences. The L-rules jointly decide how the game starts, what the players are supposed (allowed) to do in its different stages, and who wins and who loses.23 If Martha has managed to devise a viable game, she has created a ready-made normative space that can be entered by people who decide to play. The game at the point of its invention does not exist as a social phenomenon, but Martha’s invention still has in a way changed the world. A new game is ready to be played and different people can, under some conditions, enter the normative space created by Martha. We can say that the normative space of the game “exists” in a “standby mode”—SB-exists.24 We can then say that a certain L-rule is valid within a certain SB-existing normative space (SB-system), while another is not. To some extent the situation is analogous to the case depicted in figure 13.1. This time we confront an L-rule not with a normative context formed by a couple of agents but with a certain potential normative space. But even if we conclude that the L-rule is valid within the given SB-system (is relatively valid), the question as to whether it is applicable or followed do not arise. These questions arise only when some agents enter the space—when the relevant L-rules get “actualized” (operative). Whenever people enter such a space (begin to play, for example, Martha’s game), a network of F-rules—a part of a social reality—is temporarily established. The players assume both the role of the Doer who is bound by the F-rules and of the Prescriber who requires other players to respect them.25 People who engage in playing Martha’s game— similarly as people who engage in playing chess or basketball—together create a piece of social reality. (Of course, if nobody wants to play the game, the ready-made normative space stays idle.) Appearance of human languages opened the possibility of setting versatile normative spaces by means of L-rules expressed by rule sentences. The SB-existence of the systems opens the possibility that agents enter quite complex systems of regulative relationships in one fell swoop. Our world is crammed full of different kinds of ready-made normative spaces, most of which, at least from time to time, get “materialized” in complex networks of actual regulative relationships among agents. Companies, sport clubs, or monastic orders tend to form their own normative spaces.

270  Vladimír Svoboda It may be useful to distinguish between two kinds of SB-systems: (1) SB-systems prepared to guide behavior within an independently existing social space, and (2) SB-systems determining (establishing) a certain (potential) social space. A code determining what visitors of a forthcoming village festival are allowed and/or obliged to do can serve as an example of the first kind of SB-system. We assume that the social environment that gets formed by people who will take part in the festival will exist independently of the specific SB-system set down by the organizers. The festival would presumably take place even if no SB-system gets proposed and adopted.26 On the other hand, some (potential) social spaces, those formed, for example, by systems of L-rules governing games such as chess, can be said to be formed by constitutive rules—relatively valid L-rules that together constitute a specific (potential) practice. L-rules valid within an SB-system of the first ­(village festival) kind can then be called regulative.27 The game of chess provides an example of a system of L-rules that have been intentionally formed and fixed (though the SB-system received its present shape over a long period of time). We can say that the intentional rule-creating activity preceded the rule-following activity. In other cases, the normative spaces that can be from a certain perspective viewed as SB-­systems have grown from social practice. They were not designed but shaped within complex processes of social interaction that fixed them primarily as systems of F-rules that even don’t have to be explicitly articulated.28 I am going to say more about this in the following section.

5.  Explicit and Implicit F-Rules Though situations when a regulative relationship is set by an utterance of a certain human or institutional agent represent the most transparent cases of establishing F-rules, they are just one among various courses of events through which F-rules get established. Regulative relationships are commonly established by a concurrence of corrective reactions of different kinds. Typically, the “negative” corrective reactions—admonitions or penalizations of different kinds—are easier to discern, but “positive” corrective reactions like approvals, rewards, or instructive examples are not less important. In everyday life, these reactions are typically interpreted as intentional manifestations of certain attitudes, but they are often spontaneous, that is, not (fully) intentional. Parents typically regulate the actions of their small children automatically. They, for example, continuously teach their children to speak by rectifying the ways in which they express themselves—they correct them, formulate the right statements or questions on their behalf, give them different hints as to what to say or to suggest what “we do not say.” They spontaneously assume the position of the Prescriber and demand that their child observes F-rules (typically articulable as L-rules) governing the natural language that is to become her/his mother tongue. It is quite

The Nature and Diversity of Rules  271 unessential what their motivation might be; whether they deliberately want their children to speak correctly (to take part in the “game” as competent players), whether they would say that they do it in the interest of the child, or whether they behave without a rational motive (their educational/corrective reactions are instinctive). It is worth noticing that we can view languages from two p ­ erspectives— as potential normative spaces (SB-systems) or as actual normative spaces (systems of F-rules). In the case of a living language, the second perspective is primary as the practice of using the language is ubiquitous and the regulative relationships get continuously manifested in corrective reactions of the agents (speakers of the language). In the case of dead or artificial languages, the first perspective seems somewhat more natural. What has been said about the different ways in which F-rules can originate allows us to clearly articulate a further terminological distinction: F-rules can be schematically divided into two categories—explicit rules and implicit rules. Our model F-rule concerning Philip’s tree climbing can serve as a paradigmatic example of an explicit F-rule. Implicit F-rules are more difficult to pin down. F-rules of this sort are not established by speech acts consisting in an utterance of a rule sentence. Imagine that in Martha’s family the adults have almost unconsciously established certain F-rules concerning their sitting around the family table. If they have made Philip reseat himself whenever he has sat in the place that his father likes to sit, and the father does not sit down until “his place” is vacated, Philip is sure to understand that his parents demand that he doesn’t sit there during family dinners. Similarly, they can teach him not to speak out loud in church simply by lowering their voices whenever they enter the church and by reacting with gestures of disapproval when he raises his voice. In this way, they may establish an implicit F-rule.29 We commonly encounter both explicit and implicit F-rules on the macro-level of developed societies.30 Typically, both kinds of F-rules are interwoven into networks of different complexities. Individuals belonging to the societies normally play—constantly or under some conditions—the roles of the Doers within different regulative relationships establishing such F-rules. In the case of explicit F-rules, different institutions normally play the role of the Prescriber. Legal norms are the paradigmatic example here.31 In the case of implicit social F-rules (norms), the individual agents typically occupy the role of the Doers but they also, as members of the society, jointly play the role of the collective Prescriber. From what has been said, it should be clear that the basic feature that distinguishes explicit F-rules from implicit ones concerns their genesis— the history of their establishing and reinforcing. It is not uncommon that F-rules that originated as implicit get, at some point, articulated in the form of an explicitly voiced requirement (for example, Martha says at some point to Philip, “You ought to speak quietly when you are in a church”). Though such an explicit articulation doesn’t establish a new F-rule, it is capable of changing its “status.”

272  Vladimír Svoboda Implicit F-rules come into being in various ways—they are typically rooted in habitual practices and stereotypes that have become perceived as patterns to be imitated (and so deviant behavior tends to evoke corrective reactions). These F-rules are, so to say, “self-supporting”—we learn to follow them, as Wittgenstein says, blindly (cf. Wittgenstein 1953). The task of individuating and “explicitating” the F-rules embedded in complex systems of implicit F-rules may turn out to be very difficult. One of the reasons is that the mastering of the relevant rule-governed practice tends to mostly be a matter of practical know-how rather than a kind of theoretical knowledge. (Folk dances can perhaps serve as a good example here.)32 I believe that distinguishing between explicit and implicit F-rules is legitimate and important. In some cases, the categorization is unproblematic. It is, for example, clear that in communities of chimpanzees all F-rules are implicit33 and that legal F-rules or the mentioned F-rule concerning Philip’s tree climbing are clearly explicit. But in other cases, the situation may be quite indeterminate. One reason is that the process of the genesis of F-rules is often complex, and it may be quite unclear which corrective speech act should be seen just as a “hint” and which is to be regarded as an explicit articulation of an F-rule (though perhaps only a partial one). Another reason is that it is in many cases natural to view F-rules as having one “source” ­(Prescriber) but many addressees (Doers). If we adopt this picture then there, for example, arises a possibility that the same F-rule can be perceived as implicit by some addressees and as explicit by other ones, depending on how they have become acquainted with it. For such reasons we should be careful and not put too much weight on the distinction.

6. Conclusion The conceptual and terminological distinctions provided in this article point in the direction of a relatively simple and at the same time systematic solution to the so-called ontological problem of norms that is discussed by von Wright in his classic work Norm and Action.34 Rules (norms) exist in (at least) two senses. In the case of F-rules, we can talk about a full-fledged existence—F-rules are social facts established by regulative relationships among agents. In the case of SB-systems, it makes sense to talk about the weak (relative) “existence” of L-rules. These rules can be (relatively) valid but needn’t be actually binding for anybody—the relevant normative spaces needn’t be actually “inhabited” by agents. I believe that the account of rules/norms outlined in this article can be regarded as an elaboration of von Wright’s general conception according to which an utterance of certain sentences can result in the establishment of a certain relationship35 and the given norm is valid for the time of the existence of the relationship (cf. von Wright 1963, chap. 7). Terminology

The Nature and Diversity of Rules  273 provided here allows us to avoid—especially thanks to the distinction between rule sentences, L-rules, relatively valid L-rules, and F-rules— some ambiguities, which are connected with von Wright’s use of terms “norm,” “rule,” or “command.” Moreover, the framework outlined in this article allows one to address the ontological problem more comprehensively than von Wright’s framework. Although von Wright uses the term “norm” as an umbrella designation that includes rules, prescriptions, customs, and directives, he discusses the ontological problems only in connection with prescriptions (which would correspond to our explicit F-rules). I also believe that the present framework might contribute to a clarity of semantic and logical studies concerning rules/norms/commands.36 Within these studies, for example, we come across two different “semantic values” associated with deontic sentences/propositions—they are said to be valid (in force) or invalid on the one hand37 and satisfied or violated (by an agent) on the other hand. From the perspective outlined here, however, these “values” should be ascribed to somewhat different objects—only F-rules (norms) can be satisfied/followed and only L-rules can be meaningfully said to be valid/operative.38

Notes  1 Sometimes, of course, the links to Wittgenstein are not direct. This concerns especially the strong stream of philosophical studies elaborating on the heritage of another distinguished philosopher who pointed to the crucial importance of rules—Wilfrid Sellars; but also, for example, the school of economico-philosophical inquiries originated by Friedrich von Hayek.   2 This has been pointed out many times. Von Wright, for example, opens his Norm and Action by noting that “the word ‘norm’ in English and the corresponding word in other languages, is used in many senses and often with an unclear meaning” (von Wright 1963, 1). Boghossian in the opening part of his article about rules stresses that “part of the problem here is that ordinary language is not precise when it comes to the word ‘rule’—one can legitimately talk in different ways and so there is a danger of people talking past one another” (Boghossian 2015, 3).   3 Rules, for example, rules of games, are according to von Wright a standard example of a main type of norm; prescriptions (regulations) issued by an authority and directives (technical norms concerned with means to be used for the sake of achieving a certain end) are other main types of norms (von Wright 1963, 6–10).   4 Boghossian (2015) or Hage (2015) can be seen as attempts to provide such a general account, but under closer examination, we find out that they concentrate their attention on moral rules/norms (Boghossian) or legal rules/norms (Hage) even though they make claims about rules in general.   5 We are used to hearing/reading that rules have a certain content, are valid or invalid, explicit or implicit, articulated (written down) or tacit, followed or violated, known, understood or misunderstood, learned, enforced, motivationally effective, applicable, etc.

274  Vladimír Svoboda   6 An interesting survey of how different social sciences have approached the study of social norms can be found in Chung and Rimal (2016).   7 I present it in a slightly simplified version.   8 Its critical discussion can be found in Brennan et al. (2013) or in Peregrin (2014).   9 His “interactive” account substantially differs from those which take social rules (norms) to be essentially perceptions of what others do and what they (dis)approve of. Cialdini and Trost (1998) can serve as an example of such an account of social norms. 10 Another possibility, of course, is that the rule forbidding Philip to climb trees in his dress uniform already existed and was just reinforced by the speech act. But let us for simplicity disregard this option. 11 It is worth noting that individuals (social subjects) are also bound by a kind of “demandatory” relationship in cases when the relevant requirements are not general but require a particular (individual) action (“Pass me the salt!”). Relationships of this kind are (unlike rules) typically transient—they cease to exist by execution of the demanded action or when the period when it could have been reasonably executed passes by. 12 We tend to presume that only subjects having some authorization or power can successfully form a normative relationship, but it is doubtful whether this should be seen as a general condition. We can, for example, imagine that Philip managed to successfully establish a certain rule (and his mother consistently follows it). 13 Some people might perhaps find the choice of the letter “L” pointing to the linguistic nature of L-rules misleading. They might argue that meanings are in fact prelinguistic ideal entities that are only secondarily (by convention) associated with linguistic “embodiments”—paradigmatically sentences of natural languages. I don’t have space here to challenge such a picture. Thus, I can only suggest that those who wish may assume that the disambiguating “L” refers to a language of mind. 14 The well-known trouble with should/ought sentences (von Wright 1963 calls them deontic sentences) is that they are ambiguous. Prescriptively interpreted, they express L-rules; descriptively interpreted, they express (true or false) deontic propositions. This ambiguity can be the source of various misunderstandings. Some of those that arise within deontic logic are discussed in Svoboda 2017). 15 The concept of a rule sentence is related to von Wright’s concept of norm-­ formulation (see von Wright 1963, 93). In his account, however, a normformulation is identified with “the sign or symbol (the words) used in enunciating (formulating) the norm” and so, for example, a traffic-light can serve as a norm-formulation. In this respect, von Wright’s concept of normformulation is a looser concept than my concept of rule sentence. 16 Here I use the term “utterance” broadly—written declarations or regulations carried out in a specific, institutionalized way (for example, published in a codex) count as utterances. Of course, not all cases when a rule sentence is uttered result in establishing an F-rule—our Martha might, for example, pronounce the sentence too quietly to be understood (or even noticed) by Philip, she might say it during a kind of “let’s pretend” game or her utterance could be misplaced (if, let’s say, Philip is only a toddler). 17 This terminology is my modification of the terminology introduced by David Lewis who distinguishes the roles of the Master and the Slave in his discussion of scorekeeping in deontic language games (cf. Lewis 1979). It is worth noting that the roles needn’t always be divided. In the specific case of autonomous F-rules the same subject can simultaneously play both the role of the

The Nature and Diversity of Rules  275 Prescriber and the role of the Doer—for example, if one imposes on herself the duty to abstain from drinking any alcoholic beverages. 18 If a proposition is understood as “that which two sentences in different languages must have in common in order to be correct translations each of the other” (Church 1956, 25), then L-rules may be seen as that which some imperative sentences in different languages have in common. 19 Of course, often the relevant F-rule gets established by an utterance of a certain rule sentence—perhaps one that straightforwardly expresses the L-rule in question but possibly one that is more general or more complex. 20 Some F-rules are categorical—applicable in any circumstances. In situations in which a certain F-rule exists but the conditions of its application do not arise, we can say that the F-rule is trivially followed. 21 Nicholas Rescher distinguishes cases when a certain command is addressed to one group collectively and a situation when it is addressed distributively (Rescher 1966, chap. 1). 22 Searle (1990), Tuomela (1995), and Pettit and List (2011) deal with the issues of decision-making and actions of “super-individual” subjects. 23 This last rule has a specific status. It is a rule that cannot be followed within the game but only on the meta-level. Put very simply—those who take part in the game are bound to aim at winning. If they manifestly break this metarule, they can be said to spoil the game and may be punished for that (though not within the game). 24 It should be clear that SB-existence is different from Meinong’s subsistence. The difference is analogous to one between musical pieces that have been composed and those that only might be composed. 25 We can imagine that a further authority (also) assumes the role of the Prescriber. For example, Martha can supervise the players. In cases of games that are to a certain extent “institutionalized,” referees or organizers supervise the game (uphold the applicable F-rules). Thus, they assume the role of the principal Prescriber. This, however, doesn’t imply that regulative relationships among the players are unessential, what is primarily concentrated in hands of the referee (organizer) is the control over the penalizing of transgressions against the F-rules. 26 In fact, the two cases deserve to be distinguished as L-rules pertaining to an SB-system that has just been formed and proposed are apparently valid in a somewhat weaker sense than those pertaining to an SB-system that was officially approved by the organizers of the festival (even if the festival is only to take place in the future). Let us, however, keep things as simple as possible here. 27 The distinction between constitutive rules and regulative rules is discussed, for example, in Searle (1969). From our perspective, it is worth pointing out that L-rules valid within a certain “regulative” SB-system don’t have to ever regulate any actual behavior (though such a situation is not common). 28 Processes of this kind are vividly depicted in Peregrin (2014). 29 The fact that an F-rule is implicit, of course, doesn’t preclude that it can serve as the truth-maker for the claim that a certain L-rule is operative/valid. We should be careful to distinguish implicit F-rules from F-rules that are implied by L-rules that were explicitly promulgated (we could speak about explicitly valid L-rules). If Martha, for example, addresses Philip with the commands, “Visit your granny every Sunday!” and “Whenever you are visiting your granny, bring her some flowers!” we can say that the two L-rules entail the L-rule “Bring your granny some flowers every Sunday!” and hence that there exists the F-rule that might be directly introduced by a “promulgation” of the last rule sentence. This F-rule is, however, not implicit in the sense that

276  Vladimír Svoboda I have tried to pin down by the just proposed terminological convention. I thus propose to distinguish between implicit F-rules and implied L-rules. 30 Von Wright calls such implicit F-rules customs and says that they are “acquired by the community in the course of its history, and imposed on its members rather than acquired by them individually” (von Wright 1963, 8). 31 It is, nevertheless, worth noting that the explicitness of legal rules is not as straightforward as one might expect. Legal codes are often formulated not by sentences that provide straightforward guidelines for action (rule sentences) but use, for example, sentences speaking about sanctions that will be introduced if some kind action takes place or definitions of different kinds. Thus, saying which L-rules are valid in a certain code may require a nontrivial interpretative effort. 32 What has been said suggests that the scheme presented in figure 13.1 needn’t be generally applicable. It can, nevertheless, be generalized: the two topmost boxes (containing “rule sentences” and “L-rules”) may be replaced by one box containing the text “behavioral pattern.” It is, of course, difficult to specify the concept of a behavioral pattern. The human practice of recognizing such patterns is much more advanced than theorizing about them. 33 Of course, some might doubt whether communities of chimpanzees are capable of establishing any relationships that should be classified as F-rules. 34 “The existence of a norm is a fact. The truth-grounds of normative statements and of norm-propositions are thus certain facts. In the facts which make such statements and propositions true lies the reality of norms. The problem of the nature of these facts can therefore conveniently be called the ontological problem of norms” (von Wright 1963, 106). 35 Von Wright speaks about a “relationship under norm” (von Wright 1963, chap. 7). 36 Concerning the general question of the nature of the rules (laws) of logic that I have had to omit here due to a lack of space, I can refer the reader to Peregrin and Svoboda (2017). 37 Von Wright (1963, 196) summarizes this picture: “Statements of facts (propositions) are true or false; norms, it is said, are not true or false but valid or invalid.” 38 I am grateful to Georg Brun and Jaroslav Peregrin for number of very helpful comments on drafts of this chapter. My work on the chapter was supported by research grant no. 13-20785S of the Czech Science Foundation (GAČR).

References Bicchieri, Cristina. 2005. The Grammar of Society: The Nature and Dynamics of Social Norms. Cambridge: Cambridge University Press. Boghossian, Paul. 2015. “Rules, Norms and Principles: A Conceptual Framework.” In Problems of Normativity, Rules and Rule-Following, edited by Michał Araszkiewicz, Pavel Banaś, Tomasz Gizbert-Studnicki, and Krzysztof Pleszka, 3–12. Cham: Springer. Brennan, Geoffrey, Lina Eriksson, Robert E. Goodin, and Nicholas Southwood. 2013. Explaining Norms. Oxford: Oxford University Press. Chung, Adrienne, and Rajiv N. Rimal. 2016. “Social Norms: A Review.” Review of Communication Research 4, 1–28. Advance Online Publication. doi:10.12840/issn.2255-4165.2016.04.01.008. Church, Alonzo. 1956. Introduction to Mathematical Logic. Princeton, NJ: Princeton University Press.

The Nature and Diversity of Rules  277 Cialdini, Robert B., and Melanie R. Trost. 1998. “Social Influence: Social Norms, Conformity and Compliance.” In The Handbook of Social Psychology, 4th ed., edited by Susan T. Fiske, Daniel T. Gilbert, and Gardner Lindzey, 151–192. Boston: McGraw-Hill. Foucault, Michel. 1977. Discipline and Punishment: The Birth of the Prison. Translated by Adam Sheridan. New York: Vintage Books. Original edition, 1975. Hage, Jaap. 2015. “Separating Rules from Normativity.” In Problems of Normativity, Rules and Rule-Following, edited by Michał Araszkiewicz, Pavel Banaś, Tomasz Gizbert-Studnicki, and Krzysztof Pleszka, 13–29. Cham: Springer. Hayek, Friedrich A. 1973. Law, Legislation and Liberty: Rules and Order. Vol. 1. Chicago: University of Chicago Press. Lewis, David. 1979. “A Problem about Permission.” In Essays in Honour of Jaakko Hintikka, edited by Esa Saarinen, Risto Hilpinen, Illka Niiniluoto, and Merrill Provence, 163–175. Dordrecht: Reidel. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan. Peregrin, Jaroslav, and Vladimír Svoboda. 2017. Reflective Equilibrium and the Principles of Logical Analysis: Understanding the Laws of Logic. New York: Routledge. Pettit, Philip, and Christian List. 2011. Group Agency: The Possibility, Design, and Status of Corporate Agents. Oxford: Oxford University Press. Raz, Joseph. 1990. Practical Reason and Norms. Oxford: Oxford University Press. Rescher, Nicholas. 1966. The Logic of Commands. London: Routledge and Kegan Paul. Searle, John R. 1969. Speech Acts: An Essay in the Philosophy of Language. Cambridge: Cambridge University Press. Searle, John R. 1990. “Collective Intentions and Actions.” In Intentions in Communication, edited by Philip R. Cohen, Jerry Morgan, and Martha Pollack, 401–415. Cambridge, MA: MIT Press. Svoboda, Vladimír. 2017. “A Lewisian Taxonomy for Deontic Logic.” Synthese. Advanced online publication. doi: 10.1007/s11229-017-1370-7. Tuomela, Raimo. 1995. The Importance of Us: A Philosophical Study of Basic Social Notions. Palo Alto: Stanford University Press. von Wright, Georg H. 1963. Norm and Action: A Logical Enquiry. London: Routledge and Kegan Paul. Wittgenstein, Ludwig. 1953. Philosophical Investigations. Oxford: Blackwell.

14 Governed by Rules, or Subject to Rules? Ondřej Beran

1. Introduction “Man is a creature not of habits, but of rules,” says Sellars (1949, 297), or, as Peregrin (2014) would rephrase it, “man is a normative creature.” These insights are sometimes made more specific by an inspiration loosely derived from Kant’s idea of the dual nature of human beings: claiming that we are not only subject to necessity resulting from the (causal) laws of nature, but that we also reshape the world we live in and our practices by constraints we freely impose on ourselves. These rules express not what we must do (and what cannot be otherwise) but what we ought to do, assuming that violations are possible and anticipating the measures to be taken (sanctions, etc.). However, if we try to clarify this insight, it might turn out that several rather different things are meant when we say that one’s actions are rules-governed or that one is following a rule in her actions. The second section of this text is devoted to discussing some examples of rules that can highlight the heterogeneous character of our normative practice, which we might be tempted, too hastily perhaps, to label generally as “rule-following.” The examples of rules that seem most problematic with regard to the expectation of their being literally followed suggest that the standard picture of normative practice as being comprised of a rule, the actions in accordance with the rule, and the sporadic violations of it (followed by sanctions) may not be exhaustive. The Wittgensteinian account of language holds a prominent position among the sources that have inspired the inferentialist tradition. In the third section, I will discuss some criticisms of Wittgenstein that were proposed by his student and follower Rush Rhees, who has shown that some important distinctions applied to our linguistic practice do not tally with the difference between following and violating a rule. These distinctions, which make our language what it is, concern the very point of speech practices, as suggested by Rhees: to make oneself intelligible to another. In the fourth section, I try to apply Rhees’ criticisms in a broader context, reflecting on a variety of normative practices. I try to show that

Governed by Rules, or Subject to Rules?  279 some explicit statements of rules do not serve the purpose of describing a practice that actually follows the rule that was made explicit. They rather—­especially in the cases where the concerned practice clearly and regularly fails to conform to the rule—express what is the point of the practice, what the practice is “about.” The important difference that the statement of the rule captures is not the difference between those who follow the rule and those who violate it, but between those who care about what the rule is about and those who are indifferent to it. This difference of attitude particularly concerns the contexts to which we attach a relatively higher importance than to conventional practices such as games or sports: the paramount example is the normative standard of morality (being a good person).

