Is quantum logic producing interesting/different mathematics?
Is it different from the intuitionist approach to mathematics? How?
Is quantum logic producing interesting/different mathematics?
Is it different from the intuitionist approach to mathematics? How?
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.