Single Idea 17776

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics]

Full Idea

The ultimate principles upon which mathematics rests are those to which mathematicians appeal without proof; and the primitive concepts of mathematics ...themselves are grasped directly, if grasped at all, without the mediation of definition.

Gist of Idea

The ultimate principles and concepts of mathematics are presumed, or grasped directly


John Mayberry (What Required for Foundation for Maths? [1994], p.405-1)

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.405

A Reaction

This begs the question of whether the 'grasping' is purely a priori, or whether it derives from experience. I defend the latter, and Jenkins puts the case well.