What are the practical uses of Categorical Syllogisms?

[BaalChatzaf]

I have been doing mathematics since I was 11 years old, when I taught myself differential calculus. In all that time (some 62 years) I have yet to use categorical syllogisms to prove a theorem. I have yet to see a single mathematical proof in the journals using categorical syllogisms. Most of the reasoning in the math journals is an informal version of Natural Deduction which is ground on first order predicate logic. In my own work I have used First and Second Order logic, modal logic, Boolean algebra and relational algebra (the underlying formalism of relational databases). This is in addition to the usual mathematical equipment such as real and complex analysis, number theory, topology, differential equations and such like. I have yet to resort to explicit use of categorical syllogisms except for standard like chained set inclusion and stuff easily expressible in set algebra. Almost all my reasoning is based on conditional logic with modus ponens, univesal instantiation and existential instantiation and generalization being the main workhorses. Well.... every now and again I resort to a Venn diagram.

Perhaps one of you scholars out there who is well grounded in classical logic (the logic of Categorical Statements and Categorical Syllogisms) could give a brief account of the practical applications of classic categorical logic.

Ba'al Chatzaf