Commentary Aristotle Posterior Analytics
Lecture 2. Extent and order of the preexistent knowledge required for obtaining science
71a11. The preexistent knowledge required is of two kinds. In some cases admission of the fact must be assumed, in others comprehension of the meaning of the term used, and sometimes both assumptions are essential.
Thus, we assume that every predicate can be either truly affirmed or truly denied of any subject, and that “triangle” means so and so. As regards “unit,” we have to make the double assumption of the meaning of the word and the existence of the thing. The reason is that these several objects are not equally obvious to us.
71a17. Recognition of a truth may in some cases contain as factors both previous knowledge and also knowledge acquired simultaneously with that recognition—knowledge, this latter, of the particulars actually falling under the universal and therein already virtually known. For example, the student knew beforehand that the angles of every triangle are equal to two right angles, but it was only at the actual moment at which he was being led on to recognize this as true in the instance before him that he came to know “this figure inscribed in the semicircle” to be a triangle. For some things (namely, the singulars finally reached which are not predicable of anything else as subject) are only learnt in this way; that is, there is here no recognition through a middle of a minor term as subject to a major.
13. The preexistent knowledge required. After showing that every discipline is developed from knowledge already existing, the Philosopher shows what is the extent of this preexisting knowledge (71a11).
Concerning this he does two things.
First, he determines the extent of preexisting knowledge in regard to the things that must be known in order to attain knowledge of the conclusion, of which scientific knowledge is sought.
Second, he determines the extent of preexisting knowledge of the conclusion, of which scientific knowledge is sought through demonstration, at: before he was led on to recognition (71a24; [22]).
Now two things are included in preexisting knowledge, namely, the knowledge and the order of the knowledge.
First, therefore, he determines the extent of preexisting knowledge so far as the knowledge itself is concerned.
Second, he determines the extent of preexisting knowledge so far as the order of the knowledge is concerned: recognition of a truth (71a17; [20]).
14. In regard to the first, it should be noted that the object of which scientific knowledge is sought through demonstration is some conclusion in which a proper attribute is predicated of some subject, which conclusion is inferred from the principles. And because the knowledge of simple things precedes the knowledge of compound things, it is necessary that the subject and the proper attribute be somehow known before knowledge of the conclusion is obtained. In like manner it is required that the principle be known from which the conclusion is inferred, for the conclusion is made known from a knowledge of the principle.
15. Now, the extent of preexistent knowledge of these three items, that is, of the principle, of the subject, and of the proper attribute, is limited to knowing two things about them, namely, that each is and what each is.
But, as stated in Metaphysics 7, complex things are not defined. For there is no definition of white man, much less of an enunciation (proposition). Hence since a principle is an enunciation, there cannot be preexisting knowledge of what it is but only of the fact that it is true.
But in regard to the proper attribute, it is possible to know what it is, because, as is pointed out in the same book, accidents do have some sort of definition. Now, the being of a proper attribute and of any accident is being in a subject; and this fact is concluded by the demonstration. Consequently, it is not known beforehand that the proper attribute exists, but only what it is.
The subject, too, has a definition; moreover, its being does not depend on the proper attribute—rather its own being is known before one knows the proper attribute to be in it. Consequently, it is necessary to know both what the subject is and that it is, especially since the medium of demonstration is taken from the definition of the subject of the proper attribute.
16. This, therefore, is why the Philosopher says that the preexistent knowledge required is of two kinds (71a11); because two items are known beforehand concerning things of which we have preexisting knowledge, namely, that it is and what it is.
There are some things concerning which it is necessary first to know that they are, such as principles, concerning which he then gives examples, citing as one example the first of all principles, namely that there is true affirmation or negation about everything.
Again, there are other things, namely, proper attributes, concerning which it is necessary to know what is said to be predicated, that is, what is signified by their name.
And he does not say unqualifiedly, “what it is”, but “what is said to be predicated”, because one cannot properly know of something what it is before it is known that it is. (For there are no definitions of non-beings.) Hence the question “whether it is” precedes the question “what it is.” But whether a thing is cannot be shown unless it is known beforehand what is signified by its name. On this account the Philosopher teaches in Metaphysics 4 that in disputing against those who deny principles one must begin with the meanings of names.
An example of this is “triangle,” concerning which one must know beforehand that its name signifies such and such, namely, what is contained in its definition.
But since accidents are referred to their subjects in a definite order, it is not impossible for something which is an accident in relation to one thing to be a subject in relation to something else: for example, a surface is an accident in relation to a bodily substance, but in relation to color it is the first subject. However, that which is a subject in such a way as never to be an accident of anything else is a substance. Hence in those sciences whose subject is a substance, that which is the subject can never be a proper attribute, as in first philosophy and in natural science, which treats of mobile being.
