Single Idea 18156

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

Full Idea

A modern axiomatisation of geometry, such as Hilbert's (1899), does not need to claim the existence of real numbers anywhere in its axioms.

Gist of Idea

Modern axioms of geometry do not need the real numbers

Source

David Bostock (Philosophy of Mathematics [2009], 9.B.5.ii)

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.295


A Reaction

This is despite the fact that geometry is reduced to algebra, and the real numbers are the equivalent of continuous lines. Bostock votes for a Greek theory of proportion in this role.

Related Idea

Idea 18150 Actual measurement could never require the precision of the real numbers [Bostock]