Full Idea
The constructivist position I defend claims that mathematics is an idealized science of operations which can be performed on objects in our environment. It offers an idealized description of operations of collecting and ordering.
Gist of Idea
My constructivism is mathematics as an idealization of collecting and ordering objects
Source
Philip Kitcher (The Nature of Mathematical Knowledge [1984], Intro)
Book Reference
Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.12
A Reaction
I think this is right. What is missing from Kitcher's account (and every other account I've met) is what is meant by 'idealization'. How do you go about idealising something? Hence my interest in the psychology of abstraction.