It is well known that classical inferentialist semantics runs into problems regarding abnormal valuations. It is equally well known that the issues can be resolved if we construct the inference relation in a multiple-conclusion sequent calculus. The latter has been prominently developed in recent work by Restall, with the guiding interpretation that the valid sequent says that the simultaneous assertion of all of Γ with the denial of all of Δ is incoherent. However, such structures face significant interpretive challenges, and (...) they do not provide an adequate grasp on the machinery of the duality of assertions and denials that could provide an abstract account of inferential semantics; show why the dual treatment is semantically superior. This paper explores a slightly different tack by considering a dual-calculus framework consisting of two, single-conclusion, inference relations dealing with the preservation of assertion and the preservation of denial, respectively. In this context, I develop an abstract inferentialist semantics, before going on to show that the framework is equivalent to Restall’s, whilst providing a better grasp on the underlying proof-structure. (shrink)

In this paper, I develop an account of linguistic content based on the active inference framework. While ecological and enactive theorists have rightly rejected the notion of content as a basis for cognitive processes, they must recognize the important role that it plays in the social regulation of linguistic interaction. According to an influential theory in philosophy of language, normative inferentialism, an utterance has the content that it has in virtue of its normative status, that is, in virtue of the (...) set of commitments and entitlements that the speaker undertakes by producing this utterance. This normative status is determined by the normative attitudes shared by members of the utterer’s linguistic community. I propose here an account of such normative attitudes based on the ecological interpretation of the active inference framework. I explain how social normativity can be understood in that framework as the way in which members of a group shape their social niche to make it more predictable. Finally, I apply this account of social normativity to basic communicative practices, thereby explaining how social normative expectations can emerge to regulate these communicative practices, eventually leading to the institution of the sort of normative statuses constitutive of linguistic content. (shrink)

Drawing on various resources and requirements (as expressed by Dewey, Wittgenstein, Sellars, and Brandom), this paper proposes an externalist view of conceptual mental episodes that does not equate them, even partially, with vehicles of any sort, whether the vehicles be located in the environment or in the head. The social and pragmatic nature of the use of concepts and conceptual content makes it unnecessary and indeed impossible to locate the entities that realize conceptual mental episodes in non-personal or subpersonal contentful (...) entities (vehicles). Persons, who engage in social practices of deontic scorekeeping (Brandom), and who are thus able to produce appropriate inferential behaviour, enact conceptual mental episodes and the basis of their supervenience. (shrink)

I present and defend here a thesis named vehicleless externalism for conceptual mental episodes. According to it, the constitutive relations there are between the production of conceptual mental episodes by an individual and the inclusion of this individual in social discursive practices make it non-necessary to equate, even partially, conceptual mental episodes with the occurrence of physical events inside of that individual. Conceptual mental episodes do not have subpersonal vehicles; they have owners: persons in interpretational practices. That thesis is grounded (...) on inferentialism and on the endorsement of the idea that "meaning is normative". After having recapitulated this heritage and after having presented that thesis, the paper especially attempts to articulate how, in that framework, we may then positively conceive the relations there are between conceptual mental episodes, intracranial events and inferential behaviour. (shrink)

This paper offers an interpretation of multiple-conclusion sequents as a kind of meta-inference rule: just as single-conclusion sequents represent inferences from sentences to sentences, so multiple-conclusion sequents represent a certain kind of inference from single-conclusion sequents to single-conclusion sequents. The semantics renders sound and complete the standard structural rules of reflexivity, monotonicity (or thinning), and transitivity (or cut). The paper is not the first one to attempt to account for multiple-conclusion sequents without invoking notions of truth or falsity—but unlike earlier (...) such efforts, which have typically helped themselves to primitive notions of both acceptance and rejection, the present one makes do with the former alone. For technical reasons, the treatment is limited to sequents with non-empty succedents. (shrink)

I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.

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. (shrink)

The entire development of modern logic is characterized by various forms of confrontation of what has come to be called proof theory with what has earned the label of model theory. For a long time the widely accepted view was that while model theory captures directly what logical formalisms are about, proof theory is merely our technical means of getting some incomplete grip on this; but in recent decades the situation has altered. Not only did proof theory expand into new (...) realms, generalizing the concept of proof in various directions; many philosophers also realized that meaning may be seen as primarily consisting in certain rules rather than in language-world links. However, the possibility of construing meaning as an inferential role is often seen as essentially compromised by the limits of prooftheoretical means. The aim of this paper is to sort out the cluster of problems besetting logical inferentialism by disentangling and clarifying one of them, namely determining the power of various inferential frameworks as measured by that of explicitly semantic ones. (shrink)

Formal semantics is an enterprise which accounts for meaning in formal, mathematical terms, in the expectation of providing a helpful explication1 of the concept of the meaning of specific word kinds (such as logical ones), or of words and expressions generally. Its roots go back to Frege, who proposed exempting concepts, meanings of predicative expressions, from the legislation of psychology and relocating them under that of mathematics. This started a spectacular enterprise, fostered at first within formal logic and later moving (...) into the realm of natural languages, and featuring a series of eminent scholars, from Tarski and Carnap to Montague and David Lewis. Partly independently of this, Frege set the agenda for a long-term discussion of the question of what a natural language is, his own contribution being that language should be seen not as a matter of subjective psychology, but rather as a reality objective in the sense in which mathematics is objective. His formal semantics, then, was just an expression of this conception of language. And many theoreticians now take it for granted that formal semantics is inseparably connected with a Platonist conception of language. Moreover, the more recent champions of formal semantics, Montague and David Lewis, took for granted that natural language is nothing else than a structure of the very kind envisaged by the theories of formal logicians. While Montague claims quite plainly that there is no substantial difference between formal and natural languages ("I reject the contention," he says, 1974, p. 188, "that an important theoretical difference exists between formal and natural languages"), Lewis states that it is fully correct to say that a linguistic community entertains a language in the form of a mathematical structure ("we can say", states Lewis, 1975, p.. (shrink)

