Single Idea 18068

[catalogued under 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism]

Full Idea

I want to suggest both that arithmetic owes its truth to the structure of the world and that arithmetic is true in virtue of our constructive activity.

Gist of Idea

Arithmetic is made true by the world, but is also made true by our constructions

Source

Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2)

Book Reference

Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.108


A Reaction

Well said, but the problem seems no more mysterious to me than the fact that trees grow in the woods and we build houses out of them. I think I will declare myself to be an 'empirical constructivist' about mathematics.