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2Logic-as-Modeling: A New Perspective on FormalizationDissertation, The Ohio State University. 2000.I propose a novel way of viewing the connection between mathematical discourse and the mathematical logician's formalizations of it. We should abandon the idea that formalizations are accurate descriptions of mathematical activity. Instead, logicians are in the business of supplying models in much the same way that a mathematical physicist formulates models of physical phenomena or the hobbyist constructs models of ships. ;I first examine problems with the traditional view, and I survey some pri…Read more
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67The Yablo Paradox: An Essay on CircularityOxford University Press. 2012.Roy T Cook examines the Yablo paradox--a paradoxical, infinite sequence of sentences, each of which entails the falsity of all others that follow it. He focuses on questions of characterization, circularity, and generalizability, and pays special attention to the idea that it provides us with a semantic paradox that involves no circularity
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31Monads and Mathematics: The Logic of Leibniz's MereologyStudia Leibnitiana 32 (1). 2000.Es bestehen tiefgreifende Zusammenhänge zwischen Leibniz' Mathematik und seiner Metaphysik. Dieser Aufsatz hat das Ziel, das Verständnis für diese beiden Bereiche zu erweitern, indem er Leibniz' Mereologie (die Theorie der Teile und des Ganzen) näher untersucht. Zunachst wird Leibniz' Mereologie primär anhand seiner Schrift “Initia rerum mathematicarum metaphysica" rekonstruiert. Dieses ehrgeizige Programm beginnt mit dem einfachen Begriff der Kompräsenz, geht dann iiber zu komplexeren Begriffen…Read more
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16A Dictionary of Philosophical LogicEdinburgh University Press. 2009.This dictionary introduces undergraduate and post-graduate students in philosophy, mathematics, and computer science to the main problems and positions in philosophical logic. Coverage includes not only key figures, positions, terminology, and debates within philosophical logic itself, but issues in related, overlapping disciplines such as set theory and the philosophy of mathematics as well. Entries are extensively cross-referenced, so that each entry can be easily located within the context of…Read more
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186The T-schema is not a logical truthAnalysis 72 (2): 231-239. 2012.It is shown that the logical truth of instances of the T-schema is incompatible with the formal nature of logical truth. In particular, since the formality of logical truth entails that the set of logical truths is closed under substitution, the logical truth of T-schema instances entails that all sentences are logical truths
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59Necessity, Necessitism, and NumbersPhilosophical Forum 47 (3-4): 385-414. 2016.Timothy Williamson’s Modal Logic as Metaphysics is a book-length defense of necessitism about objects—roughly put, the view that, necessarily, any object that exists, exists necessarily. In more formal terms, Williamson argues for the validity of necessitism for objects (NO: ◻︎∀x◻︎∃y(x=y)). NO entails both the (first-order) Barcan formula (BF: ◇∃xΦ → ∃x◇Φ, for any formula Φ) and the (first-order) converse Barcan formula (CBF: ∃x◇Φ → ◇∃xΦ, for any formula Φ). The purpose of this essay is not to a…Read more
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18Groensteen, Thierry. Comics and Narration. Trans. Ann Miller. University Press of Mississippi, 2013, ix + 205 pp., 16 b&w illus., $55.00 cloth (review)Journal of Aesthetics and Art Criticism 72 (3): 337-340. 2014.
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1Universals and AbstractIn Robert Barnard Neil Manson (ed.), Continuum Companion to Metaphysics, . pp. 67. 2012.
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124There Are Non-circular Paradoxes (But Yablo’s Isn't One of Them!)The Monist 89 (1): 118-149. 2006.
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90Abstraction and Four Kinds of InvariancePhilosophia Mathematica 25 (1). 2017.Fine and Antonelli introduce two generalizations of permutation invariance — internal invariance and simple/double invariance respectively. After sketching reasons why a solution to the Bad Company problem might require that abstraction principles be invariant in one or both senses, I identify the most fine-grained abstraction principle that is invariant in each sense. Hume’s Principle is the most fine-grained abstraction principle invariant in both senses. I conclude by suggesting that this par…Read more
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152Impure Sets Are Not Located: A Fregean ArgumentThought: A Journal of Philosophy 1 (3): 219-229. 2012.It is sometimes suggested that impure sets are spatially co-located with their members (and hence are located in space). Sets, however, are in important respects like numbers. In particular, sets are connected to concepts in much the same manner as numbers are connected to concepts—in both cases, they are fundamentally abstracts of (or corresponding to) concepts. This parallel between the structure of sets and the structure of numbers suggests that the metaphysics of sets and the metaphysics of …Read more
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3Embracing revenge: on the indefinite extendibility of languageIn J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox, Oxford University Press. pp. 31. 2007.
