•  2217
    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 (al…Read more
  •  1010
    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 Naï…Read more
  •  889
    The inexpressibility of validity
    Analysis 74 (1): 65-81. 2014.
    Tarski's Undefinability of Truth Theorem comes in two versions: that no consistent theory which interprets Robinson's Arithmetic (Q) can prove all instances of the T-Scheme and hence define truth; and that no such theory, if sound, can even express truth. In this note, I prove corresponding limitative results for validity. While Peano Arithmetic already has the resources to define a predicate expressing logical validity, as Jeff Ketland has recently pointed out (2012, Validity as a primitive. An…Read more
  •  658
    More Reflections on Consequence
    Logique Et Analyse 57 (227): 223-258. 2014.
    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 …Read more
  •  484
    Categoricity by convention
    Philosophical Studies 178 (10): 3391-3420. 2021.
    On a widespread naturalist view, the meanings of mathematical terms are determined, and can only be determined, by the way we use mathematical language—in particular, by the basic mathematical principles we’re disposed to accept. But it’s mysterious how this can be so, since, as is well known, minimally strong first-order theories are non-categorical and so are compatible with countless non-isomorphic interpretations. As for second-order theories: though they typically enjoy categoricity results…Read more
  •  365
    Generalized Revenge
    Australasian Journal of Philosophy 98 (1): 153-177. 2020.
    Since Saul Kripke’s influential work in the 1970s, the revisionary approach to semantic paradox—the idea that semantic paradoxes must be solved by weakening classical logic—has been increasingly popular. In this paper, we present a new revenge argument to the effect that the main revisionary approaches breed new paradoxes that they are unable to block.
  •  345
    Naïve validity
    Synthese 199 (Suppl 3): 819-841. 2017.
    Beall and Murzi :143–165, 2013) introduce an object-linguistic predicate for naïve validity, governed by intuitive principles that are inconsistent with the classical structural rules. As a consequence, they suggest that revisionary approaches to semantic paradox must be substructural. In response to Beall and Murzi, Field :1–19, 2017) has argued that naïve validity principles do not admit of a coherent reading and that, for this reason, a non-classical solution to the semantic paradoxes need no…Read more
  •  326
    It is sometimes held that rules of inference determine the meaning of the logical constants: the meaning of, say, conjunction is fully determined by either its introduction or its elimination rules, or both; similarly for the other connectives. In a recent paper, Panu Raatikainen (2008) argues that this view - call it logical inferentialism - is undermined by some "very little known" considerations by Carnap (1943) to the effect that "in a definite sense, it is not true that the standard rules o…Read more
  •  309
    Two Flavors of Curry’s Paradox
    with Jc Beall
    Journal of Philosophy 110 (3): 143-165. 2013.
    In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn’t automatically solved by solving c-curry. A unified treatment of curry paradox thus calls for a unified treatment of both c-Curry and v-Curry. If, as is often thought, c-Curry paradox is to be solved via non-classical logic, then v-Curry may require a lesson about the structure—indeed, the substructure—of the validity…Read more
  •  295
    Inferentialism without Verificationism: Reply to Prawitz
    In Emiliano Ippoliti & Carlo Cellucci (eds.), Logic and Knowledge, Cambridge Scholars Press. pp. 285-90. 2011.
    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.
  •  278
    How basic is the basic revisionary argument?
    Analysis 68 (4): 303-309. 2008.
    Anti-realists typically contend that truth is epistemically constrained. Truth, they say, cannot outstrip our capacity to know. Some anti-realists are also willing to make a further claim: if truth is epistemically constrained, classical logic is to be given up in favour of intuitionistic logic. Here we shall be concerned with one argument in support of this thesis - Crispin Wright's Basic Revisionary Argument, first presented in his Truth and Objectivity. We argue that the reasoning involved in…Read more
  •  266
    The paradox of idealization
    Analysis 69 (3): 461-469. 2009.