2.  Different Kinds of Rules What forms can rule-following assume? Let us first take a simple, commonplace example: a chess game (cf. Wittgenstein [1953] 2009, § 31). Playing chess is defined by a set of explicit rules like “a knight only moves in an L-pattern,” “when your king gets into a position it cannot escape, you lose,” and so on. Every action of every chess player conforms to this set of rules—if any player would persist in doing something that contradicts one of these rules, she simply could not play chess anymore.1 It is hard to imagine that one could prove oneself as a chess player unless she is aware of all of its foundational rules. Even if she cannot enumerate by heart every single one of them, she would be able to answer questions about them correctly. There are, however, more complicated examples of rules-governed activities that involve something like explicit rules. Let us take an example of being a member of an institution that has an explicit code, for example, a child attending a primary school, which—just as most primary schools do—has a long list of School Regulations. “Students are always dressed cleanly and properly.” (That was one of the Regulations of the primary school I attended.) Such requirements are often hard to satisfy, not to mention the difficulties with specifying what “properly dressed” means. And outright obscurity and vagueness is characteristic of cases like “Students always take care to preserve the good reputation of the school.” Also, plausible-looking interpretations of some rules seem to contradict plausible-looking interpretations of other rules within the same set. Can a student, on her way to school, save a drowning man (thereby preserving the school’s reputation) and then risk being dirty and muddy in the class? Rules-governed actions and explicit references to the rules in this latter case differ from chess: no child actually follows all School Regulations and she typically does not even know them. Nor are there general expectations imposed on her, such that she should comply with each of these

280 Ondřej Beran rules. Those who are in a position of authority employ certain measures and reactions that delimit a certain space for the schoolchildren’s practice; but the outline of this practice, if written down, might not be to the last letter the same as what is contained in the document with School Regulations. Now, can the School Regulations rules govern the children’s practice at all? They are too complicated for their subject agents to know and remember them; and they are too difficult to follow without exception or failure. There is no unequivocal agreement on recognizing a violation and reacting to it. The example of School Regulations also indicates that the role of sanctions, which are often supposed to play various roles in establishing and sustaining a normative practice (for example, Bicchieri 2006), may be less clear than expected. As I suggested, it is certainly not the case that sanctions enter upon the stage as soon as a student violates one of the Regulations. The pattern of the actual occurrence of significant sanctions allows us to hypothesize a rather different shape of practice than is actually expected. There is also the implicit (psychological) assumption that those agents who stay within the space delimited by the Regulations either do so out of a fear of sanctions or because they don’t mind the Regulations (they may even like them). But it might mean that we are underestimating the influence of such factors as habit, convention, or conformism and of such evaluative categories as appropriateness (in addition to mere correctness). We often avoid certain courses of action not because they are incorrect but because they are inappropriate, though permitted. And so on. It seems that rules of the School Regulations-type work (and perhaps can only work) in a somewhat different way than chess rules, which raises the question: were they ever intended to work in such a way as the rules of chess do? I don’t think so. But there is a strong connection between these rules and the concerned practice. Let us consider another example from this problematic group. Scout law typically includes some version of “a Scout is pure in thought, word, and deed.” Well, no human being actually is that—it is not in the nature of people to be completely free of mean thoughts, impolite speech, or actions harming other people. Even more clearly than with the always properly dressed students, this is not a rule expected to be maintained without slip-ups. This rule talks about certain values or character virtues that nobody exemplifies perfectly and thus may incite doubts as to whether it is a rule at all. Sellars (1969, 508 ff), however, points out that apart from specific ought-to-do rules prescribing particular actions, there are also more complex ought-to-be rules that fulfil a certain critical function and that set a standard for the agents to live up to. These rules play a distinct role. For one can learn a lot from the rule about Scout purity: what “Scouting” means; what one wants to become when she wants to be a Scout;

Governed by Rules, or Subject to Rules?  281 how to respond to those who have undertaken the commitment to Scouting. If I am to understand a person standing in front of me and if I know that she is a Scout, familiarity with Scouting rules can shed light on what she says and does. This is what the Wittgenstein ([1953] 2009) notions of “seeing connections” or “knowing one’s way about” point to: “You approach from one side and know your way about; you approach the same place from another side and no longer know your way about” (Wittgenstein [1953] 2009, § 203). Approaching from the right side gives one “that kind of understanding which consists in ‘seeing connections’ ” (Wittgenstein [1953] 2009, § 122). Familiarity with Scouting rules helps me to approach the person from such a way that I “know my way about” her and see the connections involved in her actions. I know what kind of ambient assumptions and expectations makes her actions intelligible. This “cloud” does not entail that all individual Scouts are pure in thought, word, and deed. Neither does everybody respond to the Scouts as if they actually expect such ideal behavior from them all the time. It offers an indication as to what the point of Scouting is—what is the direction of one’s activity when she is a Scout. Nobody embodies the “idea” of a Scout; but the idea of a Scout is omnipresent in the Scout’s activities and provides an inherent orientation to them. Thanks to the idea, “less Scoutlike” actions can be told from those that are “more Scout-like”; the idea provides guidance both for the agents that are in action themselves and for the others in their evaluation.2 But although the idea is made explicit in the form of a rule (or of a set of rules), it is not a rule expected to be actually kept. It provides orientation for our actions and striving. “If you are serious in your allegiance to Scouting, there should be no discussion whether you prefer slander over honesty. You might make a slip-up in your actions, but you cannot say that you preferred and intended to slander somebody because it is the better thing to do.” A person’s refusal to comply with these claims would make us conclude that she does not clearly see what Scouting is and her interlocutor would face considerable problems in seeing her as a Scout. I do not think that all rules are tools for an orientation of this kind rather than anything else. Certainly, there are rules that are (almost) without exception followed during the activities governed by them. The example of chess (or any other explicitly regimented game or sport, such as football) is of this kind. However, the rules we can see that concern the core areas of more complex life practices or attitudes (being a schoolchild, being a Scout, being a good person) work in a different way. Or, what constitutes the heart of these practices may not be the literal following of a rule as such. Some explicit rules that look quite far-reaching do not actually set the boundaries to a space of permitted moves. When we say things like “one ought to do anything for the sake of one’s family,” we don’t do so in the course of a rational deliberation about which rule should determine,

282 Ondřej Beran in advance, the domain of actions to be permitted. The agent often simply focuses on particular alternatives of action. Or she may address herself with such a rule-like kind of statement afterward, when she tries to make clear how she sees or saw a situation in which she had to make a decision (cf. Murdoch 1956). Stating the rule would then mean to offer the Wittgensteinian “perspicuous representation” for an already performed situated action.

3.  Problems with Wittgenstein’s Conception of Language Stating the rule for an action can help us understand the action under the description it had for the agent. But to more fully understand an action we may need to go further than the statement of the rule. Rhees’ (1959, 2006) critique of the later Wittgenstein’s conception of language focuses on this problem in connection with the famous example of the builders’ game (Wittgenstein [1953] 2009, § 2, § 6 ff): it might seem that the underlying rule is “when A says ‘Slab!,’ it is expected that B should bring a slab to A,” which captures the overall sense of this microcommunication between A and B. Wittgenstein gradually complicates the initial description by introducing further details, and especially, he doesn’t always work with the key concept “language game” in a consequent way. But the target of Rhees’ critique is relatively easy to outline. It is the idea that such a language as the one exhibited by the builders can be self-contained and represent a whole language (the only context where the language is used), even though it consists of hardly more than simple commands and commanded actions. Further, there is the assumption that the training, with the help of which such a builders’ game can be taught, provides a certain picture of how we learn our language. It is true that Wittgenstein discusses and investigates these hypotheses from various angles, and thus by no means does he state them uncritically as certain “theses”; but neither does he focus clearly enough on the (somewhat misleading) limitations of these “objects of comparison.” These limitations consist in overlooking certain aspects of language that are of utmost importance in Rhees’ eyes: Wittgenstein’s example doesn’t explain why such an agreement between the two builders works and why they comply with this communication pattern when others may not. Building, when you think it through, turns out to be a far more complicated enterprise then might have been initially thought. Wittgenstein presents the builders’ language game (“the whole, consisting of language and the activities into which it is woven”; Wittgenstein [1953] 2009, § 7) as a mere game of symbols. Under his description, it works, as Rhees (1959, 182 f) argues, similarly to the practice of “pretended conversations” used as an exercise in a foreign language: nobody learns anything from what is said because nobody really tells the other

Governed by Rules, or Subject to Rules?  283 anything. A mere game of symbols doesn’t make it possible to capture the difference between the pretended conversation and actually telling each other anything. Building, on the other hand, is work rather than a game. Every work meets obstacles and workers have to deal with them; some are easier and some more difficult to solve. Unlike Wittgenstein’s builders, who only have signals like “Slab!,” the workers have ways of talking through the problems they encounter. Language that provides ways of talking through problems needs a complex interconnection of one linguistic activity with many others. Being a builder truly means being a person who goes home after work and talks to their family—using much the same language as they do at work. Their activity means something: it is the construction of houses when houses are often the homes builders live in with their families and that can have considerable meaning for them. Language in which these interconnections are seen and practiced cannot consist only of signals followed by actions that are required by rules. In such a language, Rhees argues, literature or jokes wouldn’t have any place. And it is difficult to imagine that we would call something that lacks these capacities a “language.” Wittgenstein’s lists of language-games (for example, Wittgenstein [1953] 2009, § 23) often include storytelling or joking, but for a closer inquiry of the rules of language games he typically doesn’t choose these as an example. After all, the rules of poetry or telling jokes are notoriously difficult to determine. The importance of literature or jokes may have to do with their capacity to pervade so many linguistic situations: a humorous or poetical quality can accompany the way people discuss the solving of a technical problem, admonish another to get better, and so on. This capacity, I believe, highlights the fact that, despite a multitude of language games, human linguistic practices have a certain unity thanks to which various practices are interconnected rather than separated. The unity of language is not a unity of one game with one set of rules. The practices are kept together because remarks (moves) made within particular games have a bearing on one other. People say things to each other and these things are elaborated by further things said by the others in different but connected contexts. Within one conversation, it is possible to shift from exchanging factual information to telling jokes and back again and then perhaps move on to storytelling—while all these activities are elaborating on things said in the course of the preceding discussion. These activities each have their own rules; but what makes them hold together—what makes it possible for them to be a part of one conversation—is not one set of rules that would be the rules of the whole conversation. We usually explain the rules of various practices in language with reference to the purpose of the practice. But we do not learn (our native)

284 Ondřej Beran language with the help of its rules explicitly stated in a language (which we already know) and we do not learn to talk for a specific purpose. What makes linguistic communication a whole is thus not a single purpose; rather, it has to do with the speakers having an interest in saying things to each other that are relevant to the things said previously. This interest in making oneself intelligible, along with the implicit trust in mutual intelligibility, sets a practical foundation for conversation rather than representing its purpose as something to be attained (cf. Cockburn’s 2014 discussion of primitive trust in conversation). According to Rhees, if games (like chess) only consisted in governance by their rules, it might then make sense to repeat the same game, perhaps because it was played so beautifully the first time. But it makes no sense to repeat the same conversation because its sense lies in the developing course of what is being said between the speakers. Each bit of conversation follows the previous ones and advances the focus somewhat. Rhees’ criticisms of Wittgenstein culminate in pointing at what he considers the truly important differences arising within discourse: the difference between speaking to the point and chattering pointlessly, between saying deep things with the power to elucidate and being trivial, and so on. These differences are not examples of the difference between rule-­following and rule-violation. A deep speaker and a trivial speaker engaged in the course of the same conversation are participating in the same joint activity; there is no clear difference between them in terms of the rules they follow. They both form correct utterances. They both react to questions by answers. They both manifest familiarity with the connections between names and personal pronouns. They are both familiar with the differences between the different kinds of language-games, and so on. And yet, one is dull and has little to offer to those who talk to her, while the other is sharp and insightful, and what she says enables her partners to see things from unusual perspectives and will be remembered by them for a long time.3 But “you should make a profound contribution to the conversation” doesn’t seem to be a rule (of conversation) at all. If it was, each participant in a conversation would have to follow the rule or at least acknowledge (explicitly or implicitly) its relevance. They would also need a shared standard of what constitutes “profoundness.” When there is a rule that is quite frequently violated, its authority as a rule is testified to by further responses: here, such responses would include apologizing for oneself or explaining one’s failure to say something profound, the ability to distinguish the profound from the trivial in the case of other speakers, or being confused by those who do not seem to be concerned about their triviality at all, and so on. This is not the case here. Pointless and shallow talk is neither punished by sanctions nor seen as unequivocally inappropriate. On the contrary, it’s the most normal and conventional thing there is.

Governed by Rules, or Subject to Rules?  285 Further, very different contributions—depending on the course of the particular conversation—turn out to be profound. The same utterance can contribute profoundly to one conversational context, while in another it can be utterly trivial and abstaining from the remark would add more to the profoundness of the conversation. To have this sense of the profound requires the identification of its proper place and time (Cavell 2002, 41), which has little to do with universal rules that could be made explicit. The endeavor to make “profound contributions to a conversation” would therefore potentially take such very different forms in differing contexts that they might even seem incompatible (such as answering as opposed to not answering a question that is, in both cases, “materially” the same). Hence, a rule governing it would be so general that it would say nothing in particular: “You ought to be profound.” Yet, the value of making profound contributions is not questioned, and the distinction is not rendered illusory. If there is a rule underlying it at all, it might be of the kind characterized by Wittgenstein ([1953] 2009, II., § 355) as follows: “What one acquires here is not a technique; one learns correct judgements. There are also rules, but they do not form a system, and only experienced people can apply them rightly. Unlike calculating rules.” Judgment and the discernment of aspects and qualities of a situation that may be difficult to perceive is needed. These capacities are of a phronetic kind, and as such they require cultivation rather than blind instilment (under the threat of sanctions). There is no general underlying “trick” that, once one “gets it,” can simply be applied in the instant.

4.  The Point of Rules-Governed Practices The impact of Rhees’ observations about language is also worth some consideration in the case of other rules-governed (normative) practices. Let’s return again to the simple example of games such as chess. What is the difference between Garri Kasparov’s performance in a master match and my performance against my seven-year-old nephew? Is it that Kasparov follows some particular rule of chess that I fail to follow? Hardly (see Ryle 1953, 176). First and foremost, there is a striking inequality in our chess skills. But, and this is perhaps more interesting for us here, I also do not take the game that seriously. How well I perform does not matter that much to me. Indeed, “you ought to take chess seriously” or “it should matter to you how well you perform or whether you win” do not occur among the rules that define chess. Cavell (2002, 28 f) might call this a principle of chess, rather than a rule thereof—it is the principles that are crucial for an insightful understanding of a game. Commonplace though these principles are, if one overlooks them, one will hardly understand what it is that chess means. Why do people play chess? What is chess about? About following its rules? No. It has to do with what is expressed by the above not-really-rules. Let us just

286 Ondřej Beran imagine what a match where both players only make haphazard—yet permitted—moves would look like. If the moves are not guided by a strategy to defeat one’s rival (if an interest in playing well, preferably so that one wins, is absent), the game becomes pointless and loses something vital that makes the game true chess. The question of what this missing component consists in brings us, I believe, back to the issue of the “impossible” rules of Scouting. With football or chess, it is relatively easy to state what the practice is “about.” Basically, the point is to win the game while having some fun during it. In the case of more complex normative practices like Scouting, the distinct character of what a practice is “about” is more difficult to see, but in that case, it also runs deeper with the agents. As I suggested, some explicit rules of Scouting orient, rather than directly govern, the practice. They also orient the outsiders’ responses to those they recognize as Scouts. The explicit reference to purity in thought, word, and deed helps us see more clearly the point of Scouting and what Scouting is about. But it doesn’t really draw the boundary between Scouts and non-Scouts. It rather helps us understand the nature of the difference between a perfunctory Scout (perhaps compelled to join a Scout group by Scouting-enthusiast parents or because she is dully following the model of an older sibling) and someone who takes the issue of purity seriously, for whom this principle plays an important role in her life. Again, the difference is not a difference of rule-conformity. Unlike in chess, it is probable that both the “perfunctory Scout” and the “serious Scout” sometimes—likely quite often—violate the rule of purity. But sanctions don’t follow in all these cases. Then, one may suggest, it is perhaps a matter of the relative frequency of the violations: the “perfunctory Scouts” simply violate the rule more often. But this is also far from evident, and at any rate would be a question for field sociology rather than philosophy. The seriousness, I think, is connected internally to, and would show itself in, the Scouts’ responses to their failures. Do they feel regret? Do they try to improve for the next time? Do they believe that their “average Scout performance” is good enough? “Yes, I avoid doing charity work, but nobody can expect anything more from me. Eugene even took the money that was collected and bought ice-cream for himself, and yet nobody wants him expelled from the group. So leave me alone!” We can imagine that a serious Scout might shirk from attending a Scouting charity event, but I don’t think we can imagine her saying such a thing except as a joke. She cannot really mean this. Scout rules do matter for her; the point of Scouting is important for her. Such a resentful indifference toward them cannot be reconciled with the concept of the seriousness of being a Scout. I think this example can help us understand a little better the role these rules play in the differences we recognize among people. Some rules can

Governed by Rules, or Subject to Rules?  287 be difficult to follow in their literal form, and virtually everybody violates them now and them. The workings of these “impossible” rules do not then concern the difference between those who follow a rule and those who do not, but between people who all follow (or violate) the same rule while some of them do it better—investing more of themselves into it—than the others. Of course, there is a problem. The “impossible” rules cannot serve as practical criteria for statuses linked to them. The status “chess player” can be attributed to an agent based on her following the rules or on admitting the authority of sanctioning measures in the (sporadic) case of rule-violations. The status “student of a school” is attributed in a different way. Some complex statuses, defined through clusters of rules, including the “impossible” ones, therefore rely on simplified criteria. Let us take the status “student of a school.” There are sets of explicit Regulations imposed upon children of particular schools, but if one wants to determine whether a child is a student of a particular school, one looks elsewhere. For example: Is she physically present for (most of) her school lessons? Does she get grades that allow her, at the least, to continue her studies in the next school year? And so on. Most schoolchildren who are not expelled function in such a regime that these questions would be answered Yes, even though they may fail under a more literal reading of the School Regulations. Affirmative answers to the above questions do not at all reflect whether the child does better or worse at school, whether it matters to her how much she learns, and what she gains from it. Enthusiastic students and academic stars do not differ from slackers or socially disadvantaged children—so long as they all keep a reasonable frequency of school attendance, and so on. The simplified criteria were not designed to capture this latter difference, because its relationship to explicit rules is opaque.4 Those who see a gap between simplified identification criteria and the point of the rules-governed activities can exploit this observation. (Related phenomena were described at length by social psychologists and behavioral economists under the name “Goodhart’s Law” or “Campbell’s Law.”) For example, being an “intellectual” involves a balanced, critical, cross-referencing, and knowledgeable dealing with the information, opinions, news, arguments, and so on, that one is confronted with. Taking this endeavor seriously is also a part of what being an intellectual means. However, intellectuals in this sense are rather difficult to recognize. Auxiliary, simplified criteria are needed and frequently used. For instance: being able to produce a university degree and willing to use it as a certificate of one’s expertise and superior intellect. Certainly, this sounds ridiculous—but it cannot be denied that when we have to decide, in real time, whether to consider someone as an “intellectual” we cannot only look at the whole record of their attempts to understand complex issues. This is why it is possible for quite suspicious

288 Ondřej Beran persons to qualify as “intellectuals.” Perceptivity of simplified practical criteria and a demonstrative conformity to these simpler rules can substitute for a lack of interest in the point of the activity. The easier the simplified rules are to make explicit, the easier, so to speak, is the parasitic exploitation of the related statuses. “Of course Eugene is a genuine intellectual. I heard him talking for two hours about Sharia law yesterday, and he appeared to know quite a lot about the Qur’an, from which he quoted at length. I could never imagine that there are such things in the Qur’an, but now that I know, I am not surprised. You see, Eugene’s got his PhD from Bob Jones University. He says it’s a top-notch college.” As I suggested, some rules, even though they can be made explicit, are probably not expected to be followed literally. Many rule sets are too complicated, and it is impossible to not violate them. However, a targeted choice of a rule from a set can also be used to mark a person whose practice is disapproved of for serious reasons. “Eugene’s speech is too filthy to be a Scout.” Many Scouts use ugly words; but to say that specifically about Eugene means to mark him as a person seriously failing, unlike the others, in his attitude to the Scouting standard. A deliberate focus on this failure can then serve as a basis for sanctions or even for banishing the person from the respective community. “Eugene should leave the group— there is no room for racist speech among Scouts.” Again, the reference to the rule with which Eugene’s behavior collides (the purity of speech) smells of a pretext. The rule is not supposed to actually be followed—not every Scout who has ever used a vulgar expression is expected to be “officially” reprimanded or even banished. This is not a standard sanction for a standard rule-violation. Why does a group, a community, or an institution feel a need to get rid of one of its own people? Sometimes the reasons are simply base and petty. But sometimes the “impossible” rules can be used to reprehend a person whose actions are at odds with the elusive point of the rules. Eugene’s presence within a Scout group can poison its atmosphere and discourage others from staying, despite many attempts to work it out with him. Having such a pretext available then becomes a blessing: “I heard him curse three times yesterday—this cannot be tolerated anymore. The time has come to expel him. He doesn’t do the group any good.”5 Eugene’s expulsion isn’t explicitly related to his being a mean person. That would be a difficult thing to demonstrate. Its justification is helped along by a reference to a rule that is rarely exercised and enforced in its literal form. This rule does not prescribe nonmeanness, but it has nonmeanness as its implicit point. Eugene’s expulsion doesn’t mean that there are clear cases of his violating the rule that justify the sanction while in the case of the other Scouts there are no such violations. But there is a connection to this rule: Eugene’s conduct—his attitude, the spirit of his actions—violates the point of the rules-governed agency that is, though indirectly, expressed by the wording of the rule. But the appropriate

Governed by Rules, or Subject to Rules?  289 application of this measure—recognition of another’s serious violation of the point of a practice—requires, again, fine phronetic judgment. If we reserve the term “governed” for the way the rules of chess function in relation to the chess game, it seems questionable whether Scouting can be characterized as genuinely governed by the rules of Scouting— such as the requirement of purity. (In this sense, Scouting is much more governed by those rules that expect Scouts to attend group meetings and trips or to wear Scout uniforms on certain occasions. However, these rules tell us little about Scouting; even less than what the explicit rules of chess tell about chess—these at least mention checkmate and its importance in the game.) Scouting is, nevertheless, clearly subject to its rules, Scout Law, in multiple and interconnected ways, often quite complicated such as the one I just sketched. These ways of subjection affect the differentiated manner of people’s responses to Scouts as opposed to their responses to non-Scouts. Scouts’ attitude toward the point of Scouting and its seriousness plays central role here. However, this particular kind of subjection to rules should be distinguished from the way in which we are subject, for example, to the laws that hold in the country where we live. Everyone probably breaks some law now and then. But one doesn’t have to do anything to become subject to these laws; one needn’t even know about them (nobody knows all the laws she is subject to). Scouting is a matter of an active choice: one chooses to work on oneself to live up to the Scouting standard. In this respect, it differs from the status of a schoolchild—children usually don’t actively and autonomously choose the school to attend (though the subjection is not as blind and automatic as it is in the case of laws). School Regulations are also not the matter of one’s decision to cultivate oneself, but of the institution’s mechanisms that are intended to keep it stable and, so to speak, looking good. In Scouting, one’s own decision for self-cultivation is central. The rules of Scouting are teleological and express a direction for a particular kind of care for one’s soul, unlike School Regulations. I introduced and discussed these various examples to highlight the fact that there are different kinds of normative statuses and practices in relationship to their respective rules. Some are not directly governed by them, but they may have a point referred to by these rules, even though the rules are difficult to follow in their literal form. Among these more complex statuses, I have already mentioned the status “being a good person.” In the case of Scouting or school attendance, there is a stronger sense of seriousness that accompanies the preference of attaining that status as opposed to a failure to get it, stronger than in the case of being a chess-player. Yet one can still be legitimately indifferent as to whether she attends a school properly or whether she is a Scout. With being a good person, it seems a trickier question. If there are some moral rules, one of them—or an aspect of each of them as a moral rule—would be something

290 Ondřej Beran like “you ought to follow these rules.” In contrast to morality, a sport is defined by a set of rules excluding this aspect. Its idea remains meaningful even if nobody cares about following its rules. As Wittgenstein (1965, 5 f) points out, it is perfectly intelligible that one doesn’t care at all that she is not good in tennis and that she is not interested in getting better. But it is a part of our idea of morality or of being good that one ought to try to be good. This idea that personal (moral) goodness is not, by definition, an “optional” achievement that finds various expressions in ethical insights propounded by many philosophers, such as Plato, Kant, or Wittgenstein (though Nietzsche or Sartre might disagree). Moral goodness is one of the most important things in our lives, vastly more important than chess. On the other hand, the explicit moral rules, coined by ethicists, (1) are typically not pregnant and specific enough to capture the richness and complexity of morally loaded situations in which we find ourselves. And many of them also (2) seem to be too ideal to be followed without any slip-ups. Instead of describing a workable practice, they rather convey its point—as human beings, we are subject to them in a complicated sense. Those who take them seriously aren’t necessarily to be recognized by their perfectly good life practices that conform to these rules, but rather by the seriousness with which they react to the cases when they have trespassed these acknowledged standards. Kant would probably also suggest that for a rule to be a moral rule, it is essential that the agent be following it because she herself sees and judges, by her own reason, the rule as being right. If another agent followed the same standard out of conformity, the rule she would follow could not then be easily considered a moral rule. The Kantian stress on reason (as opposed to emotion, for instance) is, of course, not controversial. But his suggestion underscores, if from a slightly different point of view, that with normative moral practice, what counts first and foremost is the agent’s own attitude toward the point of the practice, rather than actually following the rule in question without any slip-up. Sellars, in the same text I quoted from in the beginning, says: “To describe rules is to describe the skeletons of rules. A rule is lived, not described.” I believe that a lot is hidden in this “lived.” For a rule to be lived, a connection is required to the point of the activities that are supposed to be governed by it. To understand a normative practice, we thus often ought to take into account something that the rules express only indirectly.6

Notes 1 Naturally, chess is a human practice, and as such it is (1) open to alterations and shifts and is (2) sustained by having a broader context connected to it. If two players in a particular match “officially repudiate” such a chess rule as castling (they may proclaim it “idiotic” or “obsolete”), the meaning of the ­situation—that it is a “chess match” that they are involved in—probably wouldn’t vanish completely. The other moves they perform don’t lose the status

Governed by Rules, or Subject to Rules?  291 of “chess moves,” and the players don’t lose the status of “chess players” in the observers’ eyes. Their practice doesn’t simply become meaningless through the repudiation, and neither does it assume the status of a distinctly different game. The way the observers understand the situation will remain: they are playing chess, they just don’t acknowledge one of its (minor) rules. Of course, with the repudiation of a more fundamental rule (checkmate) or of a larger number of rules, the collapse of the situation’s meaning could be expected. Cf. Cavell (2002, 25). 2 Just as the idea of the good provides, according to Murdoch (1970, chap. 1), an inherent orientation to our moral agency. This talk of ideas and how they work is, of course, nothing strikingly novel—being, as it is, a broadly Platonic conception. 3 Ryle (1953, 179 f) draws attention to the difference between words and sentences: what we say things with and the things we say. The use of words, not of sentences, is governed by rules; the things we say (sentences) can be stupid, while our words are as such neither stupid nor intelligent. 4 But neither, as I tried to point out, do the School Regulations seem to capture it neatly, at least not if we focus on the issue of their simply being followed versus their violation. 5 In a similar vein, Cavell (1999, 303 ff) points out that references to rules bypass justifications of actions in moral terms and only serve as excuses. 6 Work on this chapter was supported by grant no. 13-20785S of the Czech Science Foundation (GAČR). An earlier version of the chapter was presented at the conference Why Rules Matter in November 2016 in Prague. Comments on the talk, made by Robert Brandom, Hans-Johann Glock, Wolfgang Huemer, Juraj Hvorecký, Kamila Pacovská, Mark Risjord, and Vladimír Svoboda, were of considerable help to me.

