more from Immanuel Kant

Single Idea 16917

[catalogued under 6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics]

Full Idea

Space and time are the two intuitions on which pure mathematics grounds all its cognitions and judgements that present themselves as at once apodictic and necessary.


'apodictic' means demonstrable

Gist of Idea

All necessary mathematical judgements are based on intuitions of space and time


Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 284)

Book Reference

Kant,Immanuel: 'Prolegomena to Any Future Metaphysic', ed/tr. Lucas,Peter G. [Manchester UP 1971], p.39

A Reaction

This unlikely proposal seems to be based on the idea that mathematics must arise from the basic categories of our intuition, and these two are the best candidates he can find. I would say that high-level generality is the basis of mathematics.