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; [504]).

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; [492]).

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.

In regard to this he does two things.

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; [500]).

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; [497]).

Third, he does the same in regard to the efficient cause, at: why did the Athenians (95a36; [497]).

Fourth, in regard to the final cause, at: this is no less true (95b8; [498]).

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; [494]).

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.

This, proof, therefore, the Philosopher uses here, saying that in this way it is shown why “that is right which falls in a semicircle,” that is, why the angle which falls in a semicircle is a right angle, when that is given which, when it exists, it follows that it is a “right.” Therefore, let right angle be A, the major extreme; the half of two right angles, the middle, be B; and angle falling in a semicircle, the minor extreme, be C. Now, the cause of A’s being in C, that is, of the angle in the semicircle’s being right, is B, namely, that the angle of a semicircle is half of two right angles. For this half is by conversion equal to A; in like manner, C is equal to B. For B consists in being the half of two right angles. Therefore, since this is the case, it is necessary that A be in C, which is nothing else than for the angle of a semicircle to be right. He further adds that this method of demonstration can also pertain to the formal cause (which he called 'quod quid erat esse') on the ground that being half of two right angles can be taken as an expression signifying the 'quod quid' of a right angle.

Then, at: moreover, the formal cause (95a35) he returns to what has been previously established.

He states that it was shown there how the formal cause which is the 'quod quid erat esse' pertains to the middle of demonstration.

Then, at: why did the Athenians (95a36) he gives an example of the movent cause, touching on an event from the history of the Greeks, namely, that the Athenians, allying themselves with certain other Greeks, once invaded the Sardians who were subject to the king of the Medes; and for that reason the Medes invaded the Athenians.

He says, therefore, that one might ask propter quid [that is, why] the war of the Medes with the Athenians occurred; and this 'propter quid' would be the cause why the Athenians were attacked by the Medes, namely, because the former along with certain allies, namely, the Eretrians, made an assault upon the Sardians: for this was the first motive of the war. Therefore, let war be the major extreme, A, and the first to attack be the middle, B, but Athenians, the minor extreme, C. Therefore, B is in C, (so far forth namely as it belongs to the Athenians that they were the first to make an assault.) But A is in B, because namely the ones who were first to work an injustice were in turn warred upon. Thus, therefore, A is in B, inasmuch as they were attacked who first launched the war. But this, namely B, which is the middle, pertains to the Athenians who first began the war. And thus it is clear that in this example the cause which first moved is taken as middle.

Then, at: this is no less true (95b8) he manifests the same thing in the final cause.

Concerning this he does two things.

First, he sets forth an example in final cause.

Second, he shows the difference between the final cause and the cause which is the source of motion, at: incidentally, here the order (95b8; [499]).

He says therefore first (95b8) that it happens in like manner in all cases where the cause taken is the end for the sake of which something is done: for example, if we should state "propter quid [that is, for what purpose] someone walks after dinner," namely, to be made healthy; and again propter quid [that is, for what] does a house exist, namely, so that the vessels, that is, a man’s belongings, may be kept safe. Thus, therefore, this, namely, walking after dinner is done for the sake of health; this other, namely, the building of a house is for the sake of keeping belongings safe. Thus, there is no difference in saying propter quid [that is, for what purpose] one should walk after dinner and that for the sake of which this is necessary. So let 'walk after dinner' be C, the minor extreme; but 'food not to rise to the entrance of the stomach' be B, the middle; and 'be made healthy' be A, the major extreme. Hence let B be in C, because walking after dinner brings it about that food does not rise to the entrance of the stomach; and for this reason one is made healthy, which is for A to be in B. For it is seen that to walk, which is C belongs B, which is that food does not rise to the entrance of the stomach. From this follows A, which is to be made healthy. Thus, therefore, it is clear that B, namely, that the food does not rise to the entrance of the stomach is the cause why C is A, that is, why walking after dinner is healthful: and this, namely, that foods do not rise to the entrance of the stomach is involved in the notion of being kept healthy. For A, that is, to be healthful, will be thus explained, that is, made known. But the fact that B is in C is 'propter quid', namely, because to be healthy consists in being in such a state that foods do not rise to the opening of the stomach. And in order that each of these be better understood one should arrange the reasons, so that the middle will be taken as the reason of the major extreme, as appears in the above example.

Then, at: incidentally, here the order (95b8) he shows how the situation is otherwise in the cause which is the principle of motion.