References Bicchieri, Cristina. 2006. The Grammar of Society: The Nature and Dynamics of Social Norms. Cambridge: Cambridge University Press. Cavell, Stanley. 1999. The Claim of Reason: Wittgenstein, Skepticism, Morality, and Tragedy. New York: Oxford University Press. Cavell, Stanley. 2002. Must We Mean What We Say? A Book of Essays. Cambridge: Cambridge University Press. Cockburn, David. 2014. “Trust in Conversation.” Nordic Wittgenstein Review 3 (1): 47–68. Murdoch, Iris. 1956. “Vision and Choice in Morality.” Proceedings of the Aristotelian Society, Supplementary Volume 30 (1): 32–58. Murdoch, Iris. 1970. The Sovereignty of Good. London: Routledge and Kegan Paul. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave. Rhees, Rush. 1959. “Wittgenstein’s Builders.” Proceedings of the Aristotelian Society, New Series 60 (1): 171–186. Rhees, Rush. 2006. Wittgenstein and the Possibility of Discourse. Oxford: Blackwell. Ryle, Gilbert. 1953. “Ordinary Language.” The Philosophical Review 62 (2): 167–186. Sellars, Wilfrid. 1949. “Language, Rules and Behaviour.” In John Dewey: Philosopher of Science and Freedom, edited by Sidney Hook, 289–315. New York: The Dial Press.

292 Ondřej Beran Sellars, Wilfrid. 1969. “Language as Thought and as Communication.” Philosophy and Phenomenological Research 29 (4): 506–527. Wittgenstein, Ludwig. 1965. “A Lecture on Ethics.” Philosophical Review 74 (1): 3–12. Wittgenstein, Ludwig. 2009. Philosophical Investigations. Revised 4th ed. Translated by Gertrude Elizabeth Margaret Anscombe, Peter Michael Stephan Hacker, and Joachim Schulte. Oxford: Blackwell. Original edition, 1953.

Part IV

History and Present

15 Inferentialism after Kant Danielle Macbeth

In the opening chapter of Inferentialism: Why Rules Matter, Jaroslav Peregrin (2014) suggests that, historically, the first expression of inferentialism may have been Frege’s claim, in § 3 of his Begriffsschrift (Frege 1879), that the conceptual contents of two sentences are the same if they have the same inferential consequences. Throughout, Peregrin also highlights the connection of inferentialism of the sort he espouses to use theories of meaning and in particular to the concept of a language game that became prominent in philosophy in the second half of the twentieth century. Such theories of meaning aim to provide a compelling alternative to relational theories according to which words have meaning in virtue of their relationship to something, namely, their meanings. On Peregrin’s use theory, words have meaning not in virtue of their relationship to something but instead in virtue of their rule-governed roles in what, following Brandom, he thinks of as a game of giving and asking for reasons. Inferentialism so construed is, I would argue, broadly Kantian, after Kant in the sense of following in the footsteps of, or being in the manner of, Kant. Frege’s inferentialism, I argue, is different, not Kantian but instead essentially post-Kantian—hence “after Kant” in a very different sense. For example, Frege does not replace representationalism with inferentialism, as the Kantian inferentialist does, but instead splits the notion of (sentential) representation into two, into an inferentially articulated sense expressed and a truth-value designated. Further, and connected, Frege does not think of judgment as a matter of making a move in an essentially social game, as Peregrin does; he thinks of it instead as an acknowledgment of (fully objective) truth. Whereas Peregrin’s inferentialism aims to start not with truth but instead with inference, Frege’s inferentialism takes both inference and truth to be fundamental. My aim is to clarify some of the core differences between these two sorts of inferentialism, and to begin to explore their philosophical significance. Inferentialism is the view that an expression’s role in inference is constitutive of its meaning. It is the view that, as Sellars thought of it, concepts involve laws and are inconceivable without them.1 My interest is in two species of the genus. The first species of inferentialism I will consider is

296  Danielle Macbeth that which Peregrin (2014) develops. The second is largely due to Frege, though with some further developments of my own. See Macbeth (2014). On Peregrin’s account, inferentialism aims to provide an alternative to representationalist conceptions according to which words have meaning, that is, are words rather than mere noise or marks, in virtue of standing for, or representing or expressing, something that is their meaning (see Peregrin 2014, § 1.1). On Peregrin’s alternative account following Brandom, a word has meaning in virtue of its rule-governed role in the essentially social game of giving and asking for reasons. Much as we can understand the meaning of, say, the sign for conjunction by appeal to certain introduction and elimination rules—by appeal, that is, to the circumstances and consequences of making a judgment that has the logical form of a conjunction—so we are to understand the meanings of words in general by appeal to the circumstances and consequences of making judgments involving them, what judgments those judgments follow from, and what judgments follow from them. Frege has a rather different idea. Rather than opposing inferentialism to representationalism, Frege splits the representationalist conception of meaning in terms of a state of affairs pictured—what he, in the 1879 logic Begriffsschrift (Frege 1879), calls a judgeable content—into two; into, on the one hand, a thought that lays out the inference potential of any putative judgment acknowledging the truth of the thought, and on the other, a truth-value, either the True or the False (see Macbeth 2005, 118–119). We begin, in other words, with the idea that sentential meaning is to be understood in terms of truth, what is the case if a sentence is true. A sentence, then, is a kind of a picture of a state of affairs, one that pictures the state of affairs by itself being a state of affairs much as a Roman numeral numbers a collection of things by itself being a collection of things.2 It is this notion that is to be replaced, on the one hand, by the Fregean thought expressed, and on the other, by the truth-value designated. The thought is to be conceived in turn in terms of its inferential consequences, not what is the case if it is true but instead what follows if it is true. A Fregean thought is thus more fine-grained than a state of affairs. Two Fregean thoughts such as those expressed by the sentences “Hesperus is illuminated by the sun” and “Phosphorus is illuminated by the sun” are both true because both involve one and the same property, being illuminated by the sun, and in both cases that property is ascribed to one and the same object, namely, Venus. But they are nonetheless different thoughts because they have different inferential consequences. It is, furthermore, obvious that they have different inferential consequences: the one cannot be correctly inferred from the other without the additional premise that Hesperus is Phosphorus. So, again, the thought is more fine-grained than the state of affairs that obtains if that thought is true. The Bedeutung of a sentence, its truth-value, if any, is, on the other hand, much less fine-grained than any state of affairs. If Frege is right, all

Inferentialism after Kant  297 true sentences designate the same thing, namely, the True, and all false sentences similarly designate the same thing, namely, the False. On the Fregean account just outlined, individual words of the language express Fregean senses and together with their mode of combination in a sentence determine the thoughts expressed by sentences involving them. Sentences also designate truth-values. But what, then, are we to say about the designation of subsentential expressions? Frege’s answer is that it is only relative to an analysis of a sentence into function and argument that one can speak of the designation of subsentential expressions. It is just this that Frege intends by his well-known context principle: “never to ask for the meaning [Bedeutung] of a word in isolation, but only in the context of a proposition” (Frege [1884] 1953, x).3 The building blocks of a language out of which sentences are composed have, as such, only Fregean senses. Sentences composed of them express Fregean thoughts that are a function of those senses and the way the words are put together in the sentence. If, now, one provides an analysis of the sentence into function and argument, the subsentential expressions that are the fruit of the analysis will not only express senses but also designate. In some cases, those subsentential expressions designate objects; in others, they designate lower- or higher-level concepts. In sum, then, where Peregrin has inference potential instead of reference, Frege has inference potential and reference. It should not be assumed that the conception of inference potential is the same in the two cases. Another regard in which the two species of inferentialism differ concerns the relationship of the inferentialist conception of meaning to rationality. All are agreed that rationality is grounded in, somehow made possible by, inferentially articulated language. The two accounts differ nonetheless in the details regarding how exactly this is to work. As one might expect, they also differ in their most basic understanding of the nature of rationality. Peregrin has a minimalist view: Just as a creature is called carnivorous if it has been equipped by evolution with tools to digest meat and with the skills needed to kill and eat other animals, so we call an animal rational if it has been equipped, by evolution, with the tools and skills needed to reason. (Peregrin 2014, 208) To be rational, in this view, is to be capable of reasoning where to reason is, first and foremost, to play the so-called game of giving and asking for reasons. Because this game is possible at all only in light of the inferentially articulated language that is its vehicle, it follows that language is the ground of rationality. The essential link between language and rationality is forged on Peregrin’s account by the fact that without the inferentially articulated language there can be no game of giving and asking

298  Danielle Macbeth for reasons.4 And for Peregrin, that is pretty much the whole of the story: “the rules of our language are not correct or substantiated in any sense beyond this pragmatic one: without them, we could not be reasoning (hence rational), concept-mongering creatures” (Peregrin 2014, 205). Peregrin often compares our use of language to playing a game such as chess. Both are rule-governed activities and in both cases the rules are constitutive of the game. They do not determine what one ought to do, which particular move is to be made at some particular point; rather they articulate a space of what it is legal to do, what, according to the rules of the game, it is permissible to do at this or that point. But of course, chess is just a game. And one can easily imagine a community of conforming individuals who have developed various practices that together create the space of a game without imagining thereby that these conformists are rational. On the other hand, if the game really is a game of giving and asking for reasons, then the players are and must be rational. But in virtue of what is the language game, unlike chess, a game trafficking in reasons? A natural answer, the one that the Fregean gives, is that the “game” of giving and asking for reasons is not merely a game only because and insofar as it answers to the norm of truth. A rational animal, unlike its non-rational cousin, is trying to get things right, to know things as they are, not merely as we take them to be. And as both Sellars and Frege see, what is key here is the capacity for self-correction, the capacity for second thoughts about anything one thinks—even the laws of logic. As Sellars puts the point: inquiry “is rational, not because it has a foundation but because it is a self-correcting enterprise which can put any claim in jeopardy, though not all at once” (Sellars 1956, § 38). It will be worth our while to unpack this thought a bit. As Sellars is well aware, we tend to have a foundationalist conception of knowledge at the base of which are foundational truths that we somehow just know, for instance, by seeing or otherwise perceiving them to be so. In the foundationalist picture, the foundational truths are to be at once something merely caused in us, that is, items in the realm of nature, and nonetheless normatively significant, items in the space of reasons; but nothing, Sellars argues, can be like that. Nothing could be given in the way needed for foundationalism. One natural response, then, is to keep the overall foundationalist picture while rejecting the part of it that relies on the mythic Given. This, in Sellars’ imagery, is “the picture of a great Hegelian serpent of knowledge with its tale in its mouth” and is equally to be rejected. Indeed, the whole static framework of both foundationalism and coherentism is to be jettisoned, replaced by an account that is constitutively dynamic, one that is concerned not so much with the products of knowing as with the processes of knowing. Once we have in view the dynamic processes of inquiry at the heart of which is self-correction, we will be in a position to see that the rationality of inquiry is grounded in the fact that we are and

Inferentialism after Kant  299 can be answerable to the norm of truth only insofar as anything we think can be called into question as reason sees fit. Of course, there is much at any given time that we have no reason to question, and so should not question. But that is very different from taking a thought to be unquestionable in principle, that is, as Given. Suppose that we did believe something that was for us unquestionable in principle, simply Given. If that belief really were unquestionable, something we were made to think (however that comes about), then there would be no reason at all to think that it is true. As far as anything we would know in such a case, it would be as likely to be false. If, on the other hand, anything we think can be called into question as reason sees fit, then the fact that some claim survives our ongoing scrutiny is good reason to think that it is true. We could, in any given case, be wrong; and perhaps later we will discover grounds for thinking we have been wrong. There is no certainty. Nevertheless, capacities for rationally reflective criticism about anything we think are just the capacities that are needed to reveal the rationality of inquiry, of the processes that will reveal things as they are if anything will.5 And of course inference is central to such processes of rationally reflective criticism. There could be no such criticism if our languages were not inferentially articulated. On this Fregean account, then, the need for inferential links between sentences is not merely a sine qua non of a game we have evolved to play. It is the lifeblood of our investigations into what is the case, our processes of inquiry into the truth of the matter, whatever the domain. It follows directly that there is no language of thought, that language is and must be acquired, learned in the course of one’s upbringing—just as Sellars argues. It is only as learned that our conceptions, both of what is true and of what follows from what, can be unlearned as needed. As already indicated, the notion of truth on Peregrin’s inferentialist account has effectively no role to play in any adequate understanding of our cognitive comportments. Truth is not, for him, “a basic concept” (Peregrin 2014, 235). For the Fregean inferentialist, by contrast, the notion of truth is absolutely fundamental. As Frege reports in his “Notes for Ludwig Darmstaedter,” what is distinctive about my conception of logic is that I begin by giving pride of place to the content of the word “true,” and then immediately go on to introduce a thought as that to which the question “is it true?” is in principle applicable. (Frege 1979, 253) An inferentialist such as Peregrin has no use for such a conception of logic precisely because, so it is thought (following Kant), our thought simply cannot be answerable to the world, to how things actually are, in the way such a conception requires.

300  Danielle Macbeth For the Kantian, reality as it is in itself is merely causal, not in conceptual shape. And because it would be an episode in the Myth of the Given to take what is merely causal, not in conceptual shape, to have normative significance for a thinker, for instance, the significance of being that to which our thought is answerable, the Kantian holds that reality, insofar as it is merely causal, is normatively inert. Now Peregrin does say that “the relationship between language and the world [. . .] is [. . .] normative in nature” (Peregrin 2014, 37). But what he means is only that aspects of what he calls the causal world are involved in the game of giving and asking for reasons. He holds, in particular, that aspects of the world are involved in the game of giving and asking for reasons in much the way that aspects of the world are involved in sports such as football—in a way they are not involved in a game such as chess. Much as “the rules of football cannot be disentangled from the causal order in the way those of chess can” (Peregrin 2014, 36), so the rules of the language game of giving and asking for reasons cannot be disentangled from the causal order. “The normative is intertwined with the causal realm” (Peregrin 2014, 38). If, for example, one is in the presence of a dog, then one is right to say that it is a dog and wrong to say that it is, say, a cat or a cactus. And although it might seem that a robust notion of truth thereby comes into view, really it does not. Peregrin is not claiming here that one’s assertion is answerable to how things in fact are but only that it is part of the way the game is to be played that one responds to worldly things in certain particular ways, for instance, by making certain noises rather than others in certain circumstances. As Peregrin puts the point: an interface between the conceptual and the non-conceptual can only be sought within our linguistic practices, where the game of giving and asking for reasons, the game that is the home of asserting and hence propositions, and hence concepts, draws its materials from the world. (Peregrin 2014, 39) Now Peregrin does directly address the question of truth, the place that notion has in our cognitive comportments overall, but for him the question arises only in semantics. In particular, Peregrin suggests, instead of saying that consequence is a relation of truth-preservation, we can say that truth is that property that is preserved by consequence, i.e., by our loosely-criterial [that is, possibly infinitistic] inference. We may perceive the moves of the game of giving and asking for reasons as a matter of handing down, by means of sentences, a specific stuff—the truth. (Peregrin 2014, 116)

Inferentialism after Kant  301 To say that an assertion is true, on this account, is nothing more than to say that it is correct in a particular sort of way: “aiming at truth is [. . .] being correct in the sense constitutive of assertion” (Peregrin 2014, 236). Here, then, is the picture overall: Logical laws came into being [. . .] by means of certain argumentative practices developing out of rudimentary proto-practices and out of nothing. Then, argumentation developed into an implicitly standardized enterprise, rendering possible a general consensus on what is an acceptable step in an argument and what is not, gave birth to correct inferences. Specific expressions that could represent steps in arguments distinguished themselves from other expressions and became what we now call sentences. Some of the sentences, perhaps in specific contexts, came to be used as argument starters. These sentences can be called true, together with all those that are inferable from them. In this way, inferences become truth-preserving, not because there is some truth independent of them which happens to be preserved by those inferences we consider correct (and not by those we consider incorrect) but because truth was simply stipulated as that which is preserved by whatever counts as correct inference. (Peregrin 2014, 236) In the end, on this account, it really is all just a game. We saw that Peregrin opposes his inferentialism to representationalism, as if there were a kind of either/or between the two conceptions of meaning, as if one had to choose which of the two one would adopt.6 The underlying picture seems to be something like this. Imagine a web with multiple nodes, each of which is connected to other nodes by some relation or other, a relation we can visualize as lines connecting the various nodes. Pretheoretically, the items standing in the relations are to be thought of as in some way standing for or representing objects, or perhaps how things are with objects, and the relations among them are to be thought of as inferential relations. Now, both sides assume, we have a choice. We can begin with the various relations and try to understand the items that are the nodes solely in terms of those relations. Or we can begin with the nodes conceived as labels for objects or as pictures of states of affairs, aiming to understand the relations among them by appeal only to those labels or pictures. The first is the path taken by Peregrin’s inferentialist, and the second is that of his opponent, the representationalist. Now think of Kant. Kant in his way holds that one needs both inferentially articulated concepts and reference to objects as falling under those concepts, as thought through concepts. On Kant’s picture, the relations induce nodes as positions at which objects can be found and objects are given, in intuitions, to occupy those positions. It is this Kantian conception

302  Danielle Macbeth of intuitions as giving objects that can be thought only through concepts that Frege discovers is mistaken. Kant’s dichotomy of inferentially articulated concepts and given objects in fact conflates two different distinctions, that of sense (Sinn) and meaning (Bedeutung) with the distinction between concepts and objects. If Frege is right, we, following Kant, have [confounded] the division into concepts and objects with the distinction between sense and meaning [Bedeutung], so that we run together sense and concept on the one hand and meaning [Bedeutung] and object on the other. To every concept-word or proper name, there corresponds as a rule a sense and a meaning [Bedeutung] as I use these words. (Frege 1979, 118) Following Kant, we think that all objectivity lies in relations to objects and that all cognitive significance is conceptual. But this, Frege sees, is a mistake. It is to collapse into one what are in fact two essentially different distinctions. Once we distinguish the two distinctions as needed, we can begin to understand how it is that inferentially articulated language mediates our cognitive access to what is. In particular, we can now recognize two essentially different tasks that the course of inquiry must complete in order to culminate in knowledge of things as they are, one with respect to the senses of expressions in the language and the other as concerns Bedeutung or meaning. Consider, first, the fact that one can discover not only that what one had thought to be true is actually false but also that what one had thought to be one or the other, either true or false, is actually neither. Frege’s Basic Law V, for example, is not true (as Russell’s paradox shows), but nor is it false. It is not the case that the negation of Basic Law V is true. Basic Law V has no truth-value at all. And it has no truth-value because, as Frege came to see, the notion of a course of values is essentially confused; there is and can be no such concept. Thus there are, in Frege’s view, two essentially different epistemic tasks an inquirer must perform. First, she must get her conceptions right, come to grasp concepts in what Frege describes in Grundlagen as their “pure form,” stripped of all the “irrelevant accretions” that can at first attach to them (Frege [1884] 1953, vii). This is a matter of getting clear on the senses of concept words, a matter of coming to grasp their senses and achieving thereby a real relation of cognitive access to those concepts—assuming there are any. And if there are not, if the relevant concept word has no Bedeutung, it is the sense that will enable one to discover this, as, for example, in the case of the notion of a course of values. Basic Law V served to set out what Frege took to be the inference potential of the concept of a course of values, what may be inferred from the fact that something is a certain course of values. But as we now know, that axiom enables one to derive a contradiction. There is no such concept as that of a course of values.

