Commentary Aristotle Posterior Analytics
Lecture 23
How demonstrations quia and propter quid differ in the same science; demonstration quia through an effect a22. Knowledge of the fact differs from knowledge of the reasoned fact. To begin with, they differ within the same science and in two ways: (1) when the premises of the syllogism are not immediate (for then the proximate cause is not contained in them — a necessary condition of knowledge of the reasoned fact): (2) when the premises are immediate, but instead of the cause the better known of the two reciprocals is taken as the middle; for of two reciprocally predicable terms the one which is not the cause may quite easily be the better known and so become the middle term of the demonstration.
a30. Thus (2) (a) you might prove as follows that the planets are near because they do not twinkle: let C be the planets, B not twinkling, A proximity. Then B is predicable of C; for the planets do not twinkle. But A is also predicable of B, since that which does not twinkle is near — we must take this truth as having been reached by induction or sense-perception. Therefore, A is a necessary predicate of C; so that we have demonstrated that the planets are near. This syllogism, then, proves not the reasoned fact but only the fact; since they are not near because they do not twinkle, but, because they are near, do not twinkle.
a39. The major and middle of the proof, however, may be reversed, and then the demonstration will be of the reasoned fact. Thus: let C be the planets, B proximity, A not twinkling. Then B is an attribute of C, and A — not twinkling — of B. Consequently A is predicable of C, and the syllogism proves the reasoned fact, since its middle term is the proximate cause.
b3. Another example is the inference that the moon is spherical from its manner of waxing. Thus: since that which so waxes is spherical, and since the moon so waxes, clearly the moon is spherical. Put in this form, the syllogism turns out to be proof of the fact, but if the middle and major be reversed it is proof of the reasoned fact; since the moon is not spherical because it waxes in a certain manner, but waxes in such a manner because it is spherical. (Let C be the moon, B spherical, and A waxing.)
b10. Again (b), in cases where the cause and the effect are not reciprocal and the effect is the better known, the fact is demonstrated but not the reasoned fact.
Knowledge of the fact. After determining about demonstration propter quid, the Philosopher here shows the difference between demonstration quia and demonstration propter quid.
And he does two things about this.
First, he shows how they differ in the same science.
Second, in diverse sciences, at: but there is another way (78b33; [207]).
Concerning the first he does two things.
First, he states the twofold difference between the two in the same science.
Second, he clarifies this with examples, at: thus you might prove (78a30; [196]).
He says therefore first (78a22) that, as said above, demonstration is a syllogism causing scientific knowledge and proceeds from the causes both first and immediate of a thing. Now, this is to be understood as referring to demonstration 'propter quid'. But there is a difference between knowing 'that' a thing is so and 'why' it is so. Therefore, since demonstration is a syllogism causing scientific knowledge, as has been said, it is necessary that a demonstration 'quia' which makes one know that a thing is so should differ from the demonstration 'propter quid' which makes one know why. Consequently, this difference must be considered first in the same science and later in sciences that are diverse.
In one and the same science each of the above is said to differ in regard to the two things required for demonstration in the strict sense—which causes knowledge of the why—namely, that it be from causes and from immediate causes. Hence one way that scientific knowledge 'quia' differ from 'propter quid' is that it is the former if the syllogism is not through immediate principles but through mediate ones. For in that case the first cause will not be employed, whereas science propter quid is according to the first cause; consequently, the former will not be science 'propter quid'.
It differs in another way, because it is science 'quia' when the syllogism, although not through middles, that is, mediate, but through immediate things, is not through the cause but through “convertence,” that is, through effects convertible and immediate. Hence a demonstration of this kind is through the better known, namely, to us; otherwise it would not effect scientific knowledge. For we do not reach a knowledge of the unknown except through something better known. However in the case of two things equally predicable, that is, convertible, one of which is the cause and the other the effect, there is nothing to preclude that now and then the better known will not be the cause but the effect. For sometimes the effect is better known than the cause both in respect to us and according to sense-perception, although absolutely and according to nature the cause is the better known. Consequently, through an effect better known than the cause there can be demonstration which does not engender 'propter quid' knowledge but only 'quia'.
Then, at: thus you might prove (78a30) he clarifies these differences by examples.
And this is divided into two parts.
In the first he develops an example of the demonstration 'quia' which is through an effect.
