Defending the Axioms
On the Philosophical Foundations of Set Theory
Seiten
2013
Oxford University Press (Verlag)
978-0-19-967148-9 (ISBN)
Oxford University Press (Verlag)
978-0-19-967148-9 (ISBN)
Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. The axioms of set theory have long played this role, so the question of how they are properly judged is of central importance. Maddy discusses the appropriate methods for such evaluations and the philosophical backdrop that makes them appropriate.
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.
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.
Penelope Maddy is Distinguished Professor of Logic and Philosophy of Science at the University of California, Irvine. She is the author of Naturalism in Mathematics (OUP, 1997), Realism in Mathematics (OUP, 1992), and Second Philosophy (OUP, 2007).
Introduction ; 1. The Problem ; 2. Proper Method ; 3. Thin Realism ; 4. Arealism ; 5. Morals ; Bibliography
| Erscheint lt. Verlag | 13.3.2013 |
|---|---|
| Verlagsort | Oxford |
| Sprache | englisch |
| Maße | 141 x 216 mm |
| Gewicht | 202 g |
| Themenwelt | Geisteswissenschaften ► Philosophie ► Logik |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| Naturwissenschaften | |
| ISBN-10 | 0-19-967148-6 / 0199671486 |
| ISBN-13 | 978-0-19-967148-9 / 9780199671489 |
| Zustand | Neuware |
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