Single Idea 18065

[catalogued under 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism]

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]