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844Williamson on CounterpossiblesJournal of Philosophical Logic 47 (4): 693-713. 2018.A counterpossible conditional is a counterfactual with an impossible antecedent. Common sense delivers the view that some such conditionals are true, and some are false. In recent publications, Timothy Williamson has defended the view that all are true. In this paper we defend the common sense view against Williamson’s objections.
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35Valuations: Bi, Tri, and TetraStudia Logica 107 (6): 1313-1346. 2019.This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.
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28Vagueness in a Kind of ConflationLogic and Logical Philosophy 26 (1): 115-135. 2017.This paper sketches an understanding of conflation and vagueness according to which the latter is a special kind of the former. First, I sketch a particular understanding of conflation. Then, I go on to argue that vague concepts fit directly into this understanding. This picture of vagueness is related, but not identical, to a number of existing accounts.
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43Blurring: An Approach to ConflationNotre Dame Journal of Formal Logic 59 (2): 171-188. 2018.I consider the phenomenon of conflation—treating distinct things as one—and develop logical tools for modeling it. These tools involve a purely consequence-theoretic treatment, independent of any proof or model theory, as well as a four-valued valuational treatment.
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168Review of Vagueness and degrees of truth, by Nicholas J. Smith (review)Analysis 70 (1): 188-190. 2010.(No abstract is available for this citation)
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111Paraconsistent LogicJournal of Philosophical Logic 44 (6): 771-780. 2015.In some logics, anything whatsoever follows from a contradiction; call these logics explosive. Paraconsistent logics are logics that are not explosive. Paraconsistent logics have a long and fruitful history, and no doubt a long and fruitful future. To give some sense of the situation, I’ll spend Section 1 exploring exactly what it takes for a logic to be paraconsistent. It will emerge that there is considerable open texture to the idea. In Section 2, I’ll give some examples of techniques for dev…Read more
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1045Conservatively extending classical logic with transparent truthReview of Symbolic Logic 5 (2): 354-378. 2012.This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete.…Read more
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803Contractions of noncontractive consequence relationsReview of Symbolic Logic 8 (3): 506-528. 2015.Some theorists have developed formal approaches to truth that depend on counterexamples to the structural rules of contraction. Here, we study such approaches, with an eye to helping them respond to a certain kind of objection. We define a contractive relative of each noncontractive relation, for use in responding to the objection in question, and we explore one example: the contractive relative of multiplicative-additive affine logic with transparent truth, or MAALT.
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360Structures and circumstances: two ways to fine-grain propositionsSynthese 189 (1). 2012.This paper discusses two distinct strategies that have been adopted to provide fine-grained propositions; that is, propositions individuated more finely than sets of possible worlds. One strategy takes propositions to have internal structure, while the other looks beyond possible worlds, and takes propositions to be sets of circumstances, where possible worlds do not exhaust the circumstances. The usual arguments for these positions turn on fineness-of-grain issues: just how finely should propos…Read more
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299Negation, Denial, and RejectionPhilosophy Compass 6 (9): 622-629. 2011.At least since [Frege, 1960] and [Geach, 1965], there has been some consensus about the relation between negation, the speech act of denial, and the attitude of rejection: a denial, the consensus has had it, is the assertion of a negation, and a rejection is a belief in a negation. Recently, though, there have been notable deviations from this orthodox view. Rejectivists have maintained that negation is to be explained in terms of denial or rejection, rather than vice versa. Some other theorists…Read more
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61Spandrels of Truth, by Jc Beall (review)Mind 120 (478): 503-507. 2011.A review of Jc Beall's "Spandrels of Truth"
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77As we’ve seen in the last chapter, there is good linguistic reason to categorize negations (and negative operators in general) by which De Morgan laws they support. The weakest negative operators (merely downward monotonic) support only two De Morgan laws;1 medium-strength negative operators support a third;2 and strong negative operators support all four. As we’ve also seen, techniques familiar from modal logic are of great use in giving unifying theories of negative operators. In particular, D…Read more
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78Response to HeckThought: A Journal of Philosophy 1 (4): 254-257. 2012.In Heck, Richard Heck presents variants on the familiar liar paradox, intended to reveal limitations of theories of transparent truth. But all existing theories of transparent truth can respond to Heck's variants in just the same way they respond to the liar. These new variants thus put no new pressure on theories of transparent truth
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105Comparing Substructural Theories of TruthErgo: An Open Access Journal of Philosophy 2. 2015.Substructural theories of truth are theories based on logics that do not include the full complement of usual structural rules. Existing substructural approaches fall into two main families: noncontractive approaches and nontransitive approaches. This paper provides a sketch of these families, and argues for two claims: first, that substructural theories are better-positioned than other theories to grapple with the truth-theoretic paradoxes, and second—more tentatively—that nontransitive approac…Read more
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361Expectations and morality: A dilemmaBehavioral and Brain Sciences 33 (4): 346-346. 2010.We propose Knobe's explanation of his cases encounters a dilemma: Either his explanation works and, counterintuitively, morality is not at the heart of these effects; or morality is at the heart of the effects and Knobe's explanation does not succeed. This dilemma is then used to temper the use of the Knobe paradigm for discovering moral norms
