
Vagueness, Truth and Permissive ConsequenceIn T. Achourioti, H. Galinon, J. Martínez Fernández & K. Fujimoto (eds.), Unifying the Philosophy of Truth, Imprint: Springer. 2015.We say that a sentence A is a permissive consequence of a set X of premises whenever, if all the premises of X hold up to some standard, then A holds to some weaker standard. In this paper, we focus on a threevalued version of this notion, which we call stricttotolerant consequence, and discuss its fruitfulness toward a unified treatment of the paradoxes of vagueness and selfreferential truth. For vagueness, stconsequence supports the principle of tolerance; for truth, it supports the requi…Read more

59Review of Paradox and Paraconsistency (review)Notre Dame Philosophical Reviews. 2003.When physicists disagree as to whose theory is right, they can (if we radically idealize) form an experiment whose results will settle the difference. When logicians disagree, there seems to be no possibility of resolution in this manner. In Paradox and Paraconsistency John Woods presents a picture of disagreement among logicians, mathematicians, and other “abstract scientists” and points to some methods for resolving such disagreement. Our review begins with (very) short sketches of the chapter…Read more

189Nonclassical theories of truthIn Jc Beall & David Ripley (eds.), Oxford Handbook of Truth, . 2018.This chapter attempts to give a brief overview of nonclassical (logic) theories of truth. Due to space limitations, we follow a victorythroughsacrifice policy: sacrifice details in exchange for clarity of bigpicture ideas. This policy results in our giving alltoobrief treatment to certain topics that have dominated discussion in the nonclassicallogic area of truth studies. (This is particularly so of the ‘suitable conditoinal’ issue: §4.3.) Still, we present enough representative ideas t…Read more

59Formal Theories of TruthOxford University Press. 2018.Three leading philosopherlogicians present a clear and concise overview of formal theories of truth, explaining key logical techniques. Truth is as central topic in philosophy: formal theories study the connections between truth and logic, including the intriguing challenges presented by paradoxes like the Liar.

18Core Type TheoryBulletin of the Section of Logic 52 (2): 145186. 2023.Neil Tennant’s core logic is a type of bilateralist natural deduction system based on proofs and refutations. We present a proof system for propositional core logic, explain its connections to bilateralism, and explore the possibility of using it as a type theory, in the same kind of way intuitionistic logic is often used as a type theory. Our proof system is not Tennant’s own, but it is very closely related, and determines the same consequence relation. The difference, however, matters for our …Read more

20Experimental Philosophical LogicIn Wesley Buckwalter & Justin Sytsma (eds.), Blackwell Companion to Experimental Philosophy, Blackwell. 2016.This chapter explores the intersection of experimental philosophy and philosophical logic. It considers a distinction between pure and applied logic. It sketches some ways in which experimental results and empirical results more broadly, can inform and have informed debates within philosophical logic. The chapter lays out a way of looking at the situation that makes plain at least one way in which people should expect experimental and logical concerns to overlap. It turns to the phenomenon of va…Read more

113Tolerance and Mixed Consequence in the S'valuationist SettingStudia Logica 100 (4): 855877. 2012.In a previous paper (see ‘Tolerant, Classical, Strict’, henceforth TCS) we investigated a semantic framework to deal with the idea that vague predicates are tolerant, namely that small changes do not affect the applicability of a vague predicate even if large changes do. Our approach there rests on two main ideas. First, given a classical extension of a predicate, we can define a strict and a tolerant extension depending on an indifference relation associated to that predicate. Second, we can us…Read more

176Identity, Leibniz’s Law and NonTransitive ReasoningMetaphysica 14 (2): 253264. 2013.Arguments based on Leibniz's Law seem to show that there is no room for either indefinite or contingent identity. The arguments seem to prove too much, but their conclusion is hard to resist if we want to keep Leibniz's Law. We present a novel approach to this issue, based on an appropriate modification of the notion of logical consequence.

59Inferences and Metainferences in STJournal of Philosophical Logic 49 (6): 10571077. 2020.In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between metainferences holding in the stricttolerant logic of transparent truth ST+ and inferences holding in the logic of paradox LP+. They argue that LP+ is ST+’s external logic and they question whether ST+’s solution to the semantic paradoxes is fundamentally different from LP+’s. Here we establish that by parity of reasoning, ST+ can be related to LP+’s dual logic K3+. We clarify the distinction between internal and…Read more

73Tolerant reasoning: nontransitive or nonmonotonic?Synthese 199 (Suppl 3): 681705. 2017.The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approa…Read more

414Tolerant, Classical, StrictJournal of Philosophical Logic 41 (2): 347385. 2012.In this paper we investigate a semantics for firstorder logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and…Read more

202Reaching Transparent TruthMind 122 (488): 841866. 2013.This paper presents and defends a way to add a transparent truth predicate to classical logic, such that and A are everywhere intersubstitutable, where all Tbiconditionals hold, and where truth can be made compositional. A key feature of our framework, called STTT (for StrictTolerant Transparent Truth), is that it supports a nontransitive relation of consequence. At the same time, it can be seen that the only failures of transitivity STTT allows for arise in paradoxical cases

66Identity, Leibniz's Law and Nontransitive ReasoningMetaphysica 14 (2): 253264. 2013.Arguments based on Leibniz's Law seem to show that there is no room for either indefinite or contingent identity. The arguments seem to prove too much, but their conclusion is hard to resist if we want to keep Leibniz's Law. We present a novel approach to this issue, based on an appropriate modification of the notion of logical consequence.

