Commentary Aristotle Posterior Analytics
Lecture 9
Propter quid can be manifested in four genera of causes a20. We think we have scientific knowledge when we know the cause, and there are four causes: (1) the definable form, (2) an antecedent which necessitates a consequent, (3) the efficient cause, (4) the final cause. Hence each of these can be the middle term of a proof, a24. for though the inference from antecedent to necessary consequent does not hold if only one premise is assumed—two is the minimum—still when there are two it holds on condition that they have a single common middle term. So it is from the assumption of this single middle term that the conclusion follows necessarily.
a28. The following example will also show this. Why is the angle in a semicircle a right angle?—or from what assumption does it follow that it is a right angle? Thus, let A be right angle, B the half of two right angles, C the angle in a semicircle. Then B is the cause in virtue of which A, right angle, is attributable to C, the angle in a semicircle, since B=A and the other, viz. C,=B, for C is half of two right angles. Therefore, it is the assumption of B, the half of two right angles, from which it follows that A is attributable to C, that is, that the angle in a semicircle is a right angle. Moreover, B is identical with (b) the defining form of A, since it is what A’s definition signifies.
a35. Moreover, the formal cause has already been shown to be the middle.
a36. (c) ‘Why did the Athenians become involved in the Persian war?’ means ‘What cause originated the waging of war against the Athenians?’ and the answer is, ‘Because they raided Sardis with the Eretrians’, since this originated the war. Let A be war, B unprovoked raiding, C the Athenians. Then B, unprovoked raiding, is true of C, the Athenians, and A is true of B, since men make war on the unjust aggressor. So A, having war waged upon them, is true of B, the initial aggressors, and B is true of C, the Athenians, who were the aggressors. Hence here too the cause—in this case the efficient cause—is the middle term.
b8. (d) This is no less true where the cause is the final cause. e.g., why does one take a walk after supper? For the sake of one’s health. Why does a house exist? For the preservation of one’s goods. The end in view is in the one case health, in the other preservation. To ask the reason why one must walk after supper is precisely to ask to what end one must do it. Let C be walking after supper, B the non-regurgitation of food, A health. Then let walking after supper possess the property of preventing food from rising to the orifice of the stomach, and let this condition be healthy; since it seems that B, the non-regurgitation of food, is attributable to C, taking a walk, and that A, health, is attributable to B. What, then, is the cause through which A, the final cause, inheres in C? It is B, the non-regurgitation of food; but B is a kind of definition of A, for A will be explained by it. Why is B the cause of A’s belonging to C? Because to be in a condition such as B is to be in health. The definitions must be transposed, and then the detail will become clearer.
Incidentally, here the order of coming to be is the reverse of what it is in proof through the efficient cause: in the efficient order the middle term must come to be first, whereas in the teleological order the minor, C, must first take place, and the end in view comes last in time.
b27. The same thing may exist for an end and be necessitated as well. For example, light shines through a lantern (1) because that which consists of relatively small particles necessarily passes through pores larger than those particles—assuming that light does issue by penetration—and (2) for an end, namely to save us from stumbling. If then, a thing can exist through two causes, can it come to be through two causes—as for instance if thunder be a hiss and a roar necessarily produced by the quenching of fire, and also designed, as the Pythagoreans say, for a threat to terrify those that lie in Tartarus?
b35. Indeed, there are very many such cases, mostly among the processes and products of the natural world; for nature, in different senses of the term ‘nature’, produces now for an end, now by necessity. Necessity too is of two kinds. It may work in accordance with a thing’s natural tendency, or by constraint and in opposition to it; as, for instance, by necessity a stone is borne both upwards and downwards, but not by the same necessity.
a3. Of the products of man’s intelligence some are never due to chance or necessity but always to an end, as for example a house or a statue; others, such as health or safety, may result from chance as well. It is mostly in cases where the issue is indeterminate (though only where the production does not originate in chance, a7. and the end is consequently good), that a result is due to an end, and this is true alike in nature or in art. By chance, on the other hand, nothing comes to be for an end.
