A classically trained mathematician is more likely to be familiar (at least anecdotally) with an area of mathematical physics such as deformation quantization than with Intuitionistic logic. It is helpful in any sense (philosophical or mathematical) to think of Intuitionistic logic as a quantization of classical logic? Has anyone explored such an approach? Note that the idea itself of comparing the passage from classical to intuitionistic logic to denying commutativity is not new; see Richman's "Interview with a constructive mathematician" at http://www.ams.org/mathscinet-getitem?mr=1400617