59Foreword: Threevalued logics and their applicationsJournal of Applied NonClassical Logics 24 (12): 111. 2014.

290On the Ternary Relation and ConditionalityJournal of Philosophical Logic 41 (3). 2012.One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the RoutleyMeyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions o…Read more

124Vagueness, Truth and Permissive ConsequenceIn T. Achourioti, H. Galinon, J. Martínez Fernández & K. Fujimoto (eds.), Unifying the Philosophy of Truth, Imprint: Springer. pp. 409430. 2015.We say that a sentence A is a permissive consequence of a set X of premises whenever, if all the premises of X hold up to some standard, then A holds to some weaker standard. In this paper, we focus on a threevalued version of this notion, which we call stricttotolerant consequence, and discuss its fruitfulness toward a unified treatment of the paradoxes of vagueness and selfreferential truth. For vagueness, stconsequence supports the principle of tolerance; for truth, it supports the requi…Read more

90Pragmatic Interpretations of Vague Expressions: Strongest Meaning and Nonmonotonic ConsequenceJournal of Philosophical Logic 44 (4): 375393. 2015.Recent experiments have shown that naive speakers find borderline contradictions involving vague predicates acceptable. In Cobreros et al. we proposed a pragmatic explanation of the acceptability of borderline contradictions, building on a threevalued semantics. In a reply, Alxatib et al. show, however, that the pragmatic account predicts the wrong interpretations for some examples involving disjunction, and propose as a remedy a semantic analysis instead, based on fuzzy logic. In this paper we…Read more

36Qua Solution, 0Qua Has ProblemsJournal of Analytic Theology 8 (1): 405411. 2020.We present an objection to Beall & Henderson’s recent paper defending a solution to the fundamental problem of conciliar Christology using qua or secundum clauses. We argue that certain claims the acceptance/rejection of which distinguish the Conciliar Christian from others fail to so distinguish on Beall & Henderson’s 0Qua view. This is because on their 0Qua account, these claims are either acceptable both to Conciliar Christians as well as those who are not Conciliar Christians or because th…Read more

25One Step is EnoughJournal of Philosophical Logic 51 (6): 12331259. 2022.The recent development and exploration of mixed metainferential logics is a breakthrough in our understanding of nontransitive and nonreflexive logics. Moreover, this exploration poses a new challenge to theorists like me, who have appealed to similarities to classical logic in defending the logic ST, since some mixed metainferential logics seem to bear even more similarities to classical logic than ST does. There is a whole STbased hierarchy, of which ST itself is only the first step, that see…Read more

The Sorites paradox in psychologyIn Sergi Oms & Elia Zardini (eds.), The Sorites Paradox, Cambridge University Press. 2019.

27Précis of UncutAnálisis Filosófico 41 (2): 235260. 2021.Uncut is a book about two kinds of paradoxes: paradoxes involving truth and its relatives, like the liar paradox, and paradoxes involving vagueness. There are lots of ways to look at these paradoxes, and lots of puzzles generated by them, and Uncut ignores most of this variety to focus on a single issue. That issue: do our words mean what they seem to mean, and if so, how can this be? I claim that our words do mean what they seem to, and yet our language is not undermined by paradox. By developi…Read more

89One Step is EnoughJournal of Philosophical Logic 51 (6): 127. 2021.The recent development and exploration of mixed metainferential logics is a breakthrough in our understanding of nontransitive and nonreflexive logics. Moreover, this exploration poses a new challenge to theorists like me, who have appealed to similarities to classical logic in defending the logic ST, since some mixed metainferential logics seem to bear even more similarities to classical logic than ST does. There is a whole STbased hierarchy, of which ST itself is only the first step, that see…Read more

129Classical counterpossiblesReview of Symbolic Logic 15 (1): 259275. 2022.We present four classical theories of counterpossibles that combine modalities and counterfactuals. Two theories are antivacuist and forbid vacuously true counterfactuals, two are quasivacuist and allow counterfactuals to be vacuously true when their antecedent is not only impossible, but also inconceivable. The theories vary on how they restrict the interaction of modalities and counterfactuals. We provide a logical cartography with precise acceptable boundaries, illustrating to what extent n…Read more

78This paper presents a new puzzle for certain positions in the theory of truth. The relevant positions can be stated in a language including a truth predicate T and an operation that takes sentences to names of those sentences; they are positions that take the Tschema A ↔ T to hold without restriction, for every sentence A in the language. As such, they must be based on a nonclassical logic, since paradoxes that cannot be handled classically will arise. The bestknown of these paradoxes is probab…Read more

149A Counterfactual Approach to Explanation in MathematicsPhilosophia Mathematica 28 (1): 134. 2020.ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intramathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intramathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explor…Read more

44Two traditions in abstract valuational model theorySynthese 198 (S22): 52915313. 2019.We investigate two different broad traditions in the abstract valuational model theory for nontransitive and nonreflexive logics. The first of these traditions makes heavy use of the natural Galois connection between sets of valuations and sets of arguments. The other, originating with work by Grzegorz Malinowski on nonreflexive logics, and best systematized in Blasio et al. : 233–262, 2017), lets sets of arguments determine a more restricted set of valuations. After giving a systematic discussi…Read more
Areas of Specialization
Philosophy of Language 
Logic and Philosophy of Logic 
Areas of Interest
Metaphysics 
Philosophy of Mind 
Philosophy of Cognitive Science 