But in those sciences which bear upon accidents, nothing prevents a same thing from being taken as a subject in reference to one proper attribute, and as an attribute in reference to a more basic subject. Nevertheless, this must not develop into an infinite process, for one must arrive at something which is first in that science and which is taken as a subject in such a way that it is never taken as a proper attribute, as is clear in the mathematical sciences, which treat of continuous or discrete quantity. For in these sciences those things are postulated which are first in the genus of quantity; for example, unit and line and surface and the like. Once these are postulated, certain other things are sought through demonstration, such as the equilateral triangle and the square and so on in geometry. In these cases the demonstrations are said to be, as it were, operational, as when it is required to construct an equilateral triangle on a given straight line. But once it has been constructed, certain proper attributes are proved about it; for example, that its angles are equal, or something of that sort. It is clear, therefore, that in the first type of demonstration ‘triangle’ behaves as a proper attribute, and in the second type as a subject. Hence the Philosopher is using ‘triangle’ as a proper attribute and not as a subject when he says by way of example, we must assume that triangle means so and so (71a14).
He says, furthermore, that there are certain things about which we must know beforehand both what each is and whether it is. And he uses the example of ‘one,’ which is the principle in every genus of quantity. For although it is somehow an accident in reference to substance, yet in the mathematical sciences, which treat of quantity, it cannot be taken as a proper attribute but only as a subject, since in this genus [quantity] it has nothing prior to it.
The reason for this difference is shown by the fact that the manner in which the aforesaid, namely, principle, proper attribute and subject, are manifested is not the same. For the way in which they are known is not the same: for principles are known through the act of composing and dividing, but subject and proper attribute by the act of apprehending the essence. And this, too, does not belong in similar fashion to a subject and to a proper attribute, since a subject is defined absolutely, for nothing outside its essence is mentioned in its definition; but a proper attribute is defined with dependence on the subject which is mentioned in its definition. Therefore, since they are not known in the same way, it is not surprising if they are not foreknown in the same way.
Then, at: recognition of a truth (71a17), he determines the extent of foreknowledge on the part of the order which foreknowing implies.
For something is prior to another both in the order of time and in the order of nature. And this twofold order must be considered in regard to preexistent knowing.
For something is known before something else in the sense of being known prior in time. Concerning such things he says that someone could know certain things by knowing them prior to the time when he knows the things to which they are said to be foreknown. But certain others are known at one and the same time, although one is prior by nature to the other.
Concerning these he says that one acquires a knowledge of some of these foreknown things at the same time that knowledge of the things to which they are foreknown is acquired.
He indicates what these are when he adds that they are the things contained under certain universals of which we have knowledge, that is, of which it is known that they are contained under such universals.
Then he clarifies this with an example. For since two propositions are needed for inferring a conclusion, namely, a major and a minor; when the major proposition is known, the conclusion is not yet known. Therefore, the major proposition is known before the conclusion not only in nature but in time. Further, if in the minor proposition something is introduced or employed which is contained under the universal proposition which is the major, but it is not evident that it is contained under this universal, then a knowledge of the conclusion is not yet possessed, because the truth of the minor proposition will not yet be certain. But if in the minor proposition a term is taken about which it is clear that it is contained under the universal in the major proposition, the truth of the minor proposition is clear, because that which is taken under the universal shares in the same knowledge, and so the knowledge of the conclusion is had at once.
Thus, suppose that someone should begin to demonstrate by stating that every triangle has three angles equal to two right angles. When this is known, the knowledge of the conclusion is not yet known. But when it is later assumed that this figure inscribed in a semicircle is a triangle, he knows at once that it has three angles equal to two right angles. However, if it were not clear that this figure inscribed in the semicircle is a triangle, the conclusion would not be known as soon as the minor was stated; rather, it would be necessary to search for a middle through which to demonstrate that this figure is a triangle.
In giving this example of things which are known at a time prior to the conclusion the Philosopher says (71a19) that a person obtaining a knowledge of the conclusion through demonstration foreknew this proposition even according to time, namely, that every triangle has the equal of two right angles. But inducing this assumption, namely, that this figure in the semicircle is a triangle, he knew the conclusion at the same time, because this induction shares in the evidence of the universal under which it is contained, so that there is no need to search for another middle.
He adds (71a21), therefore, that some things are only learnt in this way, that is, learnt in virtue of themselves, so that it is not necessary to learn them through some other middle which is the ultimate reached by analysis in which the mediate is reduced to the immediate.
Or it can be read in such a way that the ultimate, that is, the extreme, which is subsumed under the universal middle does not need a further middle to show that it is contained under that universal.
And he manifests what those things are which always share the knowledge of their universal, saying that they are the singulars, which are not predicated of any subject, since no middle can be found between singulars and their species.