Inferentialism after Kant  303 The second task for the inquirer, assuming that the first has been successfully executed, is to formulate and acknowledge true thoughts involving the senses of those concept words.7 As we might think of it, a Fregean thought that is true has the potential to be revelatory of some aspect of reality. Actually to acknowledge such a thought, to come to see that it is true as the culmination of one’s course of inquiry, is to actualize that potential, to fully realize the power of the thought to be revelatory of an aspect of reality. Here we come to the third point of comparison I want to draw between our two species of inferentialism. On Peregrin’s view, judgment is a move in a game, an action one performs; it is to make a commitment, whether or not that commitment is entitled. On Frege’s view, we have just seen, judgment is not a move in a game, an action one performs, but is instead an acknowledgment of truth, something that has the form of an exercise of a power not unlike an instance of seeing. As seeing is not an action one performs but instead an exercise of a power one has, so judging is an exercise of a power on Frege’s view. Notice, now, that as one cannot see what is not there or know what is not so, so one cannot acknowledge the truth of what is not true. One cannot judge what is not so as Frege conceives judgment. If, on the other hand, judging is a matter of making a move, or of forming a commitment, one certainly can judge what is not so; that is just to commit oneself to something that is not true. Judging on the construal that Peregrin endorses cannot, then, put one in cognitive contact with things as they are; for it is always possible that things are not as one judges them to be on Peregrin’s account of judging. Judging as Frege conceives it can put one in cognitive contact with things. Like seeing and knowing on any standard understanding of them, to judge is to achieve a cognitive relation to some aspect of reality. It is to have some aspect of reality brought to mind. When it comes to practical matters—which car to buy, whether to mow the lawn, whom to trust—often one simply must decide, make up one’s mind by deciding what to think. Judgment in the case of a purely theoretical question seems essentially different insofar as the idea of deciding what to think in this sort of case seems deeply inappropriate. Obviously, one cannot judge what one already knows to be true because if one knows it to be true, then there is nothing further to be done. One has already judged what one knows to be true. But if one does not know a thought to be true then, as far as one knows, it might instead be false. To make a judgment in the case in which one does not know the claim to be true is, then, only to make a guess. If one is lucky, the guess is right; and if one is unlucky, the guess is wrong. In neither case can one correctly be described as having knowledge. Obviously one does not know in the case in which one’s judgment is unlucky and one gets things wrong. But neither does one have knowledge in the case in which one’s judgment is lucky precisely because luck is involved. In the case of theoretical

304  Danielle Macbeth knowledge, then, judging cannot be an act of will aimed at closing a gap between one’s evidence for a proposition and its truth; it cannot be to choose between a thought and its negation as one might choose between two entrées in a restaurant. If one does seem to be faced with a choice, if there is a gap between one’s evidence, what one is presented with, and what one takes to be so, then at least in the theoretical case, one must not judge but instead continue with the course of inquiry until it is clear where the truth lies. And once it is clear, there is no room left for judgment. One’s mind has already been made up by the course of the inquiry. To make up one’s mind on some theoretical issue is to pursue a course of inquiry that culminates, if all goes well, in one’s realizing that things are thus and so. One does not decide what to think but instead pursues an investigation aimed at revealing the truth of the matter. One makes up one’s mind through one’s inquiry, where to make up one’s mind in this way is to exercise one’s power of judgment, of knowing, in the course of a critically reflective inquiry that, if all goes well, will eventually reveal how things are. Judging is in this way not an action one performs, something one decides to do as one can decide to undertake a course of inquiry. It is an exercise of a power of knowing, one that is inherently fallible, but also efficacious, inherently potent as the power it is. I turn finally to the role the social context plays in our understanding of the nature of language and its role in cognition. We have seen that Peregrin’s inferentialism is motivated in part by the idea that it is needed for the essentially social game of giving and asking for reasons within which alone, Peregrin suggests, we can distinguish between what someone takes to be right and what is right—that is, as Peregrin puts it, between following a rule and merely thinking that one is following the rule (Peregrin 2014, § 1.4). With Brandom, Peregrin takes the idea to originate with Wittgenstein in the Philosophical Investigations (Wittgenstein 1953). But another, quite different reading of the relevant parts of Philosophical Investigations is also possible, one according to which the social plays a very different role. To understand what that role is, it is helpful to begin with an apparently very different sort of case, that of a living being, a plant, say, or a nonrational animal. As Aristotle already argued, and as is being very ably defended in some circles today, a living being is constitutively an instance of some particular form of life, a form of life that, as we now know though Aristotle did not, first emerged through processes of biological evolution through natural selection. It is only relative to the form of life that the collection of physical stuffs that make up the body of the living being is properly described as alive, only relative to the form of life that it is possible so much as to identify what the thing is and what its parts are for. Suppose, for example, that it is asked why the wings of some particular bird have grown in the way that they have. If the bird in question is an instance of a form of life the wings of which ought to have grown as they actually

Inferentialism after Kant  305 did, a good explanation would be that the bird is, say, an eagle and eagles need wings of that sort in order to hunt as they do. If instead the wings are deformed given the life form that the bird is, the explanation will instead cite, for example, a genetic defect, or some trauma the bird has suffered, or some other physical explanation for why things did not go as they ought to have done for such a form of life. When things go as they ought, then it is the form of life itself, or some aspect of it, that is explanatory. When things do not go as they ought, then an essentially different sort of explanation is needed, an explanation of a sort that is available also in cases involving only inanimate matter. To be an instance of a biologically evolved form of life is to be an ontologically distinctive kind of being. It is to be alive, where to be alive is essentially different from merely being some physical stuff in an arrangement as inanimate objects are. A living being is, for example, fragile in a way no inanimate object is or can be. A living being can be harmed; it can become ill; and it can be defective in any of a variety of ways. Inanimate beings, even those we create, merely are what they are. If they malfunction, that is only relative to our purposes, our designs. Even our machines in fact behave simply as the laws of physics dictate. Living beings, by contrast, have their own forms of life, forms of life relative to which they and their characteristic activities are explicable. And it is not only living beings that emerge through processes of biological evolution by natural selection. Various physical stuffs in the environment also acquire new, biological significances: water, for example, acquires the significance of being nourishing to animals and plants; fire is now dangerous. So it is with knowers and the known on the reading of Wittgenstein with which we are now concerned. Linguistic forms of life evolve socially in ways that are not unlike the ways biological forms of life evolve, and as they evolve things in the environment acquire linguistic significances as what things are called. And once there are such linguistic forms of life and conceptually articulated things in the environment, individuals can, through their acculturation, become instances of those forms and become thereby a radically new sort of animal, a rational one, an inhabitant of the space of reasons. Notice now that, on this account, the reality on which thought aims to bear is always already caught up in the space of reasons in a way that is essentially different from the way it is on Peregrin’s account. On our account, the realm of causes can itself become normatively significant, an aspect of the space of reasons, through processes of social evolution. Causes are not reasons. To think otherwise is the Myth of the Given. Nonetheless, causes can become also reasons through social evolution just as biologically inert stuffs such as water or fire can become also biologically significant through processes of biological evolution. And just as plants and animals can be flourishing or not relative to the norms that are provided by the forms of life of which they are instances, so a rational animal,

306  Danielle Macbeth an instance of a social, linguistic form of life, can be correct or not relative to the norm that is provided by the form of intellectual life of which it is an instance. Obviously there are disanalogies, but the general idea should be clear. On this conception, when one speaks, saying, perhaps, that a certain blue tie is green (because that is the way it appears in the lighting conditions in which it is being viewed) what one means given the rational form of life one instantiates is that the tie is green, and this is false in the situation as described. This is quite different from the sort of view Peregrin describes. On his view, because it is what we do that (as in a game) directly sets the standard of c­ orrectness—as contrasted with indirectly doing that by determining the meaning or significance of what is said—so long as one conforms to the social practices of one’s community then one is right. Again, there is no notion of truth in Peregrin’s conception of inferentialism over and above what the community as a whole takes to be true.8 I began with the idea that whereas Peregrin defends an inferentialism that is conceived by contrast to representationalism, a more Fregean inferentialism involves both inference and reference. I then focused on three themes. The first was Peregrin’s idea that what we do in the space of reasons should be thought of as an essentially social game rather than as the characteristic activities of instances of a particular rational form of life. The second theme was provided by Peregrin’s thought that inferentially articulated language is first and foremost the vehicle of the game of giving and asking for reasons. For Frege, we saw, language is and must be inferentially articulated because it is the vehicle of processes of inquiry, of critically reflective and self-­correcting courses of investigation that, if all goes well, succeed in revealing aspects of reality to a knower. Our final theme was Peregrin’s assumption that judgment is an action one performs, a move in the game of giving and asking for reasons, a making up of one’s mind in a way that closes a gap between the evidence and what one claims to know is true, rather than an acknowledgment of truth as on Frege’s account. As I have tried to indicate, there are good grounds for considering the alternatives to those views that Peregrin develops and defends. But as I have also indicated, there is a historical precedent for the kind of inferentialism Peregrin espouses. In particular, Peregrin’s inferentialism is deeply Kantian in assuming a fundamental opposition between inference and reference. What Frege helps us to see is that that Kantian distinction actually conflates two different distinctions. Frege’s inferentialism is in this regard profoundly post-Kantian. If Frege is right, the time has come to pursue inferentialism not in the manner of Kant as Peregrin does, but in Frege’s way, in a way that is genuinely beyond Kant.

Notes 1 This is, with a minor emendation, the title of one of Sellars’s papers, the actual title of which is “Concepts as Involving Laws and Inconceivable without Them.” The essay first appeared as Sellars (1948).

Inferentialism after Kant  307 2 This is explicit in Ludwig Wittgenstein’s ([1921] 1961) Tractatus LogicoPhilosophicus. 3 The original German of the whole is: “nach der Bedeutung der Wörter muss im Satzzusammenhange, nicht in ihrer Vereinzelung gefragt werden.” 4 As Peregrin (2014, 7) says, “why language must be inferentially articulated is because of its crucial role of being the vehicle of the game of giving and asking for reasons.” 5 Although I cannot pursue the point here, this idea connects directly with the insight of virtue epistemology, the idea that to understand our capacities for knowledge we must focus on the activities of virtuous knowers, not on features of the items assumed to be known. 6 In this regard, the debate is quite like that between intensionalist and extensionalist logicians. In both cases, the virtues of the one side appear to consist almost entirely in the ability of that side to avoid the defects marring the conception on the other side. 7 Of course, there are also object names that express senses and also designate. They are of less interest for our purposes and so are here set aside. 8 This is a by-now standard complaint against Brandom’s inferentialism, the model for Peregrin’s. See, for example, Haugeland (1998, 358, n. 14).

References Frege, Gottlob. 1879. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: L. Nebert. Frege, Gottlob. 1953. The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number. Translated by John Langshaw Austin. Oxford: Basil Blackwell. Original edition, 1884. Frege, Gottlob. 1979. Posthumous Writings. Edited by Hans Hermes, Friedrich Kambartel, and Friedrich Kaulbach. Translated by Peter Long and Roger White. Oxford: Blackwell. Original edition, 1969. Haugeland, John. 1998. Having Thought: Essays in the Metaphysics of Mind. Cambridge, MA: Harvard University Press. Macbeth, Danielle. 2005. Frege’s Logic. Cambridge, MA: Harvard University Press. Macbeth, Danielle. 2014. Realizing Reason: A Narrative of Truth and Knowing. Oxford: Oxford University Press. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan. Sellars, Wilfrid. 1948. “Concepts as Involving Laws and Inconceivable without Them.” Philosophy of Science 15 (4): 287–315. Sellars, Wilfrid. 1956. “Empiricism and the Philosophy of Mind.” In Minnesota Studies in the Philosophy of Science, Volume I, edited by Herbert Feigl and Michael Scriven, 253–329. Minneapolis, MN: University of Minnesota Press. Wittgenstein, Ludwig. 1953. Philosophical Investigations. Oxford: Blackwell. Wittgenstein, Ludwig. 1961. Tractatus Logico-Philosophicus. Translated by David F. Pears and Brian F. McGuinness. London: Routledge and Kegan Paul. Original edition, 1921.

16 Inferentialism, Naturalism, and the Ought-to-Bes of Perceptual Cognition James R. O’Shea

1. Inferentialism and the Meaning of Ordinary Empirical Descriptive Terms We now have at least two systematic developments of inferentialism about meaning and conceptual content in the form of Robert Brandom’s Making It Explicit (Brandom 1994) and Jaroslav Peregrin’s Inferentialism (Peregrin 2014). The following informal characterization of inferentialism about meaning by Peregrin will serve to put the view on the table for us. For the inferentialist, writes Peregrin, the question of meaningfulness of a word turns on the question of its embeddedness within networks of other words, more precisely of sentences containing the word being in inferential relationships to other sentences. Therefore inferentialism embraces the proposal that what makes something an assertion, rather than just a sound, is the fact that it is a move in a certain language game, a rule-governed game; what makes something a meaningful sentence is its capability of serving as a token playable in such a game, and what makes a word meaningful is being part of meaningful sentences. The links that are, according to the inferentialist, the most important have to do with the ability of engaging in the practices that Brandom (1994) termed the game of giving and asking for reasons. (Peregrin 2014, 30) One of the challenges for such a view, as Peregrin goes on to explain, is to account for the meaningfulness of ordinary empirical descriptive vocabulary—for example, to start simply, to account for such terms of our ordinary perceptual experience as “dog” or “apple,” and such assertions as “This apple is red.” For while it might seem plausible, for instance, that logical connectives such as the conjunction “and” might have their meaning solely in virtue of their rule-governed inferential role1 in relation to other words and sentences, it seems to be part of the very meaning of “apple” that it refers to apples. The apple itself, or some

Inferentialism, Naturalism, and the Ought-to-Bes  309 proxy or representative idea of it, seems to be part of the very meaning of the word “apple” in such sentences as “This apple is red.” Consequently, one familiar question addressed by all inferentialist views that purport to provide comprehensive accounts of meaning and conceptual content concerns how to provide an inferentialist treatment of the meaningfulness and status of ordinary perceptual knowledge claims. As any HR employee will tell you, challenges are also opportunities. In what follows, I will examine one of the most complex instances of a broadly inferentialist treatment of perception, one that I will argue also has the further advantage, in the present context, of displaying some of the original motivations of inferentialism as a general outlook on human conceptual cognition. This, of course, is the account of perceptual knowledge in Wilfrid Sellars, who is acknowledged by both Brandom and Peregrin as the inspiration for their normative inferentialist accounts of meaning. What will emerge in what follows is that one of the primary motivations for inferentialism in its Sellarsian origin concerned addressing the problem of perceptual knowledge, not so much as a challenge for an independently motivated logical or semantic inferentialism, but rather as the crux for what Sellars took to be the only possible route to a genuinely naturalistic account of human cognition in general. The aim of this chapter is to draw out those motivations and to assess their implications.

2.  Noninferential Perceptual Knowledge? In his classic 1956 article, “Empiricism and the Philosophy of Mind” (EPM), Sellars was concerned primarily with epistemological and metaphysical issues surrounding what he called the Myth of the Given, the original title of those London lectures. One prominent “givennist” target in EPM, of course, was the sort of empiricist foundationalism that was characteristic of sense-datum theories during the first half of the twentieth century. Sellars articulated the more general structure of such views as resting on the mistaken, givennist assumption that ultimately all inferences must terminate in some “stratum” of knowledge that is “not only noninferential” (that is, not inferred from other items of knowledge), but which also “presuppos[es] no knowledge of other matter of fact, whether particular or general” (Sellars 1956, VIII § 32). It is the alleged presuppositionless feature that is crucial, for as Sellars contends, it “might be thought” that “knowledge [. . .] which logically presupposes knowledge of other facts must be inferential. This, however, [. . .] is itself an episode in the Myth [of the Given]” (Sellars 1956, VIII § 32). The key mistake regarding the Myth of the Given in this respect, then, is for the givennist to assume that there cannot be noninferential knowledge that nonetheless has essential inferential epistemic presuppositions. The latter is precisely Sellars’ own view of ordinary,

310  James R. O’Shea noninferential perceptual knowledge (within any given conceptual framework).2 ­Consider the famous “space of reasons” characterization of knowledge stated by Sellars in EPM: The essential point is that in characterizing an episode or a state as that of knowing, we are not giving an empirical description of that episode or state; we are placing it in the logical space of reasons, of justifying and being able to justify what one says. (Sellars 1956, VIII §36) This passage is of course the source of Brandom’s Sellarsian phrase, “the game of giving and asking for reasons.” On Sellars’ view, accordingly, any mental state or utterance that is to be an instance of knowledge requires that one be “able to justify what one says” by means of an available supporting inference from some propositionally stateable reason that serves to justify that “episode or state”; and furthermore, that state must itself be conceptually articulable, on Sellars’ view, if it is to be fit to stand in such an inferential relation. Consider an ordinary perceptual belief, judgment, or assertion, such as that “This apple is red.”3 On Sellars’ view, such a perceptual judgment normally has, at a minimum, the following three characteristics (Sellars’ •dot quotes• serve to classify the normative-inferential role or the rulegoverned functional “use” of the quoted term): (i) a conceptually contentful, rule-governed response (a •This apple is red• thought), (ii) reliably caused by the appropriate corresponding object (that is, by red apples), and (iii) causally (not epistemically) mediated by appropriate nonconceptual sensations. Such a conceptualized perceptual response is what Sellars calls a “language entry transition” (thus using linguistic behavior as his model for conceptual thinking in general, whether “inner” or “outer,” in whatever medium), according to the following tripartite classification of semantic rule-uniformities:

• language entry transitions (world ⇒ language)—perceptual responses, • intra-linguistic transitions (language ⇒ language)—inferences, • language exit transitions (language ⇒ world)—volitions, intentional actions.

I have called these transitions “semantic rule-uniformities” (Sellars uses both “semantic rules” and “semantic uniformities”) to reflect an important principle that I have elsewhere called Sellars’ norm-nature

Inferentialism, Naturalism, and the Ought-to-Bes  311 meta-principle (O’Shea 2007). According to this principle, as Sellars puts it, the “espousal of principles,” including crucially the implicit espousal of the socially norm-reinforced “ought-to-bes” of our pattern-governed linguistic behavior, “are reflected in uniformities of performance” (Sellars 1962, 48). The upshot is that perceptual “language entry transitions” are socially reinforced and hence normally reliable noninferential conceptual responses having the schematic form: “(Ceteris paribus) it ought to be that subjects respond to ϕ items,” say, red apples, “with conceptual acts of kind C,” for example, with •this red apple• perceptual thinkings, in whatever properly patterned, norm-governed medium this might occur. To use Sellars’ (1969) terminology, the relevant ought-to-be “rule of criticism” (as opposed to a direct and explicit ought-to-do “rule of action”) is that it ought-to-be the case that speakers of English are reliably disposed to respond, ceteris paribus, to the presence of red apples with •this red apple• conceptualized perceptual responses in one form or another. More realistically, as Peregrin rightly emphasizes, the result is that such responses “tend not to occur in patterns which violate” the relevant semantic rule-uniformity transitions (Peregrin 2014, 25). The perceptual responses are noninferential because they are not conceptual responses to a propositional claim or premise, but rather to red apples themselves.4 Sellars argues in EPM that such perceptual knowings, despite being noninferential, are nonetheless not instances of the alleged presuppositionless given, on both semantic and epistemological grounds. Without entering here into the enduring pro- and con- controversies about the Myth of the Given, for Sellars the point is that perceptual experiences can provide warrant and be states of knowing only insofar as they are conceptualized, that is, have conceptual or semantic content, in a way that makes them fit for playing a role in judgments, beliefs, and assertions within the “logical space” of inferential reason-giving. One way to bring out the inferentialist semantic grounds for this view of the conceptual content of our noninferential or object-elicited perceptions is by means of Sellars’ Kantian view of concepts as involving the prescription of law (cf. O’Shea 2016a and Brandom 2015, chap. 4, on the “modal Kant-Sellars thesis”). For Sellars, as for Kant, the very idea of an object of knowledge, or more fundamentally, of any object of thought or intentionality in general (or as Kant would put it, the possibility of cognizing an object of our representations) is connected with a certain lawfulness or modal constraint the necessary representation of which, they argue, is an achievement of conceptualization. In Kantian terms, concepts are rules that prescribe laws to appearances. Sellars’ way of making the parallel point within his own inferentialist framework lies in his contention that it “is only because the expressions in terms of which we describe objects [. . .] locate these objects in a space of implications,

312  James R. O’Shea that they describe at all, rather than merely label” (Sellars 1957, 306– 307, § 108; cf. Peregrin 2014, 30–31). Brandom presses this point home further by arguing that the practice of “deploying any ordinary empirical vocabulary,” however simple (for example, “This is red”), already presupposes “counterfactually robust inferential practices-or-abilities—more specifically, the practical capacity to associate with materially good inferences ranges of counterfactual robustness” (Brandom 2015, 160, italics in original).5 Without going into the details, Brandom’s argument relies upon his inferentialist semantics such that “to count as deploying any vocabulary at all”—for example, to count as describing anything as opposed to merely labeling or parroting—“one must treat some inferences involving it as good and others as bad. Otherwise, one’s utterances are wholly devoid conceptual content” (Brandom 2015, 163). Or as Brandom had put the underlying inferentialist point it in Making It Explicit: To grasp or understand a concept is, according to Sellars, to have practical mastery over the inferences it is involved in—to know, in the practical sense of being able to distinguish, what follows from the applicability of a concept, and what it follows from. The parrot does not treat “That’s red” as incompatible with “That’s green,” nor as flowing from “That’s scarlet” and entailing “That’s colored.” Insofar as the repeatable response is not, for the parrot, caught up in practical proprieties of inference and justification, and so of the making of further judgments, it is not a conceptual or a cognitive matter at all. (Brandom 1994, 89) The result of these reflections is that the possibility of even the most minimal of empirical conceptions, such as that “This is red,” requires that one already implicitly be able to make moves in the language game that are “lawful” in the sense of being counterfactually robust. Or as Brandom puts it in his analytic pragmatist terms, the “expressive role characteristic of alethic modal vocabulary is to make explicit semantic, conceptual connections and commitments that are already implicit in the use of ordinary empirical vocabulary” (Brandom 2015, 157–158). Contrary to Hume and Quine, then, there exists no empirical “stratum” of “data” that is innocent of modal commitments of this kind on this Kant-Sellars inferentialist view of conceptual content.6 We are now in a position to return to the question of an inferentialist account of noninferential perceptual cognition with which we started, for the corresponding epistemological view of perceptual warrant in Sellars tracks the above view of the requirements on conceptual content quite closely. In this sense Sellars’ inferentialist semantics forms the basis of his “logical space of reasons” conception of knowledge, although the latter epistemic dimension raises distinctive normative and conceptual issues

Inferentialism, Naturalism, and the Ought-to-Bes  313 of its own. We began this section with Sellars’ remark that it “might be thought” that “knowledge [. . .] which logically presupposes knowledge of other facts must be inferential. This, however, [. . .] is itself an episode in the Myth [of the Given]” (Sellars 1956, VIII § 32). This implies that Sellars holds that there is such a thing as noninferential knowledge—­ paradigmatically, this would be the case with our adult perceptual responses to nearby visible medium-sized dry goods in normal conditions. However, other things that Sellars says indicate that he holds that all justification is inferential, as for instance when he once remarked, “I am arguing, in effect, that all justification is inferential” (Sellars 2015, 184, § 185). This was during a question-and-answer session following his original presentation in the early 1970s of the lectures that became “Structure of Knowledge,” but as he also puts it in the lectures themselves, “the concept of a reason seems so clearly tied to that of an inference or argument that the concept of non-inferential reasonableness seems to be a contradictio in adjecto” (Sellars 1975, III § 16). However, I think the “seems” is important here, as is the “in effect” in the previous quote. For Sellars also writes in this lecture that as “has been pointed out since time immemorial, it is most implausible to suppose that all epistemic justification is inferential, at least in the sense of conforming to the [usual] patterns” of inductive, deductive, and theoretical inference (Sellars 1975, III §13). So Sellars took his task to be that of explaining “how there can be,” as he puts this in scare-quotes, “ ‘non-inferentially reasonable beliefs’ ” (Sellars 1975 III § 16, § 15). Clearly a distinction is required here, one that turns out to track closely distinctions that more recent inferentialists such as Brandom and Peregrin have sought to draw in order to bring noninferential perceptual cognitions under the umbrella of “inferentialism,” so that the latter view can be put forward as a fully general account of meaning and conceptual content. Brandom, for instance, distinguishes between “weak” versus “strong” versus “hyper” inferentialism, and across these, between “broad” versus “narrow” inferentialism. Brandom’s own “strong” inferentialist view is that inferential articulation broadly construed is sufficient to account for conceptual content. [. . .] The broad sense focuses attention on the inferential commitment that is implicitly undertaken in using any concept whatever, even those with noninferential circumstances or consequences of application. (Brandom 2000, 28)7 So, for example, S’s assertion that “This is red” uttered in response to the presence of a red object—that is, a noninferential circumstance of the application of “x is red”—implicitly commits either S, or (Brandom wants to include) someone vouching for S, to the availability of a reliable

314  James R. O’Shea inference from S’s so asserting in these sorts of circumstances, to there in fact being a red object present to S. Sellars can be seen, despite many differences between the two philosophers, to have drawn a broadly similar distinction to Brandom’s in at least the above epistemic respect.8 Sellars’ detailed, cross-career views on the question of the justification of our noninferential perceptions by means of the relevant reliability and other epistemic principles are as rich as they are controversial.9 It is true that, unlike Brandom, Sellars requires that S herself have the requisite implicit (meta-)knowledge of her own general reliability in the relevant sorts of circumstances. But the resulting implicit normative “reasonableness,” as Sellars put it above, of the initial perceptual judgment is for Sellars, as for Brandom, supported by the availability of a warranting reliability inference of the appropriate kind (cf. Sellars 1975, III). The availability of the implicit reliability inference for both of them is ultimately grounded—and this is the key point—in the inferentialist sources of the very conceptual contents that constitute the initial noninferential perceptual judgment or “perceptual taking-tobe” itself, and thus has its ultimate source in the sorts of socio-­linguistic practices that have generated and which sustain the norm-parasitic, causal reliability of such rule-uniformity “language entry” responses in the first place (cf. O’Shea 2016b).10 It should be noted that in this respect the inferentialist outlook of Sellars has generated controversy in relation to some currently influential views in epistemology, including among some Sellars-influenced philosophers. In particular, for example, John McDowell has recently come to think, “with disappointment,” that Sellars’ systematic account of perceptual knowledge does indeed rest, as explained above, on an implicitly inferential warrant for our noninferential perceptual beliefs (McDowell 2016, 100). This is disappointing to McDowell in that he takes it to be inconsistent with his own (“disjunctivist”) view of the warrant for our knowledgeable perceptual believings, according to which a subject’s perceptual experience of an object, when all goes well, makes “present to her an environmental reality such that, in having it present to her, she has a conclusive warrant for believing” that there is such an object “in front of her” (McDowell 2016, 101). On McDowell’s view there is thus noninferential perceptual knowledge of the object, based on the experience, full stop, without recourse to available inferential support; and he had previously thought that this was Sellars’ view, at least in EPM. I have defended the plausibility of Sellars’ own inferential view of that particular matter elsewhere (O’Shea 2016b), and my concern in this section is not to resolve that particular epistemological dispute. Rather, my aim in this section has been to examine Sellars’ original approach to some of the key issues and distinctions that arise for inferentialism when it tackles the problem of accounting for the content and status of

Inferentialism, Naturalism, and the Ought-to-Bes  315 our noninferential perceptual cognitions with inferentialist resources. To close this section, let us return to Peregrin’s presentation of this general problem for inferentialism (Peregrin 2014, chap. 2), from which we took our start. Peregrin seeks to resolve the tensions that arise for an inferentialist account of noninferential perceptual cognition by “broaden[ing] the sense of inference so that we are able to talk about inferences from situations to utterances and from utterances to actions,” so that it [is] possible to say that the inferential role of an empirical term like dog consists both of (material) rules of inferences of the standard kind, [. . .] and also of some “inferential rules” linking types of situations to sentences or sentences to types of actions. (Peregrin 2014, 32) This proposal requires some care, however, for we have seen (1) that on Sellars’ view our perceptual responses in the form of language entry transitions are not inferences, and it seems to me that it would stretch the notion of “inference” beyond recognition to treat those first-order ruleuniformity transitions as inferences. We also examined (2) the role of the relevant “ought-to-be” rule—roughly, that (ceteris paribus) it oughtto-be that subjects respond to ϕ items (say, red apples) with conceptual acts of kind C (say, with •this red apple. . . • thoughts or utterances)—in generating and sustaining such transitions in practice, as “semantic uniformities.” This ought-to-be rule is not an inference, but a norm that generates actions (for example, in linguistic “training”) via corresponding “ought-to-do” rules of action. And (3) we rehearsed the ordinary, unbroadened inferentialist account of the conceptual content that is constitutive of any given perceptual response as being a perception of this or that kind of object; but that account does not involve any “inferences from situations to utterances.” Finally, (4) we saw that with these sorts of rule-induced “ought-to-be” uniformities in place in a practice, we also have the resources to account for the availability of the requisite reliability inference that warrants our perceptual beliefs. It seems that it is really only (4) that involves an inference in connection with the perceptual cognition, but even this will typically arise only when the question of the perceiver’s reliability in such and such circumstances has arisen and been made explicit. So it is not clear that broadening our notion of inference to include “inferences from situations to utterances” is really required in order to assemble all of the requisite pieces in Sellars’ or Brandom’s inferentialist accounts of perception. Yet it seems to me that (1) to (4) are all the justification needed for conceiving of this account of perceptual cognition as an inferentialist account of the content and status of our perceptual cognitions. Using the inferentialist concepts already discussed,

316  James R. O’Shea (1) brings the object properly into the account, hence the inferentialism is “broad”; (2) displays the normative bases for the semantic uniformities or transitions involved in (1), hence the inferential roles are “normative” rather than merely “causal;” (3) indicates how inferential articulation is supposed on this view to be sufficient to account for the conceptual contents involved in our perceptual experiences and beliefs, hence the inferentialism is “strong”; and (4) displays the role of an available reliability inference involved in the status of the perceptual response as warranted, or as a case of knowledge, thus reinforcing the inferentialist character of the account. Possibly this is in effect what Peregrin means by his proposal to “broaden the sense of inference so that we are able to talk about inferences from situations to utterances,” but it is less misleading to display the inferentialist pedigree of this account of perceptual knowledge as in (1) to (4), which I take to show that such a broadening is unnecessary. With the above Sellarsian inferentialist account of our noninferential perceptual knowledge in place, it is time finally to address the naturalistic motivations foreshadowed at the outset of this chapter. What has all of the above to do with naturalism?

