Predication and Ontology: Categories

Predication and Ontology: The Categories

A theory of ontology attempts to answer, in the most general possible terms, the question what is there? A theory of predication attempts to answer the question what is it to say something about something? This is a book about ontology and predication.

Ontology: The Ten Categories
In the Categories, we get this list (1b25):
1. Substance
2. Quality
3. Quantity
4. Relation
5. Where
6. When
7. Position
8. Having
9. Action
10. Passion
This is presumably a list of the ten fundamentally different kinds of things that there are. 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 understand what Aristotle says about predication.
Predication
- A subject (hupokeimenon) is what a statement is about.
- A predicate (katêgoroumenon) is what a statement says about its subject.
Examples:
- 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.
Two kinds of predication
Consider the following pair of simple (atomic) sentences:
- “Socrates is a human being”
- “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.
According to Plato, predication, in general, is explicated in terms of the notion of participating in a Form. In response, Aristotle thinks this oversimplifies. On Aristotle’s account:
- “Socrates is a human being” tells us something fundamental about what kind of a thing Socrates is: it is an essential predication.
- “Socrates is wise” tells us something less fundamental, something that merely happens to be the case: it is an accidental predication.
This idea emerges in the Categories distinction between what is said of a subject and what is in a subject, introduced as part of the four-fold distinction drawn at 1a20. Since Aristotle is using the terms ‘said of’ and ‘in’ in a somewhat technical way, we will write them, from now on, in SMALL CAPS in order to indicate this technical use.
Two fundamental relations
Aristotle distinguishes two fundamental relations: being SAID OF a subject and being PRESENT IN a subject. These correspond, respectively, to the notions (that Aristotle later develops) of essential and accidental predication, and they cut across all ten categories.
1. SAID OF a subject
  - This is a relation of fundamental ontological classification. It is the relation between a kind and a thing that falls under it.
  - It is a transitive relation (i.e., if x is SAID OF y and y is SAID OF z, it follows that x is SAID OF z).
  - Its relata belong to the same category. A universal in a given category is SAID OF the lower-level universals and individuals that fall under it.
  - What is SAID OF a subject is essential to that subject.
  Examples:
  1. Man is SAID OF Socrates.
  2. Animal is SAID OF man.
  3. (Hence) animal is SAID OF Socrates.
  4. White is SAID OF this (particular) color.
  5. Color is SAID OF white.
2. PRESENT IN a subject
  - This is a relation of fundamental ontological dependence. What is PRESENT IN a subject, Aristotle says, belongs to it “not as a part, and cannot exist separately from what it is in” (1a24).
  - This is a cross-categorial relation; things PRESENT IN a subject are non-substances; the things they are PRESENT IN are substances: non-substances are PRESENT IN substances.
  - What is PRESENT IN a subject is accidental (non-essential) to that subject.
  Examples:
  1. This grammatical knowledge is PRESENT IN a soul.
  2. This white is PRESENT IN a body.
  3. Color is PRESENT IN body.
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:
- A universal is what is SAID OF some subject
- 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 (Aristotle calls them “secondary substances.”)
  - Callias and “this horse” are particular substances. (Aristotle calls them “primary substances.”)
  - White and color are universal qualities.
  - “This white” is a particular quality.
Category Trees
1. Each category can be thought of as having a tree structure. The category itself can be divided into its fundamental kinds (e.g., substance can be divided into plants and animals). Each of these kinds can in turn be divided (e.g., animal can be divided into the various broad genera of animals). Each of these can in turn be divided into the fundamental species of the category in questions (e.g., into such basic kinds as tiger, and horse, and human being). (All of these kinds—animal, tiger, horse—are what Aristotle calls “secondary substances”.) Finally, we can divide these lowest-level kinds into the basic individuals in the category (e.g., human being can be divided into Socrates, Callias, Coriscus, etc.).
2. Similarly, the category of quality can be divided into subcategories such as color, which can in turn be divided into red, green, etc. Aristotle thinks that these specific qualities can be further divided into individuals (analogous to individual substances) such as this individual bit of white.
3. Thus, each category is ultimately divisible into the individual members of that category.
4. Here’s a useful chart that illustrates the tree structure of the categories.

The fourfold division

This can be found in Categories, Ch. 2.

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

Universal substances (“secondary substances”)
Particular non-substances
Universal non-substances
Particular substances (“primary substances”)

The chart below summarizes the fourfold division of Aristotle’s ontology:

The Ontology of Aristotle’s Categories
(a) SAID OF a subject
not PRESENT IN a subject
man, horse, animal

Universal Substances
(c) SAID OF a subject
PRESENT IN a subject

knowledge, white
Universal non-Substances

(d) not SAID OF a subject
not PRESENT IN a subject

this man,
this horse

Individual Substances
(b) not SAID OF a subject
PRESENT IN a subject

this knowledge of grammar,
this white

Individual non-Substances

The Ontology of Aristotle’s *Categories*
(a) SAID OF a subject not PRESENT IN a subject man, horse, animal Universal Substances	(c) SAID OF a subject PRESENT IN a subject knowledge, white Universal non-Substances
(d) not SAID OF a subject not PRESENT IN a subject this man, this horse Individual Substances	(b) not SAID OF a subject PRESENT IN a subject this knowledge of grammar, this white Individual non-Substances

Notice the following facts about these relations:

x is SAID OF something → x is a universal.
x is not SAID OF anything → x is a particular.
x is PRESENT IN y → x is a non-substance and y is a substance.
x is not PRESENT IN anything → x is a substance.
x is neither PRESENT IN anything nor SAID OF anything → x is a particular substance (primary substance).
x is PRESENT IN y and x is SAID OF z → y≠z.