    A well-known proof by Alonzo Church, first published in 1963 by Frederic Fitch, purports to show that all truths are knowable only if all truths are known. This is the Paradox of Knowability. If we take it, quite plausibly, that we are not omniscient, the proof appears to undermine metaphysical doctrines committed to the knowability of truth, such as semantic anti-realism. Since its rediscovery by Hart and McGinn (1976), many solutions to the paradox have been offered. In this article, we presen…Read more
  •  256
    Surprise, surprise: KK is innocent
    with Leonie Eichhorn and Philipp Mayr
    Thought: A Journal of Philosophy 10 (1): 4-18. 2021.
    The Surprise Exam Paradox is well-known: a teacher announces that there will be a surprise exam the following week; the students argue by an intuitively sound reasoning that this is impossible; and yet they can be surprised by the teacher. We suggest that a solution can be found scattered in the literature, in part anticipated by Wright and Sudbury, informally developed by Sorensen, and more recently discussed, and dismissed, by Williamson. In a nutshell, the solution consists in realising that …Read more
  •  133
    Is logical knowledge dispositional?
    Philosophical Studies 166 (S1): 165-183. 2013.
    In a series of recent papers, Corine Besson argues that dispositionalist accounts of logical knowledge conflict with ordinary reasoning. She cites cases in which, rather than applying a logical principle to deduce certain implications of our antecedent beliefs, we revise some of those beliefs in the light of their unpalatable consequences. She argues that such instances of, in Gilbert Harman’s phrase, ‘reasoned change in view’ cannot be accommodated by the dispositionalist approach, and that we …Read more
  •  127
    Coming True: A Note on Truth and Actuality
    Philosophical Studies 163 (2): 403-427. 2013.
    John MacFarlane has recently presented a novel argument in support of truth- relativism. According to this, contextualists fail to accommodate retrospective reassessments of propositional contents, when it comes to languages which are rich enough to express actuality. The aim of this note is twofold. First, it is to argue that the argument can be effectively rejected, since it rests on an inadequate conception of actuality. Second, it is to offer a more plausible account of actuality in branchin…Read more
  •  120
    Validity and Truth-Preservation
    In D. Achourioti, H. Galinon & J. Martinez (eds.), Unifying the Philosophy of Truth, Springer. pp. 431-459. 2015.
    The revisionary approach to semantic paradox is commonly thought to have a somewhat uncomfortable corollary, viz. that, on pain of triviality, we cannot affirm that all valid arguments preserve truth (Beall2007, Beall2009, Field2008, Field2009). We show that the standard arguments for this conclusion all break down once (i) the structural rule of contraction is restricted and (ii) how the premises can be aggregated---so that they can be said to jointly entail a given conclusion---is appropriatel…Read more
  •  108
    Manifestability and Epistemic Truth
    Topoi 31 (1): 17-26. 2012.
    I argue that the standard anti-realist argument from manifestability to intuitionistic logic is either unsound or invalid. Strong interpretations of the manifestability of understanding are falsified by the existence of blindspots for knowledge. Weaker interpretations are either too weak, or gerrymandered and ad hoc. Either way, they present no threat to classical logic
  •  107
    Denial and Disagreement
    Topoi 34 (1): 109-119. 2015.
    We cast doubts on the suggestion, recently made by Graham Priest, that glut theorists may express disagreement with the assertion of A by denying A. We show that, if denial is to serve as a means to express disagreement, it must be exclusive, in the sense of being correct only if what is denied is false only. Hence, it can’t be expressed in the glut theorist’s language, essentially for the same reasons why Boolean negation can’t be expressed in such a language either. We then turn to an alternat…Read more
  •  105
    Logical orthodoxy has it that classical first-order logic, or some extension thereof, provides the right extension of the logical consequence relation. However, together with naïve but intuitive principles about semantic notions such as truth, denotation, satisfaction, and possibly validity and other naïve logical properties, classical logic quickly leads to inconsistency, and indeed triviality. At least since the publication of Kripke’s Outline of a theory of truth , an increasingly popular dia…Read more
  •  99
    In this paper, I focus on some intuitionistic solutions to the Paradox of Knowability. I first consider the relatively little discussed idea that, on an intuitionistic interpretation of the conditional, there is no paradox to start with. I show that this proposal only works if proofs are thought of as tokens, and suggest that anti-realists themselves have good reasons for thinking of proofs as types. In then turn to more standard intuitionistic treatments, as proposed by Timothy Williamson and, …Read more
  •  99
    Reflection Principles and the Liar in Context
    Philosophers' Imprint 18. 2018.
