Commentary Aristotle Posterior Analytics
Lecture 9
How something is said to be predicated of all a21. Since the object of pure scientific knowledge cannot be other than it is, the truth obtained by demonstrative knowledge will be necessary. And since demonstrative knowledge is only present when we have a demonstration, it follows that demonstration is an inference from necessary premises. So we must consider what are the premises of demonstration—that is, what is their character:
and as a preliminary, let us define what we mean by an attribute ‘true in every instance of its subject’, an ‘essential’ attribute, and a ‘commensurate and universal’ attribute.
a28. I call “true in every instance” what is truly predicable of all instances—not of one to the exclusion of others — and at all times, not at this or that time only; e.g., if animal is truly predicable of every instance of man, then if it be true to say ‘this is a man’, ‘this is an animal’ is also true, and if the one be true now the other is true now. A corresponding account holds if point is in every instance predicable as contained in line.
a32. There is evidence for this in the fact that the objection we raise against a proposition put to us as true in every instance is either an instance in which, or an occasion on which, it is not true.
Since the object of pure scientific knowledge. After showing what a demonstrative syllogism is, the Philosopher in this section begins to show the nature and characteristics of the things that comprise a demonstration.
Concerning this he does three things.
First, he connects this with what has already been established.
Second, he explains certain matters that must be understood first, at: and as a preliminary (73a25; [78]).
Third, he establishes what he had in mind, namely, to show what and of what sort are the things that constitute a syllogism, at: demonstrative knowledge must rest (74b5; [109]).
He says therefore first (73a21), that since the definition of scientific knowledge given above spoke of that which cannot be otherwise, that which is scientifically known through demonstration will be necessary. Then he explains what it is to know something in a scientific way through demonstration, saying that demonstrative science is what we possess in having a demonstration, that is, what we acquire through demonstration. Consequently, it follows that the conclusion of a demonstration is necessary.
Now, although the necessary could be syllogized from the contingent, it is not possible through a contingent middle to obtain scientific knowledge of the necessary, as will be proved later. Furthermore, because the conclusion of a demonstration is not only necessary, but, as has been said, is known through demonstration, it follows that a demonstrative syllogism proceeds from necessary things. Consequently, we must establish from what and from what sort of necessary things a demonstration proceeds.
Then, at: and as a preliminary (73a25) he interjects certain things that must be understood as preliminaries to the matters to be discussed.
Apropos of these he does two things:
First, he states his intention (73a25), saying that before determining specifically the nature and characteristics of the things that form a demonstrative syllogism, we must indicate what is meant when we say, “of all,” and “per se,” that is, in virtue of itself, and “commensurately universal.”
For if we are to understand the nature of the things that form a demonstration, we must know what these terms mean, because they describe things that must be observed in demonstrations. For in the propositions of a demonstration it is required that something be predicated universally—which he signifies by the term 'said of all'—and 'per se,' that is, in virtue of itself, and 'first'—which he signifies by the words, “commensurately universal.” But these three things are related by adding something to the previous one. For whatever is predicated per se is predicated universally [that is, of all], but not vice versa. Again, whatever is predicated first is predicated per se, but not vice versa. This, therefore, shows why they are arranged as they are.
But why there are three and wherein they differ are explained by the fact that something is said to be predicated “of all” or universally in relation to things contained under the subject. For, as it is stated in Prior Analytics, something is said “of all,” when there is nothing under the extension of the subject that does not receive the given predicate. But it is in relation to the subject that something is said to be predicated per se, because the subject is mentioned when this predicate is defined, or vice versa, as will be explained below. Finally, something is said to be predicated of another thing “first” in relation to items that are prior to the subject and embrace or include it, as the more universal includes the less. Thus to have three angles equal to two right angles is not predicated “first” of isosceles, because it is previously predicated of something prior to isosceles, namely, of triangle.
Second, at: I call 'true in every instance' (73a28), he establishes his proposition.
And his treatment is divided into three parts.
First, he shows what is meant by “said of all.”
Second, what is meant by “said per se,” that is, in virtue of itself, at: essential attributes are (73a34; [84]).
Third, what is meant by “commensurately universal,” at: I term “commensurately universal” (73b27; [90]).
Concerning the first he does two things.
First (73a28), he states what it is to be 'said of all'.
And it should be noted that the phrase, 'said of all', is taken here in a sense somewhat different from the sense it has in Prior Analytics, where it is taken in a very general sense so as to accommodate both the dialectician and the demonstrator. Therefore, no more is mentioned in its definition than that the predicate be found in each of the things included under its subject. But that might be verified only at a given moment—which is the sense in which the dialectician sometimes uses it; or it might be verified absolutely and at all times—which is the sense to which the demonstrator must always limit himself.
Accordingly, two things are mentioned in the definition of 'said of all': one is that there is nothing within the extension of the subject that the predicate does not apply to. And he indicates this when he says, not of one to the exclusion of others;
the other is that there is no time in which the predicate does not belong. And this he indicates when he says, not at this or that time only.
And he gives the example of “man” and “animal,” saying that animal is predicated of every man; and of anything of which it is true to say that it is a man, it is true to say that it is an animal, and whenever it is a man, it is an animal. The same is true between line and point: for a point is in every line and always in every line.
Second, at: there is evidence for this (73a32), he explains this definition, using as evidence the techniques employed in rebuttals. For a universal proposition is not rebutted unless one or other of things it states is not verified. For when we are asked whether something is said “of all” in a demonstration, we can say, “No,” for two reasons, that is, either because it is not true of each instance of the subject, or because now and then it is not true. Hence it is clear that 'being said of all' signifies each of these.