We think we have scientific knowledge. After showing how the 'quid est' functions relative to demonstration, the Philosopher now shows how the 'propter quid', which signifies the cause, functions relative to demonstration.
In regard to this he does two things.
First, he shows how causes are taken in a demonstration.
Second, how diversely in diverse things, at: the effect may be still (96a10).
Concerning the first he does two things.
First, he proposes what he intends.
Second, he manifests what he has proposed, at: for though the inference (95a24).
He says therefore first (95a20) that, as was established in the first book, because we think we know in a scientific manner when we know the cause, and a demonstration is a syllogism causing us to know in a scientific manner, the consequence is that the middle of a demonstration is a cause. But there are four genera of causes as is more fully explained in Physics II and Metaphysics V. One of these is the 'quod quid erat esse', that is, the formal cause, which is the completeness of a thing’s essence. Another is the cause which, if placed, the caused must also be placed: this is the material cause, because things which follow on the necessity of matter are necessary absolutely, as is established in Physics II. The third is the cause which is the source of motion, that is, the efficient cause. But the fourth is that for the sake of which something is performed, namely, the final cause. And so it is clear that through the middle in a demonstration all these causes are manifested, because each of these causes can be taken as the middle of a demonstration.
Then, at: for though the inference (95a24) he manifests what he had said.
First, he shows how the various causes are taken as middles of demonstration in various things.
Second, he shows how there can be various causes of the same thing, at: the same thing may exist (95b27).
Concerning the first he does four things.
First, he shows how the material cause is taken in demonstration.
Second, he manifests his point in regard to the formal cause, at: moreover, the formal cause (95a35).
Third, he does the same in regard to the efficient cause, at: why did the Athenians (95a36).
Fourth, in regard to the final cause, at: this is no less true (95b8).
Regarding the first he does two things.
First, he sets forth the way in which the material cause is taken in a demonstration; a way, namely, that applies also to the other causes.
Second, he presents an example, at: the following example (95a28).
He says therefore first (95a24) that that which once it exists, something else must also exist, namely, a material cause, is not to be so taken that something follows of necessity if one proposition alone is taken; rather, one must take at least two which are so related that they communicate in one middle. Therefore, if one middle which is the material cause be taken in two propositions, a conclusion follows of necessity; as if we were to say: “Everything composed of contraries is corruptible; but a stone is such: therefore, a stone is corruptible.” Now, it is required that two propositions be taken, not only because the syllogistic form demands it, but also because not all things which are from matter have necessity from the matter, as is proved in Physics II. And therefore, besides the proposition in which it is stated that this has matter, another must be taken which declares that from such matter something follows of necessity.
Then (95a28) he presents an example from mathematics, at: the following example.
Now this does not conflict with the statement in Metaphysics III that mathematical sciences do not demonstrate through material cause: for although mathematics abstracts from sensible matter, yet not from intelligible matter, as it is stated in Metaphysics VI. This matter is considered intelligible precisely insofar as something divisible is taken in numbers or in continua. Therefore, in mathematics whenever something is demonstrated of a whole through the parts, it seems to be a demonstration through material cause: for the parts are compared to the whole according to the notion of matter, as is stated in Physics II. And because matter is more properly said of sensible things, he preferred not to name it material cause, but a cause of necessity.
To understand the example in the text it should be noted that every angle inscribed in a semicircle is a right angle, as is proved in Euclid III in the following way: Given a semicircle ABC such that its chord, namely, the diameter of the whole circle, is cut in half at the point D which is the center of the circle. From this point D draw a perpendicular line which touches the circumference of the circle at point B, from which are drawn two lines, one to point A and one to point C. He says, therefore, that angle ABC which falls within the semicircle is a right angle. And the proof is this: Triangle BDC has three angles equal to two right angles; but its angle BDC is a right angle, because BD is perpendicular to DC. Therefore, its other two angles, namely, DBC and BCD are equal to one right angle. But these two angles are equal, because the lines BD and DC are equal; since they proceed from the center to the circumference. It follows therefore that angle DBC equals one half a right angle. In the same way it is proved that angle ABD equals one half a right angle. Therefore, the entire angle ABC is a right angle.