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Is there more than one form of logic in mathematics? I would be inclined that mathematics only cover one type of formal logic, but I would be interested to know if there are variants thereof or completely different logics than what we're taught in university. In philosophy, there are several logics, but in mathematics it seems there's only one, or at least only one that's prevalent.

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    Hard to say what you mean by "form of logic", but there are parts of mathematics that are based on non-classical logics, constructive mathematics and paraconsistent mathematics are the most prominent. – Conifold Dec 15 '20 at 5:22
  • There is the syntactic and semantic. – Elliot Dec 15 '20 at 5:45
  • Mathematics is not limited to any kind of logical system since it doesn't describe directly any phenomena. Scientist uses mathematical tools to interpret and describe the phenomena they're studying. In fact, with math, you can conceive any kind of logic! Richard Feynman described this nicely in his lectures on the character of physical law. – Marino Proton Dec 15 '20 at 6:47
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