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Full Idea
I think logic, arithmetic and geometry are subject to Quine's empirical revisability argument: quantum logic may turn out to be the best overall theory; so these things are justified a posteriori.
Clarification
Quantum logic is built on the uncertainties of quantum mechanics
Gist of Idea
Logic, arithmetic and geometry are revisable and a posteriori; quantum logic could be right
Source
comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Paul Horwich - Stipulation, Meaning and Apriority §11
Book Ref
'New Essays on the A Priori', ed/tr. Boghossian,P /Peacocke,C [OUP 2000], p.168
A Reaction
Not much of an argument, because 'quantum logic' may also turn out to be a will-o'-the-whisp. Until it is established (which I doubt, because quantum theory is so poorly understood), I think we should be highly suspicious of the Quinean view.
| 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] |