3. Inferentialism, Naturalism, and Perceptual Intentionality At the outset I suggested that the task outlined above of providing an inferentialist account of perceptual content was, as Sellars saw it, a challenge that represented an opportunity for defending a thoroughgoing naturalist conception of human cognition. How so? Returning to the setting of EPM and the Myth of the Given, Sellars briefly outlined a version of his broadly later-Wittgensteinian, inferentialist conception of meaning in Part VII, “The Logic of ‘Means’.” There he remarks that the real test of a theory of language lies not in its account of what has been called (by H. H. Price) “thinking in absence,” but in its account of “thinking in presence”—that is to say, its account of those occasions on which the fundamental connection of language with nonlinguistic fact is exhibited. (Sellars 1956, VII § 30) Sellars’ rejection of the Myth of the allegedly presuppositionless yet knowledge-constituting given, as we saw briefly earlier, depends in large part on his inferentialist conception of both the conceptual contents involved in perceptual cognition and the positive epistemic status and warrant-yielding character of our noninferential perceptual experiences and judgments. Assuming at this stage that we abandon the Myth, Sellars follows up the above remark by suggesting that

Inferentialism, Naturalism, and the Ought-to-Bes  317 once we have abandoned the idea that learning to use the word “red” involves antecedent episodes of the awareness of redness—not to be confused, of course, with sensations of red—there is a temptation to suppose that the word “red” means the quality red by virtue of these two facts: briefly, the fact that it has the syntax of a predicate, and the fact that it is a response (in certain circumstances) to red objects. (Sellars 1956, VII § 31) In this connection let us distinguish four general approaches that are guiding Sellars’ thinking in EPM on the question, “by virtue” of what does “the word ‘red’ means the quality red?” The first two general styles of approach I have in mind include all of the various targets of Sellars’ critique of the Myth of the Given that appeal to irreducible semantic or intentional relations to the real, and which can be classed under the two different headings of givennist rationalist and givennist empiricist approaches to the intentionality that is involved in the “awareness of redness.” The third sort of approach is the “temptation” referred to in the passage above, which as far as semantic content is concerned seeks to appeal only to (syntax and) causal relations to the world, including behavioral conditioning causally conceived. And the fourth is Sellars’ own normative-inferentialist conception of noninferential perceptual cognition, examined in the previous sections. Recognizing that these broad distinctions involve useful idealizations, Sellars argues that both classical rationalist and classical empiricist commitments to the Myth of the Given typically presuppose naturalistically dubious semantic and intentional relations to objects. These mental and/ or semantic objects have typically been conceived as Platonist or quasiPlatonist abstract entities in the rationalist versions (including Fregean senses as abstracta, possible worlds, et al.), or as sensibilia in one form or another (for example, sense-data, or perhaps physical objects directly) in the empiricist versions. As far as the rationalist versions are concerned, Sellars offered a complex alternative account of meaning and abstract entities in terms of his normative inferential role semantics, one that attempts to avoid all reification of abstract entities and involves only the sorts of commitments outlined in the previous section. As far the empiricist versions are concerned, Sellars offered his well-known (if not uncontroversial) arguments in the first half of EPM that there are no direct mental or semantic relations to putative objects of sensation or of sense perception that are semantically or epistemically significant, except insofar as, and only insofar as, there is normative conceptualization involved in the ways outlined in the previous section.11 And on that view, that is, Sellars’ own view, the only real relations between the conceptualizer and the object conceptualized are naturalistically unproblematic causal relations. According to Sellars’ normative inferential role semantics, all the ostensibly world-relational grammar that is involved in ordinary

318  James R. O’Shea statements about intentionality, meaning, and reference are cashed out in terms of metalinguistic (metaconceptual) normative-inferential role classifications. The classical empiricist versions tended to appeal ultimately to immediate, preconceptual “mental act/object” relations to sense-data (which are also naturalistically problematic), or to appeal to relations of appearing, as alleged instances of, or as entailing, knowledge, which Sellars rejects on familiar grounds that should be familiar from the previous section. These are the primary underlying reasons why Sellars contends that his own inferentialist account of “those occasions on which the fundamental connection of language with non-linguistic fact is exhibited” (quoted above) is not only epistemically but also naturalistically superior to both the rationalist and empiricist varieties of the Myth of the Given as a comprehensive philosophy of mind and intentionality. And finally, the third, purely causal alternative is a “temptation” to Sellars due to its naturalistic credentials, but it fails to capture the constitutive normative dimensions that we have seen to be essential to Sellars’ inferential role semantics and epistemology. These reflections leave us with a final difficult question, however, one that I have attempted to address, at least in part, elsewhere (beginning with O’Shea 2007) but that I can only point to in closing here. Namely, why was Sellars confident that his own fundamental normative inferentialist position, even supposing that we grant its naturalist credentials relative to the Platonist, quasi-Platonist, and classical empiricist views he criticizes, would be accepted as a species (as he certainly held it to be) of a thoroughgoing scientific naturalist outlook from top to bottom— especially given the irreducible and constitutive normative “ought”s that are essential to his account? Brandom’s apparent characterization of his normative inferentialist position as one according to which it is “norms all the way down” (Brandom 1994, 44) has subsequently heightened the pressing nature of this last question for normative inferentialists.12 It is one of the virtues of Peregrin’s writings that he attempts to tackle the naturalistic questions raised by normative inferentialism, particularly in relation to questions concerning the evolutionary origins of our rulefollowing, pattern-governed linguistic behavior, which I think Sellars, too, regarded as a crucial scientific and philosophical explanandum for the naturalistically convinced normative inferentialist (cf. Peregrin 2014, chap. 6). My own view is that ultimately Sellars thought that the behavioral patterns brought about by the institution of “ought” principles could itself be exhaustively described in naturalistic terms, involving a sophisticated account of the behavioral patterns that result from the motivating force of “ought”s conceived as an abstract generalization of community intentions (“we shalls”). To understand them as “ought”s is indeed to take an irreducibly and constitutively normative rather than a naturalistic stance toward such principles. But when or if we were to come to understand, naturalistically, how such behavioral-linguistic phenomena

Inferentialism, Naturalism, and the Ought-to-Bes  319 produce the relevant specific patterns of (as it were) “ought”-caused ­linguistic-behavioral and other rule-uniformities that they do, then we would have explained naturalistically the same phenomena that we conceive in intentional and normative terms when we are engaged in all the rational activities that make us rational animals. Sellars’ own way of framing this general approach to the natural and the normative was thus to argue that, seen in this light, the normative dimensions of our thought and agency are conceptually irreducible but causally (explanatorily) reducible to what would be an adequate, purely naturalistic, extensional, scientific description of the same phenomena (cf. Sellars 1953b for this terminology). These last remarks, however, must remain here as open questions, though pressing ones, as to whether a constitutively normative inferentialism in the end really can, as Sellars envisaged, provide the framework for an exhaustively scientific naturalist conception of the nature of human cognition. What we have seen here is: first, that any normative inferentialism confronts a challenge in the form of how to account for the sort of ordinary empirical descriptive vocabulary that is involved, paradigmatically, in our noninferential perceptual responses and knowledge claims; second, that Sellars’ original multilayered account of such noninferential responses in the context of his normative inferentialist semantics and epistemology displays how the inferentialist can plausibly handle those sorts of cases without stretching the notion of inference beyond its standard uses; and finally, that for Sellars there were deeply naturalistic motivations for his own normative inferentialism, though the latter ends up raising further questions as to its naturalistic credentials that are currently hotly disputed.

Notes   1 As a preliminary clarification, see Peregrin (2014, 8–11) on the distinction between “normative” or rule-governed inferentialism, which is the Sellars-­ Brandom-Peregrin outlook to be discussed in this chapter, and what Peregrin characterizes as the “causal” inferentialist views of, for instance, Peacocke (1992) and Boghossian (1993), which focus rather “on inferences individual human subjects really carry out, or have dispositions to carry out” (Peregrin 2014, 9). The relevant sense of “inferential role” in this chapter will be that of the Sellarsian normativist view.   2 There are issues raised by the relativity to conceptual frameworks, but I wish to set these aside for now.   3 One could also discuss this matter in terms of the simpler, sub-propositional “perceptual takings-to-be” that are involved in perception, according to Sellars: for example, “This red apple [is so-and-so],” or “Lo! an apple!” But since for Sellars these “perceptual takings” must themselves be conceptualized and be able to function in propositional states and reasonings if they are to be candidates for perceptual knowings, we can focus on propositional judgments and utterances for present purposes.   4 Likewise, but in the reverse direction, an intentional action or “language exit transition” (that is, language ⇒ world) such as an •I’ll answer the phone•

320  James R. O’Shea intention or volition, followed ceteris paribus by the appropriate behavior, is not an inference but an instance of a socially inculcated and maintained rule-uniformity.  5 A material inference, such as “If a is copper, then a conducts electricity,” as opposed to a logically valid formal inference (in which the descriptive terms occur “vacuously,” to use Quine’s phrase, for example, “If A and B, then A”), is one the validity of which depends upon the content of the descriptive terms or concepts involved (copper, electricity). The idea that material inferences are basic—for example, that the material inference above is not merely derivative from or an enthymeme for a logically valid, formal inference such as “for all x, if x is copper, then x conducts electricity; a is copper; so, a conducts electricity”—is essential to the inferentialist semantics of Sellars, Brandom, and Peregrin. The locus classicus for this contention is Sellars (1953a); see also Brandom (1994, 97–102).   6 In this paragraph I have borrowed from my analysis in O’Shea (2016c).   7 By contrast, “weak” inferentialism takes inferential articulation, “broadly” construed, to be merely necessary (not sufficient) to account for conceptual content; and “hyper” inferentialism takes inferential articulation narrowly construed (thus as not including our noninferential perceptual responses to objects) to be sufficient by itself to account for conceptual content.   8 But as far as Sellars’ view of meaning and conceptual content is concerned, the matter is more complicated. Brandom (2000, 206 n. 10) suggests that because Sellars’ “Inference and Meaning” (1953a) “does not make these distinctions, [. . .] it may be subject to the criticism that it assembles evidence for weak inferentialism, and then treats it as justifying a commitment to strong inferentialism, or even hyperinferentialism.” The matter is further complicated, I would think, by Sellars’ remarks on “conceptual status” in “Is there a Synthetic A Priori?” (see Sellars 1963, section 9, 316–317). Here he states that “the position I wish to defend” claims that “the conceptual status” of descriptive predicates is “completely constituted, by syntactical rules,” and so, in effect, by intra-linguistic material inference transitions (italics in original). Sellars goes on to indicate here, however, that the meaning of the predicate “red” requires in addition that it is in general “applied [. . .] to red objects,” so that he concludes: “Thus, the ‘conceptual status’ of a predicate does not exhaust its ‘meaning’.” This way of marking the relevant distinctions looks to be, in Brandom’s sense, either a “weak” or a “strong” inferentialism about “meaning,” combined with a “hyper” inferentialism about “conceptual content.” I will not attempt to explore this further complication here.   9 For my take on the details and the controversies involved here, see O’Shea (2007, chap. 5; 2016b). 10 There are also important Kantian and evolutionary dimensions to Sellars’ systematic account of our perceptual knowledge that I develop in O’Shea (2016b) but will not explore here. 11 For more detailed discussion of Sellars’ arguments against both empiricist and rationalist versions of the Myth of the Given, conducted in terms of what in EPM he calls his psychological nominalism, see O’Shea (2017). And see the same work (O’Shea 2017, 35) for how some otherwise strongly Sellars-­influenced philosophers (for example, John McDowell, Michael Williams) reject Sellars’ argument, in his “nonrelational” semantics, that reference, truth, meaning, etc., do not involve any basic relations to the world (for example, McDowell 2009, chap. 11–12 on Sellars’ “blind spot” about ­Tarski-Davidson semantics, and the alternative deflationary accounts of Williams 2016). I offered a brief overview of Sellars’ views on meaning and abstract entities in O’Shea (2007, chap. 3).

Inferentialism, Naturalism, and the Ought-to-Bes  321 12 I say “apparently” because Brandom in the context cited says only that it “is possible to interpret a community as instituting normative statuses by their attitudes of assessment, even though each such status that is discerned is responded to by sanctions that involve only other normative status. It is compatible with the sanctions paradigm of assessment, and so of normative attitude, that it should be ‘norms all the way down.’ Such an interpretation would not support any reduction of normative status to nonnormatively specifiable dispositions, whether to perform or to assess, whether individual or communal” (Brandom 1994, 44). The wider context seems to suggest that “norms all the way down” is Brandom’s own view, but in other locations he stresses that this outlook is nonetheless supposed to be consistent with a naturalistic account of how we came to have such capacities in the first place.

References Boghossian, Paul. 1993. “Does an Inferential Role Semantics Rest upon a Mistake?” Mind and Language 8 (1): 27–40. Brandom, Robert. 1994. Making It Explicit: Reasoning, Representing, and Discursive Commitment. Cambridge, MA: Harvard University Press. Brandom, Robert. 2000. Articulating Reasons: An Introduction to Inferentialism. Cambridge, MA: Harvard University Press. Brandom, Robert. 2015. From Empiricism to Expressivism: Brandom Reads Sellars. Cambridge, MA: Harvard University Press. Maher, Chauncey. 2015. “Jaroslav Peregrin, Inferentialism: Why Rules Matter.” Notre Dame Philosophical Reviews 2015.04.01. http://ndpr.nd.edu/news/ 56764-inferentialism-why-rules-matter/. McDowell, John. 2009. Having the World in View: Essays on Kant, Hegel, and Sellars. Cambridge: Polity Press. McDowell, John. 2016. “A Sellarsian Blind Spot.” In Sellars and his Legacy, edited by James O’Shea, 100–118. Oxford: Oxford University Press. O’Shea, James. 2007. Wilfrid Sellars: Naturalism with a Normative Turn. Cambridge: Polity Press. O’Shea, James. 2016a. “Concepts of Objects as Prescribing Laws: A Kantian and Pragmatist Line of Thought.” In Pragmatism, Kant, and Transcendental Philosophy, edited by Robert Stern and Gabriele Gava, 196–216. London: Routledge. O’Shea, James. 2016b. “What to Take Away from Sellars’s Kantian Naturalism.” In Sellars and his Legacy, edited by James O’Shea, 130–148. Oxford: Oxford University Press. O’Shea, James. 2017. “Psychological Nominalism and the Given, from Abstract Entities to Animal Minds.” In Wilfrid Sellars, Idealism and Realism: Understanding Psychological Nominalism, edited by Patrick J. Reider, 19–39. London: Bloomsbury. Peacocke, Christopher. 1992. A Study of Concepts. Cambridge, MA: MIT Press. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan. Sellars, Wilfrid. 1953a. “Inference and Meaning.” Mind 62 (247): 313–338. Sellars, Wilfrid. 1953b. “A Semantical Solution of the Mind-Body Problem.” Methodos 5: 45–84.

322  James R. O’Shea Sellars, Wilfrid. 1956. “Empiricism and the Philosophy of Mind.” In Minnesota Studies in the Philosophy of Science, Vol. I, edited by Herbert Feigl and Michael Scriven, 253–329. Minneapolis, MN: University of Minnesota Press. Sellars, Wilfrid. 1957. “Counterfactuals, Dispositions, and the Causal Modalities.” In Minnesota Studies in the Philosophy of Science, Vol. II, edited by Herbert Feigl, Michael Scriven, and Grover Maxwell, 225–308. Minneapolis, MN: University of Minnesota Press. Sellars, Wilfrid. 1962. “Truth and ‘Correspondence’.” Journal of Philosophy 59 (2): 29–56. Sellars, Wilfrid. 1963. Science, Perception and Reality. Atascadero, CA: Ridge­ view Publishing. Sellars, Wilfrid. 1969. “Language as Thought and as Communication.” Philosophy and Phenomenological Research 29 (4): 506–527. Sellars, Wilfrid. 1975. “The Structure of Knowledge: (1) Perception; (2) Minds; (3) Epistemic Principles.” In Action, Knowledge and Reality: Studies in Honor of Wilfrid Sellars, edited by Hector-Neri Castañeda, 295–347. Indianapolis: Bobbs-Merrill. Sellars, Wilfrid. 2015. Wilfrid Sellars: The Notre Dame Lectures 1969–1986. Edited by Pedro Amaral. Atascadero, CA: Ridgeview Publishing. Williams, Michael. 2016. “Pragmatism, Sellars, and Truth.” In Sellars and His Legacy, edited by James O’Shea, 223–260. Oxford: Oxford University Press.

17 Inferentialism and Its Mathematical Precursor Vojtěch Kolman

Like every particular “-ism” that has become sufficiently established, Brandom’s inferentialism is difficult to circumscribe by mere verbal definition. This is because, besides the list of its essential features, it depends on a rather contingent and often heterogeneous list of particular philosophical problems, the philosophers who addressed them, and the types of solutions they offered. As for such a delimitation, Peregrin’s book Inferentialism: Why Rules Matter (Peregrin 2014), in its first part, combines both these approaches—that is, an intensional and extensional one—and adjusts them, in the second part, by some technical results concerning the inferential foundations of logic. Throughout the book, many historical references are made tracing the origins of the inferentialist doctrine to the doctrines of the (relatively recent) past, such as Carnap’s logical syntax or Lorenzen’s dialogical semantics, all of them in some way connected to the development of modern logic and the analytical movement in philosophy. In this chapter, I would like to deepen these historical remarks by pointing out that, within this tradition, there is an evident precedent to inferentialism: namely, so-called axiomatism, particularly in the form advocated by Hilbert. Per se, this will probably come as no surprise to anybody and might rather be seen as a contingent fact; however, as I will claim, this is not the case if you take into account the role that axiomatism has played in the development of mathematics. In this case, its kinship with Brandom’s inferentialism turns out to be rather substantial, and it will hopefully win the sympathetic eye of those who find inferentialism to be something that is hard to swallow while at the same time taking the idea of axiomatization as being a rather natural and unproblematic one. In this undertaking, I will draw on the stipulated fact that i­ nferentialism— besides the central explanatory role it attributes to inference—adopts the following characteristics of knowledge as its grounding principles: (1) every knowledge has a mediated nature; that is, there are no immediately given and incorrigible parts of it; (2) every knowledge is a holistic enterprise; that is, no single part of it is intelligible outside its relations to other parts, for example, in terms of some direct insight, impulse, or intuition;

324 Vojtěch Kolman (3) every knowledge is clothed in social agency; that is, it cannot be intelligible outside the whole of human practices and the phenomenon of normativity. None of this, of course, is unprecedented, the precedent lying most transparently in the philosophy of Hegel, whom Brandom, not coincidentally, considers one of his most important predecessors. The specific quality of a given -ism lies in the circumstance that it sees the given principles embedded into a linguistic frame as stemming from the so-called linguistic turn and the very enterprise of analytic philosophy. Hence, one might think of inferentialism as a readjustment of principles (1)–(3) by the explicit linguistic clause to the extent that:

(•) language is the canonic medium, linguistic inference the canonic mediator.

Now, as for the first two principles—including their linguistic ­specification—they are to be easily traced back to the very rebirth of axiomatism in the work of Hilbert. The third is a more complicated, indirect one to which I will come in the last section.

1. Mediation In the beginning, there was Hilbert’s and Poincaré’s reaction to the phenomenon of Non-Euclidian geometries and the doubts that their emergence had cast on the role of intuition in grounding mathematical knowledge. As for intuition, there is, of course, an intrinsic ambivalence both in the philosophy of mathematics as well as in philosophy proper about what intuition is and what it might be. I would like to start with the supposition, as phrased by Peirce, that it is both the source and the example of noninferentially grounded knowledge, to be found in the direct and incorrigible evidence of the senses (“intueri” meaning “to gaze at”) and its spatial and temporal form. The famous example that Kant gave to justify, in this very sense, the intuitive nature of mathematics is the proof of the sentence that the sum of all angles in a triangle equals two right angles. See figure 17.1. β

α

Figure 17.1 

γ

β

α

Inferentialism and Its Mathematical Precursor  325 According to Kant, it is impossible to justify this truth by means of a mere verbal definition of a triangle, that is, conceptually. What one needs is the intuition of space in which the justifying construction is to be carried out. Only then, he claims, does the conclusion follow. But, as we know—and this is where the mere possibility of Non-Euclidian geometries comes forward—such a construction depends on the validity of the Parallel Postulate. Hence, the truth of the given sentence does not directly result from the simple carrying out of the given construction in the intuition of space, but is mediated by an additional theoretical statement such as the Parallel Postulate. To give another example, according to the Intermediate Value Theorem, a continuous function f(x) adopting the values of the opposite signs must intersect the x-axis, that is, to take the value of 0 for some of its arguments. See figure 17.2.

f (x) = 0

Figure 17.2 

At first, this principle looks intuitive enough so that one needs to give serious reasons, as Bolzano did, for even attempting to prove it on analytic grounds. But on closer inspection, one sees that in its validity it depends substantially on the previous specification of what are the points that the given continuous functions might intersect and what are these intersecting functions. If one limits oneself only to the polynomials, as, for example, Lagrange did, the theorem holds—by definition—for continuum defined algebraically, but it fails to hold for its extension by transcendental numbers. Hence, the vital principle behind these extensions is not (only) some phenomenology of the real axis but (also) the intended validity of some principles. (For a detailed account of this point, see my paper Kolman 2010.) Based on such examples, the generalization follows: the mathematical knowledge including the most notorious “intuitive” facts such as the validity of the parallel postulate or intermediate value theorem is mediated by theoretical statements—possibly even of the opposite “value.” This prospectively makes these statements and the question of their mutual coherence the true object of investigation. The sentences alone, though possibly stemming from the sensuous experience, are not directly

326 Vojtěch Kolman supported by that. That is, they are intuitively “underdetermined,” finding their justification in their conventionally given whole. There is a lot of work to be done before some theorems might be held for true or even intuitively given, or to put it in Hegel’s words, “true thoughts and scientific insight can only be won by labor of the concept” (Hegel [1807] forthcoming, § 70). In the history of mathematics, this finding led to the extreme and rather exaggerated resolution of leaving intuition completely out of the picture. While Frege, in his logicism, restricted himself to arithmetic, Hilbert and Poincaré focused mainly on geometry, stressing the important role of axioms in framing geometrical knowledge and thus pointing out its overall inferential structure. The sentences in which mathematical knowledge is expressed are dependent on other sentences and are thus justified not by a direct insight—immediately—but by means of an inference. According to this principle, the given sentences are divided into (1) the inferred ones, theorems, and (2) the non-inferred ones, axioms. The traditional axiomatism of Aristoteles and Euclid stops here, declaring axioms as justified by induction (epagoge), that is, immediately, thus only postponing the given problem of intuition’s reliability. Hilbert and Poincaré, however, declare the axioms to be chosen conventionally, which means they are noninferred—and thus intuitive—only in the relative sense of the word. For axioms, there is no immediate and incorrigible justification but only practical grounds to choose this rather than another set of axioms in which the original axioms might be theorems and vice versa. In this sense, there is no intuitive knowledge in the absolute sense of the word, as C. S. Peirce (1868) within his concept of semiotics— and the distinction between sign and its interpretant—has argued against Descartes.

