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The topic of this paper is the question whether there is a logic which could be justly called the logic of inference. It may seem that at least since Prawitz, Dummett and others demonstrated the proof-theoretical prominency of intuitionistic logic, the forthcoming answer is that it is this logic that is the obvious choice for the accolade. Though there is little doubt that this choice is correct (provided that inference is construed as inherently single-conclusion and complying with the Gentzenian structural rules), I do not think that the usual justification of it is satisfactory. Therefore, I will first try to clarify what exactly is meant by the question, and then sketch a conceptual framework in which it can be reasonably handled. I will introduce the concept of 'inferentially native' logical operators (those which explicate inferential properties) and I will show that the axiomatization of these operators leads to the axiomatic system of intuitionistic logic. Finally, I will discuss what modifications of this answer enter the picture when more general notions of inference are considered.

Inferentialism, which I am going to present in detail in the following sections, is the view that meanings are, roughly, roles that are acquired by types of sounds and inscriptions in virtue of their being treated according to rules of our language games, roughly in the sense in which wooden pieces acquire certain roles by being treated according the rules of chess. The most important consequences are that (i) a meaning is not an object labeled (stood for, represented ...) by an expression; and that (ii) meaning is normative in the sense that to say that an expression means thus and so is to say that it should be used so and so. The founding father of inferentialism is Brandom (1994; 2000). (However, nothing in this paper hinges on the fact that the version of inferentialism defended here is identical with Brandom's). This position provokes two kinds of objections. First there are general objections towards the very normativity of meaning, which do not target especially inferentialism; these I have addressed elsewhere 1. Besides this, there are objection targeted more specifically at inferentialism. Probably the most discussed specimen of such objections is the objection - repeatedly raised especially by Jerry Fodor and Ernest LePore and others - to the effect that though meanings should be compositional, the compositionality of inferential roles is unattainable. This is the kind of objection I am going to deal with here 2. (Hand in hand with this objection then go various allegations of circularity of inferentialism, which we will also discuss.) To do this, I will exploit the long-standing comparison of language to chess, as it seems particularly helpful for making the inferentialist account of language plausible3. This comparison, to be sure, has its limits beyond which it may become severely misleading; but as long as we keep them in mind, it can serve us very well.

1.1 INFERENTIALISM AND REPRESENTATIONALISM 1.2 INFERENTIALISM AND LOGIC 1.3 FROM PROOF THEORY TO SEMANTICS 1.4 BRANDOM'S NORMATIVE INFERENTIALISM..

Two opposing tendencies in the philosophy of language go by the names of ‘referentialism’ and ‘inferentialism’ respectively. In the crudest version of the contrast, the referentialist account of meaning gives centre stage to the referential semantics for a language, which is then used to explain the inference rules for the language, perhaps as those which preserve truth on that semantics (since a referential semantics for a language determines the truth-conditions of its sentences). By contrast, the inferentialist account of meaning gives centre stage to the inference rules for the language, which are then used to explain its referential semantics, perhaps as the semantics on which the rules preserve truth. On pain of circularity, we cannot combine both directions of explanation.

One of the central themes of Brandom’s work is that we should construct our sematic theories around material validity and incompatibility, rather than reference, truth, and satisfaction. This approach to semantics is motivated in part by Brandom’s pragmatism about the relation between semantics and the more general study of language use—what he calls “pragmatics”: Inferring is a kind of doing. . . . The status of inference as something that can be done accordingly holds out the promise of securing an appropriate relation between pragmatics, the study of the practices, and semantics, the study of the corresponding contents. (MIE, 91)1 Although Brandom does not go so far as to say that a pragmatist attitude to the relation between semantics and pragmatics requires an inferentialist semantics, his motivating arguments strongly suggest that a pragmatist ought to be an inferentialist. In what follows, I discuss the connections between Brandom’s pragmatism and his inferentialism. I’ll argue that pragmatism, as Brandom initially describes it—the view that “semantics must answer to pragmatics”—does not favor an inferentialist approach to semantics over a truth-conditional one. I’ll then consider whether inferentialism might be..

After putting forward his celebrated deflationary theory of truth (Horwich, 1998a), Paul Horwich added a compatible theory of meaning (Horwich, 1998b). I am calling also this latter theory deflationism (although it may be a slightly misleading name in that, as Paul himself notes, his theory of meaning is deflationary more in the sense of being forced by the deflationary theory of truth than of being particularly deflationary in itself). In contrast, what I call inferentialism is the theory of meaning which I am going to advocate here – the view, in a nutshell, that meaning is a matter of inferential role. Various versions of this theory have been defended by Wilfried Sellars, Robert Brandom and a couple of other philosophers including myself. And the thesis I wish to present in this paper – to put it as a provocation right off – is that Paul is an inferentialist led astray. Both deflationism and inferentialism can be seen as elaborations of what can be called the use theory of meaning; for both seem to agree that.

The perennial question – What is meaning? – receives many answers. In this paper I present and discuss inferentialism – a recent approach to semantics based on the thesis that to have ( such and such ) a meaning is to be governed by ( such and such ) a cluster of inferential rules . I point out that this thesis presupposes that looking for meaning requires seeing language as a social institution (rather than, say, a psychological reality). I also indicate that this approach may be seen as a new embodiment of the old ideas of structuralism.

The perennial question What is meaning? receives many answers. In this paper we present and discuss inferentialism - a recent approach to semantics based on the thesis that to have (such or another) meaning is to be governed by (such or another) cluster of inferential rules. We point out that this thesis presupposes that looking for meaning requires seeing language as a social institution (rather than, say, a psychological reality). We also indicate that this approach may be see as a new embodiment of the old ideas of structuralism.

While according to the inferentialists, meaning is always a kind of inferential role, proponents of other approaches to semantics often doubt that actual meanings, as they see them, can be generally reduced to inferential roles. In this paper we propose a formal framework for considering the hypothesis of the.

Brandom's "inferentialism"—his theory that contentfulness consists in being governed by inferential norms—proves dubiously compatible with his own deflationary approach to intentional objectivity. This is because a deflationist argument, adapted from the case of truth to that of correct inference, undermines the criterion of adequacy Brandom employs in motivating inferentialism. Once that constraint is abandoned, moreover, the very constitutive-explanatory availability of Brandom's inferential norms becomes suspect. Yet Brandom intertwines inferentialism with a separate explanatory project, one that in explaining the pragmatic significance of meaning-attributions does yield a convincing construal of the claim that the concept of meaning is normative.