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]