2. Holism In the phrasing of his early axiomatic approach—within his famous and often-quoted correspondence with Frege—Hilbert is rather explicit about his axiomatist motivations, claiming that he does not believe in the possibility of defining the mathematical concept in isolation, but always within the axiomatic scheme taken as their implicit definition. See Frege (1976). At the same time, he completely ignores the role of inference in this, which is rather symptomatic because in his axiomatization of geometry, he—like Euclid before him—does not make these rules explicit. And in fact, he cannot do that unless he has a clear idea of what the logical form of the given sentences is because the inferential rules are not capturing the transfer between particular sentences, say from A to B, but

Inferentialism and Its Mathematical Precursor  327 between classes of them, say from sentences of the form A, A → B to sentences of the form B. This is the moment where Frege and his logical system enter the stage. Frege’s logic represents both the tool that makes the axiomatic approach possible and the very example of such an approach. What is even more important and goes unnoticed is the fact that Frege’s choice of logical vocabulary reflects the recently established inferential practice of the mathematical analysis. I do not have time to substantiate this point in detail (see my paper Kolman 2015), so I will just refer to the fact that he uses transfer from the uniform convergence (or continuity) to the pointwise one (S) ∃x∀yA(x, y)/∀y∃xA(x, y)

repeatedly as an example by which the expressive power of the logical system might be defended. This is of some significance for the following reason: in the reformed calculus of Cauchy, one differentiated, on the practical level, between uniform and pointwise convergence (or continuity) as well as between the fact that the latter is entailed by the former and not vice versa. Due to the inadequacy of natural language, however, these differences remained basically unexpressed, which caused the confusions about the validity of some theorems made famous by Lakatos (1978). Frege disposed of such problems by making these quantificational as well as inferential dependencies explicit by means of schemes such as (S). Since the same kind of inferential regularity found in the transfer from uniform to pointwise convergence also applies to continuity and other concepts, one could justify them all without appealing to the content of A. Only by this move has he made the axiomatization of (higher) arithmetic possible. In all of these first steps toward axiomatism in its modern form, there are some deep insights into the substantial role played by language in the development of knowledge, all of them corresponding to the grounding principles of inferentialism: (1) If knowledge is to be more than just a sum of some unconnected observations—as suggested already in its traditional delimitation as justified true belief—there must be a means which makes this connection possible. These means are the inferential rules both in an implicit and explicit form. (2) The explicit rules such as (S) are mediating knowledge also in the sense of making its whole more perspicuous, that is, accessible to our effective control. They are allowing us to apply them to cases that one does not have an immediate experience with. In this very way, knowledge is becoming “infinite” while still manageable by “finite” means.

328 Vojtěch Kolman All these points, implicitly developed by Frege (particularly in his remarks about the creativity of language that were later borrowed by Chomsky; see Frege 1976, 127; 1983, 243), were used by Hilbert to explicitly justify his axiomatism by means of a transcendental deduction sui generis. (1) First, he claims that the harmony between knowledge (theory) and it object (nature) lies exactly in the transcendental fact that they are both finite. (2) In the second step, the seeming infinity of human knowledge ­(particularly in the realm of mathematics) is to be traced back to its finite roots to be identified with a finite (or finitely describable) system of rules and axioms, and finite deductions from them. (3) The whole deduction is closed by a paraphrase of Goethe’s Faust: “At the beginning was a sign,” as a kind of programmatic expression of his previously found conventionalist approach to axioms. (For further details, see my paper Kolman 2009.) I myself read this progression and final proclamation as marking the moment when axiomatism self-consciously went down in the history of mathematics as a precursor of inferentialism.

3.  Symbolic Turn To appreciate that what might be called Hilbert’s symbolic turn, I suggest understanding Hilbert’s reference to signs in the more generous spirit of Peirce. Then, the role of signs in the history of mathematics might be basically seen as oscillating between two general approaches, as is described in Kvasz’s (2008) interesting book Patterns of Change. There is an iconic approach treating mathematics as dealing with spatio-temporal phenomena such as geometrical figures, diagrams, curves, and so on, and there is a symbolic approach stressing the analytic, calculating nature of mathematics. These approaches are, of course, characteristic of specific fields of mathematics such as, in the first case, synthetic geometry and in the second one, symbolic algebra; but they are obviously not exclusive to them, as the figural numbers of Greeks and the symbolic expressions of analytic geometry sufficiently exemplify. At the same time, these approaches oscillate between treating the arithmetical signs as standing for something existing independently of them (which is why the geometrically oriented mathematics of the Greeks led to Plato’s theory of forms) and as producing the very objects they are about (as the symbolic algebra of the Arabs and Indians did, with the negative numbers or 0 as the most obvious consequences). (For a broader context of this development, see my book Kolman 2016.) These extremes are both present in the possibility of understanding equations such as as x2 = 2 in two ways:

Inferentialism and Its Mathematical Precursor  329 (1) as naming the pre-existent square of 2, (2) as introducing such a quantity into the old system of natural numbers. The essence of Hilbert’s symbolic turn might be identified with his later decision to reconcile this primordial tension by observing that empty symbols—in their opposition to meaningful intuitions and other sensuous phenomena—are also of a sensuous nature. In this way, the seemingly sharp delimitation between the iconic and symbolic approaches seems to disappear in favor of the latter one reinterpreted to provide a genuinely Faustian solution to the given dilemma: as the meaningful parts of language, its symbols stand neither for something else nor for themselves but for their use as given, in Hilbert’s case, by their position and role in the axiomatic game. From this, the idea of constructivist foundations of mathematics with its broad pragmatic insight into the nature of meaning follows. Unluckily, this advanced form of axiomatism suffered too from some unresolved issues that were yet to be made explicit. First, Hilbert did not recognize the different roles that inferences and sentences, in contrast to other parts of the language, play in the symbolic treatment of mathematics. From the inferentialist point of view, the inferential rules must be superior to other rules, such as that for generating numerals from 1, as the ultimate source of their normativity. This is exactly the point made by Frege (1893/1903, § 93) against Thomae’s formalism, namely that it is one thing to deduce some symbol according to the given rules and it is another thing to say that that this deduction was correct. Second, Hilbert did not realize that a sign’s use is not a natural but a social phenomenon, believing one can reduce the axiomatic problems of derivability to mere intuitive manipulations with finite symbols within the so-called “finite attitude” (Hilbert 1930). This led his axiomatism back to the unsustainable original idea of intuition’s immediate and incorrigible power. Hence, the lesson given by Non-Euclidian geometries had to be learned the hard way again. The moment at which this happened is the same moment at which the neglected propositional and social features of axiomatism became transparent, namely the crisis of Hilbert’s axiomatism with respect to Gödel theorems. Let me close my contribution with several remarks on this.

4.  The Sociality of Knowledge The usual reading of Gödel’s results traces the following regressive pattern: they allegedly show that the idea of purely symbolic foundations for mathematics, as urged by the Hilbert program, is unsustainable. What Gödel has accordingly proven is that there is always something that Hilbert’s axiomatic systems cannot completely cover—namely, the arithmetical reality or intuition behind the symbols as manifested in the

330 Vojtěch Kolman existence of the sentence, which is unprovable and yet true according to the usual preaxiomatic standards. And this looks like a repeat of the original pre-Hilbertian split between the sign and the signified, but this time in the more general form of a split between the inferentially articulated knowledge (which changes all the time—even in the realm of mathematics) and its object (that—­unmovable and fixed—can never be captured in its entirety). What Hegel taught us about this difference amounts to the insight that the given gap or cognitive discontinuity between our knowledge and its object is only apparent, simply because it is again a product of knowledge. Hence, as Hegel would say, the suggested discontinuity is the continuity of the object as we know it with the object as we take it to be in itself. Knowledge thus—in the best tradition of German idealism—turns out to be the reflective enterprise or self-knowledge, developing itself from the interplay of its subjective (for us) and objective (in itself ) poles. Now, the point of my exposition is exactly that Gödel theorems rephrase Hegel’s insight in a form that takes into account all the grounding principles of inferentialism as stated in the introduction (for details, see Kolman 2016, chap. 11): (1) In Gödel theorems, the split between the sign and the signified appears again, but this time centered around the sentence in its inferential, truth-preserving relations to other sentences as provided by the given axiomatic system. Because of this, truth is, from the very beginning, treated as a holistic enterprise and the existence of the arithmetical sentences that are unprovable (for us) but true (in itself) leads us directly through the new form of discontinuity to its final resolution: the improvability of the sentence and the fact it is true must be and in fact, has been, obviously proven as a part of the argument; hence, truth-talk is only a different kind of proof-talk, and vice versa. (2) Along these lines, Hilbert’s symbolic approach was further refined by Paul Lorenzen, first in his operative and later in his dialogical concepts of logic (see Lorenzen 1955; Lorenzen and Lorenz 1978). In these endeavors, Lorenzen started with exactly the insight neglected by both Hilbert and Frege that neither truth nor proof somehow happen to a sentence but are rather something that one does with it against other people. The resulting idea to model knowledge on a dialogue of two idealized dialogue partners—one who claims something as true and the other who asks for its justification—corresponds directly to Hegel’s final step in his reflective account of knowledge: knowledge is a reflection of one subject into another—that is, a social enterprise. (3) With this future development in sight, one can look at Gödel theorems as something that—within the context of Hilbert’s ­inferentialism— brought this reflective and social analysis into play. Based on the

Inferentialism and Its Mathematical Precursor  331 construction of a sentence that says about itself “I am not provable,” these theorems force us to differentiate between a proof in the narrower sense of the word (as given in the axiomatism of Hilbert basically working with the concept of recursive function) and a proof in the broader sense of the word (or a truth, for that matter) as represented in the very proof of the validity of the Gödel theorem. These “proofs” represent two kinds of inferential commitments corresponding, in technical terms, to Schütte’s (1960) and Lorenzen’s (1962) idea of full- and semi-formalism, with the former working only with schematically controllable axioms and rules such as the generalization A(x)/∀xA(x) and the latter employing the rules with infinitely many premises, particularly the (ω)-rule. (4) This line of thought leads directly to the concept of knowledge that Brandom (2000, 119) describes as “a complex, essentially socially articulated stance or position in the game of giving and asking for reasons.” In this game, knowledge is not some property of minds but basically a relation obtaining between two agents. One of them attributes an inferential commitment (for example, to the critical sentence of Gödel theorems) and an entitlement to that commitment (for example, to be deducible in the full-formal system of Peano arithmetic) and at the same time, undertakes the same commitment oneself. This distribution of commitments between two parties can be seen as the inner differentiation into the concepts of proof and truth that exist only in their opposition to each other. What Gödel theorems show us, by way of self-referential construction, is how the truth-side of the dialogue always exceeds the proof-side, thus leading to the inner dynamic and the further development of knowledge but not to its traversing beyond the dialogue itself. The unprovable sentence of Gödel is of the so-called Goldbach type ∀xA(x), where A(x) is a decidable property of numbers. Gödel’s argument shows that this decision has already been done by the given full-formal system (Peano axioms) in the sense that all the instances A(N) are deducible in it. This makes the critical sentence ∀xA(x) provable by means of the (ω)-rule interpreted effectively (all of the premises are probably true, so is the consequence), but not in the original, full-form way. The fact that the sentence is not provable in this particular, full-formal way is a substantial part of the argument and more importantly, of the sentence’s own truth.

5. Conclusion The purpose of my contribution was to demonstrate how the main principles (1)–(3) of inferentialism are not only instantiated but consciously advocated in Hilbert’s doctrine within the philosophy of mathematics and exact sciences, thus anticipating its broader, philosophical phrasing, including its linguistic specification (•). The question was what role this

332 Vojtěch Kolman doctrine has had in the development of mathematics, particularly with respect to principle (3), which is even less obvious in the mathematical case. My suggestion was to read this principle against the phenomenon of Gödel theorems. I have claimed that these are not the end of Hilbert’s finitist approach but rather its correction, underlining the mediated and social nature of our experience. Following Hegel, one can call this feature “infinite” not in the sense that it leads us beyond our “finite” ­experience— which is the sign of Hegel’s famous concept of “bad” ­infinity—but that it leads beyond its too-narrow delimitation in the sense in which I am not independent of the understanding of others in what I say or mean, thus always leaving space for something that is not under my immediate, finite control. It is this very dependence that provides for my meaning’s infinite quality as represented here by the (ω)-rule infinite nature. And this infinity is, basically, what the whole social aspect of the symbolic turn is about.1

Note 1 Work on this chapter was supported by the grant no. 16-12624S of the Czech Science Foundation (GAČR).

References Brandom, Robert. 2000. Articulating Reasons: An Introduction to Inferentialism. Cambridge, MA: Harvard University Press. Frege, Gottlob. 1893/1903. Grundgesetze der Arithmetik I–II: Begriffsschriftlich abgeleitet. Jena: H. Pohle. Frege, Gottlob. 1976. Wissenschaftlicher Briefwechsel. Edited by Gottfried Gabriel, Hans Hermes, Friedrich Kambartel, Christian Thiel, and Albert Veraart. Hamburg: Felix Meiner. Frege, Gottlob. 1983. Nachgelassene Schriften. 2nd ed. Edited by Hans Hermes, Friedrich Kambartel, and Friedrich Kaulbach. Hamburg: Felix Meiner. Hegel, Georg Wilhelm Friedrich. Forthcoming. The Phenomenology of Spirit. Translated by Terry Pinkard. http://terrypinkard.weebly.com/phenomenologyof-spirit-page.html. Original edition, 1807. Hilbert, David. 1930. “Naturerkennen und Logik.” Die Naturwissenschaften 18: 959–963. Kolman, Vojtěch. 2009. “What Do Gödel Theorems Tell Us About Hilbert’s ­Solvability Thesis?” In Logica Yearbook 08, edited by Michal Peliš, 83–94. London: College Publications. Kolman, Vojtěch. 2010. “Continuum, Name, Paradox.” Synthese 175 (3): 351–367. Kolman, Vojtěch. 2015. “Logicism as Making Arithmetic Explicit.” Erkenntnis 80 (3): 487–503. Kolman, Vojtěch. 2016. Zahlen. Berlin: de Gruyter. Kvasz, Ladislav. 2008. Patterns of Change. Linguistic Innovations in the Development of Classical Mathematics. Basel: Birhäuser.

Inferentialism and Its Mathematical Precursor  333 Lakatos, Imre. 1978. “Cauchy and the Continuum: The Significance of NonStandard Analysis for the History and Philosophy of Mathematics.” Mathematical Intelligencer 1 (3): 151–161. Lorenzen, Paul. 1955. Einführung in die operative Logik und Mathematik. Berlin: Springer. Lorenzen, Paul. 1962. Metamathematik. Mannheim: Bibliographisches Institut. Lorenzen, Paul, and Kuno Lorenz. 1978. Dialogische Logik. Darmstadt: Wissenschaftliche Buchgesellschaft. Peirce, Charles Sanders. 1868. “Some Consequences of Four Incapacities.” Journal of Speculative Philosophy 2 (3): 140–157. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan. Schütte, Kurt. 1960. Beweistheorie. Berlin: Springer.

18 Inferentialism and the Reception of Testimony Leila Haaparanta

1.  Introduction: The Two Inferentialisms Inferentialism has various forms in contemporary philosophy. This chapter discusses the inferentialist philosophy of language, or inferentialism as philosophy, and inferentialism in the epistemology of testimony. The relations between theories of assertion and epistemology of testimony have been studied a great deal, but the connection between the two inferentialisms have been less in focus. An inferentialist philosopher of language like Robert Brandom or Jaroslav Peregrin holds the view that the meaning of a word consists in its inferential role and that language is normative in the sense that its vocabulary is governed by inferential rules.1 A normative inferentialist emphasizes the irreducibility of normative attitude; that attitude is the core of the game of giving and asking for reasons, and it amounts to treating our own and others’ utterances as correct or incorrect (Brandom 1994, 37). The vocabulary used in Brandomian inferentialism is ethical—one could also call it juridical—prime examples being the words “commitment,” “entitlement,” “responsibility,” and “authority.” Peregrin also notes that normative attitudes toward our own and others’ utterances cannot be generally propositional attitudes, although they may be propositional (Peregrin 2014, 78). Besides searching for meanings in the chains of inferences, a normative inferentialist is interested in the items that give or that are given justification in those chains—that is, in judgments and their linguistic counterparts, namely, assertions. Therefore, the normativity that is the inferentialist’s concern extends beyond the normativity of meaning. It could also be called epistemic normativity. Apart from seeking to understand propositions and to judge their semantic correctness, one who has a normative attitude searches for justifications for propositions; in fact, for a normative inferentialist, the two goals are linked together. In contemporary epistemology, there is a debate between inferentialists and anti-inferentialists. Some philosophers, for example, Elizabeth Fricker, argue that the adoption of a testimonial belief is the result of an inferential process in which the premises include beliefs about the

Inferentialism and the Reception of Testimony  335 testifier’s trustworthiness. Others, such as C. A. J. Coady, claim that we adopt testimonial beliefs directly without making any such inferences. The former view is called inferentialism, while the latter is labeled as antiinferentialism.2 An interesting link between Brandom’s inferentialism and epistemology of testimony is formed by Brandom’s theory of assertion. On that account, assertions are sayings that are accompanied by certain commitments, such as the commitment to justify the assertion if it is seriously challenged. This chapter begins with a defense of the view that if assertions are testimonies, and if we wish to explain the phenomena of buck-passing and blame, we need a normative theory of assertion, as Sanford C. Goldberg has argued, or preferably, a theory of assertion held by inferentialist philosophers in which assertions come with certain commitments. It then studies Gottlob Frege’s and W. V. O. Quine’s semantic views and seeks to make explicit some of their ideas that might help us to find a balanced view between inferentialism and anti-inferentialism in the epistemology of testimony. If understanding an expression involves knowing its role in inferences, that also holds for testimonies; for an inferentialist, our testimonial beliefs are not direct in the sense that we would adopt them as detached from inferential chains. However, that is not yet to say that beliefs based on testimony would need to be tied to beliefs about the testifier’s competence or epistemic and other virtues. A Brandomian inferentialist need not be an inferentialist in the epistemology of testimony, who has a skeptical attitude and who thus searches for inferential justification for the testifier’s competence or sincerity in order to be licensed to believe what the speaker claims. However, besides arguing for the theory of assertion proposed by inferentialism, this chapter seeks to show that the normative attitude emphasized by Brandom and Peregrin and the evaluative attitude toward the testifier are related. This chapter utilizes Gottlob Frege’s and W. V. O. Quine’s views on our ways of seeing objects and persons and elaborates the idea that the adoption of a testimonial belief involves the recipient’s seeing the testifier as a certain kind of person; still, the evaluative attitude toward the testifier need not generate an explicit premise into the inferential chain. This conclusion is related to how Peregrin understands the normative attitude. Some comments are also made on Miranda Fricker’s views on the evaluative attitude toward the testifier.

2.  Theories of Assertion and Testimonial Knowledge Gottlob Frege distinguished between the thought (der Gedanke), the judgment (das Urteil), which is the acknowledgment of the truth of the thought, and the assertion (die Behauptung), which is the linguistic expression of the judgment.3 In his posthumous paper “Meine grundle­ genden logischen Einsichten” (1915), he wrote that in language assertoric force is tied to the predicate (Frege 1969, 272). Frege was certainly not the

336  Leila Haaparanta only philosopher who adopted that distinction. It has been a commonplace in the analytic tradition that the distinction between a proposition and asserting the proposition catches something important and that it is one of philosophers’ tasks to find out what makes the difference between the two. Theories of assertion are meant to explain the phenomena of language, such as why it is not correct to say: “p but I do not know that p.” We are to blame if we assert that p, even if we lack what is required for knowing that p. One exception is Herman Cappelen’s view; Cappelen rejects the idea that it is theoretically useful to single out a subset of sayings as assertions. He argues that what philosophers have tried to capture by the term “assertion” is “largely a philosophers’ invention” and it is not a useful category if we wish to explain our linguistic practice (Cappelen 2011, 21). On his view, there are sayings and sayings are governed by variable norms, but those norms are not essential to the act of saying. Cappelen argues that sayings are evaluated by non-constitutive norms, which vary over time and across contexts and cultures, even across possible worlds (Cappelen 2011, 22). I will not raise any detailed arguments against Cappelen’s criticism in this chapter. However, one comment is in order. What is a problem in Cappelen’s attack against theories of assertion is that it ignores the original motivation for the very distinction between the thought, the judgment, and the assertion. He does not take into account that it was introduced because philosophers, such as Frege, realized that it is one thing to say something, namely, to utter a proposition, and another thing to say something with assertoric force. Moreover, Cappelen does not seem to pay much attention to the fact that in everyday linguistic practice what philosophers call assertions are primary to merely expressions of thoughts. It is one thing to say out loud what one is thinking or to suggest a thought for consideration, and another thing to make a claim for truth. Language users are interested in the difference, and they normally recognize it; Frege, among others, made that distinction visible by introducing a conceptual distinction that catches the difference. There was a moral motivation for making the distinction. We are responsible for our actions, including our assertings, but the mere expressing of thoughts does not bring us similar responsibility. However, Cappelen is right in that what is demanded from a speaker cannot be captured by any single norm, which would reveal the essence of assertion. It is sensible philosophical activity to propose, if not theories, then at least accounts of assertion. The word “theory” is often used precisely for the reason already mentioned that, like theories in general, most accounts of assertion seek to explain phenomena of language. John MacFarlane has identified four main accounts of assertion, which Sanford Goldberg calls the attitudinal account, the common ground account, the commitment account, and the constitutive rule account (MacFarlane 2011, 80; Goldberg 2015, 9–10). The commitment account, which is represented

Inferentialism and the Reception of Testimony  337 by Brandom and MacFarlane, and the constitutive rule account, are both normative. However, they are normative in different ways; as MacFarlane points out, while the constitutive rule account looks at norms for making assertions, the commitment account looks at normative effects of making assertions (MacFarlane 2011, 91). The norms that constitutive rule accounts propose vary from belief norms to knowledge norms; for example, assertions may be regarded as sayings that are governed by the following norm: “Assert p only if you know that p.” On the commitment account, assertions are sayings that are accompanied by certain commitments, such as the commitment to give reasons when challenged.4 Sanford Goldberg and Jennifer Lackey both suggest that normative theories are useful if we think of assertions as testimonies. Goldberg argues that if an asserter is a testifier, it does not suffice to require that what she asserts is something that she only believes. Nor does he regard it as sufficient to require that what is asserted just happens to be true. What is needed on his view is either knowledge, or if that is too strong a requirement, a justified or warranted belief.5 Goldberg’s thesis is that if a speech act is a case of testimony, it is an assertion and governed by an epistemic norm, and this also explains the phenomena of epistemic buckpassing and blame. This is how he characterizes the case of buck-passing: Suppose that hearer H accepts speaker S’s testimony that p, under conditions in which H had the epistemic right to accept that testimony; that some individual T later queries H regarding the truth of H’s testimony-based belief that p; that, in response, H exhausts all of her reasons for regarding S’s testimony trustworthy; and that even so T remains unsatisfied. In this situation H is epistemically entitled—is within her epistemic rights—to pass the epistemic buck on to S (by representing S as having more in the way of epistemic support for the truth of p). (Goldberg 2011, 178) Goldberg’s characterization of the case of blame is the following: Suppose that H accepts speaker S’s testimony that p, under conditions in which H had the epistemic right to accept that testimony; and that it turns out that S’s testimony to this effect had insufficient epistemic support. In this situation H is entitled—is within her epistemic rights—to blame S for the insufficient epistemic support of her (H’s) own belief. (Goldberg 2011, 178) Goldberg stresses that it is not only the case that he as a philosopher is making claims about what testifying is. He also argues that it is common

338  Leila Haaparanta knowledge that this is how testifying works. In other words, he claims that it is common knowledge that a speech act that constitutes testimony must satisfy a norm that is at least as strong as that governing assertion. He also argues that this knowledge is implicit. It is in our practices (Goldberg 2011, 184). However, it seems that the commitment account is as able to explain the two phenomena as any other normative theory; in fact, Goldberg also refers approvingly to Brandom’s early article on “Asserting,” even if he does not discuss Brandom’s inferentialism (Goldberg 2015, 74). Before giving reasons for the thesis that the commitment account has explanatory power in the cases of buck-passing and blame, I will outline Brandom’s views on assertion and testimony. In Brandom’s account, the key vocabulary consists of the terms “commitment,” “entitlement,” “deontic status,” “deontic attitude,” and “normative status.” A belief is modeled on a commitment that is acknowledged by making an assertion. Commitment and entitlement, which correspond to obligation and permission, are two sorts of deontic statuses; entitlements come with authority, while commitments come with responsibility. What this means, among other things, is that an asserter is entitled to make inferences from her assertion and use her assertion as a reason, and she is committed to give reasons for her assertion if they are asked for. On Brandom’s account, a deontic attitude is a person’s attitude of taking or treating an asserter, whether that asserter is the person herself or another person, as committed or entitled. The asserter’s normative status is understood in terms of the addressee’s deontic attitude toward her, and that status may change as a consequence of her and the addressee’s actions. On Brandom’s view, assertions are fit to be reasons; they are “fodder for inferences” (Brandom 1994, 157–168). From the addressee’s point of view, assertions are commitments whose reasons may be asked for, because they come with responsibilities; moreover, they can also be used as reasons for further inferences. For a Brandomian inferentialist, all assertions are testimonies, even if the authority and the burden of responsibility that they carry may vary across contexts. Assertional speech acts license others to undertake the same doxastic commitments as the testifier. On Brandom’s view, the testimonial authority of an assertional act is balanced by a responsibility to exhibit one’s entitlement to the commitment, if the recipient challenges it. Brandom distinguishes between three ways of exhibiting entitlement: one may offer an inferential justification, present the commitment as the result of exercising a reliable noninferential perceptual ability, or refer to a testifier’s assertion and thus defer the responsibility to her. The last alternative also allows buck-passing, if that is needed when the assertion is challenged. Deferrals may also be explicit; for example, the speaker may say that she, the speaker herself, is a competent perceiver. Brandom

Inferentialism and the Reception of Testimony  339 also states that we inherit authority from the testifier (Brandom 1994, 532). Testimony thus involves a kind of inherited entitlement. Blame can be easily explained in terms of the commitment account, because the risk of blame comes with responsibility. The speaker is responsible for her assertions, and she is therefore also to blame if it turns out that she does not manage to take care of her responsibility. Because the addressee who has inherited authority may defer the responsibility to the testifier, the model presented by Brandom also takes into account the cases of buck-passing. The commitment account is not essentialist as the constitutive rule account; therefore, it is not hit by Cappelen’s most serious attack.

