Defending the Axioms

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.