Philosophy 433
Philosophy of Aristotle

University of Washington

Predication and Ontology: The Categories

1. The Ten Categories

The list (even the precise number) of categories varies in different works. In the Categories, we get this list (1b25):

2. Linguistics or Ontology?

Is this linguistics or ontology? What are the categories categories of?

  1. Things in the world?
  2. Linguistic expressions?
  3. Concepts?

A likely account: Aristotle is classifying things in the world on the basis of linguistic considerations. (The idea seems to be that the structure of language mirrors the structure of reality.)

3. Substance vs. the other 9 Categories

The first category - substance - is the most important in Aristotle’s ontology. Substances are, for Aristotle, the fundamental entities. To see why this is so, we will have to introduce some important Aristotelian distinctions.

4. Subjects and predicates

These are non-linguistic entities: not the subjects and predicates of sentences, but the entities referred to by linguistic subjects and predicates.

A subject (hupokeimenon) is what a statement is about.
A predicate (kategoroumenon) is what a statement says about its subject.


This (particular animal) is a man.
Man is an animal.
This (particular color) is white.
White is a color.

The same thing may be both a subject and a predicate. E.g., man and white above. Some things are subjects but are never predicates, e.g., this (particular) animal, or this (particular) color.

5. Overview: two kinds of predication

Consider the following pair of simple (atomic) sentences:

“Socrates is a man”
“Socrates is wise”

Do both of these atomic sentences have the same kind of ontological underpinning? I.e., is the structure of the fact that Socrates is a man the same as the structure of the fact that Socrates is wise? Plato’s account suggests that it is. For Plato

x is F” means that x partakes of the Form, F-ness.

For Plato, predication, in general, is explicated in terms of the notion of participating in a Form. In response, Aristotle thinks this oversimplifies. The superficial similarity between these two sentences disguises an important ontological difference in the facts they express. (In Greek, the sentences look even more similar than in English, since Greek lacks the indefinite pronoun: “Socrates man (is)” vs. “Socrates wise (is).”)

For Aristotle, man is what Socrates IS; wise, on the other hand, is not what he IS (even though we say he is wise). Rather, it is something he HAS. (Cf. Grice and Code on IZZing and HAZZing.)

This idea emerges in the Categories distinction between what is said of a subject and what is in a subject.

6. Two fundamental relations: SAID OF and IN a subject.

There are two basic ontological relations that cut across all ten categories. These correspond to the notions (that Aristotle later develops) of essential and accidental predication.

  1. SAID OF a subject

    This is a relation of fundamental ontological classification.


    Man is SAID OF Socrates.
    Animal is SAID OF man.
    (Hence) animal is SAID OF Socrates.
    White is SAID OF this (particular) color.
    Color is SAID OF white.
  2. IN a subject

    This is a relation of fundamental ontological dependence. What is IN a subject, Aristotle says, belongs to it “not as a part, and cannot exist separately from what it is in” (1a24).


    This grammatical knowledge is IN a soul.
    This white is IN a body.
    Color is IN body.

    This is a cross-categorial relation; things IN a subject are non-substances; the things they are IN are substances: non-substances are IN substances.

7. Universals and Particulars

Although Aristotle does not use these terms in the Categories, it is clear that he intends to capture the notions of universal and particular with his SAID OF locution. Cf. these passages:

De Int. 17a38: “Now of actual things some are universal, others particular (I call universal that which is by its nature predicated of a number of things, and particular that which is not; man, for instance, is a universal, Callias a particular).”

Met. B, 1000a1: “For this is just what we mean by the individual - the numerically one, and by universal we mean that which is predicable of the individuals.”

An. Pr. A27, 43a26ff: “Of all the things which exist some are such that they cannot be predicated of anything else . . ., e.g. Cleon and Callias, i.e. the individual and sensible, but other things may be predicated of them (for each of these is both man and animal); and some things are themselves predicated of others, but nothing prior is predicated of them; and some are predicated of others, and yet others of them, e.g. man of Callias and animal of man. It is clear then that some things are naturally not said of anything; for as a rule each sensible thing is such that it cannot be predicated of anything....”

So a universal is what is SAID OF some subject, and a particular is what is not SAID OF any subject.  Note that there are universals and particulars in all the categories:

Man and animal are universal substances.
Callias and “this horse” are particular substances.

White and color are universal qualities.
“This white” is a particular quality.

8. The fourfold division (Categories, Ch. 2)

The SAID OF relation divides entities into universals and particulars; the IN relation divides them into substances and non-substances. Hence, the fourfold division at 1a20ff produces (in the order of presentation):

  1. Universal substances
  2. Particular non-substances
  3. Universal non-substances
  4. Particular substances

9. Primary Substances: the basic individuals

The last class (things neither SAID OF nor IN any subject) Aristotle calls “primary substances” (protai ousiai). Primary substances are fundamental in that “if they did not exist it would be impossible for any of the other things to exist” (2b5).

