nLab
Platonism

Contents

Contents

Idea

Platonism is a position in philosophy committed to the existence of abstract entities that derives from the theory of ideas of the Greek philosopher Plato.

Since this attitude provides a convenient ontological underpinning for mathematical concepts, platonism is one of the major schools of thought in the philosophy of mathematics as well as in spontaneous affinity with the practice of ‘every-day mathematics’ with its feel of objectivity and free availability of non-constructive classical modes of reasoning.

Famous mathematicians like Georg Cantor, Gottlob Frege, Kurt Gödel or more recently Alain Connes and Roger Penrose have advocated views akin to platonism.

References

A classical reference is

  • Paul Bernays , Sur le platonisme dans les mathématiques , L’enseignement mathématique 34 (1935) pp.52-69. (pdf)

Other texts include

  • Mark Balaguer, Platonism & Anti-Platonism in Mathematics , Oxford University Press, 1998.

  • Barry Mazur, Mathematical Platonism and its Opposites . (pdf)

Last revised on October 8, 2018 at 06:02:10. See the history of this page for a list of all contributions to it.