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37AbstractionismInternet Encyclopedia of Philosophy. 2021.Abstractionism is a philosophical account of the ontology of mathematics according to which abstract objects are grounded in a process of abstraction. Abstraction involves arranging a domain of underlying objects into classes and then identifying … Continue reading Abstractionism →
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37PATRICIA A. BLANCHETTE. Frege's Conception of Logic. Oxford University Press, 2012. ISBN 978-0-19-926925-9 . Pp. xv + 256 (review)Philosophia Mathematica 22 (1): 108-120. 2014.
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36Embracing intensionality: Paradoxicality and semi-truth operators in fixed point modelsLogic Journal of the IGPL 28 (5): 747-770. 2020.The Embracing Revenge account of semantic paradox avoids the expressive limitations of previous approaches based on the Kripkean fixed point construction by replacing a single language with an indefinitely extensible sequence of languages, each of which contains the resources to fully characterize the semantics of the previous languages. In this paper we extend the account developed in Cook, Cook, Schlenker, and Tourville and Cook via the addition of intensional operators such as ``is paradoxica…Read more
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36Introduction to Special Issue: Reconsidering Frege's Conception of NumberPhilosophia Mathematica 24 (1): 1-8. 2016.
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34Vagueness and MeaningIn Giuseppina Ronzitti (ed.), Vagueness: A Guide, Springer Verlag. pp. 83--106. 2011.
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34Hilary Putnam on Logic and Mathematics (edited book)Springer Verlag. 2018.This book explores the research of Professor Hilary Putnam, a Harvard professor as well as a leading philosopher, mathematician and computer scientist. It features the work of distinguished scholars in the field as well as a selection of young academics who have studied topics closely connected to Putnam’s work. It includes 12 papers that analyze, develop, and constructively criticize this notable professor's research in mathematical logic, the philosophy of logic and the philosophy of mathemati…Read more
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33Frege's Concept-Script (Grundgesetze der Arithmetik)In Bruno Woltzenlogel Paleo & Giselle Reis (eds.), Encyclopedia of Proof Systems, College Publications. 2022.
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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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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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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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25ParadoxesPolity. 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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19Lego and Philosophy: Constructing Reality Brick by Brick (edited book)Blackwell Publishers. 2017.LEGO and Creativity -- LEGO, Ethics, and Rules -- LEGO and Identity -- LEGO, Consumption, and Culture -- LEGO, Metaphysics, and Math.
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19Groensteen, 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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18CRITICAL NOTICE: Humberstone, Lloyd, The Connectives, Cambridge, MA: MIT Press, 2011, pp. xvii + 1492, $US65.00, £44.95 (hardback) (review)Australasian Journal of Philosophy 91 (2): 395-405. 2013.
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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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16The 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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14There Are Non-circular Paradoxes (But Yablo’s Isn't One of Them!)The Monist 89 (1): 118-149. 2006.
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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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3Foundational theories of classical and constructive mathematics, edited by Giovanni Sommaruga, Springer, 2011. xi + 314 pp (review)Bulletin of Symbolic Logic 18 (1): 128-131. 2012.
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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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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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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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1Universals and AbstractIn Robert Barnard & Neil Manson (eds.), Continuum Companion to Metaphysics, Continuum Publishing. pp. 67. 2012.
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Extendability and ParadoxIn John Burgess (ed.), Hilary Putnam on Logic and Mathematics, Springer Verlag. 2018.
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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 |