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person1970s-present

Penelope Maddy

Disciplines:
philosophy of science
philosophy of mathematics

Summary

American philosopher who developed a naturalistic account of mathematics — defending mathematical realism on empiricist grounds — and then moved to a second philosophy naturalizing the study of mathematical practice.

Core Contribution

Realism in Mathematics: sets are perceivable physical objects (set-theoretic realism grounded in cognition). Second Philosophy: philosophy should adopt the methods of natural science; mathematical practice should be studied as it actually unfolds, not judged by external philosophical standards.

Key Spikes & Highlights

  • Argued that the axiom of choice and the axiom of foundation can be evaluated by their role in mathematical practice, not by metaphysical argument — a genuinely naturalistic approach.
  • Changed her mind significantly between Realism in Mathematics (1990) and Second Philosophy (2007) — the set-theoretic realism of the first was abandoned for a more thoroughgoing naturalism.

Notable Works & Achievements

Realism in Mathematics

Naturalism in Mathematics

Second Philosophy

Defending the Axioms

Historical Influences

W. V. O. Quine Paul Benacerraf Kurt Gödel

Intellectual Lineage

Analytic Philosophy Quinean Naturalism

Contemporaries & Peers

Stewart Shapiro Hartry Field

Minds Influenced

No recorded minds influenced.

Intellectual Posterity

Naturalism in Mathematics Second Philosophy

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