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.