Aristotle, Boole, and Categories
نویسنده
چکیده
We propose new axiomatizations of the 24 assertoric syllogisms of Aristotle’s syllogistic, and the 2 n n-ary operations of Boole’s algebraic logic. The former organizes the syllogisms as a 6 × 4 table partitioned into four connected components according to which term if any must be inhabited. We give two natural-deduction style axiomatizations, one with four axioms and four rules, the second with one axiom and six rules. The table provides immediately visualizable proofs of soundness and completeness. We give an elementary category-theoretic semantics for the axioms along with criteria for determining the term if any required to be nonempty in
منابع مشابه
Notes oN the FouNdiNg oF Logics aNd MetaLogic: aristotLe, BooLe, aNd tarski
This paper is more a series of notes than a scholarly treatise. It focuses on certain achieve‐ ments of Aristotle, Boole and Tarski. The notes presented here using concepts introduced or formalized by Tarski contribute toward two main goals: comparing Aristotle’s system with one Boole constructed intending to broaden and to justify Aristotle’s, and giving a modern perspective to both logics. ...
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