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402Absence perception and the philosophy of zeroSynthese 197 (9): 3823-3850. 2020.Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent work i…Read more
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316Independence and Ignorance: How agnotology informs set-theoretic pluralismJournal of the Indian Council of Philosophical Research 34 (2): 399-413. 2017.Much of the discussion of set-theoretic independence, and whether or not we could legitimately expand our foundational theory, concerns how we could possibly come to know the truth value of independent sentences. This paper pursues a slightly different tack, examining how we are ignorant of issues surrounding their truth. We argue that a study of how we are ignorant reveals a need for an understanding of set-theoretic explanation and motivates a pluralism concerning the adoption of foundational …Read more
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255Richness and ReflectionPhilosophia Mathematica 24 (3): 330-359. 2016.A pervasive thought in contemporary philosophy of mathematics is that in order to justify reflection principles, one must hold universism: the view that there is a single universe of pure sets. I challenge this kind of reasoning by contrasting universism with a Zermelian form of multiversism. I argue that if extant justifications of reflection principles using notions of richness are acceptable for the universist, then the Zermelian can use similar justifications. However, I note that for some f…Read more
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University of OsloDepartment of Philosophy, Classics, History of Art and IdeasPost-doctoral Fellow
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Singapore, Singapore
Areas of Specialization
Science, Logic, and Mathematics |
Metaphysics and Epistemology |
Areas of Interest
Science, Logic, and Mathematics |
Metaphysics and Epistemology |
Philosophy, Misc |