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I'm looking for references on applications of logic (e.g. intuitionistic logic, toposes) to physics (especially quantum physics, as this is the area that I'm aware can be helped by logical considerations, but I'm open to other areas as well).

My motivation is that I read/heard multiple times that quantum physics could be well apprehended through, say, topos theory (I've heard the following sentence, which was probably an exageration : "The laws of quantum physics are the same laws as those of classical physics, but interpreted in a different topos"); but also I know that there's a thing called quantum logic even though I don't know much about it.

The references could be either technical ones (but if possible self-contained, or at least not requiring too much bagage in physics) or sort of vulgarized, not too technical ones (though I would want a bit more than "oh it can be applied, and it's interesting"), I don't really mind.

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  • $\begingroup$ Not certain, but I understand the quantum logic isn't used much by physicists these days. It looks like classical logic reigns supreme in physics as in most other fields. $\endgroup$ – Dan Christensen Aug 28 '18 at 22:27
  • $\begingroup$ @DanChristensen : yes surely classical logic reigns supreme but other logics could have some interesting insights/applications $\endgroup$ – Max Aug 28 '18 at 22:41
  • $\begingroup$ Are there any proofs obtained using these other logics that could not be obtained through more conventional means with a bit of effort? It seems that proofs in all formal logics can be verified using ordinary digital computers (turing machines?) which themselves are based on classical logic. Just a hunch, but perhaps there is something universal about classical logic. $\endgroup$ – Dan Christensen Aug 29 '18 at 2:30
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    $\begingroup$ @DanChristensen not half the rules, just one. But removing a rule allows you to add axioms that would otherwise be contradictory. I know for a fact that some people are envisioning topos theory for instance as a way of making sense of quantum physics, so if you're just going to say "classical logic is enough", it's really not going to be useful for my question $\endgroup$ – Max Aug 29 '18 at 17:05
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    $\begingroup$ @Max There are tons of references to this kind of thing on nLab e.g. the Bohr Topos, the Geometry of Physics, and various works by Urs Schreiber. A lot of these are fairly technical, geared more at addressing issues in quantum field theory. More generally are ideas related to cohesion. Also what's produced is usually an intuitionistic type theory, not just a logic. $\endgroup$ – Derek Elkins Aug 29 '18 at 21:44

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