In the second of demonstration 'quia' which is through a mediate cause, at: this also occurs when the middle (78b13; [201]).
In the first he gives an example of a syllogism which is through a convertible effect.
In the second of a syllogism through a nonconvertible effect, at: again, in cases where the cause (78b10; [200]).
The first is divided into two parts according to the two examples he gives, the second of which begins at: another example is the inference (78b3; [199]).
Concerning the first he does two things.
First, he gives an example of demonstration 'quia' which is through an effect.
Second, he states when it can be converted into a demonstration 'propter quid', at: the major and middle of the proof (78a39; [198]).
He says therefore first (78a30) that demonstration 'quia' is through an effect if one concludes for example that the planets are near because they do not twinkle. For 'non-twinkling' is not the cause why the planets are near, but vice versa: for the planets do not twinkle because they are near. For the fixed stars twinkle because in gazing at them the sight is beclouded on account of the distance. Therefore, the syllogism might be formed in the following way: “Whatever does not twinkle is near; but the planets do not twinkle: therefore, they are near.” Here we let C be the planets, that is, let 'planets' be the minor extreme, and let B consist in not twinkling, and A “to be near” be the major extreme. Then the proposition, “Every C is B,” is true, namely, the planets do not twinkle. Also it is true that “Every B is A,” that is, every star that does not twinkle is near. However, the truth of such a proposition must be obtained through induction or through sense perception, because the effect here is better known than the cause. And so, the conclusion, “Every C is A,” follows. In this way, then, it has been demonstrated that the planets, that is, the wandering stars, are near. Consequently, this syllogism is not “propter quid” but “quia.” For it is not because they do not twinkle that planets are near but rather, because they are near, they do not twinkle.
Then, at: the major and middle of the proof (78a39) he teaches how a demonstration 'quia' is changed to a demonstration 'propter quid'. And he says that it is possible to demonstrate the one through the other, that is, to demonstrate that they do not twinkle, because they are near. Then the demonstration will be 'propter quid'. Thus let C be the wanderers, that is, let 'wandering star' be the minor extreme; let B consist in being near, that is, let 'to be near', which was the major extreme above, be the middle term; and let A consist in not twinkling, that is, let 'not to twinkle', which above was the middle term, now be the major term. Therefore, B is in C, that is, “Every planet is near”; and A is in B, that is, “Any planet which is near does not twinkle.” Wherefore, it follows that A is in C, that is, “A planet does not twinkle.” In this way we have a syllogism 'propter quid', since it rests on the first and immediate cause.
Then, at: another example is the inference (78b3) he presents another example of this, saying that in this way (that is, by means of a demonstration 'quia'), one demonstrates that the moon is round because of its phases, according to which it waxes and wanes every month. They argue thus: “Everything which waxes thus circularly is circular; but the moon waxes thus: therefore, it is circular.” Put in this form it is a syllogism demonstrating 'quia'. But if the middle be interchanged, that is, if 'circular' be made the middle term and 'waxes' the major term, it becomes a demonstration 'propter quid'. For the moon is not circular because it waxes in that way, but because it is circular it undergoes such phases. Therefore, let C be the moon, that is, the minor extreme; let waxing be A, that is, the major extreme, and let circular be B, the middle term. This will be the situation in the syllogism propter quid.
Then, at: again, in cases where the cause (78b10) he shows that a demonstration through a non-convertible effect is quia. He says, therefore, that even in those syllogisms in which the middles are not converted with the extremes, and in which an effect rather than a cause is taken as the middle better known in reference to us, even in those cases the demonstration is “quia” and not “propter quid.”
If the middle be such that it can be converted with the major extreme and it exceeds the minor, then obviously it is a fitting syllogism; for example, if one proves that Venus is near because it does not twinkle. On the other hand, if the minor exceeded the middle, it would not be a fitting syllogism: for one cannot conclude universally of stars that they are near because they do not twinkle. Quite the contrary is true in comparison to the major term: for if the middle is in less things than is the major term, the syllogism is fitting, as when it is proved that someone has a sensible soul on the ground that he is capable of progressive local motion. But if it is in more, then the syllogism is not fitting, for from an effect which can proceed from several causes, one of them cannot be concluded. Thus, one cannot conclude from a rapid pulse that he has a fever.