    Contextualist approaches to the Liar Paradox postulate the occurrence of a context shift in the course of the Liar reasoning. In particular, according to the contextualist proposal advanced by Charles Parsons and Michael Glanzberg, the Liar sentence L doesn’t express a true proposition in the initial context of reasoning c, but expresses a true one in a new, richer context c', where more propositions are available for expression. On the further assumption that Liar sentences involve propositiona…Read more
  •  93
    On Heck's New Liar
    Thought: A Journal of Philosophy 1 (2): 258-269. 2012.
    Richard Heck has recently drawn attention on a new version of the Liar Paradox, one which relies on logical resources that are so weak as to suggest that it may not admit of any “truly satisfying, consistent solution”. I argue that this conclusion is too strong. Heck's Liar reduces to absurdity principles that are already rejected by consistent paracomplete theories of truth, such as Kripke's and Field's. Moreover, the new Liar gives us no reasons to think that (versions of) these principles can…Read more
  •  75
    Conservative deflationism?
    Philosophical Studies 177 (2): 535-549. 2020.
    Deflationists argue that ‘true’ is merely a logico-linguistic device for expressing blind ascriptions and infinite generalisations. For this reason, some authors have argued that deflationary truth must be conservative, i.e. that a deflationary theory of truth for a theory S must not entail sentences in S’s language that are not already entailed by S. However, it has been forcefully argued that any adequate theory of truth for S must be non-conservative and that, for this reason, truth cannot be…Read more
  •  62
    Classical Harmony and Separability
    Erkenntnis 85 (2): 391-415. 2020.
    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 thesis—requirements, however, that standard single-conclusion and assertion-based formalizations of classical logic provably fail to satisfy :1035–1051, 2011). On the plausible assumption that our logical practice is both single-conclusion and assertion…Read more
  •  48
    Non-reflexivity and Revenge
    Journal of Philosophical Logic 51 (1): 201-218. 2021.
    We present a revenge argument for non-reflexive theories of semantic notions – theories which restrict the rule of assumption, or initial sequents of the form φ ⊩ φ. Our strategy follows the general template articulated in Murzi and Rossi [21]: we proceed via the definition of a notion of paradoxicality for non-reflexive theories which in turn breeds paradoxes that standard non-reflexive theories are unable to block.
  •  36
    Non-contractability and Revenge
    Erkenntnis 85 (4): 905-917. 2020.
    It is often argued that fully structural theories of truth and related notions are incapable of expressing a nonstratified notion of defectiveness. We argue that recently much-discussed non-contractive theories suffer from the same expressive limitation, provided they identify the defective sentences with the sentences that yield triviality if they are assumed to satisfy structural contraction.
  •  20
    Inferentialism
    In Bob Hale, Crispin Wright & Alexander Miller (eds.), A Companion to the Philosophy of Language, Wiley. 2017.
    This chapter introduces inferential role semantics (IRS) and some of the challenges it faces. It also introduces inferentialism and places it into the wider context of contemporary philosophy of language. The chapter focuses on what is standardly considered both the most important test case for and the most natural application of IRS: logical inferentialism, the view that the meanings of the logical expressions are fully determined by the basic rules for their correct use, and that to understand…Read more
  •  8
    On Heck’s New Liar
    Thought: A Journal of Philosophy 1 (4): 258-269. 2012.
    Richard Heck has recently drawn attention on a new version of the Liar Paradox, one which relies on logical resources that are so weak as to suggest that it may not admit of any ‘‘truly satisfying, consistent solution’’. I argue that this conclusion is too strong. Heck’s Liar reduces to absurdity principles that are already rejected by consistent paracomplete theories of truth, such as Kripke’s and Field’s. Moreover, the new Liar gives us no reasons to think that these principles cannot be consi…Read more