The Categories, traditionally interpreted as an introduction to Aristotle’s logical work, divides all of being into ten categories. These ten categories are as follows:

Substance, which in this context means what something is essentially (e.g., human, rock)

Of the ten, Aristotle considers substance to be primary, because we can conceive of a substance without, for example, any given qualities but we cannot conceive of a quality except as it pertains to a particular substance. One important conclusion from this division into categories is that we can make no general statements about being as a whole because there are ten very different ways in which something can have being. There is no common ground between the kind of being that a rock has and the kind of being that the color blue has.

Aristotle’s emphasis on the syllogism leads him to conceive of knowledge as hierarchically structured, a claim that he fleshes out in the Posterior Analytics. To have knowledge of a fact, it is not enough simply to be able to repeat the fact. We must also be able to give the reasons why that fact is true, a process that Aristotle calls demonstration. Demonstration is essentially a matter of showing that the fact in question is the conclusion to a valid syllogism. If some truths are premises that can be used to prove other truths, those first truths are logically prior to the truths that follow from them. Ultimately, there must be one or several “first principles,” from which all other truths follow and which do not themselves follow from anything. However, if these first principles do not follow from anything, they cannot count as knowledge because there are no reasons or premises we can give to prove that they are true. Aristotle suggests that these first principles are a kind of intuition of the universals we recognize in experience.

Aristotle believes that the objects of knowledge are also structured hierarchically and conceives of definition as largely a process of division. For example, suppose we want to define human. First, we note that humans are animals, which is the genus to which they belong. We can then take note of various differentia, which distinguish humans from other animals. For example, humans walk on two legs, unlike tigers, and they lack feathers, unlike birds. Given any term, if we can identify its genus and then identify the differentia that distinguish it from other things within its genus, we have given a definition of that term, which amounts to giving an account of its nature, or essence. Ultimately, Aristotle identifies five kinds of relationships a predicate can have with its subject: a genus relationship (“humans are animals”); a differentia relationship (“humans have two legs”); a unique property relationship (“humans are the only animals that can cry”); a definition, which is a unique property that explains the nature or essence of the subject; and an accident relationship, such as “some humans have blue eyes,” where the relationship does not hold necessarily.

While true knowledge is all descended from knowledge of first principles, actual argument and debate is much less pristine. When two people argue, they need not go back to first principles to ground every claim but must simply find premises they both agree on. The trick to debate is to find premises your opponent will agree to and then show that conclusions contrary to your opponent’s position follow necessarily from these premises. The Topics devotes a great deal of attention to classifying the kinds of conclusions that can be drawn from different kinds of premises, whereas the Sophistical Refutations explores various logical tricks used to deceive people into accepting a faulty line of reasoning.

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.