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.

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.

Logicians' training is so different from philosophers' that it should be considered a separate discipline, or under the branch of computer science.