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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
Source
William D. Hart (The Evolution of Logic [2010], 2)
Book Ref
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.
| 24138 | Strongly believed a priori is not certain; it may just be a feature of our existence [Nietzsche] |
| 23485 | No pictures are true a priori [Wittgenstein] |
| 9338 | Quine's objections to a priori knowledge only work in the domain of science [Horwich on Quine] |
| 9337 | Science is empirical, simple and conservative; any belief can hence be abandoned; so no a priori [Quine, by Horwich] |
| 9340 | Logic, arithmetic and geometry are revisable and a posteriori; quantum logic could be right [Horwich on Quine] |
| 20961 | What is considered a priori changes as language changes [Habermas, by Bowie] |
| 18272 | Platonism defines the a priori in a way that makes it unknowable [Coffa] |
| 9356 | The idea of the a priori is so obscure that it won't explain anything [Devitt] |
| 19564 | Some knowledge must be empirical; naturalism implies that all knowledge is like that [Devitt] |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| 9384 | We may have strong a priori beliefs which we pragmatically drop from our best theory [Boghossian] |