Defending the Axioms: On the Philosophical Foundations of Set Theory

Oxford University Press (2011)
Abstract
Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. For nearly a century, the axioms of set theory have played this role, so the question of how these axioms are properly judged takes on a central importance. Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolates the appropriate methods for such evaluations and investigates the ontological and epistemological backdrop that makes them appropriate. In the end, a new account of the objectivity of mathematics emerges, one refreshingly free of metaphysical commitments.
Keywords Axiomatic set theory  Axiomatic set theory Philosophy  Axioma's  Axiomatische methode  Axiomatische Methode  Mengenlehre  Philosophie
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Call number QA248.M276 2011
ISBN(s) 9780199596188
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Rodrigo A. Freire (2012). On Existence in Set Theory. Notre Dame Journal of Formal Logic 53 (4):525-547.
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