(6) may require amplification. The reason is that if x is PRESENT IN y, then y is a substance and x is a non-substance (e.g., a quality). But if x is a quality and is SAID OF z, then z is a (more specific) quality. So y is a substance and z is a quality. And no quality is a substance. For example, knowledge is PRESENT IN the soul (a substance), and SAID OF grammar (a kind of knowledge). But knowledge is not SAID OF the soul (for the soul is not a kind of knowledge), and knowledge is not PRESENT IN grammar (for grammar is not a substance).

Cross-categorial predication
1. Predication within a category (“Socrates is a human,” “a tiger is an animal,” “red is a color”) involves classifying something (whether a particular or a universal) under some higher universal within the same category tree. Predication is a matter of classification.
2. Cross-categorial predication (“Socrates is wise,” “This horse is white”) is more complicated. Here we are predicating an accident (something PRESENT IN a subject) of a substance in which it inheres.
3. Are such (accidental) predications still a matter of classification? Yes. But we are classifying something PRESENT IN a substance, rather than the substance itself.
4. Example: “This horse is white” classifies a particular bit of color, inhering in this horse, under the color-universal white.
5. That is: White is SAID OF an individual bit of color that is PRESENT IN this horse.
Primary Substances: the basic individuals
Things that are neither SAID OF nor PRESENT 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). That is, on Aristotle’s account, primary substances have priority. Aristotle gives this 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 PRESENT IN some primary substance or other.
3. That is, everything other than primary substance is either SAID OF or PRESENT IN primary substances.
4. Therefore, if primary substances did not exist, neither would anything else.
Comparison with Plato
1. The ontological priority is reversed. For Plato, particulars (participants in Forms) are the dependent entities; the Forms in which they participate are the independent entities. For Aristotle, it is individuals that are ontologically primary or basic.
2. Aristotle has two kinds of predication relation; Plato’s theory, although less clearly articulated, seems to have only one.
3. The difference can be seen most clearly if we read Aristotle’s Categories as a response to the dilemma of participation that Plato brings up in the Parmenides.
The dilemma of participation
1. Here is Plato’s presentation of the problem (Parm. 131a-c):
  Do you think, then, that the form as a whole - one thing - is in each of the many ... so, being one and the same, it will be at the same time, as a whole, in things that are many and separate, and thus it would be separate from itself?
  
  Socrates replies with the suggestion that a Form may be “in” many things in the way that many people may all be covered with one sail. To which Parmenides replies:
  In that case, would the sail be, as a whole, over each person, or would a part of it be over one person and another part over another? [“A part,” Socrates replies.] So the forms themselves are divisible, Socrates, and the things that partake of them would partake of a part; no longer would a whole form, but only a part of it be in each thing.
2. As Plato has Parmenides present the dilemma, both horns are unattractive:
  1. If the whole Form is in each participant, then the Form will be “separate from itself,” which seems impossible.
  2. If only a part of each Form is in each participant, then the Form will be many, and not one, which also seems impossible. (An even more important problem, that Plato does not mention: if two different participants have two different things in them, what makes them have one and the same thing in common? The theory will not explain what it is supposed to.)
3. Aristotle’s solution goes between the horns of this dilemma: it is not precisely correct to say that the whole universal is in each particular of which it is predicated, nor is it precisely correct to say that it is “only” a part of the universal that is in a given particular.
4. On Aristotle’s account: white (the genus or universal) is SAID OF the particular color that is PRESENT IN this horse. So, for one and the same thing, whiteness, to be in both this horse and that horse (Plato’s problem case) is just for the color of this horse and the color of that horse both to be classified as white. (White is SAID OF both of these two individual instances of color.) Whiteness is therefore in both horses without being “separate from itself” for it is just the common classification of the particular bits of color in them both.
5. According to Aristotle, what is PRESENT IN individual substances is, ultimately, individual. But just as individual substances can be classified under universals (like horse and animal), so too can the qualities, etc., of substances be classified under universals (like white and color).
6. For more detail on this interpretation of Aristotle’s Categories as a response to Plato’s Dilemma of Participation, see Matthews and Cohen, “The One and the Many” p. 644, on reserve.
Substances and Change
In Cat. 5, Aristotle points out the hallmarks of substance, one of which is that substances are the subjects that undergo change [“Most characteristic of substance seems to be the fact that something one and the same in number can receive contraries” (4a10).]
Thus in the ontology of the Categories, substances are the continuants - the individuals that persist through change remaining one and the same in number. But, as we will see, Aristotle’s investigation of the topic of change begins to exert pressure on this ontology. A claimant (viz., matter) will emerge to challenge the place of individual plants and animals as the basic subjects of predication and change.