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 Reference
'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.