Commentary Aristotle Posterior Analytics
Lecture 10
How something is said to be predicated per se of a thing a34. Essential attributes are (1) such as belong to their subject as elements in its essential nature (e.g., line thus belongs to triangle, point to line; for the very being or ‘substance’ of triangle and line is composed of these elements, which are contained in the formulae defining triangle and line):
a38. (2) such that, while they belong to certain subjects, the subjects to which they belong are contained in the attribute’s own defining formula. Thus straight and curved belong to line, odd and even, prime and compound, square and oblong, to number; and also the formula defining any one of these attributes contains its subject—e.g., line or number as the case may be.
Extending this classification to all other attributes, I distinguish those that answer the above description as belonging per se to their respective subjects; whereas attributes related in neither of these two ways to their subjects I call accidents or ‘coincidents’; e.g., musical or white is a ‘coincident’ of animal.
b5. Further, that is essential which is not predicated of a subject other than itself: e.g., ‘the walking [thing]’ walks and is white in virtue of being something else besides; whereas substance, in the sense of whatever signifies a ‘this somewhat’, is not what it is in virtue of being something else besides. Things, then, not predicated of a subject I call essential; things predicated of a subject I call accidental or ‘coincidental’.
b10. In another sense again, a thing consequentially connected with anything is essential; one not so connected is ‘coincidental’. An example of the latter is ‘While he was walking it lightened’: the lightning was not due to his walking; it was, we should say, a coincidence.
If, on the other hand, there is a consequential connexion, the predication is essential; e.g., if a beast dies when its throat is being cut, then its death is also essentially connected with the cutting, because the cutting was the cause of death, not death a ‘coincident’ of the cutting.
b16. So far, then, as concerns the sphere of connexions scientifically known in the unqualified sense of that term, all attributes which (within that sphere) are essential either in the sense that their subjects are contained in them, or in the sense that they are contained in their subjects, are necessary as well as consequentially connected with their subjects.
For it is impossible for them not to inhere in their subjects either simply or in the qualified sense that one or other of a pair of opposites must inhere in the subject; e.g., in line must be either straightness or curvature, in number either oddness or evenness. For within a single identical genus the contrary of a given attribute is either its privative or its contradictory; e.g., within number what is not odd is even, inasmuch as within this sphere even is a necessary consequent of not-odd. So, since any given predicate must be either affirmed or denied of any subject, essential attributes must inhere in their subjects of necessity.
b25. Thus, then, we have established the distinction between the attribute which is ‘true in every instance’ and the ‘essential’ attribute.
Essential attributes. After determining about 'said of all', the Philosopher now determines about 'said per se' [that is, said in virtue of itself] and does three things.
About this he does two things.
First, he shows the number of ways something is said per se.
Second, how the demonstrator makes use of these ways, at: so far then as concerns the sphere of connexions (73b16; [89]).
In regard to the first it should be noted that this preposition per [“in virtue of” or “by”] denotes a causal relationship, although sometimes it also signifies a state, as when someone is said to be per se, that is, by himself, when he is alone.
But when it designates a relationship to a cause, sometimes the cause is formal, as when it is stated that the body lives in virtue of the soul; sometimes the relationship is to a material cause, as when it is stated that a body is colored in virtue of its surface, that is, because the surface is the subject of color; again, it might even designate a relationship to an extrinsic cause, particularly an efficient cause, as when it is said that water is made hot in virtue of fire.
But just as this preposition per designates a relationship to a cause, when something extrinsic is the cause of that which is attributed to the subject, so also when the subject or something pertaining to the subject is the cause of that which is attributed to the subject. This latter is what per se, that is, in virtue of itself, signifies.
Therefore, the first way of saying something per se (73a34) is when that which is attributed to a subject pertains to its form. And because the form and essence of a thing are signified by its definition, the first mode of that which is per se is when the definition itself or something expressed in the definition is predicated of the thing defined.
This is what he means when he says, Essential attributes are such as belong to their subject as elements in its essential nature, that is, included in the definition which indicates what it is, whether those elements are stated in the nominative case or in one of the oblique cases. Thus, line is stated in the definition of triangle. Hence line is in triangle per se. Again, in the definition of line, point is mentioned; hence point is per se in line.
And the reason why they are mentioned in the definition is stated when he says, for the very being or substance [that is, the essence, which the definition signifies] of triangle and line is composed of these elements, namely, of lines and points. However, this does not mean that a line is formed out of points, but that point is involved in the very notion of line, just as line is involved in the very notion of triangle. And he asserts this in order to exclude things which are part of a thing’s matter and not of its species: thus, semicircle is not mentioned in the definition of circle, or finger in the definition of man, as it is stated in Metaphysics VII. He states further that all those items which are found universally in the definition expressing what a thing is are attributed to it per se.
The second mode of saying per se is when this preposition 'per' implies a relationship of material cause, in the sense that that to which something is attributed is its proper matter and subject.
