### Single Idea 18760

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

Full Idea

One of the culminating achievements of Euclidean geometry was categorical axiomatisations, that describe the geometric structure so completely that any two models of the axioms are isomorphic. The axioms are second-order.

Gist of Idea

The culmination of Euclidean geometry was axioms that made all models isomorphic

Source

Vann McGee (Logical Consequence [2014], 7)

Book Reference

'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.45

A Reaction

[He cites Veblen 1904 and Hilbert 1903] For most mathematicians, categorical axiomatisation is the best you can ever dream of (rather than a single true axiomatisation).

Related Idea

Idea 10246
The limit of science is isomorphism of theories, with essences a matter of indifference **[Weyl]**