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.