more from Peter Geach

Single Idea 10735

[catalogued under 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism]

Full Idea

For an understanding of arithmetic the grasp of an operation's being performed 'so many times' is quite indispensable; and abstraction of a feature from groups of nuts cannot give us this grasp.

Gist of Idea

Abstraction from objects won't reveal an operation's being performed 'so many times'


Peter Geach (Abstraction Reconsidered [1983], p.170)

Book Reference

'Knowledge and Mind', ed/tr. Ginet,C/Shoemaker,S [OUP 1983], p.170

A Reaction

I end up defending the empirical approach to arithmetic because remarks like this are so patently false. Geach seems to think we arrive ready-made in the world, just raring to get on with some counting. He lacks the evolutionary perspective.