Inferentialism

This article offers an overview of inferential role semantics. We aim to provide a map of the terrain as well as challenging some of the inferentialist’s standard commitments. We begin by introducing inferentialism and placing it into the wider context of contemporary philosophy of language. §2 focuses on what is standardly considered both the most important test case for and the most natural application of inferential role semantics: the case of the logical constants. We discuss some of the (alleged) benefits of logical inferentialism, chiefly with regards to the epistemology of logic, and consider a number of objections. §3 introduces and critically examines the most influential and most fully developed form of global inferentialism: Robert Brandom’s inferentialism about linguistic and conceptual content in general. Finally, in §4 we consider a number of general objections to IRS and consider possible responses on the inferentialist’s behalf

Inferentialism without Verificationism: Reply to Prawitz

I discuss Prawitz’s claim that a non-reliabilist answer to the question “What is a proof?” compels us to reject the standard Bolzano-Tarski account of validity, andto account for the meaning of a sentence in broadly verificationist terms. I sketch what I take to be a possible way of resisting Prawitz’s claim---one that concedes the anti-reliabilist assumption from which Prawitz’s argument proceeds

Maximally Consistent Sets of Instances of Naive Comprehension

Paul Horwich (1990) once suggested restricting the T-Schema to the maximally consistent set of its instances. But Vann McGee (1992) proved that there are multiple incompatible such sets, none of which, given minimal assumptions, is recursively axiomatizable. The analogous view for set theory---that Naïve Comprehension should be restricted according to consistency maxims---has recently been defended by Laurence Goldstein (2006; 2013). It can be traced back to W.V.O. Quine(1951), who held that Naïve Comprehension embodies the only really intuitive conception of set and should be restricted as little as possible. The view might even have been held by Ernst Zermelo (1908), who,according to Penelope Maddy (1988), subscribed to a ‘one step back from disaster’ rule of thumb: if a natural principle leads to contra-diction, the principle should be weakened just enough to block the contradiction. We prove a generalization of McGee’s Theorem, anduse it to show that the situation for set theory is the same as that for truth: there are multiple incompatible sets of instances of Naïve Comprehension, none of which, given minimal assumptions, is recursively axiomatizable. This shows that the view adumbrated by Goldstein, Quine and perhaps Zermelo is untenable

More Reflections on Consequence

This special issue collects together nine new essays on logical consequence :the relation obtaining between the premises and the conclusion of a logically valid argument. The present paper is a partial, and opinionated,introduction to the contemporary debate on the topic. We focus on two influential accounts of consequence, the model-theoretic and the proof-theoretic, and on the seeming platitude that valid arguments necessarilypreserve truth. We briefly discuss the main objections these accounts face, as well as Hartry Field’s contention that such objections show consequenceto be a primitive, indefinable notion, and that we must reject the claim that valid arguments necessarily preserve truth. We suggest that the accountsin question have the resources to meet the objections standardly thought to herald their demise and make two main claims: (i) that consequence, as opposed to logical consequence, is the epistemologically significant relation philosophers should be mainly interested in; and (ii) that consequence is a paradoxical notion if truth is

Intuitionism and logical revision.

The topic of this thesis is logical revision: should we revise the canons of classical reasoning in favour of a weaker logic, such as intuitionistic logic? In the first part of the thesis, I consider two metaphysical arguments against the classical Law of Excluded Middle-arguments whose main premise is the metaphysical claim that truth is knowable. I argue that the first argument, the Basic Revisionary Argument, validates a parallel argument for a conclusion that is unwelcome to classicists and intuitionists alike: that the dual of the Law of Excluded Middle, the Law of Non-Contradiction, is either unknown, or both known and not known to be true. As for the second argument, the Paradox of Knowability, I offer new reasons for thinking that adopting intuitionistic logic does not go to the heart of the matter. In the second part of the thesis, I motivate an inferentialist framework for assessing competing logics-one on which the meaning of the logical vocabulary is determined by the rules for its correct use. I defend the inferentialist account of understanding from the contention that it is inadequate in principle, and I offer reasons for thinking that the inferentialist approach to logic can help model theorists and proof-theorists alike justify their logical choices. I then scrutinize the main meaning-theoretic principles on which the inferentialist approach to logic rests: the requirements of harmony and separability. I show that these principles are motivated by the assumption that inference rules are complete, and that the kind of completeness that is necessary for imposing separability is strictly stronger than the completeness needed for requiring harmony. This allows me to reconcile the inferentialist assumption that inference rules are complete with the inherent incompleteness of higher-order logics-an apparent tension that has sometimes been thought to undermine the entire inferentialist project. I finally turn to the question whether the inferentialist framework is inhospitable in principle to classical logical principles. I compare three different regimentations of classical logic: two old, the multiple-conclusions and the bilateralist ones, and one new. Each of them satisfies the requirements of harmony and separability, but each of them also invokes structural principles that are not accepted by the intuitionist logician. I offer reasons for dismissing multiple-conclusions and bilateralist formalizations of logic, and I argue that we can nevertheless be in harmony with classical logic, if we are prepared to adopt classical rules for disjunction, and if we are willing to treat absurdity as a logical punctuation sign

Classical Harmony and Separability

According to logical inferentialists, the meanings of logical expressions are fully determined by the rules for their correct use. Two key proof-theoretic requirements on admissible logical rules, harmony and separability, directly stem from this thesisrequirements, however, that standard single-conclusion and assertion-based formalizations of classical logic provably fail to satisfy (Dummett in The logical basis of metaphysics, Harvard University Press, Harvard, MA, 1991; Prawitz in Theoria, 43:140, 1977; Tennant in The taming of the true, Oxford University Press, Oxford, 1997; Humberstone and Makinson in Mind 120(480):10351051, 2011). On the plausible assumption that our logical practice is both single-conclusion and assertion-based, it seemingly follows that classical logic, unlike intuitionistic logic, cant be accounted for in inferentialist terms. In this paper, I challenge orthodoxy and introduce an assertion-based and single-conclusion formalization of classical propositional logic that is both harmonious and separable. In the framework I propose, classicality emerges as a structural feature of the logic.(VLID)283667

Naïve validity

P2971-G24(VLID)239640