philosophy of mathematics

This article is about philosophical issues raised by the nature of mathematics. For influences of mathematical studies and methods on philosophy, see Mathematical philosophy.

The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics, and purports to provide a viewpoint of the nature and methodology of mathematics, and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.

Contents

• 1Recurrent themes
• 2History
  • 2.1Contemporary philosophy
• 3Major themes
  • 3.1Mathematical realism
  • 3.2Mathematical anti-realism
• 4Contemporary schools of thought
  • 4.1Platonism
  • 4.2Mathematicism
  • 4.3Logicism
  • 4.4Formalism
  • 4.5Conventionalism
  • 4.6Intuitionism
    • 4.6.1Constructivism
    • 4.6.2Finitism
  • 4.7Structuralism
  • 4.8Embodied mind theories
    • 4.8.1Aristotelian realism
    • 4.8.2Psychologism
    • 4.8.3Empiricism
  • 4.9Fictionalism
  • 4.10Social constructivism
  • 4.11Beyond the traditional schools
    • 4.11.1Unreasonable effectiveness
    • 4.11.2Popper's two senses
    • 4.11.3Philosophy of language
• 5Arguments
  • 5.1Indispensability argument for realism
  • 5.2Epistemic argument against realism
• 6Aesthetics
• 7Journals
• 8See also
  • 8.1Related works
  • 8.2Historical topics
• 9Notes
• 10Further reading
• 11External links