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9The Routledge Companion to Comics (edited book)Routledge. 2016.This cutting-edge handbook brings together an international roster of scholars to examine many facets of comics and graphic novels. Contributor essays provide authoritative, up-to-date overviewsof the major topics and questions within comic studies, offering readers a truly global approach to understanding the field.
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1Logic-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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7The 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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3Monads 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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5A 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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12The 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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19Hume’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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16Curry, 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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16Vagueness 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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4Canonicity and Normativity in Massive, Serialized, Collaborative FictionJournal of Aesthetics and Art Criticism 71 (3): 271-276. 2013.
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6There Are Non-circular Paradoxes (But Yablo’s Isn't One of Them!)The Monist 89 (1): 118-149. 2006.
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12Abstraction 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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16Patterns 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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21Let 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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20Frege'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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22What’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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137Comments 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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7B. 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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12Should 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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12ParadoxesPolity. 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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6If 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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12Do Comics Require Pictures? Or Why Batman #663 Is a ComicJournal of Aesthetics and Art Criticism 69 (3): 285-296. 2011.
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6Vagueness and MeaningIn Giuseppina Ronzitti (ed.), Vagueness: A Guide, Springer Verlag. pp. 83--106. 2011.
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5The 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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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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4Hintikka's Revolution: The Priciples of Mathematics Revisited (review)British Journal for the Philosophy of Science 49 (2): 309-316. 1998.
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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 |