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You mean mathematicians? CS majors also all study logic to some degree. I think we have enough of both in AI. Philosophers of mind, not so much.
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Logicians are typically part of the philosophy department, at least in the US.
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You do realize that propositional logic, set theory, and mapping the limits of formal systems are philosophy, right? You're literally describing mathematical logic and philosophy of language.
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Logicians' training is so different from philosophers' that it should be considered a separate discipline, or under the branch of computer science.
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When I was a young man I took three philosophy courses from a very old man who, when he was a young man, was the dissertation director of Alan Turing. The latter, by the way, was an habitué of the seminar of Wittgenstein.
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I studied it getting my CS degree - you can literally write mathematical formulas using symbols and you can perform operations in logic. Very different from a philosophy class - excuse me if you were already aware.
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