more from David Hilbert

Single Idea 9546

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry]

Full Idea

Hilbert's geometrical axioms were existential in character, asserting the existence of certain geometrical objects (points and lines). Euclid's postulates do not assert the existence of anything; they assert the possibility of certain constructions.

Gist of Idea

Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects


report of David Hilbert (Foundations of Geometry [1899]) by Charles Chihara - A Structural Account of Mathematics 01.1

Book Reference

Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.9

A Reaction

Chihara says geometry was originally understood modally, but came to be understood existentially. It seems extraordinary to me that philosophers of mathematics can have become more platonist over the centuries.