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178Sorting out the soritesIn Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications, Springer. pp. 329-348. 2012.Supervaluational theories of vagueness have achieved considerable popularity in the past decades, as seen in eg [5], [12]. This popularity is only natural; supervaluations let us retain much of the power and simplicity of classical logic, while avoiding the commitment to strict bivalence that strikes many as implausible. Like many nonclassical logics, the supervaluationist system SP has a natural dual, the subvaluationist system SB, explored in eg [6], [28].1 As is usual for such dual systems, t…Read more
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56Naive Set Theory and Nontransitive LogicReview of Symbolic Logic 8 (3): 553-571. 2015.In a recent series of papers, I and others have advanced new logical approaches to familiar paradoxes. The key to these approaches is to accept full classical logic, and to accept the principles that cause paradox, while preventing trouble by allowing a certain sort ofnontransitivity. Earlier papers have treated paradoxes of truth and vagueness. The present paper will begin to extend the approach to deal with the familiar paradoxes arising in naive set theory, pointing out some of the promises a…Read more
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67Contraction and closureThought: A Journal of Philosophy 4 (2): 131-138. 2015.In this paper, I consider the connection between consequence relations and closure operations. I argue that one familiar connection makes good sense of some usual applications of consequence relations, and that a largeish family of familiar noncontractive consequence relations cannot respect this familiar connection
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193Responsibility and the brain sciencesEthical Theory and Moral Practice 12 (5): 511-524. 2008.Some theorists think that the more we get to know about the neural underpinnings of our behaviors, the less likely we will be to hold people responsible for their actions. This intuition has driven some to suspect that as neuroscience gains insight into the neurological causes of our actions, people will cease to view others as morally responsible for their actions, thus creating a troubling quandary for our legal system. This paper provides empirical evidence against such intuitions. Particular…Read more
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Reply to Nicholas Smith’s Comments on 'Inconstancy and Inconsistency'In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical, and Linguistic Perspectives, College Publications. pp. 63-5. 2011.
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638Embedding DenialIn Colin R. Caret & Ole T. Hjortland (eds.), Foundations of Logical Consequence, Oxford University Press. pp. 289-309. 2015.Suppose Alice asserts p, and the Caterpillar wants to disagree. If the Caterpillar accepts classical logic, he has an easy way to indicate this disagreement: he can simply assert ¬p. Sometimes, though, things are not so easy. For example, suppose the Cheshire Cat is a paracompletist who thinks that p ∨ ¬p fails (in familiar (if possibly misleading) language, the Cheshire Cat thinks p is a gap). Then he surely disagrees with Alice's assertion of p, but should himself be unwilling to assert ¬p. So…Read more
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1876Explaining the Abstract/Concrete Paradoxes in Moral Psychology: The NBAR HypothesisReview of Philosophy and Psychology 3 (3): 351-368. 2012.For some reason, participants hold agents more responsible for their actions when a situation is described concretely than when the situation is described abstractly. We present examples of this phenomenon, and survey some attempts to explain it. We divide these attempts into two classes: affective theories and cognitive theories. After criticizing both types of theories we advance our novel hypothesis: that people believe that whenever a norm is violated, someone is responsible for it. This bel…Read more
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62The Yablo Paradox: An Essay on Circularity By Roy T. CookAnalysis 75 (3): 523-525. 2015.The Yablo Paradox (Cook 2014) is an examination of, well, the Yablo paradox. For space reasons, I’ll assume you’re familiar with the paradox already (sorry!); i.
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1235Paradoxes and Failures of CutAustralasian Journal of Philosophy 91 (1). 2013.This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory …Read more
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1021Contradictions at the bordersIn Rick Nouwen, Robert van Rooij, Uli Sauerland & Hans-Christian Schmitz (eds.), Vagueness in Communication, Springer. pp. 169--188. 2011.The purpose of this essay is to shed some light on a certain type of sentence, which I call a borderline contradiction. A borderline contradiction is a sentence of the form F a ∧ ¬F a, for some vague predicate F and some borderline case a of F , or a sentence equivalent to such a sentence. For example, if Jackie is a borderline case of ‘rich’, then ‘Jackie is rich and Jackie isn’t rich’ is a borderline contradiction. Many theories of vague language have entailments about borderline contradiction…Read more
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112Vagueness and Order Effects in Color CategorizationJournal of Logic, Language and Information 22 (4): 391-420. 2013.This paper proposes an experimental investigation of the use of vague predicates in dynamic sorites. We present the results of two studies in which subjects had to categorize colored squares at the borderline between two color categories (Green vs. Blue, Yellow vs. Orange). Our main aim was to probe for hysteresis in the ordered transitions between the respective colors, namely for the longer persistence of the initial category. Our main finding is a reverse phenomenon of enhanced contrast (i.e.…Read more
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99Revising Up: Strengthening Classical Logic in the Face of ParadoxPhilosophers' Imprint 13. 2013.This paper provides a defense of the full strength of classical logic, in a certain form, against those who would appeal to semantic paradox or vagueness in an argument for a weaker logic. I will not argue that these paradoxes are based on mistaken principles; the approach I recommend will extend a familiar formulation of classical logic by including a fully transparent truth predicate and fully tolerant vague predicates. It has been claimed that these principles are not compatible with classica…Read more
Areas of Specialization
Philosophy of Language |
Logic and Philosophy of Logic |
Areas of Interest
Metaphysics |
Philosophy of Mind |
Philosophy of Cognitive Science |