Single Idea 14151

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

Full Idea

As a branch of pure mathematics, geometry is strictly deductive, indifferent to the choice of its premises, and to the question of whether there strictly exist such entities. It just deals with series of more than one dimension.

Gist of Idea

Pure geometry is deductive, and neutral over what exists

Source

Bertrand Russell (The Principles of Mathematics [1903], §352)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.372


A Reaction

This seems to be the culmination of the seventeenth century reduction of geometry to algebra. Russell admits that there is also the 'study of actual space'.