more from Philip Kitcher

Single Idea 12392

[catalogued under 6. Mathematics / A. Nature of Mathematics / 1. Mathematics]

Full Idea

Proposals for a priori mathematical knowledge have three main types: conceptualist (true in virtue of concepts), constructivist (a construct of the human mind) and realist (in virtue of mathematical facts).

Gist of Idea

Mathematical a priorism is conceptualist, constructivist or realist

Source

Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.3)

Book Reference

Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.46


A Reaction

Realism is pure platonism. I think I currently vote for conceptualism, with the concepts deriving from the concrete world, and then being extended by fictional additions, and shifts in the notion of what 'number' means.