Author Description
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.
Menrva's Summary
THE THESIS
This book investigates the criteria used to evaluate the fundamental axioms of set theory within the framework of mathematical practice. Penelope Maddy, a prominent philosopher of mathematics, employs a naturalistic approach—often termed the 'second-philosophical' perspective—to examine how mathematicians justify their foundational assumptions. By analyzing the ontological and epistemological requirements of these axioms, she constructs an account of mathematical objectivity that avoids traditional metaphysical baggage.
THE SCOPE MAP
What You Will Find
- A naturalistic methodology for assessing mathematical foundations
- Analysis of the role of axioms in set theory
- Examination of the relationship between mathematical practice and philosophical justification
Scope Limits
- Does not provide a comprehensive history of all set-theoretic developments
- Does not engage deeply with non-naturalistic or purely platonist metaphysical arguments
THE AUTHORITY PERSPECTIVE
Experts recognize this work as a significant contribution to the philosophy of mathematics, particularly for its rigorous application of naturalism to foundational questions. Readers frequently note the technical density of the prose, which assumes a solid background in both set theory and analytic philosophy.
Page Count:
161
Publication Date:
2011-01-01
Publisher:
Oxford University Press, USA
ISBN-10:
0191616532
ISBN-13:
9780191616532
Philosophy
Logic
Set Theory
Epistemology
Mathematics
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