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107The No-No Paradox Is a ParadoxAustralasian Journal of Philosophy 89 (3): 467-482. 2011.The No-No Paradox consists of a pair of statements, each of which ?says? the other is false. Roy Sorensen claims that the No-No Paradox provides an example of a true statement that has no truthmaker: Given the relevant instances of the T-schema, one of the two statements comprising the ?paradox? must be true (and the other false), but symmetry constraints prevent us from determining which, and thus prevent there being a truthmaker grounding the relevant assignment of truth values. Sorensen's vie…Read more
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29Critical notice: Humberstone, Lloyd, the connectives, cambridge, ma: Mit press, 2011, pp. XVII + 1492, $us65.00, £44.95Australasian Journal of Philosophy 91 (2): 395-405. 2013.No abstract
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356Response to my criticsAnálisis Filosófico 32 (1): 69-97. 2012.During the Winter of 2011 I visited SADAF and gave a series of talks based on the central chapters of my manuscript on the Yablo paradox. The following year, I visited again, and was pleased and honored to find out that Eduardo Barrio and six of his students had written ‘responses’ that addressed the claims and arguments found in the manuscript, as well as explored new directions in which to take the ideas and themes found there. These comments reflect my thoughts on these responses (also collec…Read more
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111Alethic pluralism, generic truth, and mixed conjunctionsPhilosophical Quarterly 61 (244): 624-629. 2011.A difficulty for alethic pluralism has been the idea that semantic evaluation of conjunctions whose conjuncts come from discourses with distinct truth properties requires a third notion of truth which applies to both of the original discourses. But this line of reasoning does not entail that there exists a single generic truth property that applies to all statements and all discourses, unless it is supplemented with additional, controversial, premises. So the problem of mixed conjunctions, while…Read more
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1New waves on an old beach: Fregean philosophy of mathematics todayIn Ø. Linnebo O. Bueno (ed.), New Waves in Philosophy of Mathematics, . 2009.
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141Hume’s Big Brother: counting concepts and the bad company objectionSynthese 170 (3). 2009.A number of formal constraints on acceptable abstraction principles have been proposed, including conservativeness and irenicity. Hume’s Principle, of course, satisfies these constraints. Here, variants of Hume’s Principle that allow us to count concepts instead of objects are examined. It is argued that, prima facie, these principles ought to be no more problematic than HP itself. But, as is shown here, these principles only enjoy the formal properties that have been suggested as indicative of …Read more
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200Curry, Yablo and dualityAnalysis 69 (4): 612-620. 2009.The Liar paradox is the directly self-referential Liar statement: This statement is false.or : " Λ: ∼ T 1" The argument that proceeds from the Liar statement and the relevant instance of the T-schema: " T ↔ Λ" to a contradiction is familiar. In recent years, a number of variations on the Liar paradox have arisen in the literature on semantic paradox. The two that will concern us here are the Curry paradox, 2 and the Yablo paradox. 3The Curry paradox demonstrates that neither negation nor a falsi…Read more
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171Vagueness and mathematical precisionMind 111 (442): 225-247. 2002.One of the main reasons for providing formal semantics for languages is that the mathematical precision afforded by such semantics allows us to study and manipulate the formalization much more easily than if we were to study the relevant natural languages directly. Michael Tye and R. M. Sainsbury have argued that traditional set-theoretic semantics for vague languages are all but useless, however, since this mathematical precision eliminates the very phenomenon (vagueness) that we are trying to …Read more
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11There Are Non-circular Paradoxes (But Yablo’s Isn't One of Them!)The Monist 89 (1): 118-149. 2006.
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56Canonicity and Normativity in Massive, Serialized, Collaborative FictionJournal of Aesthetics and Art Criticism 71 (3): 271-276. 2013.
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327Patterns of paradoxJournal of Symbolic Logic 69 (3): 767-774. 2004.We begin with a prepositional languageLpcontaining conjunction (Λ), a class of sentence names {Sα}αϵA, and a falsity predicateF. We (only) allow unrestricted infinite conjunctions, i.e., given any non-empty class of sentence names {Sβ}βϵB,is a well-formed formula (we will useWFFto denote the set of well-formed formulae).The language, as it stands, is unproblematic. Whether various paradoxes are produced depends on which names are assigned to which sentences. What is needed is a denotation functi…Read more
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487Abstraction and identityDialectica 59 (2). 2005.A co-authored article with Roy T. Cook forthcoming in a special edition on the Caesar Problem of the journal Dialectica. We argue against the appeal to equivalence classes in resolving the Caesar Problem.
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468Let a thousand flowers Bloom: A tour of logical pluralismPhilosophy Compass 5 (6): 492-504. 2010.Logical pluralism is the view that there is more than one correct logic. In this article, I explore what logical pluralism is, and what it entails, by: (i) distinguishing clearly between relativism about a particular domain and pluralism about that domain; (ii) distinguishing between a number of forms logical pluralism might take; (iii) attempting to distinguish between those versions of pluralism that are clearly true and those that are might be controversial; and (iv) surveying three prominent…Read more
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University of St. Andrews3- Year Post-doctoral Fellow
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University of MinnesotaTenured
Ohio State University
PhD, 2000
St Andrews, United Kingdom of Great Britain and Northern Ireland
Areas of Specialization
Science, Logic, and Mathematics |
PhilPapers Editorships
Theories of Mathematics |