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Naturalism in Mathematics
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Naturalism in Mathematics

Penelope Maddy

Abstract

It is well known that certain natural statements of set theory, like Cantor's continuum hypothesis (CH), cannot be proved or disproved on the basis of the standard axioms (Zermelo–Fraenkel with Choice or ZFC). Some philosophers take this to be the end of the story on these questions, but set theorists continue to look for answers by investigating candidates for new axioms. One way to understand this work, an approach pioneered by Gödel, is to embrace some brand of realism (sometimes called ‘Platonism’) about sets: there is an objective world of sets in which the CH is either true or false; ZFC ... More

Keywords: Axiom of Constructibility, Cantor, continuum hypothesis, Zermelo–Fraenkel, Gödel, Penelope Maddy, naturalism, philosophy of mathematics, Platonism, Quine, realism, scientific method, set theory, Wittgenstein

Bibliographic Information

Print publication date: 2000 Print ISBN-13: 9780198250753
Published to Oxford Scholarship Online: November 2003 DOI:10.1093/0198250754.001.0001

Authors

Affiliations are at time of print publication.

Penelope Maddy, author
University of California, Irvine
Author Webpage