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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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68The 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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12There 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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95Frege's Cardinals and Neo-LogicismPhilosophia Mathematica 24 (1): 60-90. 2016.Gottlob Frege defined cardinal numbers in terms of value-ranges governed by the inconsistent Basic Law V. Neo-logicists have revived something like Frege's original project by introducing cardinal numbers as primitive objects, governed by Hume's Principle. A neo-logicist foundation for set theory, however, requires a consistent theory of value-ranges of some sort. Thus, it is natural to ask whether we can reconstruct the cardinal numbers by retaining Frege's definition and adopting an alternativ…Read more
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238What’s Wrong with TonkJournal of Philosophical Logic 34 (2). 2005.In “The Runabout Inference Ticket” AN Prior (1960) examines the idea that logical connectives can be given a meaning solely in virtue of the stipulation of a set of rules governing them, and thus that logical truth/consequence
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126Comments on Patricia Blanchette's Book: Frege's Conception of Logic (review)Journal for the History of Analytical Philosophy 3 (7). 2015.All contributions included in the present issue were originally presented at an ‘Author Meets Critics’ session organised by Richard Zach at the Pacific Meeting of the American Philosophical Association in San Diego in the Spring of 2014.
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110Should Anti-Realists be Anti-Realists About Anti-Realism?Erkenntnis 79 (S2): 233-258. 2014.On the Dummettian understanding, anti-realism regarding a particular discourse amounts to (or at the very least, involves) a refusal to accept the determinacy of the subject matter of that discourse and a corresponding refusal to assert at least some instances of excluded middle (which can be understood as expressing this determinacy of subject matter). In short: one is an anti-realist about a discourse if and only if one accepts intuitionistic logic as correct for that discourse. On careful exa…Read more
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49B. Jack Copeland, Carl J. Posy, and Oron Shagrir, eds, Computability: Turing, Gödel, Church, and Beyond. Cambridge, Mass.: MIT Press, 2013. ISBN 978-0-262-01899-9. Pp. x + 362 (review)Philosophia Mathematica 22 (3): 412-413. 2014.
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24ParadoxesPolity. 2013.Paradoxes are arguments that lead from apparently true premises, via apparently uncontroversial reasoning, to a false or even contradictory conclusion. Paradoxes threaten our basic understanding of central concepts such as space, time, motion, infinity, truth, knowledge, and belief. In this volume Roy T Cook provides a sophisticated, yet accessible and entertaining, introduction to the study of paradoxes, one that includes a detailed examination of a wide variety of paradoxes. The book is organi…Read more
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110If A then B: How the World Discovered LogicHistory and Philosophy of Logic 35 (3): 301-303. 2014.If A then B: How the World Discovered Logic is a historically oriented introduction to the basic notions of logic. In particular, and in the words of the authors, it is focused on the idea that ‘lo...
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34Vagueness and MeaningIn Giuseppina Ronzitti (ed.), Vagueness: A Guide, Springer Verlag. pp. 83--106. 2011.
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126Do Comics Require Pictures? Or Why Batman #663 Is a ComicJournal of Aesthetics and Art Criticism 69 (3): 285-296. 2011.
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30The Arché Papers on the Mathematics of Abstraction (edited book)Springer. 2007.Unique in presenting a thoroughgoing examination of the mathematical aspects of the neo-logicist project (and the particular philosophical issues arising from these technical concerns).
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94Hintikka's Revolution: The Priciples of Mathematics Revisited (review)British Journal for the Philosophy of Science 49 (2): 309-316. 1998.
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3Appendix: How to read GrundgesetzeIn Gottlob Frege (ed.), Basic Laws of Arithmetic, Oxford University Press. 1893.This appendix is intended to assist the reader in becoming comfortable with the notations, rules, and definitions of Frege's Grundgesetze
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49Mathematics, Models, and ModalityHistory and Philosophy of Logic 31 (3): 287-289. 2010.John P. Burgess, Mathematics, Models, and Modality: Selected Philosophical Essays. Cambridge: Cambridge University Press, 2008. xiii + 301 pp. $90.00, £50.00. ISBN 978-0-521-88034-3. Adobe eBook, $...
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79Frege's RecipeJournal of Philosophy 113 (7): 309-345. 2016.In this paper, we present a formal recipe that Frege followed in his magnum opus “Grundgesetze der Arithmetik” when formulating his definitions. This recipe is not explicitly mentioned as such by Frege, but we will offer strong reasons to believe that Frege applied it in developing the formal material of Grundgesetze. We then show that a version of Basic Law V plays a fundamental role in Frege’s recipe and, in what follows, we will explicate what exactly this role is and explain how it differs f…Read more
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118The state of the economy: Neo-logicism and inflationPhilosophia Mathematica 10 (1): 43-66. 2002.In this paper I examine the prospects for a successful neo–logicist reconstruction of the real numbers, focusing on Bob Hale's use of a cut-abstraction principle. There is a serious problem plaguing Hale's project. Natural generalizations of this principle imply that there are far more objects than one would expect from a position that stresses its epistemological conservativeness. In other words, the sort of abstraction needed to obtain a theory of the reals is rampantly inflationary. I also in…Read more
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96Conservativeness, Stability, and AbstractionBritish Journal for the Philosophy of Science 63 (3): 673-696. 2012.One of the main problems plaguing neo-logicism is the Bad Company challenge: the need for a well-motivated account of which abstraction principles provide legitimate definitions of mathematical concepts. In this article a solution to the Bad Company challenge is provided, based on the idea that definitions ought to be conservative. Although the standard formulation of conservativeness is not sufficient for acceptability, since there are conservative but pairwise incompatible abstraction principl…Read more
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156Still counterintuitive: A reply to KremerAnalysis 63 (3). 2003.In (2002) I argued that Gupta and Belnap’s Revision Theory of Truth (1993) has counterintuitive consequences. In particular, the pair of sentences: (S1) At least one of S1 and S2 is false. (S2) Both of S1 and S2 are false.1 is pathological on the Revision account. There is one, and only one, assignment of truth values to {(S1), (S2)} that make the corresponding Tarski..
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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 |