### Single Idea 21444

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 2. Geometry]

Full Idea

There is now 'pure' geometry, consisting of formal systems based on axioms for which truth is not claimed, and which are consequently not synthetic; and 'applied', a branch of physics, the truth of which is empirical, and therefore not a priori.

Gist of Idea

Modern geoemtry is either 'pure' (and formal), or 'applied' (and a posteriori)

Source

Sebastian Gardner (Kant and the Critique of Pure Reason [1999], 03 'Maths')

Book Reference

Gardner,Sebastian: 'Kant and the Critique of Pure Reason' [Routledge 1999], p.58

A Reaction

His point is that there is no longer any room for a priori geometry. Might the same division be asserted of arithmetic, or analysis, or set theory?