### Single Idea 18218

#### [catalogued under 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics]

Full Idea

Facts about geometric laws receive satisfying explanations, by the intrinsic facts about physical space, i.e. those laid down without reference to numbers in Hilbert's axioms.

Gist of Idea

Hilbert explains geometry, by non-numerical facts about space

Source

Hartry Field (Science without Numbers [1980], 3)

Book Reference

Field,Hartry: 'Science without Number' [Blackwell 1980], p.27

A Reaction

Hilbert's axioms mention points, betweenness, segment-congruence and angle-congruence (Field 25-26). Field cites arithmetic and geometry (as well as Newtonian mechanics) as not being dependent on number.