Commentary Aristotle Posterior Analytics
Lecture 6. Knowledge of immediate principles
72a25. Now, since the required ground of our knowledge—that is, of our conviction—of a fact is the possession of such a syllogism as we call demonstration, and the ground of the syllogism is the facts constituting its premises, we must not only know the primary premises—some if not all of them—beforehand, but know them better than the conclusion.
72a29. For the cause of an attribute’s inherence in a subject always itself inheres in the subject more firmly than that attribute; e.g., the cause of our loving anything is dearer to us than the object of our love.
So since the primary premises are the cause of our knowledge—that is, of our conviction—it follows that we know them better—that is, are more convinced of them—than their consequences, precisely because our knowledge of the latter is the effect of our knowledge of the premises.
72a32. Now, a man cannot believe in anything more than in the things he knows, unless he has either actual knowledge of it or something better than actual knowledge. But we are faced with this paradox if a student whose belief rests on demonstration has not prior knowledge.
72a36. A man must believe in some, if not in all, of the basic truths more than in the conclusion. Moreover, if a man sets out to acquire the scientific knowledge that comes through demonstration,
72a38. He must not only have a better knowledge of the basic truths and a firmer conviction of them than of the connexion which is being demonstrated: more than this, nothing must be more certain or better known to him than these basic truths in their character as contradicting the fundamental premises which lead to the opposed and erroneous conclusion. For indeed the conviction of pure science must be unshakable.
Now, since the required ground of our knowledge. After showing what immediate principles are, the Philosopher now determines concerning our knowledge of them.
Apropos of this he does two things.
First, he shows that immediate principles are better known than the conclusion.
Second, that the falsity of their contraries ought to be most evident, at: he must not only have a better knowledge (72a38; [59]).
Concerning the first he does three things.
First (72a25), he states his proposition and says that because we give our assent to a thing which has been concluded and we know it scientifically precisely because we have a demonstrative syllogism (and this insofar as we know the demonstrative syllogism in a scientific way), it is necessary not only to know the first principles of the conclusion beforehand, but also to know them better than we know the conclusion.
He adds, either all or some, because some principles require proof in order to be known; so that before they are proved, they are not better known than the conclusion. Thus the fact that an exterior angle of a triangle is equal to its two opposite interior angles is, until proved, as unknown as the fact that a triangle has three angles equal to two right angles. But there are other principles which, once they are posited, are better known than the conclusion.
Or, in another way, there are some conclusions which are most evident; for example, those based on sense perception, as that the sun is eclipsed. Hence the principle through which this is proved is not better known absolutely—the principle being that the moon is between the sun and the earth—although it is better known within the reasoning process that goes from cause to effect.
Or, in another way, he says this because he had said above that in the order of time certain principles are known before the conclusion, but others are known along with the conclusion at the same moment of time.
Second, at: for the cause of an attribute’s inherence (72a29), he proves his proposition in two ways:
First, with an ostensive argument, thus: that in virtue of which something is so, is itself more so; for example, if we love someone because of someone else, as a master because of his disciple, we love the disciple more. But we know conclusions and give our assent to them because of the principles. Therefore, we know the principles with more conviction and give them stronger assent than the conclusion.
Apropos of this reason it should be noted that a cause is always more noble than its effect. When, therefore, cause and effect have the same name, that name is said principally of the cause rather than of the effect; thus fire is primarily called hot rather than things heated by fire. But sometimes the name of the effect is not attributed to the cause. In that case, although the name the effect has does not belong to the cause, nevertheless, something more noble belongs to it. For example, although the sun does not possess heat, nevertheless, there is in it a certain power which is the principle of heat.
Then, at: now, a man cannot believe in anything more (72a32) he proves the same thing with a principle which leads to an impossibility. He reasons thus: Principles are known prior to the conclusion, as has been shown above; consequently, when the principles are known, the conclusion is not yet known. If, therefore, the principles were not more known than the conclusion, it would follow that a man would know things he does not know either as well as or better than the things he does know. But this is impossible. Therefore, it is also impossible that the principles not be better known than the conclusion.
Phrase by phrase this is explained in the following manner: a man who knows scientifically or even one who knows in a way superior to this, if such there be (he says this, having in mind the person who has the intuition of principles, a state he has not yet explained), cannot give more credence to things he does not know than to things he does know. But this will be the case if one who assents to a conclusion obtained through demonstration did not foreknow, that is, did not know the principles better.
In Greek it is stated more clearly: but no one, whether he has scientific knowledge or that form of knowledge which is better than the scientific (if there be such), can believe anything more firmly than the things he knows.
Third, at: a man must believe in some (72a36), he clarifies what he had said, saying that his statement to the effect that it is more necessary to believe the principles (either all or some) than the conclusion should be understood as referring to a person who is to acquire a discipline through demonstration. For if the conclusion were more known through some other source, such as sense-perception, nothing would preclude the principles not being better known than the conclusion in that case.
Then, at: he must not only have a better knowledge (72a38) he shows that it is not only necessary to know the principles more than the demonstrative conclusion, but nothing should be more certain than the fact that the opposites of the principles are false. And this because the scientific knower must not disbelieve the principles, but assent to them most firmly. But anyone who doubts the falseness of one of two opposites cannot assent firmly to the other, because he will always fear that the opposite one might be true.