philosophy of mathematics

Introduction
Mathematical Platonism
- Formal definition
- Nontraditional versions
Mathematical anti-Platonism
- Realistic anti-Platonism
- Nominalism
Logicism, intuitionism, and formalism
Mathematical Platonism: for and against
- The Fregean argument for Platonism
- The epistemological argument against Platonism
- Ongoing impasse

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philosophy of mathematics summary

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External Websites

Stanford Encyclopedia of Philosophy - Philosophy of Mathematics

Gottlob Frege German philosopher of mathematics, logic, and language Gottlob Frege.

philosophy of mathematics

Written by

Mark Balaguer

Professor of Philosophy, California State University, Los Angeles. Author of Platonism and Anti-Platonism in Mathematics.

Mark Balaguer

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History

philosophy of mathematics, branch of philosophy that is concerned with two major questions: one concerning the meanings of ordinary mathematical sentences and the other concerning the issue of whether abstract objects exist. The first is a straightforward question of interpretation: What is the best way to interpret standard mathematical sentences and theories? In other words, what is really meant by ordinary mathematical sentences such as “3 is prime,” “2 + 2 = 4,” and “There...

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