more from James Robert Brown

Single Idea 9641

[catalogued under 2. Reason / D. Definition / 2. Aims of Definition]

Full Idea

The standard requirement of definitions involves 'eliminability' (any defined terms must be replaceable by primitives) and 'non-creativity' (proofs of theorems should not depend on the definition).

Gist of Idea

Definitions should be replaceable by primitives, and should not be creative


James Robert Brown (Philosophy of Mathematics [1999], Ch. 7)

Book Reference

Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.94

A Reaction

[He cites Russell and Whitehead as a source for this view] This is the austere view of the mathematician or logician. But almost every abstract concept that we use was actually defined in a creative way.