3. Lessons from Excursions into Frege’s and Quine’s Semantics As Brandom (2000, 50) and Peregrin (2014, 3–4) both emphasize, Frege seems to speak in favor of inferentialism in his Begriffsschrift (Frege 1879). Frege writes there as follows: The contents of two judgments can differ in two ways: it may be the way that the consequences which can be derived from the first judgment combined with certain others can always be derived also from the second judgment combined with the same others; secondly, this may not be the case. The two propositions “At Plataea, the Greeks defeated the Persians” and “At Plataea, the Persians were defeated by the Greeks” differ in the first way. Even if one can perceive the slight difference in sense, the agreement still predominates. Now I call the part of the contents which is the same in both, the conceptual content. (Frege 1879, § 3) In this passage Frege suggests that the logically relevant content of a sentence is determined by what can be inferred from the sentence. Frege’s distinction between Sinn and Bedeutung is normally taken to be a representationalist view. In the Begriffschrift Frege notes that in an identity statement the two symbols have the same Inhalt, but different Bestimmungsweisen (Frege 1879, § 8). In “Über Sinn und Bedeutung” (Frege 1892), he claims that in an identity statement the two names have the same Bedeutung and different Sinne or different Bezeichnungsweisen (Frege 1967, 143). Frege remarks that the sense of a proper name is a way in which the object to which this expression refers is presented, a way the object is given, or a way of “looking at” the object. As is well known, Frege gives examples of senses, like “the Evening Star” and “the Morning Star,” as senses expressed by “Venus” and “the teacher of Alexander

340  Leila Haaparanta the Great” and “the pupil of Plato” as senses expressed by “Aristotle” (Frege 1967, 144). If I see Venus as the Morning Star and even judge that it is the Morning Star, my judgment implies several things, primarily that Venus is a star and that it is visible in the morning. If objects are given via their senses as Frege (1969, 135) tells us in “Ausführungen über Sinn und Bedeutung” (1892–1895), they are thereby given in a conceptual framework, and in that framework, we are allowed to make inferences concerning the “location” of each object. Therefore, Frege’s inferentialism and representationalism turn out to be connected. Frege regards it as possible for an object to be given to us in a number of different ways. He observes that it is common in our natural language that one single proper name expresses many senses. For Frege, to each way in which an object is presented there corresponds a special sense of the sentence that contains the name of that object. The different thoughts we get from the same sentence have the same truth-value. In his article “Der Gedanke” (1918), he notes that we must sometimes stipulate that for every proper name there is just one associated manner of presentation of the object denoted by the proper name (Frege 1967, 350). However, in his paper “Über den Begriff der Zahl” (1891/92) he states that different names for the same object are unavoidable because one can be led to the object in a variety of ways (Frege 1969, 95). One sense or a number of senses provides us only with one-sided knowledge (einseitige Erkenntnis) of an object. Frege argues that complete knowledge of the reference would require us to be able to say whether any given sense belongs to it but that we never attain to such knowledge (Frege 1967, 144).6 Frege does not discuss errors concerning the senses of objects, or attitudes, including prejudices, toward persons. We cannot tell whether he would have distinguished between seeing an object as something and judging that an object is such-and-such. However, it seems that for him, one’s attaching a sense to an object, one’s seeing an object a as P amounts to believing truly that a is P. If that view were true, then seeing somebody as something would mean that one would be willing to acknowledge the thought, that is, to judge, or even to assert, that the person is such-as-such. That, however, does not hold. It is possible that one has a prejudice toward a person, a nonpropositional attitude, but one is not willing to make the corresponding judgment. However, inferentialism in the epistemology of testimony requires that attitudes toward testifiers are propositional attitudes. Quine’s behavioral theory of meaning is quite distant from what Frege was after. It heavily relies on what I would call our attitudes toward persons, even our beliefs about persons. Guesses and hypotheses play a more important role in Quine’s theory of linguistic behavior than Quine explicitly admits. First of all, the linguist must recognize native assent and dissent. Quine writes that the linguist must simply set forth a hypothesis as to what is assent and what is dissent (Quine 1960, 29–30). The linguist must also try to guess what the questions of the native’s language are like,

Inferentialism and the Reception of Testimony  341 whether they are formed out of declarative sentences by changing the intonation or by grammatical transformations. Hence, what the scientist interprets as assent and dissent is a mere guess, on which the very concept of stimulus meaning is based. It makes sense to assume that, even if the native answers, truthfully or untruthfully, to the linguist’s query, she may have no idea of why the stranger makes her utterances. Still, Quine seems to presuppose in his behavioral theory of meaning that the native has a propositional or a nonpropositional attitude toward the linguist. Quine presupposes that the native sees the linguist as one who asks questions to find out the meanings of the expressions of the native’s language. This implicit assumption of Quine’s can be shown by the following example. Quine gives a separate consideration for situations of language learning and linguistic research. In language learning, the child who turns to her mother when hearing the word “Mama” is rewarded by the adult’s approving of her response. However, according to Quine, the child’s learning to look at an object named does not necessarily have to be operant behavior; the child can also be directed to look at the object (Quine 1960, 82). The adult points at the object and names it, and the child learns to look at the object and at the same time, learns its name. Quine also writes that no two people can learn the language in the same way, and in a sense, no one finishes learning language while she lives (Quine 1960, 13). Let us suppose that the linguist has not made any guesses at how the questions of the native’s language are formed. Further, let us suppose that the native does not see the linguist under any kind of description—that is, she does not see the linguist as a person asking questions. Since we, according to Quine, learn language all our lives and since the native does not see the linguist as a querying scientist, she might as well behave as if the linguist taught her the language. Furthermore, since the child can learn language so that the adult directs her to look at an object and names that object, we could perfectly well assume that the linguist teaches the native in the very same way. However, Quine does not propose anything of that kind. Let us imagine a situation in which the linguist asks a native child her semantic questions. Could the native child learn the language from the linguist? We must assume that either belief or alief, to use Tamar Szabó Gendler’s term, the one that the person is an adult or the one that she is an outsider, determines the child’s attitude. Hence, in order to avoid the difficulties, Quine must implicitly presuppose that the native sees the linguist as a querying person, not as an authority coming from the outside of the tribe to tell the natives “the correct names of things.” From what has been said above, it follows that the linguist and the native have what could be called attitudes toward the person. On the one hand, the linguist sees the native either as an assenting or as a dissenting person. On the other, the native sees the linguist as an inquiring person, not as an adviser. That basic attitude can be construed either as propositional or nonpropositional.

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4. The Normative Attitude and the Attitude Toward the Speaker If understanding an expression involves knowing its role in inferences, testimonial beliefs are not direct in the sense that we would adopt them as detached from other beliefs, and hence, that we would not consider them in terms of other beliefs we have. However, that is not yet to say that beliefs based on testimony have beliefs about the testifier’s competence or epistemic and other virtues as their premises. The question will be raised whether the normative attitude that Brandom and Peregrin emphasize includes such beliefs. Peregrin points out that the normative attitude might be similar to Tamar Szabó Gendler’s alief or Hubert Dreyfus’ idea of absorbed coping (Peregrin 2014, 78). Normative attitudes must also be taken into account when we seek to find out how the inferentialist commitment account would evaluate inferentialism in the epistemology of testimony. Brandom argues that to be one of us is to be the subject of normative attitudes. Being such a subject means being capable of acknowledging proprieties and improprieties of conduct, being able to treat a performance as correct or incorrect. On his view, such attitudes are implicit; this means that Brandom seeks to deintellectualize the idea of normativity. He notes that the normative attitude must be “construed as somehow implicit in the practice of the assessor, rather than explicit as the endorsement of a proposition” (Brandom 1994, 32–33). I argued above that “seeings as” need not be acknowledgments of any thoughts or endorsements of propositions and that Frege’s thought about our attitudes toward objects as references can be interpreted either way. I also argued that Quine’s semantics depends on the interlocutors taking attitudes toward persons; those persons are taken to be authorities or advisors, hence, competent testifiers, or as those to whom the language is taught. Quine cannot avoid taking these evaluations as the basis of what he regards as linguistic hypotheses. As an attitude toward a speech act, an inferentialist attitude is deontic; it concerns the speaker’s commitments and entitlements, or her obligations and permissions. If it were an attitude toward a person, it would be an evaluative attitude along the lines of virtue ethics. The question to be asked is whether it would be a propositional attitude, a belief about a person, or a seeing a person as such-and-such without endorsing any proposition that the person is such-and-such. If it need not be such an endorsement, then strictly speaking a Brandomian inferentialist is not an inferentialist in the epistemology of testimony. Brandom mentions, though, that tropes may be introduced that express authority. For example, one may say, “I am a reliable reporter of red things under circumstances like these” (Brandom 1994, 532). Similarly, one might think that the addressee could express her judgment on the testifier’s competence. That expression would then

Inferentialism and the Reception of Testimony  343 be a further reason for the assertion originally made and an item in the inferential chain of the recipient. As noted above, in the receiver-centered epistemology of testimony, an anti-inferentialist simply accepts what the testifier says. However, this is a simplified interpretation of the anti-inferentialist’s thesis. The rival inferentialist position is reductive or internalist as it claims that testimonial knowledge depends on the fact that the receiver possesses an independent justification for the testifier’s competency and sincerity.7 Coady, who is an anti-inferentialist, does not support any naïve view that a person should believe just any and every thing he is told. On the contrary, he also accepts the idea that the addressee considers the veracity of the witness, the probability of what he says, and other similar things. However, unlike an anti-inferentialist, an inferentialist has a skeptic’s attitude; she doubts everything the other says. In the commitment account, it is not the case that the skeptical attitude dominates; in that respect, a Brandomian inferentialist is not an inferentialist in the epistemology of testimony. Stephen Napier summarizes an anti-inferentialist position with the following description of the case of perception: [. . .] if one believes that there is a tomato on the table, we clearly do not require that the believer justifiably believe that her faculties are functioning properly, the environment is conducive to veridical perception or that no one has deceptively replaced the real tomato on the table with the fake one. (Napier 2008, 80) Such things are taken for granted. An anti-inferentialist like Coady admits, though, that we are interested in such things as the credit of witness, confirmation received from other witnesses, and the consistency of what the witness tells us. However, unlike an inferentialist, Coady is not constructing a theory of the speaker and thus intellectualizing the process of the reception of testimony. Miranda Fricker (2003, 2007) seeks to avoid intellectualism and therefore criticizes the inferentialists’ view on testimonial knowledge. However, she also emphasizes that “the mere absence of explicit signals for doubt is not enough to justify a general habit of uncritically accepting what other people tell one” (Fricker 2003, 155). She seeks to find a way to understand what testimonial knowledge ought to be like, if it is noninferential and yet critical. That project amounts to an effort to describe what the addressee’s rationality should be if it is not inferential or argumentative rationality. Her position is an interesting point of comparison to normative inferentialism. Fricker suggests that some mode of rational sensitivity is needed that yields spontaneous, noninferential judgments. On her view, a virtuous person need not work out that an act was cowardly; she just sees that this

344  Leila Haaparanta is the case. She speaks in favor of the skill of critical openness to the word of others but admits that giving up the demand for inferences also opens the door for prejudices, stereotypes, and the influence of power (Fricker 2003, 160, 165). She admits that epistemic trust has an affective aspect that is influenced by how the hearer sees the testifier. What she is looking for is a virtuous recipient, an expert addressee, along the lines suggested by Hubert and Stuart Dreyfus, who has an intuitive grasp of the situation and who thus need not use such faculties as inference in order to see whether the testifier is reliable. Fricker pays attention to the hearer’s virtues and responsibility. Brandom and Peregrin, for their part, are interested in what normative statuses the hearers give to the asserters when they evaluate the asserters’ actions. In inferentialism it is the commitment to give reasons and the entitlement to ask for reasons that matters. It is required from the two interlocutors that they take their respective roles. Brandom states that testimony provides reasons when it is reliable (Brandom 2000, 100). The commitment account of assertion, hence, also normative inferentialism, which focuses on the speaker’s commitments and entitlements, is concerned about the moral status of the speaker’s acts from a deontological point of view, how the speaker manages with the responsibility and the authority that have come with her assertion. As for the recipient’s status, a normative inferentialist would not favor the skeptical attitude in the epistemology of testimony; nor would she slip to naïve reliance. Miranda Fricker, who seeks a balance between inferentialism and antiinferentialism in the epistemology of testimony, focuses on what happens at the receiver’s end. What Fricker is interested in are the receiver’s spontaneous judgments and “seeings as” concerning the speaker’s reliability and other virtues; those “seeings as” may be prejudiced, if the hearer is not virtuous. She thinks that an evaluative attitude, which is nonpropositional, not a link in any inferential chain, is needed in order to avoid the intellectualism of inferentialism and the gullibility of anti-inferentialism. However, to avoid prejudices and to argue against them requires that nonpropositional attitudes are made propositional; at this point Miranda Fricker favors inferentialism over anti-inferentialism. The normative attitude emphasized in the inferentialist philosophy of language and the evaluative attitude toward the testifier suggested by Miranda Fricker are related. The main difference lies in what kind of moral theory they emphasize. However, if assertions are testimonies, one who supports the commitment account also has to consider the reliability and other virtues of the testifier; hence, she also has to adopt some of the virtue ethicist’s viewpoint. The adoption of a testimonial belief involves the recipient’s seeing the testifier as a certain kind of person; still, the “seeing as,” the evaluative attitude toward the testifier, need not have the role of a premise in an inferential chain. It may work as a precondition on which all inferring relies. There are such basic

Inferentialism and the Reception of Testimony  345 attitudes as trust that keep communities alive. They are transcendental conditions for any inferences. Occasionally, however, there are power and other relations that are parts of the very inferences as hidden premises and that should be made explicit. This conclusion is related to how Peregrin understands the normative attitude; they may be propositional attitudes, but they are not generally propositional attitudes.

Notes 1 See Peregrin’s characterization of Brandomian normative inferentialism in Peregrin (2014, 6–14). 2 See Fricker (1987, 1994, 2006) and Coady (1992). Also see Kusch (2002, 20–28) and Napier (2008, 77–105). 3 See, for example, Frege (1879, § 2), and “Der Gedanke” (1918) in Frege (1967, 346). 4 For theories of assertion, see Brown and Cappelen (2011). In this section, I have used extracts from my article Haaparanta (forthcoming). 5 See Lackey (2008, 103–140) and Goldberg (2011; 2015, 72–92). 6 For Frege’s distinction between senses and references and its connection with the so-called context principle, see, for example, Haaparanta (1985, 2001, 2006). 7 For detailed comparisons of the two views, see Napier (2008).

References Brandom, Robert. 1994. Making It Explicit. Reasoning, Representing, and Discursive Commitment. Cambridge, MA: Harvard University Press. Brandom, Robert. 2000. Articulating Reasons: An Introduction to Inferentialism. Cambridge, MA: Harvard University Press. Brown, Jessica, and Herman Cappelen, eds. 2011. Assertion: New Philosophical Essays. New York: Oxford University Press. Cappelen, Herman. 2011. “Against Assertion.” In Assertion: New Philosophical Essays, edited by Jessica Brown and Herman Cappelen, 21–47. New York: Oxford University Press. Coady, Cecil Antony John. 1992. Testimony: A Philosophical Study. Oxford: Clarendon Press. Frege, Gottlob. 1879. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: L. Nebert. Frege, Gottlob. 1892. “Über Sinn und Bedeutung.” Zeitschrift für Philosophie und philosophische Kritik 100 (1): 25–50. Frege, Gottlob. 1967. Kleine Schriften. Edited by Ignacio Angelelli. Hildesheim: Georg Olms. Frege, Gottlob. 1969. Nachgelassene Schriften. Edited by Hans Hermes, Friedrich Kambartel, and Friedrich Kaulbach. Hamburg: Felix Meiner. Fricker, Elizabeth. 1987. “The Epistemology of Testimony.” Proceedings of the Aristotelian Society, Supplementary Volume 61: 57–83. Fricker, Elizabeth. 1994. “Against Gullibility.” In Knowing from Words, edited by Bimal Krishna Matilal and Arindam Chakrabarti, 125–161. Dordrecht: Kluwer.

346  Leila Haaparanta Fricker, Elizabeth. 2006. “Testimony and Epistemic Autonomy.” In The Epistemology of Testimony, edited by Jennifer Lackey and Ernest Sosa, 225–250. Oxford: Oxford University Press. Fricker, Miranda. 2003. “Epistemic Injustice and a Role for Virtue in the Politics of Knowing.” Metaphilosophy 34 (1–2): 154–173. Fricker, Miranda. 2007. Epistemic Injustice: Power and the Ethics of Knowing. Oxford: Oxford University Press. Goldberg, Sanford C. 2011. “Putting the Norm of Assertion to Work: The Case of Testimony.” In Assertion: New Philosophical Essays, edited by Jessica Brown and Herman Cappelen, 175–195. New York: Oxford University Press. Goldberg, Sanford C. 2015. Assertion: On the Philosophical Significance of Assertoric Speech. Oxford: Oxford University Press. Haaparanta, Leila. 1985. “Frege’s Context Principle.” Communication and Cognition 18 (1–2): 81–94. Haaparanta, Leila. 2001. “Existence and Propositional Attitudes: A Fregean Analysis.” Logical Analysis and History of Philosophy 4: 75–86. Haaparanta, Leila. 2006. “Compositionality, Contextuality and the Philosophical Method.” In Truth and Games: Essays in Honour of Gabriel Sandu, edited by Tuomo Aho and Ahti-Veikko Pietarinen. Acta Philosophical Fennica 78: 289–301. Haaparanta, Leila. Forthcoming. “Testimonies of Faith and Contemporary Theories of Assertion.” In Origins of Religion, edited by Hanne Appelqvist and Dan-Johan Eklund, 199–210. Helsinki: Luther-Agricola Society. Kusch, Martin. 2002. Knowledge by Agreement: The Programme of Communitarian Epistemology. Oxford: Oxford University Press. Lackey, Jennifer. 2008. How to Learn Things from Words: Testimony as a Source of Knowledge. Oxford: Oxford University Press. MacFarlane, John. 2011. “What Is an Assertion?” In Assertion: New Philosophical Essays, edited by Jessica Brown and Herman Cappelen, 79–96. New York: Oxford University Press. Napier, Stephen E. 2008. Virtue Epistemology, Motivation, and Knowledge. London: Continuum. Peregrin, Jaroslav. 2014. Inferentialism: Why Rules Matter. Basingstoke: Palgrave Macmillan. Quine, Willard Van Orman. 1960. Word and Object. Cambridge, MA: MIT Press.

Contributors

Ondrˇej Beran is a researcher, currently based at the Centre for Ethics ­(University of Pardubice). His publications, ongoing work, and areas of research interest include the philosophy of language, ethics, the philosophy of religion, and feminist philosophy. He is author of the book Living with Rules (Peter Lang 2018) and research articles in international journals (Sophia and Ethical Perspectives). He has also translated some of Wittgenstein’s works into Czech. Robert Brandom is distinguished Professor of Philosophy at the University of Pittsburgh. His books include Making It Explicit (Harvard University Press 1994), Between Saying and Doing: Towards an Analytic Pragmatism (Oxford University Press 2008), Reason in Philosophy  (Harvard University Press 2009), Perspectives on Pragmatism  (Harvard University Press 2011), Widererrinerter Idealismus (Suhrkamp 2014), and From Empiricism to Expressivism: Brandom Reads Sellars (Harvard University Press 2014). Christopher Gauker is Professor for Theoretical Philosophy at the University of Salzburg. He works in the philosophy of language, philosophy of mind, and philosophical logic. His books include Words without Meaning (MIT 2003), Conditionals in Context (MIT 2005), and Words and Images: An Essay on the Origin of Ideas (Oxford University Press 2011). Hans-Johann Glock is Professor of Philosophy and head of Department at the University of Zurich (Switzerland), and visiting professor at the University of Reading (UK). He is the author of A Wittgenstein Dictionary (Blackwell 1996), Quine and Davidson (Cambridge University Press 2003), La mente de los animals (KRK Ediciones 2009), and What is Analytic Philosophy? (Cambridge University Press 2008). He has edited The Rise of Analytic Philosophy (Blackwell 1997), Wittgenstein: A Critical Reader (Blackwell 2001), and Strawson and Kant (Oxford University Press 2003), and coedited Wittgenstein’s Philosophical Investigations (Routledge 1991), Wittgenstein and Quine

348 Contributors (Routledge 1996), Wittgenstein and Analytic Philosophy (Oxford University Press 2009), and The Blackwell Companion to Wittgenstein (Blackwell 2017). He has published numerous articles on Wittgenstein, analytic philosophy, the philosophy of language, and the philosophy of mind. He is currently working on a book on animal minds. Leila Haaparanta is Professor of Philosophy at the University of Tampere and Docent at the University of Helsinki. She works in the history of logic, late nineteenth– and early twentieth–century philosophy, epistemology, philosophy of mind and language, and philosophy of religion. She is the author of Frege’s Doctrine of Being (Acta Philosophica Fennica 1985) and the editor of Mind, Meaning and Mathematics (Kluwer 1994), The Development of Modern Logic (Oxford University Press 2009), and Rearticulations of Reason (Acta Philosophica Fennica 2010). Her coedited works include Frege Synthesized (with J. Hintikka, Reidel 1986), Analytic Philosophy in Finland (with I. Niiniluoto, Rodopi 2003), and Categories of Being: Essays on Metaphysics and Logic (with H. J. Koskinen, Oxford 2012). She has published articles in anthologies and journals, including Dialectica, Logical Analysis and History of Philosophy, The Philosophical Quarterly, and Synthese. Ole Hjortland is an associate professor at the University of Bergen. His work is primarily in the philosophy of logic, including logical pluralism, inferentialism, and proof theory. Together with Colin Caret, he is the editor of the Oxford University Press volume Foundations of Logical Consequence. Kareem Khalifa is an associate professor of philosophy at Middlebury College. He has published articles on various topics in the philosophy of science, the philosophy of social science, and epistemology. He is the author of Understanding, Explanation, and Scientific Knowledge (Cambridge University Press 2017). Gary Kemp is a senior lecturer at the University of Glasgow. He has published on Quine, Frege, Wittgenstein, and Davidson, on problems in the philosophy of language and metaphysics, and also on aesthetics. Recent books include Quine versus Davidson: Truth, Reference and Meaning (Oxford University Press 2012), What is This Thing Called Philosophy of Language? (Routledge 2013), Wollheim, Wittgenstein and Pictorial Representation (Routledge 2016), and coedited with Frederique Janssen-Lauret, Quine and His Place in History (Palgrave-Macmillan 2016). Vojteˇch Kolman is Associate Professor of Logic at the Faculty of Arts, Charles University in Prague. His research focuses mainly on themes from the philosophy of mathematics, the history of logic, pragmatism,

Contributors  349 and the philosophy of the arts. He is author of the book Zahlen (de Gruyter 2016) and numerous articles in international journals ­(Synthese, Erkenntnis, Hegel-Bulletin, Allgemeine Zeitschrift für Philosophie, and others). Ladislav Korenˇ is the chair of the Department of Philosophy and Social Sciences at the University of Hradec Králové and a researcher at the Czech Academy of Sciences. His areas of interest include epistemology, philosophy of language, philosophy of logic, philosophy of mind, and philosophy of social sciences. His publications include research articles in international journals (Synthese, Journal of Social ­Ontology) and Volumes (Routledge). Danielle Macbeth is the T. Wistar Brown Professor of Philosophy at Haverford College in Pennsylvania, USA. She is the author of Frege’s Logic (Harvard University Press 2005) and Realizing Reason: A Narrative of Truth and Knowing (Oxford University Press 2014), as well as many essays on a variety of issues in the philosophy of language, the philosophy of mind, the history and philosophy of mathematics, and other topics. She was a fellow at the Center for Advanced Study in the Behavioral Sciences in Palo Alto in 2002–2003 and has been awarded an American Council of Learned Societies (ACLS) Burkhardt Fellowship as well as a Fellowship from the National Endowment for the Humanities (NEH). Peter Milne has held a chair in philosophy at the University of Stirling in Scotland for ten years. Before moving to Stirling, he held a readership in philosophy at the University of Edinburgh and, prior to that, held teaching positions at various colleges of the University of London and at the University of Liverpool and a research position at Massey University in Palmerston North, New Zealand. He has published numerous articles on philosophy of probability, on confirmation theory, on philosophy of logic, especially on proof-theoretic semantics and on conditionals, and on the history of twentieth-century logic and its philosophy. Jared Millson is currently the Kirk Postdoctoral Fellow in Philosophy at Agnes Scott College in Atlanta, Georgia, USA. His published work contributes to the fields of philosophy of language, logic, and philosophy of science. His work focuses, in particular, on developing inferentialist accounts of nondeclarative expressions, such as interrogatives. James O’Shea is Professor of Philosophy at University College Dublin (UCD). He has published widely on twentieth-century American pragmatism and naturalism, as well as on Kant, Hume, and Wilfrid Sellars. His books include Kant’s Critique of Pure Reason: A Critical Guide, editor (Cambridge University Press 2017), Sellars and his Legacy, editor (Oxford University Press 2016), Kant’s Critique

350 Contributors of Pure Reason: An Introduction and Interpretation (Routledge 2014),  Self, Language, and World: Problems from Kant, Sellars, and Rosenberg, coeditor (Ridgeview 2010), and Wilfrid Sellars: Naturalism with a Normative Turn (Wiley/Polity 2007). Jaroslav Peregrin is the head of the Department of Logic of the Institute of Philosophy of the Czech Academy of Sciences and a professor at the Faculty of Philosophy of the University of Hradec Králové, Czechia. He is the author of Doing Worlds with Words (Kluwer 1995), Meaning and Structure (Ashgate 2001), Inferentialism: Why Rules Matter (Palgrave Macmillan 2014), and, with Vladimír Svoboda, Reflective Equilibrium and the Principles of Logical Analysis (Routledge 2017). His current research focuses on logical and philosophical aspects of inferentialism and on more general questions of normativity. Mark Risjord is a professor in the Department of Philosophy at Emory University, and he is director of the Institute for the Liberal Arts. He is also affiliated faculty at the University of Hradec Králové. His research in the philosophy of social science has concerned the role of rationality and normativity in explanation, the explanation of intentional action, and the role of values in the sciences. His books include Woodcutters and Witchcraft: Rationality and Interpretive Change in the Social Sciences (SUNY 2000), Nursing Knowledge: Science, Practice, and Philosophy (Blackwell 2010), and Philosophy of Social Science: A Contemporary Introduction (Routledge 2014). With Stephen Turner, he coedited The Philosophy of Anthropology and Sociology (Elsevier 2007), and he edited Normativity and Naturalism in the Philosophy of the Social Sciences (Routledge 2016). Lionel Shapiro is Associate Professor of Philosophy at the University of Connecticut. His research interests center around the conceptual tools used in theorizing about intentionality. He has published articles on topics in the philosophy of language, philosophical logic, early modern philosophy, and the philosophy of Wilfrid Sellars. Shawn Standefer is a postdoctoral research fellow working for the Meaning in Action Project, headed by Professor Greg Restall, at the University of Melbourne. He primarily works on philosophical logic and philosophy of language. Vladimír Svoboda is a researcher at The Institute of Philosophy of the Academy of Sciences of the Czech Republic. His main areas of interest include the philosophy of logic, deontic logic, meta-ethics, and the logical analysis of natural language. For many years he has been one of the main organizers of the annual Logica symposium. In Czech, he has published Logic and Ethics (Filosofia 1997, with Petr Kolář), From Language to Logic (Academia 2009, with Jaroslav Peregrin),

Contributors  351 and Logic for Masters, Slaves, and Kibitzers (Filosofia 2013). With Jaroslav Peregrin, he coauthored the book Reflective Equilibrium and the Principles of Logical Analysis: Understanding the Laws of Logic (Routledge 2017). Bernhard Weiss is currently Professor of Philosophy at the University of Cape Town. He is interested in conceptions of meaning and use and his publications include: Michael Dummett (Acumen and Princeton 2002); How to Understand Language (Acumen and McGill-Queen’s 2010) and, as coeditor with Jeremy Wanderer, Reading Brandom (Routledge 2010).

