Commentary Aristotle Posterior Analytics
Lecture 3. Preexistent knowledge of the conclusion
71a24. Before he was led on to recognition or before he actually drew a conclusion, we should perhaps say that in a manner he knew, in a manner not. If he did not in an unqualified sense of the term know the existence of this triangle, how could he know without qualification that its angles were equal to two right angles? No: clearly he knows not without qualification but only in the sense that he knows universally.
71a29. If this distinction is not drawn, we are faced with the dilemma in the Meno: either a man will learn nothing or what he already knows.
71a30. For we cannot accept the solution which some people offer. A man is asked, ‘Do you, or do you not, know that every pair is even?’ He says he does know it. The questioner then produces a particular pair, of the existence, and so a fortiori of the evenness, of which he was unaware. The solution which some people offer is to assert that they do not know that every pair is even, but only that everything which they know to be a pair is even.
71a34. Yet what they know to be even is that of which they have demonstrated evenness, that is, what they made the subject of their premise, viz. not merely every triangle or number which they know to be such, but any and every number or triangle without reservation.
For no premise is ever couched in the form ‘every number which you know to be such’, or ‘every rectilinear figure which you know to be such’: the predicate is always construed as applicable to any and every instance of the thing.
71b5. On the other hand, I imagine there is nothing to prevent a man in one sense knowing what he is learning, in another not knowing it.
The strange thing would be, not if in some sense he knew what he was learning, but if he were to know it in that precise sense and manner in which he was learning it.
Before he was led on to recognition. Having shown the manner in which certain other things must be known before knowledge of the conclusion is obtained, the Philosopher now wishes to show how we know even the conclusion beforehand, that is, before knowledge of it is obtained through a syllogism or induction.
Concerning this he does two things:
First (71a24), he establishes the truth of the fact, saying that before an induction or syllogism is formed to beget knowledge of a conclusion, that conclusion is somehow known and somehow not known: for, absolutely speaking, it is not known; but in a qualified sense, it is known. Thus, if the conclusion that a triangle has three angles equal to two right angles has to be proved, the one who obtains science of this fact through demonstration already knew it in some way before it was demonstrated; although absolutely speaking, he did not know it. Hence in one sense he already knew it, but in the full sense he did not.
And the reason is that, as has been pointed out, the principles of the conclusion must be known beforehand. Now, the principles in demonstrative matters are to the conclusion as efficient causes in natural things are to their effects; hence in Physics II the propositions of a syllogism are set in the genus of efficient cause. But an effect, before it is actually produced, preexists virtually in its efficient causes but not actually, which is to exist absolutely. In like manner, before it is drawn out of its demonstrative principles, the conclusion is preknown virtually, although not actually, in its self-evident principles. For that is the way it preexists in them. And so it is clear that it is not preknown in the full sense, but in some sense.
Second, at: if this distinction (71a29), in virtue of this established fact, he settles a doubt which Plato maintained in the book Meno, which gets its title from the name of his disciple.
The doubt is presented in the following manner: A person utterly ignorant of the art of geometry is questioned in an orderly way concerning the principles known in themselves from which a geometric conclusion is concluded. By starting with principles that are known in themselves, to each of which this person ignorant of geometry gives a true answer, and leading him thus by questions to the conclusion, he gives the true answer step by step. From this, therefore, he would have it that even those who seem to be ignorant of certain arts really have a knowledge of them before being instructed in them.
And so it follows that either a man learns nothing or he learns what he already knew.
In dealing with this problem he does four things.
First, he suggests that it cannot be settled unless we grant the truth established above, namely, that the conclusion which a person learns through demonstration or induction was already known, not absolutely, but as it was virtually known in its principles concerning which a person ignorant of a science can give true answers. However, according to Plato’s theory the conclusion was preknown absolutely, so that no one learns afresh but is led to recall by some rational process of deduction. This is similar to Anaxagoras’ position on natural forms, namely, that before they are generated, they already preexisted in the matter absolutely, whereas Aristotle says that they preexist in potency and not absolutely.
Second, at: for we cannot accept the solution (71a30), he shows that the way some have answered Plato’s problem is false, namely, by saying that a conclusion is not in any sense known before it is demonstrated or learned by some method or other. For they might face the following objection based on Plato’s problem: If an unlearned person were asked by someone, “Do you know that every duo (pair) is an even number?” and, if upon answering that he does know this, he were presented with a duo which the person interrogated did not know existed, for example, the duo which is one third of six, the conclusion would be that he knew one third of six to be an even number, a fact which had not been known by him but which he learned through the demonstration proposed to him. And so it seems to follow that he either did not freshly learn this or that he learned what he already knew. To avoid this dilemma, they would answer that the person who was questioned and who answered that he knew every duo to be an equal number did not say that he knew every duo to be even absolutely, but only those he knew to be duos. Hence, since that duo which was proposed was utterly unknown to him, he did not in any sense know that this duo was an even number. And so it follows that when one knows the principles, the conclusion is not in any sense preknown, either absolutely or in a qualified sense.
Third, at: yet what they know to be even (71a34), he refutes this solution in the following way: That is known, concerning which a demonstration is had, or concerning which a demonstration is for the first time received.
And this is said on account of those learners who begin to know scientifically. But learners do not obtain a demonstration touching every duo they happen to know but every duo absolutely; and the same applies to every number or every triangle. Therefore, it is not true that he knows something about every number which he knows to be a number, or of every duo which he knows to be a duo, but he knows it about every one absolutely.
And that he knows it not only of every number he happens to know is a number, but of every number absolutely, is proved, at: for no premise is ever couched (71b4), on the ground that the conclusion agrees with the premises in its terms. For the subject and predicate of the conclusion are the major and minor extremes in the premises. But in the premises no proposition concerning number or straight line is stated with the addition, “which you know”, but it is stated of all without qualification. Neither, therefore, is the conclusion of the demonstration asserted with the aforesaid qualification, but it is asserted of all without reservation.
Fourth, at: on the other hand, I imagine (71b5), he presents the true solution of the problem under discussion in terms of the truth already established, saying that there is nothing to prevent a person from somehow knowing and somehow not knowing a fact before he learns it. For it is not a paradox if one somehow already knows what he learns, but it would be, if he already knew it in the same way that he knows it when he has learned it.
For learning is, properly speaking, the generation of science in someone. But that which is generated was not, prior to its generation, a being absolutely, but somehow a being and somehow non-being: for it was a being in potency, although actually non-being. And this is what being generated consists in, namely, in being converted from potency to act. In like fashion, that which a person learns was not previously known absolutely, as Plato preferred; but neither was it absolutely unknown, as they maintained whose answer was refuted above. Rather it was known in potency, that is, virtually, in the preknown universal principles; however, it was not actually known in the sense of specific knowledge. And this is what learning consists in, namely, in being brought from potential or virtual or universal knowledge to specific and actual knowledge.