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Structuralism and the notion of dependencePhilosophical Quarterly 58 (230): 59-79. 2008.This paper has two goals. The first goal is to show that the structuralists’ claims about dependence are more significant to their view than is generally recognized. I argue that these dependence claims play an essential role in the most interesting and plausible characterization of this brand of structuralism. The second goal is to defend a compromise view concerning the dependence relations that obtain between mathematical objects. Two extreme views have tended to dominate the debate, namely the…Read more
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Abstraction and GroundingPhilosophy and Phenomenological Research. forthcoming.The idea that some objects are metaphysically “cheap” has wide appeal. An influential version of the idea builds on abstractionist views in the philosophy of mathematics, on which numbers and other mathematical objects are abstracted from other phenomena. For example, Hume’s Principle states that two collections have the same number just in case they are equinumerous, in the sense that they can be correlated one-to-one: (HP) #xx=#yy iff xx≈yy. The principal aim of this article is to use the noti…Read more
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Review: Fraser MacBride (ed.): Identity and Modality (review)Mind 117 (467): 705-708. 2008.
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The limits of abstraction (review)Australasian Journal of Philosophy 82 (4): 653-656. 2004.
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Early Analytic Philosophy (review)Philosophical Review 109 (1): 98-101. 2000.Analytic philosophy has traditionally been little concerned with the history of philosophy, including that of analytic philosophy itself. But in recent years the study of the early period of the analytic tradition has become an active and lively branch of Anglo-American philosophy. Early Analytic Philosophy, a collection of papers presented in honor of professor Leonard Linsky at the University of Chicago in April 1992, is an example of this. The contributors, many of them leading scholars in th…Read more
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Mending the master: John P. Burgess, fixing Frege. Princeton, N. J.: Princeton university press, 2005. ISBN 0-691-12231-8. Pp. XII + 257 (review)Philosophia Mathematica 14 (3): 338-351. 2006.Fixing Frege is one of the most important investigations to date of Fregean approaches to the foundations of mathematics. In addition to providing an unrivalled survey of the technical program to which Frege's writings have given rise, the book makes a large number of improvements and clarifications. Anyone with an interest in the philosophy of mathematics will enjoy and benefit from the careful and well-informed overview provided by the first of its three chapters. Specialists will find the boo…Read more
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Review of P. Maddy, Defending the Axioms: On the Philosophical Foundations of Set Theory (review)Philosophy 87 (1): 133-137. 2012.
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Platonism in the Philosophy of MathematicsStanford Encyclopedia of Philosophy. forthcoming.Platonism about mathematics (or mathematical platonism) isthe metaphysical view that there are abstract mathematical objectswhose existence is independent of us and our language, thought, andpractices. Just as electrons and planets exist independently of us, sodo numbers and sets. And just as statements about electrons and planetsare made true or false by the objects with which they are concerned andthese objects' perfectly objective properties, so are statements aboutnumbers and sets. Mathemati…Read more
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The modal logic of set-theoretic potentialism and the potentialist maximality principlesReview of Symbolic Logic 15 (1): 1-35. 2022.We analyze the precise modal commitments of several natural varieties of set-theoretic potentialism, using tools we develop for a general model-theoretic account of potentialism, building on those of Hamkins, Leibman and Löwe [14], including the use of buttons, switches, dials and ratchets. Among the potentialist conceptions we consider are: rank potentialism, Grothendieck–Zermelo potentialism, transitive-set potentialism, forcing potentialism, countable-transitive-model potentialism, countable-…Read more
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New waves in philosophy of mathematics (edited book)Palgrave-Macmillan. 2009.Thirteen up-and-coming researchers in the philosophy of mathematics have been invited to write on what they take to be the right philosophical account of mathematics, examining along the way where they think the philosophy of mathematics is and ought to be going. A rich and diverse picture emerges. Some broader tendencies can nevertheless be detected: there is increasing attention to the practice, language and psychology of mathematics, a move to reassess the orthodoxy, as well as inspiration fr…Read more
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Philosophy of MathematicsPrinceton University Press. 2017.Mathematics is one of the most successful human endeavors—a paradigm of precision and objectivity. It is also one of our most puzzling endeavors, as it seems to deliver non-experiential knowledge of a non-physical reality consisting of numbers, sets, and functions. How can the success and objectivity of mathematics be reconciled with its puzzling features, which seem to set it apart from all the usual empirical sciences? This book offers a short but systematic introduction to the philosophy of m…Read more
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Dummett on Indefinite ExtensibilityPhilosophical Issues 28 (1): 196-220. 2018.
Oslo, Norway
Areas of Specialization
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Science, Logic, and Mathematics |
Logic and Philosophy of Logic |
Philosophy of Mathematics |
Metaphysics |
Ontology |
Metaontology |
Modality |
Gottlob Frege |
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PhilPapers Editorships
Philosophy of Mathematics |