Penelope Maddy

in Defending the Axioms

Published in print January 2011 | ISBN: 9780199596188
Published online May 2011 | e-ISBN: 9780191725395 | DOI:

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philogLogic/Philosophy of MathematicsphimetMetaphysics/Epistemology

Mathematics, as we all know, depends on proofs. And proofs, as we all know, have to begin somewhere, from some fundamental assumptions. In contemporary pure mathematics, the axioms of set theory are particularly salient, for reasons traced in Chapter I. In this case, the Euclidean ideal of postulates that are simply obvious or self-evident can't be the whole story, which raises two basic questions: what are the proper methods for defending set-theoretic axioms? and, why are these the proper methods? The first of these is the subject of ...

Chapter.  247 words. 

Subjects: Philosophy of Mathematics and Logic ; Metaphysics

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