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Defending the Axioms
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Defending the Axioms: On the Philosophical Foundations of Set Theory

Penelope Maddy

Abstract

Mathematics depends on proofs, and proofs have to begin somewhere, from some fundamental assumptions. Chapter I traces the historical rise of pure mathematics and the development of set theory, eventually axiomatic set theory, to play this foundational role for contemporary classical mathematics. Here 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? Chapter II introduces the meta-philosophical perspective, ca ... More

Keywords: axioms, epistemology, mathematical existence, mathematics, set-theoretic methods, objectivity, ontology, Second Philosophy, set theory, mathematical truth

Bibliographic Information

Print publication date: 2011 Print ISBN-13: 9780199596188
Published to Oxford Scholarship Online: May 2011 DOI:10.1093/acprof:oso/9780199596188.001.0001

Authors

Affiliations are at time of print publication.

Penelope Maddy, author
University of California, Irvine
Author Webpage