For in the order of generation the final cause and the cause which is the principle of motion behave in contrary ways. For there, namely, in the demonstration which is based on the cause which is the principle of motion, the middle must eventuate first, that is, be first in the order of generation, just as the Athenians assaulted the Sardians before being attacked by the Medes. But here, in the demonstration which is based on final cause, the first to be taken in the order of generation is C, which is the minor extreme; and the last, the effect of the final cause. But in the way of generation the last thing is the end for the sake of which something is done. For it is obvious that one first of all walks after dinner, and on that follows the fact that foods do not rise to the entrance of the stomach, upon which further follows the man’s health which is the chief end.

Then, at: the same thing may exist (95b27) he shows how for the same effect several of the aforesaid causes can be taken.

In regard to this he does two things.

First, he manifests that there are several causes of a same thing.

Second, he shows the cases in which this is applicable, at: indeed, there are very many (95b35; [501]).

He says therefore first (95b27), that it happens that one and the same effect exists because of an end or for its sake, and also from the necessity of some prior cause: thus, the fact that light appears through the skin of a lantern comes about of necessity; for it is necessary that a tiny body pass through pores that are larger. Now, this is said according to the opinion of those who posit light as a subtle body, and the appearance of light through a transparency as occurring because of the size of the pores which are regarded as openings. But a subtle body seems to be comprised of tiny parts. And because this is not according to his own opinion, he adds that this arises from that sort of necessity, namely, if light does appear by passing through, that is, by the passing of its parts through the pores of the transparency. But the appearing of light through the skin of a lantern occurs for some end, namely, in order that with the help of the light we might walk at night without stumbling. In such cases, therefore, it is possible to argue in two ways: in one way from a preexisting cause, as when we say that if this occurs then this other will occur; for example, if a light is set in a lantern, it follows that it will be diffused through the pores of the skin. In another way from a posterior cause which is posterior in the order of becoming. According to this, one will argue that if some ultimate end comes to pass, it is required that those items precede through which the end is attained, as is clear in thunder; which if it is quenched fire, it is necessary that it hiss, that is, make the sound and roar of fire being quenched. And if the opinion of the Pythagoreans is true that thunder takes place to strike terror into the denizens of Tartarus, then one should say that thunder takes place to the end that the men in Tartarus shudder.

Then, at: indeed, there are very many (95b35) he shows in which things this occurs that has been said.

In regard to this he does three things.

First, he shows how this is in regard to things which are from nature.

Second, with things that are done intentionally, at: of the products of man’s intelligence (96a3; [502]).

Third, he draws a corollary, at: and the end is consequently (96a7; [503]).

He says therefore first (95b35), that very many of these, namely, which are from necessity and are done for an end, are found chiefly in things which subsist by nature and in things which are constructed by nature. For nature makes certain things, acting for an end, and certain things it makes from the necessity of prior causes.

This latter is twofold:

one, according to nature, which is according to the condition of the matter;

the other, according to movent cause as a stone is moved by necessity sometimes upwards and sometimes downwards, but not on account of the same type of necessity: it is moved downward on account of a necessity of nature, but upward on account of a necessity of the mover, that is, of the one casting it.

Then, at: of the products of man’s intelligence (96a3) he shows how this is in regard to things that proceed from intention.

And he says that in things that are done through reason (as works of art are), some are such that they never occur by chance; for example, a house and a statue, and never from the necessity of nature: but they are always done for an end, because they are always done by reason, which does not act without intending an end. However, there are certain things which can indeed be produced from the reasoning of art, but can also come about through fortune: as in the case of health, which can sometimes be produced by the art of medicine; but because it can occur from a natural cause, it can happen that someone be healed not intending it, as if a leper should be healed from eating a serpent which he ate to die. The same can happen in regard to safety, namely, when a person entering a house for some other purpose is saved from the hands of enemies hunting him. And this happens mainly in all cases in which something can happen one way or another, when it is not due to fortune, that is, when a same effect might happen without fortune from various causes. For example, a person might enter a house not by chance in order to be saved from the hand of his enemies or to eat or to rest. Hence, if in intending one of these something else occurs, it will be from fortune. But a house and a statue cannot be produced except by identical causes and therefore such things cannot be done by fortune.

Then, at: and the end is consequently (96a7; [503]), he concludes from the foregoing that arrival at a good is either by nature or by art. For art and nature operate in similar fashion for an end, as is stated in Physics II. But what is done by fortune is not done of set purpose. He says this because even though fortune may be involved in things that are being done for something, as it is stated in Physics II, nevertheless that which is said to be done by fortune is not intended as an end, but happens outside one’s intention.