Single Idea 14153

[catalogued under 6. Mathematics / A. Nature of Mathematics / 2. Geometry]

Full Idea

The approach to practical geometry of the empiricists, notably Mill, was to show that no other set of premisses would give results consistent with experience.

Gist of Idea

In geometry, empiricists aimed at premisses consistent with experience

Source

Bertrand Russell (The Principles of Mathematics [1903], §353)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.373


A Reaction

The modern phrase might be that geometry just needs to be 'empirically adequate'. The empiricists are faced with the possibility of more than one successful set of premisses, and the idealist don't know how to demonstrate truth.

Related Idea

Idea 14152 In geometry, Kant and idealists aimed at the certainty of the premisses [Russell]