Full Idea
I propose that a very limited amount of our mathematical knowledge can be obtained by observations and manipulations of ordinary things. Upon this small base we erect the powerful general theories of modern mathematics.
Gist of Idea
We derive limited mathematics from ordinary things, and erect powerful theories on their basis
Source
Philip Kitcher (The Nature of Mathematical Knowledge [1984], 05.2)
Book Reference
Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.92
A Reaction
I agree. The three related processes that take us from the experiential base of mathematics to its lofty heights are generalisation, idealisation and abstraction.
Related Idea
Idea 18069 Arithmetic is an idealizing theory [Kitcher]