Aristotle’s treatment of logical categories commits him to asserting a strong link between language and reality. To take a salient point, it is not clear whether his ten categories are meant to denote the ten kinds of being that exist or the ten kinds of predicates we can use in language. It seems most likely that he is suggesting both. That is, there are ten kinds of predicates we can use in language, and these ten predicates denote the ten kinds of being that exist. In other words, the structure of language mirrors the structure of the world. This is not a ridiculous assumption to make, but neither is it an obvious one. There has been much philosophical debate in the twentieth century as to the degree to which ordinary language reveals the structure of the world to us and the degree to which it obscures the structure of the world from us. As we see in the Metaphysics, Aristotle’s ten categories, his conception of definition, his five “predicables,” and his conception of first principles all loom large not just as means of making sense of the world but also as the fundamental struts on which reality itself is built.

When Aristotle talks about knowledge as requiring demonstration, he is using the word knowledge in a much narrower sense than what we usually think of when we use the word. This term is a rough translation of the Greek term epistêmê, which specifically denotes knowledge of a scientific or rigorously proven kind. In saying that such knowledge requires demonstration, Aristotle is showing the influence of his teacher, Plato, who insists on distinguishing knowledge, which must be justified, from mere true belief. Demonstration establishes that we not only know a certain fact but can show why it must necessarily be so and why it could not be otherwise. This conception of scientific knowledge is quite a step away from our current conception of science, which relies fundamentally on hypothesis and experiment rather than on logically rigorous demonstration. As a means of showing that something is necessarily as it is and could not possibly be otherwise, demonstration is closely linked with Aristotle’s conception of definition. Both of these terms intend to get to the heart of a matter, to show what it really is rather than what it appears to be on the surface.

Aristotle’s claim that substance is the primary category figures prominently in his Metaphysics, but the claim itself is far from certain. On the surface, it makes intuitive sense. We are inclined to think that rocks and trees and pigeons are more real somehow than the colors or qualities or numbers that we might associate with them. However, it is very difficult to show exactly how and why substances are primary. Aristotle argues that substance can exist without quality or any of the other categories, but none of those categories can exist without substance. Certainly, it is hard to imagine any of those other categories in a universe without substance, but it is equally difficult to imagine a substance that has no qualities, or no location, or that sits outside of time. In the Metaphysics, Aristotle reconsiders his conception of substance, so that species, and not individual particulars, become the fundamental substances that make up reality, but this does not help to resolve the difficulty of showing why substance should be prior to the other categories in the first place.