In this paper I present how the normative inferentialist can make the distinction between sentence meaning and content of the utterance. The inferentialist can understand sentence meaning as a role conferred to that sentence by the rules governing inferential transitions and content of the utterance as just a part of sentence meaning. I attempt to show how such a framework can account for prominent scenarios presented by contextualists as a challenge to semantic minimalism/literalism. I argue that inferentialism can address contextualist (...) challenges in a simple and effective manner by understanding sentence meaning as broad, but invariant. (shrink)

In this paper, I show how normative inferentialism could be used to explain several phenomena related to natural languages. First, I show how the distinction between the inferential potential and the inferential significance fits the standard distinction between the meaning of a sentence and the content of an utterance. Second, I show how the distinction could be used to explain ambiguity and free pragmatic enrichment from the perspective of normative inferentialism. The aim of this paper is to establish theoretical foundations (...) that enable normative inferentialism to enter the discussions within the literalism-contextualism debate. As I argue, the biggest advantage of inferentialism is that it provides one general framework for the representation of meaning/content that naturally incorporates contextual information and so it can be used to represent meanings of various types of context-dependent sentences. (shrink)

How many notions of cause are there? The causality literature is witnessing a flourishing of pluralist positions. Here I focus on a recent debate on whether interpreting causality in terms of inferential relations commits one to semantic pluralism (Reiss 2011) or not (Williamson 2006). I argue that inferentialism is compatible with a ‘weak’ form of monism, where causality is envisaged as one, vague cluster concept. I offer two arguments for this, one for vagueness, one for uniqueness. Finally, I qualify in (...) what sense the resulting form of monism is ‘weak’.¿Cuántas nociones de causa hay? Hay un resurgir de posiciones pluralistas en la bibliografía sobre causalidad. Me ocuparé aquí de un debate reciente sobre si la interpretación de la causalidad en términos de relaciones inferenciales nos compromete con el pluralismo semántico (Reiss 2011) o no (Williamson 2006). Defiendo que el inferencialismo es compatible con una forma ’debil’ de monismo, donde la causalidad se presenta como un único concepto vago y de agrupación (cluster). Ofrezco para ello dos argumentos, uno sobre vaguedad y otro sobre unicidad. Finalmente, matizaré en qué sentido esta forma demonismo es ’débil’. (shrink)

When dealing with ‘meaning’ or related notions, one cannot ignore what for a long time was the dominant paradigm in semantics. According to such paradigm, truth-conditional formal semantics for natural language is a theory of semantic competence. In this article, I shall discuss a foundational problem for such semantic program. I shall first be following authors who claim that truth-conditional formal semantics is unable to provide a complete account of lexical competence, and, therefore, it suffers from incompleteness. Moreover, as a (...) few authors observed, a coherent completion of lexical meaning/competence cannot be easily provided in the philosophical framework of truth-conditional semantics. The problem is a consequence of Kripke’s and Putnam’s arguments against the view that semantic values of words are cognitively determined. I shall argue that these arguments undermine the notion that formal semantics can be, at the same time, a theory of truth-conditions and a theory of semantic competence. I shall outline and critically discuss two general attempts to solve this problem, which I shall refer to as the social/ideal route and the concepts route. The conclusions of the article are deliberately open. I shall argue that both these attempts are exposed to conceptual troubles and counterintuitive consequences, and so the lexical problem still remains a deep and unresolved issue for semantics. (shrink)

I present an account of truth values for classical logic, intuitionistic logic, and the modal logic s5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.

In this paper, after having outlined the theoretical framework of Brandom’s philosophy, I examine his attempt to reconcile semantic perspectivism, which is at the core of his inferentialist semantics, with the idea that objectivity transcends the practical normative attitudes of the participants in the so-called game of giving and asking for reasons.

ABSTRACT: A traditional objection to inferentialism states that not all inferences can be meaning-constitutive and therefore inferentialism has to comprise an analytic-synthetic distinction. As a response, Peregrin argues that meaning is a matter of inferential rules and only the subset of all the valid inferences for which there is a widely shared corrective behaviour corresponds to rules and so determines meaning. Unfortunately, Peregrin does not discuss what counts as “widely shared”. In the paper, I argue for an empirical plausibility of (...) Peregrin’s proposal. The aim of the paper is to show that we can find examples of meaning-constitutive linguistic action, which sustain Peregrin’s response. The idea is supported by examples of meaning modulation. If Peregrin is right, then we should be able to find specific meaning modulations in which a new meaning is publicly available and modulated in such a way that it has a potential to be widely shared. I believe that binding modulations – a specific type of meaning modulations – satisfy this condition. (shrink)

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. (shrink)

The proof of correctness and completeness of a logical calculus w.r.t. a given semantics can be read as telling us that the tautologies (or, more gen erally, the relation of consequence) specified in a model theoretic way can be equally well specified in a proof theoretic way, by means of the calculus (as the theorems, resp. the relation of inferability of the calculus). Thus we know that both for the classical propositional calculus and for the clas sical predicate calculus theorems (...) and tautologies represent two sides of the same coin. We also know that the relation of inference as instituted by any of the common axiom systems of the classical propositional calculus coin cides with the relation of consequence defined in terms of the truth tables; whereas the situation is a little bit more complicated w.r.t. the classical predicate calculus (the coincidence occurs if we restrict ourselves to closed ∀xFx is inferable from Fx without being its conse formulas; otherwise.. (shrink)