Categorical Logic was invented by Aristotle, and presupposes his system of categories. To understand how it works, we have to know the method Aristotle used to classify things into categories. For Aristotle, an individual substance is not just an individual. It is always a member of a kind or category. Fido is not just Fido, he is also a dog. Socrates is not just Socrates, he is also a man. By itself, this principle was probably not very innovative even in Aristotle’s time. In order to talk about the world at all, we need words that refer to the kinds of things that we encounter in it: words like dog, chair, football…