### Single Idea 18221

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

Full Idea

There are two approaches to axiomatising geometry. The 'metric' approach uses a function which maps a pair of points into the real numbers. The 'synthetic' approach is that of Euclid and Hilbert, which does without real numbers and functions.

Gist of Idea

'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space

Source

Hartry Field (Science without Numbers [1980], 5)

Book Reference

Field,Hartry: 'Science without Number' [Blackwell 1980], p.42

Related Idea

Idea 18218
Hilbert explains geometry, by non-numerical facts about space **[Field,H]**