syllogism

In his book "Prior Analytics," Aristotle works out the logic of “the categorical syllogism.”

A syllogism is any argument that has a conclusion supported by two premises.

A syllogism is “categorical” if the conclusion and two premises are of categorical form, that is, is a sentence of the type “All A are B,” “No A are B,” “Some A are B,” or “Some A are not B.”

It turns out that there are 256 ways to arrange three categorical sentences into a syllogism.

A categorical syllogism includes three categories, call them A, B, and C. One premise would involve A and B, the other would relate B and C, and then the conclusion would be a statement about A and C. So, if we were going to move from representing single propositions to illustrating the entire syllogism, we need a new sort of diagram, the one with three interlocking circles that Vice President Harris is so enamored with.