•  844
    Williamson on Counterpossibles
    Journal 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.
  •  35
    Valuations: Bi, Tri, and Tetra
    Studia 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.
  •  28
    Vagueness in a Kind of Conflation
    Logic 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.
  •  43
    Blurring: An Approach to Conflation
    Notre 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.
  •  34
    Something Is Wrong With The Way We Think
    The Philosophers' Magazine 77 98-103. 2017.
  •  67
    Contraction and closure
    Thought: 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
  •  193
    Responsibility and the brain sciences
    Ethical 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
  •  213
    Tolerating Gluts
    with Zach Weber, Graham Priest, Dominic Hyde, and Mark Colyvan
    Mind 123 (491): 813-828. 2014.
  • 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.
  •  638
    Embedding Denial
    In 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
  •  1876
    Explaining the Abstract/Concrete Paradoxes in Moral Psychology: The NBAR Hypothesis
    Review 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
  •  62
    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.
  •  1235
    Paradoxes and Failures of Cut
    Australasian 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
  •  1021
    Contradictions at the borders
    In 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
  •  112
    Vagueness and Order Effects in Color Categorization
    with Paul Egré and Vincent de Gardelle
    Journal 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
  •  99
    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
  •  102
    Inconstancy and inconsistency
    In Petr Cintula, Christian Fermuller, Lluis Godo & Petr Hajek (eds.), Reasoning Under Vagueness, College Publications. pp. 41-58. 2011.
    In everyday language, we can call someone ‘consistent’ to say that they’re reliable, that they don’t change over time. Someone who’s consistently on time is always on time. Similarly, we can call someone ‘inconsistent’ to say the opposite: that they’re changeable, mercurial. A student who receives inconsistent grades on her tests throughout a semester has performed better on some than on others. With our philosophy hats on, though, we mean something quite different by ‘consistent’ and ‘inconsist…Read more
  •  825
    Anything Goes
    Topoi 34 (1): 25-36. 2015.
    This paper consider Prior's connective Tonk from a particular bilateralist perspective. I show that there is a natural perspective from which we can see Tonk and its ilk as perfectly well-defined pieces of vocabulary; there is no need for restrictions to bar things like Tonk.
  •  264
    How Mathematics Can Make a Difference
    Philosophers' Imprint 17. 2017.
    Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We …Read more
  •  168
    Review of Vagueness and degrees of truth, by Nicholas J. Smith (review)
    Analysis 70 (1): 188-190. 2010.
    (No abstract is available for this citation)
  •  111
    Paraconsistent Logic
    Journal 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
  •  1045
    Conservatively extending classical logic with transparent truth
    Review 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
  •  803
    Contractions of noncontractive consequence relations
    Review 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.
  •  360
    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
  •  299
    Negation, Denial, and Rejection
    Philosophy 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
  •  22
    Book Reviews (review)
    Studia Logica 94 (1): 139-145. 2010.
  •  61
    Spandrels of Truth, by Jc Beall (review)
    Mind 120 (478): 503-507. 2011.
    A review of Jc Beall's "Spandrels of Truth"
  •  77
    As 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
  •  78
    Response to Heck
    Thought: 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
  •  105
    Comparing Substructural Theories of Truth
    Ergo: 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