Where Aristotle saw problems in Plato’s theory, he was not shy to point them out. Quickly he seems to have elaborated his own theory of basic realities, his ontology, in contrast to Plato’s Theory of Forms. In his treatise The Categories, Aristotle offered an elegant and attractive theory to rival Plato’s. It was a short treatise, but dense, not at all reader-friendly like Plato’s best dialogues. Almost unintelligible on a first reading, it nonetheless introduced startling new conceptions with new vocabulary that would become Aristotle’s trademark jargon. It was undeniably brilliant, from start to finish.
Aristotle starts by distinguishing between words (legomena) and things (onta). Words can be either simple or combined. By ‘combined’ he means joined into a sentence, for instance the simple words ‘man’ and ‘runs’ can make up the sentence ‘(a) man runs.’ Things, on the other hand, can be either said-of a subject or in a subject—or not. [1] This distinction of things seems to make no sense, until he gives examples. The sentence ‘Socrates is pale’ implies that paleness is in Socrates. Being ‘in,’ in this sense, means the subject has it as a property. In the sentence ‘Socrates is a man,’ humanity is said-of Socrates. Humanity, in this case, is not just an incidental property, but it classifies Socrates, telling us what kind of thing he is. Similarly, ‘Paleness is a color’ tells what kind of thing paleness is. But paleness is an incidental property, not a defining characteristic.
Moreover, some things are always subjects and some things are always predicates, while some things can be both. Thus Socrates is always a subject, color is always a predicate, and Socrates’ paleness can be both: it is a predicate for Socrates, but a subject for color. Putting this all together, we get four classes arranged on two axes, as follows:
| universal | c) Man “secondary substance” | d) Whiteness |
| individual | a) Socrates “primary substance” | b) Soc’s pale complexion |
| substance (thing) | accident (attribute, property) |
This table, known as “the ontological square,” offers us a basic scheme of what there is in the world, according to Aristotle at least.[2] Aristotle designates the first column ‘substance’ (ousia), a word used by Plato with a different sense.[3] A substance for Aristotle is a particular object, (usually) a concrete physical thing like Socrates. The designates the second column ‘accident,’ signifying in incidental property something like Socrates has, such as his pale complexion.
The bottom row of the table presents particular or individual things; the top row presents kinds or classes of things. For instance, Socrates is a Man, i.e., a human being; his paleness is a Color. Aristotle invents a new name for the upper row: ‘universal’ (katholou, derived from the phrase kath’ holou ‘in general’).[4] While items on the bottom row are unique, those on the top row have, or can have, multiple instances: there are many human beings and many complexions. So typically things in the bottom row will be referred to by a proper noun or name (“Socrates,” “Socrates’ complexion”), those on the top row will be referred to by a common noun (“man,” “color”).
[1] Aristotle Categories 1a16-24.
[2] See Lowe 2006.
[3] The term in general usage means ‘possessions, property.’ Plato uses the term in its pregnant sense (it is the abstract noun from the verb ‘to be’) to signify something like ‘essence’: Euthyphro 11a8. For Aristotle it comes to signify the ultimate reality.
[4] Aristotle does not actually introduce this term until he writes an apparent sequel to the Categories, namely On Interpretation, 17a38-40. (The term appears in Categories 12a27, but not in a technical sense.)