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Frege and arbitrary functionsIn William Demopoulos (ed.), Frege's philosophy of mathematics, Harvard University Press. pp. 89--107. 1995.
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Set TheoryCambridge University Press. 2022.Set theory is a branch of mathematics with a special subject matter, the infinite, but also a general framework for all modern mathematics, whose notions figure in every branch, pure and applied. This Element will offer a concise introduction, treating the origins of the subject, the basic notion of set, the axioms of set theory and immediate consequences, the set-theoretic reconstruction of mathematics, and the theory of the infinite, touching also on selected topics from higher set theory, con…Read more
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Mathematics, Models, and Modality: Selected Philosophical EssaysCambridge University Press. 2008.John Burgess is the author of a rich and creative body of work which seeks to defend classical logic and mathematics through counter-criticism of their nominalist, intuitionist, relevantist, and other critics. This selection of his essays, which spans twenty-five years, addresses key topics including nominalism, neo-logicism, intuitionism, modal logic, analyticity, and translation. An introduction sets the essays in context and offers a retrospective appraisal of their aims. The volume will be o…Read more
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A Subject with No Object. Strategies for Nominalistic Interpretations of MathematicsNoûs 33 (3): 505-516. 1999.
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Logic, Mathematics, Science. Quine's Philosophy of Logic and MathematicsIn Gilbert Harman & Ernest LePore (eds.), A Companion to W. V. O. Quine, Wiley-blackwell. 2013.
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