more from William D. Hart

Single Idea 13476

[catalogued under 12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori]

Full Idea

In the case of the parallels postulate, Euclid's fifth axiom (the whole is greater than the part), and comprehension, saying was believing for a while, but what was said was false. This should make a shrewd philosopher sceptical about a priori knowledge.

Gist of Idea

The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori


William D. Hart (The Evolution of Logic [2010], 2)

Book Reference

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.53

A Reaction

Euclid's fifth is challenged by infinite numbers, and comprehension is challenged by Russell's paradox. I can't see a defender of the a priori being greatly worried about these cases. No one ever said we would be right - in doing arithmetic, for example.