For it is required, when defining an accident, to mention its proper subject in one of the oblique cases: thus when an accident is defined abstractly, we say that “aquilinity” is a curvature of a nose, but when it is defined concretely, the subject is put in the nominative case, so that we say that “the aquiline is a curved nose.” Now, the reason for this is that since the being of an accident depends on its subject, its definition—which signifies its being—must mention that subject. Hence it is the second mode of saying per se, when the subject is mentioned in the definition of a predicate which is a proper accident of the subject.
And this is what he means when he states (73a38), essential attributes are those such that while they belong to certain subjects, that is, to subjects of accidents, the subjects to which they belong are contained in the attribute’s own defining formula, that is, in the expression which describes what the accident is, that is, in the definition of the accident. Thus straight and curved belong to line per se. For line is mentioned in their definition. For the same reason odd and even belong per se to number, because number is mentioned in their definition. Again, prime and compound are predicated per se of number, and number is mentioned in their definition. (For a prime number, for example, seven, is one which is exactly divisible by no other number but one; but a compound number, for example, nine, is one which is exactly divisible by some number greater than one. Again, isoplural, that is, equilateral, and scalene, that is, having three unequal sides, belong per se to triangle, 93and triangle is mentioned in their definition.)
Accordingly, he adds that their respective subjects belong to each of the aforesaid accidents and are mentioned in the expression which states what each is, that is, in the definition: thus line belongs to some of them, and number to others. In each of these subjects that have been mentioned, I say that its accident is in it per se.
But those predicates which are neutral, that is, of such a nature as not to be mentioned in the definition of their subjects, nor the subjects in their definition, are accidents, that is, are predicated per accidens: for example, musical and white are predicated per accidens of animal.
Then, at: further, that is essential (73b5) he sets down another mode of that which is per se, that is, the sense in which it signifies something in isolation. Thus something which is a singular in the genus of substance and which is not predicated of any subject is said to be per se. The reason for this is that when I say, walking or white, I do not signify either of them as something isolated or apart, since something else which is walking or white is understood. But this is not the case with terms which signify a “this something,” that is, with terms that signify first substance. For when I say, “Socrates” or “Plato,” it is not to be supposed that there is something else, over and above what they really are, which would be their subject.
Therefore, things which are thus not predicated of any subject are per se, but things which are predicated of a subject, as being in the subject, are accidents. However, not all things predicated of a subject, as universals of their inferiors, are accidents. It should be noted, however, that this mode is not a mode of predicating, but a mode of existing; hence at the very start he said that they exist per se and not that they are said per se.
Then, at: in another sense again (73b10) he gives the fourth mode, according to which the preposition 'per' designates a relationship of efficient cause or of any other. Consequently, he says that whatever is attributed to a thing because of itself, is said of it per se; but whatever is not so attributed is said per accidens, as when I say, “While he was walking, it lightened.” For it is not the fact that he walks that causes lightning, but this is said by coincidence. But if the predicate is in the subject because of itself, it is per se, as when we say, “Slaughtered, it died.” For it is obvious that because something was slaughtered, it died, and it is not a mere coincidence that something slaughtered should die.
Then, at: so far, then, as concerns the sphere (73b16) he shows how the demonstrator uses the aforesaid modes.
But first it should be noted that, since science bears on conclusions, and understanding [intuition] bears on principles, the scientifically knowable are, properly speaking, the conclusions of a demonstration wherein proper attributes are predicated of their appropriate subjects. Now, the appropriate subjects are not only placed in the definition of attributes, but they are also their causes. Hence the conclusions of demonstrations involve two modes of predicating per se, namely, the second and the fourth.
And this is what he means when he says that the predications in the scientifically knowable in the strict sense, that is, in the conclusions of demonstrations are per se in the sense of something contained in the predicates, that is, in the way that subjects are contained in the definition of accidents which are predicated of the former; or are present on account of them, that is, in the way that predicates are in a subject by reason of the subject itself, which is the cause of the predicate.
Then he shows that such scientifically knowable things are necessary, because it is impossible for a proper accident not to be predicated of its subject. But this can occur in two ways: sometimes it is absolute, as when the accident is convertible with its subject, as “having three angles equal to two right angles” is convertible with triangle, and “risible” with man. At other times, two opposites stated disjunctively are of necessity in the subject, as straight or oblique in line, and odd or even in number. He shows that the reason for this is the fact that contrariety, privation and contradiction are in the same genus. For privation is nothing more than a negation in a determinate subject. Again, a contrary is equivalent to a negation in some genus, as in the genus of numbers, odd is the same as not even by way of consequence. Therefore, just as it is necessary, either to affirm or deny, so it is necessary that one of two things that belong per se, be in its proper subject.
Then, at: thus, then, we have established (73b25) he summarizes, and the text is clear.