Index

action 8, 26, 30 – 31, 31, 59 – 60, 74, 88, 190, 197, 206, 239 – 243, 246, 247n4, 263 – 268, 270, 274n11, 276n31, 288, 291n5, 303 – 304, 306, 310 – 311, 315, 319n4, 336, 338, 344 Adorno, T. 39 agency 2, 242, 288, 291n2, 319, 324 analyticity 81 – 83, 192n11 analytic/synthetic distinction (dichotomy) 9, 64, 67 Aristotle 20, 147, 304, 340 assertibility (assertability) 8, 12, 101, 111n7, 221; and denial conditions (deniability) 97, 99 – 104; and superassertibility 11, 105, 106; and truth 99, 101, 104, 105, 107; see also assertion assertion: and acceptance 51, 55 – 56, 59; and denial 97 – 104, 122 – 123, 127, 132, 136n29, 212, 217n23; and force (mode, form) 98 – 101, 132; norms of 122, 132, 224; retraction of 107; and superassertion 105 – 107 assessment, normative 103, 142 – 143 attitudes: deontic 216n13; normative 6, 19 – 22, 24 – 25, 84, 207, 213, 242, 256, 334, 342; practical 6, 19 – 20, 179, 185, 198, 200, 206; propositional 93 – 94, 334, 340, 344 – 345 authority 22, 147, 186, 198, 220, 244, 267, 273n3, 275n25, 280, 284, 287, 341 – 342; and entitlement 19, 334, 338; and responsibility 6, 19, 334, 338 – 339, 344 Begriffsschrift 27 – 28, 144, 295 – 296, 339 belief: de dicto/de re attribution 22, 38, 215n5; degree of 221, 223, 231 – 232;

justified (warranted, reasonable) 313, 315, 337; knowledge as justified true belief 36, 38, 327; norms of 85, 224, 337; (non–inferential) perceptual 310, 314 – 315; revision of 227 – 228; testimonial 42, 334 – 335, 342, 344; and valuation (value) 88 – 90 Belnap, N. 12, 115, 124, 149, 217n22, 225 Bicchieri, C. 262 – 263, 280 Brandom, R. 1 – 10, 12 – 41, 63 – 64, 78, 97, 111n11, 116 – 117, 123, 132 – 133, 135n17, n18, 136n27, 155 – 156, 162, 179 – 190, 191n2, n4, n5, 192n12, n14, n16, n17, 196 – 197, 200 – 202, 204 – 206, 211 – 212, 215n2, n7, n8, n10, 216n11, n19, 217n22, 220 – 221, 225, 239 – 240, 242, 244, 246, 249 – 251, 258, 258n2, 295 – 296, 304, 308 – 315, 318, 319n1, 320n5, n8, 321n12, 323 – 324, 331,  334 – 335, 337 – 339, 342 – 344 Cappelen, H. 336, 339 Carnap, R. 83, 183, 259n3, 323 Cartwright, N. 144 causality 155, 242; causal (natural) order 19, 24, 300; causal explanation 71; causal processes 66, 240, 242; causal realm 240, 300; causal terms 155; causal theories 78n1 Cavell, S. 285, 291n5 Chomsky, N. 83 – 84, 91, 258n3, 328 claims: making of 6, 206, 211, 337; see also assertion Coady, C. A. J. 335, 343 cognition: conceptual 41, 309; human 2, 49, 254, 309, 316, 319;

Index  353 imagistic 51, 54, 59; nonconceptual (preconceptual) 51; perceptual 312 – 313, 313, 315 – 317 commitment: collateral 21, 199, 208 – 209, 217, 240; conditional–task responsibility to justify it 6, 208, 216n16; discursive 6, 198, 200, 208, 242, 244; undertaking and attributing of 6, 36, 198, 200, 204, 207, 208; see also entitlement communication, linguistic 51, 60, 266; and cooperation (collective goals) 50 – 52; and interpretation 5 – 6, 22, 197, 241; rules governing communication 63 – 64 community, linguistic 60, 66, 78n2, 83, 92, 225 concepts: logical vs. non–logical 14, 117, 141 – 143, 181 conceptual (inferential) role semantics 4, 11, 63 – 64, 317 – 318; see also inferential role conditionals: classical 120 – 121, 125; expressive role of 147, 180; indicative 19, 219, 228 – 233; intuitionistic 120, 123, 142; two– valued 142, 147; see also sentence consequence relation: logical (formal) 17 – 19, 30, 115, 127, 143, 146, 153, 159 – 162, 166 – 171, 179 – 180, 183, 189, 198 – 199, 219, 223 – 224, 226 – 228, 230, 233n2; material 6 – 8, 17, 144 – 146, 149, 151 – 153, 181 – 190, 191n4, n7, 192n13, 193n30; monotonic vs. nonmonotonic 17, 144, 148 – 149, 151 – 153, 161; see also inferential role conservativeness: conservative (vs. non–conservative) extension 13, 17, 115 – 118, 120, 122, 127, 130, 132, 133, 152, 174 – 175; as a criterion for inferential rules 12, 14, 122 – 123, 149, 165, 174, 176; and harmony 13, 16 – 17, 116, 119 content: assertible (assertable, claimable) 7 – 9, 13, 180, 187, 189, 191n3, n5, 197; conceptual 3 – 4, 7, 19 – 20, 27 – 28, 34, 115 – 116, 119 – 121, 143 – 144, 147, 181, 196 – 197, 205, 207, 240, 295, 308 – 309, 311 – 316, 320n7; inferentially articulated 13, 15, 200; judgeable 22, 296; propositional 3, 8, 11, 14, 18, 54, 97, 193n30,

196 – 197, 200 – 205, 207, 209 – 210, 215, 240; representational 3, 38 conversation: context of 61, 82, 243, 285; conversational implicatures 68 – 69; conversational maxims 68, 79n3, 87 culture 25, 253, 256, 258, 336 Davidson, D. 78n1, 93, 94n7, 241, 320n11 denial: conditions of 11, 97, 99, 101 – 104; and incompatibility (negation) 18, 212 – 214 Descartes, R. 242, 326 Dewey, J. 40 dispositions: linguistic 10, 81, 83; to overt behavior 10, 81; Quinean 84 – 85; and regularities 10, 19, 24 Dreyfus, H. 342, 344 Dudman, V. 220 – 224, 233n2 Dummett, M. 12 – 13, 103, 111n3, 116, 120, 123, 133, 155, 220 endorsement: of conditional 185, 215n7; of content 181, 185; of incompatibility relations 13; of inference 184, 216n19 entitlement: to a commitment 6 – 8, 13, 19, 22 – 24, 36 – 37, 198 – 200, 208, 212, 216n16, 239 – 240, 242, 331, 334, 338 – 339, 342, 344; default 8, 198, 208, 216n16 experience 1, 20, 31 – 32, 37, 40, 55 – 56, 60, 308, 311, 314, 316, 325, 327, 332 explicitation 17, 29, 145 – 146, 149, 152, 188; see also expressivism expressivism 27, 143, 155 – 156, 180, 185; regarding implicit content 179 – 183, 192n14; regarding inferential attitude 179 – 180, 184 – 185, 192n14; logical expressivism 141 – 142, 147, 153, 179 – 181, 183 – 186, 189 – 191, 191n2, 192n8, n16, n17 Fodor, J. 4, 9, 61n1, 67, 76 form (way) of life 239, 245 – 247, 304 – 306 formalization 40, 120, 169 foundationalism 36, 298, 309 Frege, G. 27 – 28, 30, 32, 34, 40 – 41, 66, 97, 144, 225, 295 – 299, 302 – 303, 306, 326 – 330, 335 – 336, 339 – 340

354 Index Fricker, E. 334 Fricker, M. 343 – 344 game (practice) of giving and asking for reasons 5, 9 – 11, 14, 18 – 20, 32 – 34, 36 – 37, 39, 41 – 42, 185, 189 – 190, 196 – 197, 199 – 200, 205 – 211, 213 – 214, 217n24, 240, 295 – 298, 300, 304, 306, 307n4, 308, 310, 331, 334 Gendler, T. S. 341 – 342 Gentzen, G. 12 – 13, 17, 134n9, 143, 145, 147 – 148, 150 – 153, 154n2, 159, 161, 226, 255 Glüer, K. 9, 73 Gödel, K. 42, 329 – 332 Goldberg, S. 335 – 338 Goldman, A. 35 Grice, P. 68 – 69, 78n1, 79n3, 83 Habermas, J. 40 Harman, G. 15, 19, 142, 219, 223, 226 – 228, 230, 234n10 harmony: as a constraint on inference rules 116 – 118, 121, 127; harmony between inference rules 13, 16 – 17, 117 – 119, 126, 130 – 131, 133, 134n2; see also conservativeness Hattiangadi, A. 9, 74, 77 Haugeland, J. 40, 241 Hayek, F. A. 262, 273n1 Hegel, G. W. F. 1 – 2, 26, 31 – 37, 34, 39 – 40, 191n4, 324, 326, 330, 332 Heidegger, M. 37 – 38, 40 Hempel, C. 157 – 158 Henrich, J. 253 – 254 Hilbert, D. 41 – 42, 323 – 324, 326, 328 – 332 Hlobil, U. 148 – 150, 152, 217n22 holism 9, 27 – 28, 82, 121 idealism 10, 32; German 27, 249, 330 images, mental 51 – 54, 61n3; imagistic thinking (cognition, representation) 10, 51 – 60 incompatibility: incompatibility entailment 7, 135n18, 205n2; incompatibility semantics 132, 135n18; (material) relations of 7, 11, 13, 16 – 17, 33 – 34, 57, 143 – 154, 162, 179, 191n4, 197 – 198, 200, 206, 208, 212 – 213, 244 inference: to the best explanation 18, 156; deductive 7; inductive

(defeasible) 7, 18, 18, 146, 160, 215n6; reliability 215n3, 314 – 316; substitutional (symmetric vs. asymmetric) inferences 15, 29 inferentialism: Brandomian 25, 40, 116, 133, 249, 258, 334, 345n1; logical 12, 115, 120, 122, 141; naturecultural 25, 243 – 246; normative 12, 41, 318 – 319, 343 – 344, 345n1; Peregrin’s 81, 264, 295, 304, 306, 308 inferential relations 5, 7.8, 11, 14, 16 – 18, 29, 33, 67, 97, 117, 141, 179, 181, 191n3, 191n4, 192n10, 197, 211, 213 – 215, 215n7, 217n25, 225, 240, 245, 301, 310 inferential role 5, 9, 11 – 14, 16, 19, 21, 30, 63, 115, 123, 135n18, 155, 197, 199, 202 – 203, 215n1, 240, 308, 310, 315 – 318, 319n1, 334 intentionality 3, 8, 214, 241, 257, 311, 317 – 318 intuition (in mathematics) 101, 104, 324, 329 Jackson, F. 221, 233, 234n11 Kant, I. 27, 40 – 41, 63, 187, 278, 290, 295, 299, 301, 302, 306, 311 – 312, 324 – 325 Kaplan, D. 150, 152 knowledge: as justified true belief 36, 38, 327; mediated vs. intuitive (immediately given) 30, 33 – 35, 326; non–inferential 34, 309, 313; perceptual 41, 309; testimonial 335, 343 Kukla, R. 9, 217n22 Lance, M. 9, 135n17, 217n22 language: and culture 25, 258; learning (acquisition) 10, 243 – 244, 341; rules (norms) governing language (linguistic communication) 12, 63 – 64, 71, 82, 201, 255, 270, 283 language entry/exit transitions 8, 11, 37, 67, 197, 215n3, 310 – 311, 315, 319n4 language game 8 – 9, 21, 32, 39, 85 – 87, 201, 206, 274n17, 282 – 284, 295, 298, 300, 308, 312; see also game (practice) of giving and asking for reasons

Index  355 laws: and causes 155, 247, 305; of logic 14, 276, 308; moral 89 – 90; of nature 144, 155, 278 Lepore, E. 9, 67 Lewis, D. 26, 142, 221, 256, 274n17 logic: deductive (formal) 14, 227 – 228; expressive conception (treatment) of 13 – 14, 16 – 18, 156, 159, 196, 214; expressivist 148, 153; inductive 227; modal 130 – 132; substructural 17, 117, 125 – 126, 129, 134, 150; see also expressivism Lorenzen, P. 40, 42, 323, 330 – 331 Macbeth, D. 9, 41, 296 MacFarlane, J. 336 – 337 manifest image of man, vs. scientific image of man 22 – 24 McDowell, J. 9, 22, 26, 32, 35, 37, 204 – 206, 240, 314, 320n11 meaning: explanation of 10, 63, 65, 69, 71; knowledge of 68, 69, 71; normativity of 73, 76, 78, 242, 334; theories of 8, 40, 64, 78n1, 84, 101, 225, 295, 340; as use 78n1 Millikan, R. G. 4, 247n1 mind 3 – 4, 31 – 32, 34, 36, 53, 60, 68, 241, 253 – 254, 258, 261, 318, 331 modality 94, 131 Murdoch, I. 282, 291n2 Myth of the Given 34, 242, 300, 305, 309, 311, 316 – 318, 320n11 naturalism 25, 85, 239, 244, 316 negation: classical 17, 120 – 123, 128, 133; and incompatibility (relations) 13, 33 – 34, 57 – 58, 143, 147 – 148, 179, 200, 206, 209, 212 – 213, 215; intuitionistic 120 – 121 niche construction 25, 239, 242 – 244, 247 normativism 64, 72, 73, 78, 250 normativity 1, 15, 20, 25 – 26, 65, 72 – 73, 76 – 78, 81 – 83, 85, 90 – 94, 190, 242, 244 – 246, 250 – 251, 257 – 258, 324, 329, 334, 342 norm psychology 253, 256 – 257 norms (rules): of discourse 10, 20, 51, 61, 211; explicit and implicit 14, 20 – 26, 87, 159, 199 – 200, 264, 271 – 272, 279, 281, 286 – 287, 289, 311, 327; governing language (linguistic communication) 12, 63 – 64, 71, 82, 201, 255, 270,

283; intersubjective 18, 207, 211, 213 – 214; social 252, 257, 263 – 264 objectivity 21 – 22, 38, 91, 302 observation: observation sentences 56, 92; Quine on observation sentences 82, 91; reports of 8, 35, 342 Peirce, C. S. 30, 32 – 36, 40, 120 – 121, 324, 326 perception 31, 53, 56, 239 – 242, 309, 315, 317, 343 Peregrin, J. 2, 9 – 10, 12, 14 – 16, 24 – 26, 41, 63 – 64, 68, 78, 81 – 85, 87, 92, 94, 94n2, n3, 97, 135n18, 141, 143, 155 – 156, 179 – 184, 186 – 188, 190, 191n4, n7, n8, n9, 196 – 197, 201 – 204, 210, 217n23, 225 – 227, 239 – 240, 242, 244, 246, 249, 251 – 252, 264, 278, 295 – 301, 303 – 306, 308 – 309, 311 – 313, 315 – 316, 318, 319n1, 320n5, 323, 334 – 335, 339, 342, 344 – 345 Plato 20, 29, 147, 290, 328, 340 Poincaré, H. 324, 326 practices: material–inferential 200 – 201; normative (norm-governed, rulegoverned) 26, 32, 103, 196, 272, 278, 280, 285 – 286, 290; social 1, 5 – 6, 18, 22, 24, 181, 183, 186, 197, 215n3, n7, 270, 306 pragmatism: American 26 – 27, 31; normative 6, 11 Prawitz, D. 118, 120, 155 predicate 15, 28 – 29, 54, 74, 93, 182, 202, 215n9, 317, 335; consequence predicate 183 – 184, 190; metalinguistic predicate 101; truth predicate 126, 136n23, 184, 189 Price, H. 11, 101 – 102, 104, 111n2, n7, 185, 191n2, 192n17, 208, 212 – 213, 251, 316 Prior, A. N. 12, 115 proposition 27 – 28, 54, 71 – 72, 74, 99 – 101, 111n4, 163, 167, 171, 186, 191n4, 193n29, 202, 221 – 224, 226 – 227, 229, 232, 233n2, 267, 273, 274n14, 275n18, 276n34, 297, 300, 304, 334, 336, 339, 342 proprieties: inferential 8, 11, 82, 196 – 197, 200, 207 – 209, 213 – 215, 240, 242, 312, 320n8; of (governing) use of expressions (language) 7, 14 provability 101, 105, 161

356 Index Quine, W. V. O. 10, 64, 72, 77, 78n1, 81 – 94, 94n2, n3, 184, 250, 312, 320n5, 335, 340 – 342 rationality 24 – 25, 27, 85, 204 – 206, 239, 297 – 299, 343, 350 reason: space of 5 – 6, 23, 37, 85, 196, 198, 201 – 204, 210, 214 – 215, 239 – 242, 298, 305 – 306, 310, 312 reasoning: deductive 17, 142, 227, 232; defeasible 17, 110 – 111, 161, 166; inductive 18, 227 regularism, vs. regulism (about norms) 10, 20, 25 relationships, regulative 265 – 272 representation: committive 52, 55; imagistic 52 – 58; mental 49 – 50, 54 representationalism, vs. inferentialism 32, 41, 295 – 296, 301, 306, 340 Restall, G. 122, 126 – 127, 132, 135n15 Rhees, R. 26, 39, 278, 282 – 285 Ripley, D. 126 – 127, 212 Rorty, R. 26 Rouse, J. 25, 239, 241 – 242, 244, 247, 247n5 rule–following 26, 35, 76, 207, 267, 270, 278 – 279, 284 rules: F–rules 266 – 273, 267, 274n16, n17, 275n19, n20, n25, n29, 276n30, n33; of inference (inferential) 2, 12 – 15, 16, 32, 67, 81 – 82, 85, 115 – 123, 156, 159 – 160, 174, 202 – 203, 226 – 227, 251, 255, 315, 326 – 327, 329, 334; L–rules 265 – 270, 267, 272 – 273, 274n13, n14, 275n18, n19, n26, n27, n29, 276n31, n32; rules governing communication 63 – 64, 68 – 69; rules of games 85, 256, 262, 264, 273n3, 279, 283 – 285, 298, 300, 308; social rules 250 – 253, 262 – 264, 274n9 rule sentence 265 – 269, 271, 273, 274n15, n16, 275n19, n29, 276n31 Rumfitt, I. 11, 97 – 102, 104, 111n4, 212 Ryle, G. 65, 78n2, 185 – 187, 189, 193n21, 209, 285, 291n3 sanctions 24, 253, 276n31, 278, 280, 284 – 286, 288, 321n12 Sartre, J.–P. 38, 290 scientific image of man see manifest image of man, vs. scientific image of man

scorekeeping, deontic (practices of) 6, 8 – 9, 13, 19, 21 – 22, 197 – 198, 200, 211, 213 Searle, J. 69, 255 self-consciousness, semantic 29, 117, 204 – 205, 210 – 211, 213 – 214 Sellars, W. 4, 7 – 8, 20, 22 – 23, 25 – 27, 31 – 32, 34 – 35, 37, 40 – 41, 63, 67, 78, 82, 143, 155, 184 – 185, 187, 192n16, 239, 247, 251 – 254, 257, 273n1, 278, 280, 290, 295, 298 – 299, 309 – 319, 319n1, n3, 320n5, n8, n11 semantics: incompatibility 132, 135n18; inferentialist 41, 240, 312, 319, 320n5; see also conceptual (inferential) role semantics semiosis 30, 34 sentence: assertible (assertable) 12, 103; atomic 16, 17, 55 – 57, 60, 148, 150, 160; conditional 18, 58, 181 – 182, 215n7; declarative (indicative) 11, 98, 100, 197, 219, 341; deontic (proposition) 273, 274n14; logically complex (compound) 101, 104, 111, 149, 151, 153; nonlogical 7, 9, 13, 21, 29, 200 – 201, 204, 207; rule 265 – 269, 271, 273 Sinn (and Bedeutung) 302, 339, 340 space of reasons 4 – 6, 23, 37, 85, 196, 198, 201 – 204, 210, 214 – 215, 239 – 242, 298, 305 – 306, 310; logical 202 – 203, 310 – 312 speech acts 6, 68, 78n1, 221 status: deontic 133, 338; normative 7, 21, 24, 70, 82, 103, 185, 198, 289, 321, 338, 344 subject-object distinction (dichotomy) 32, 34, 37 subject-subject distinction (difference) 32, 34, 37 substitution: and inference 14, 15, 22, 240; technique (analysis, procedure, strategy) 28 – 30 syntax, logical 259n3, 323 Tarski, A. 17, 78n1, 143, 145, 147, 320n11 Tennant, N. 13, 123 terms, singular 15, 29, 54 – 56 testimony 42, 334 – 335, 337 – 345 thought (thinking): conceptual 2 – 3, 5, 8, 10, 19, 23; propositional 4, 197 Tomasello, M. 252, 257

Index  357 truth: logical 32, 83, 224, 228; norm of 224, 298 – 299; notion of 184, 299 – 300, 306; theories of 16, 78n1; truth conditions 3, 75, 107; truth predicate 126, 136n23, 136n25, 184, 193n26 validity 14, 42, 61, 161 – 162, 166, 186 – 187, 193n21, 320n5, 325, 327, 331

von Wright, G. H. 233n1, 262, 272 – 273, 273n2, n3, 274n15, 276n30 Wilson, M. 144 Wittgenstein, L. 4, 10, 20, 26, 32, 35, 39 – 40, 63 – 67, 69, 71 – 72, 78, 78n2, 86, 92, 99 – 100, 102, 207, 224 – 225, 261, 272, 278 – 279, 281 – 285, 290, 304 – 305, 316 Wright, C. 11, 104 – 106