We’ve begun categorical syllogisms. Don’t worry if you’re still not getting the whole thing; there are a lot of working parts, but once you start keeping track of them, they snap together beautifully.

To diagram categorical propositions, we used biliteral diagrams, two-term diagrams. That makes sense: categorical propositions have a subject term and a predicate term. But categorical syllogisms have three propositions (two premises and a conclusion), each with their own subject term and predicate term. How are we going to handle that?

Each of the three has its own subject and predicate terms, so we need a new vocabulary to help us keep things straight. Take an argument like the following:

All birds fly. All things that fly have feathers. Therefore all birds have feathers.

Assume that the universe of discourse is ‘Things’. Notice that terms show up more than once. ‘Birds’ is in the first premise and the conclusion. ‘(Things that) fly’ is in the first and second premise. And ‘(things that) have feathers’ is in the second premise and the conclusion.

The minor term of the argument is the term we find in the subject of the conclusion. So the minor term of this argument is ‘Birds’. The minor term is always in one of the premises. This premise is called the minor premise.

The major term of the argument is the term we find in the predicate of the conclusion. So the major term of this argument is ‘(Things that) have feathers’. The major term is always in the other premise. This premise is called the major premise. By tradition the major premise is listed first, but we won’t worry about that for our class, so I haven’t bothered with it here.

There is a third term that is not found in the conclusion, but is shared by the premises. This is called the middle term. It’s what makes the argument work: it’s the in-between term that links the minor term and the major term. Without it, they would be stuck in separate premises; but with the middle term, they can be united into a conclusion. Note that the middle term is never found in the conclusion.

A categorical syllogism is an argument that links a minor term and a major term using a middle term. To diagram it we need a diagram that includes each of these three terms. Thus we get our triliteral diagram. So far in class we’ve just looked at one example: we’ll need to look at more to get a better view of what is going on.