10. Aristotle’s argument for the ontological priority of primary substances (2a34-2b7)

  1. Every secondary (universal) substance is predicated of (i.e., SAID OF) some primary substance or other.
  2. Every non-substance (whether universal or particular) is IN some primary substance or other.
  3. That is, everything other than primary substance is either SAID OF or IN primary substances.
  4. Therefore, if primary substances did not exist, neither would anything else.

11. Amplifications on Aristotle’s argument:

It is clear that a non-substance can exist only IN a substance. For the only subject a non-substance can be IN is a substance, and things IN a subject (i.e., non-substances) cannot exist if they are not IN subjects.

What about universals? Aristotle’s premises seems to leave open the possibility that they might exist even though they are not SAID OF anything. But he clearly seems to be assuming an ontological dependence condition for universals analogous to the one he assumes for non-substances:

12. Some important features of substances

See esp. Categories ch. 5:

  1. Substances are not IN subjects (they are not dependent entities.)

  2. Differentiae are not IN subjects either. Why does Aristotle say this? After all, differentiae are (typically) qualities, and qualities can exist only by being IN substances. So it would seem to follow that differentiae are IN subjects.

    The precise status of differentiae in Aristotle’s system is hard to pin down. But there are some good reasons for him to say that differentiae are not IN subjects:

    1. It seems to be a corollary of (a). For Aristotle thinks that a definition consists of genus + differentia (cf. Topics A.8, 103b15). So a differentia of a substance is part of what the substance IS, and not something it HAS.

    2. When Aristotle talks about “parts of substances” in the Categories, he is probably thinking of “conceptual” parts, and differentiae would be such parts (cf. Frede, “Individuals in Aristotle”). But Aristotle says that the things IN a subject are not parts of the subject, i.e., not differentiae.

      Perhaps Aristotle can say about differentiae (of substances) what he says about secondary substances (3b14-22): a secondary substance signifies a poion - lit. quality, but here it pretty clearly means sort. He certainly does not think that horse (the species) is a quality - he thinks it is a type or sort of substance. (That’s why he says that a species like horse is not simply a poion, but a poion with respect to substance - 3b21).

      Similarly, a differentia is not simply a poion, but a poion with respect to substance. That means that it is not a quality (in the way that white is a quality); and hence it does not count as being IN a subject.

    3. Substances have no contraries (opposites).

    4. Substances do not admit of degree. (If F is a substance term, nothing can be more or less F.)

    5. “Most distinctive” Aristotle says (4a10) is that “substances remain one and the same while admitting contraries.”

      By this Aristotle means that a distinctive feature of substances is that they undergo change. That is, they persist through changes. They can be subjects of change. We will examine this.

13. Substances and Change

Presumably, in the Categories Aristotle thinks that only substances can undergo change. Since he holds that change requires that one property of a subject be replaced by another, opposed, property, what he has to prove is this:

if x goes from being F at one time to being not-F at a later time, then x is a substance.

[One might think that Aristotle can obtain this conclusion easily, since it might appear that only substances can be subjects. But although he is tempted by this equation of substancehood with subjecthood, he realizes that it will not work. Cf. Topics A9: the “what is it?” question can be raised about qualities, quantities, etc. So any item from any category can be a subject.]

The argument he gives in the Categories consists in choosing some non-substances as values of x, and then showing that for a choice of values of F (with respect to which we would expect there to be change) x does not go from being F at one time to being not-F at another time.

These are his examples:

  1. x = a color
    F = white
    not-F = black

  2. x = an action
    F = good
    not-F = bad

But these examples beg the question. For the choices of values for x and F are from the same category. [This is certainly clear in the case of example (a).] Yet when Aristotle gives an example of change, x and F are from different categories, with x a substance and F a non-substance.

The principle on which Aristotle’s point seems to depend is this:

A thing never changes with respect to what it IZZes, but only with respect to what it HAZZes.

And this seems to guarantee that substances can change (since every substance HAZZes some accidental properties); but it doesn’t show that only substances can change. For it hasn’t been proved that non-substances can’t also HAZZ accidental properties.

14. A defense of Aristotle

What can be said in behalf of Aristotle’s argument? There is still an intuition that substances play a special role as subjects. One might defend that intuition in the following way:

In those cases in which a non-substance (e.g. a quality) seems to change (i.e. goes from being F to being not-F), the change doesn’t really seem to be in the non-substance that is the apparent subject, but in some (unspecified) substance. E.g., cf. “Purple has become unpopular.” Here, it seems that purple itself hasn’t changed. Rather, people (substances) have changed their attitudes about colors.

So we can analyze “Purple has become unpopular” as “Most people no longer like purple.” In this case, a more defensible thesis for Aristotle might be:

Every (apparent) change which a non-substance undergoes can be analyzed as a (real) change that a substance undergoes.

But even this thesis (as we shall see) will not stand up. The criterion of “ultimate subject of change” for substancehood will have to be given up.

15. Aristotle’s Ontology after the Categories.

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