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Is quantum logic producing interesting/different mathematics?

Is it different from the intuitionist approach to mathematics? How?

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    $\begingroup$ I'm not sure I understand the question. Quantum logic is a branch of mathematics, and it is different from other branches (that's why it has its own name), so in that sense, it is certainly producing interesting and different mathematics. $\endgroup$ Feb 26, 2011 at 22:05
  • $\begingroup$ Why would you expect quantum logic to be the same as intuitionism? $\endgroup$ Feb 26, 2011 at 23:26
  • $\begingroup$ @Qiaochu I was under the impression that if you change the laws of logic, a lot of proofs become invalid, and that makes different mathematics. @Jim From the little I know, quantum logic talks about prepositions that neither have true nor false value, which reminds me of the intuitionist approach. $\endgroup$
    – Uri
    Feb 27, 2011 at 9:49
  • $\begingroup$ I don't think people use quantum logic that way, but I could be wrong. $\endgroup$ Feb 27, 2011 at 12:22

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There is an approach to quantum logic where you get topoi with quantum logic. An elementary topos is sometimes regarded as a "place" where you can do mathematics, but where classical logic doesn't necessarily apply. Thus you get a different sort of mathematics.

I know very little about these quantum topoi, so I cannot detail in what way their mathematics differ from the classical one. But I think the two articles referenced in the below PlanetMath articles may (or may not - I haven't read them) answer your question.

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