Defending the Axioms: On the Philosophical Foundations of Set Theory

Defending the Axioms: On the Philosophical Foundations of Set Theory
Genre: 
Language: 
ISBN10: 
0199596182
ISBN13: 
9780199596188
Pages: 
144
Published: 
January 27th 2011 by OUP Oxford
Rating: 
3.73

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.

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