Commentary Aristotle Posterior Analytics
Lecture 19
Whether upon unity of cause follows unity of effect, and vice versa; how cause and effect follow upon one another a1. Can the cause of an identical effect be not identical in every instance of the effect but different? Or is that impossible?
a2. Perhaps it is impossible if the effect is demonstrated as essential and not as inhering in virtue of a symptom or an accident—because the middle is then the definition of the major term—though possible if the demonstration is not essential.
a4. Now, it is possible to consider the effect and its subject as an accidental conjunction, though such conjunctions would not be regarded as connexions demanding scientific proof. But if they are accepted as such, the middle will correspond to the extremes, and be equivocal if they are equivocal, generically one if they are generically one. Take the question why proportionals alternate. The cause when they are lines, and when they are numbers, is both different and identical; different in so far as lines are lines and not numbers, identical as involving a given determinate increment. In all proportionals this is so. Again, the cause of likeness between color and color is other than that between figure and figure; for likeness here is equivocal, meaning perhaps in the latter case equality of the ratios of the sides and equality of the angles, in the case of colors identity of the act of perceiving them, or something else of the sort. Again, connexions requiring proof which are identical by analogy have middles also analogous.
a17. The truth is that cause, effect, and subject are reciprocally predicable in the following way. If the species are taken severally, the effect is wider than the subject (e.g., the possession of external angles equal to four right angles is an attribute wider than triangle or square), but it is coextensive with the species taken collectively (in this instance with all figures whose external angles are equal to four right angles). And the middle likewise reciprocates, for the middle is a definition of the major; which is incidentally the reason why all the sciences are built up through definition. We may illustrate as follows. Deciduous is a universal attribute of vine, and is at the same time of wider extent than vine; and of fig, and is of wider extent than fig: but it is not wider than but coextensive with the totality of the species. Then if you take the middle which is proximate, it is a definition of deciduous. I say that, because you will first reach a middle next the subject, and a premise asserting it of the whole subject, and after that a middle—the coagulation of sap or something of the sort—proving the connexion of the first middle with the major: but it is the coagulation of sap at the junction of leaf-stalk and stem which defines deciduous.
a30. If an explanation in formal terms of the inter-relation of cause and effect is demanded, we shall offer the following. Let A be an attribute of all B, and B of every species of D, but so that both A and B are wider than their respective subjects. Then B will be a universal attribute of each species of D (since I call such an attribute universal even if it is not commensurate, and I call an attribute primary universal if it is commensurate, not with each species severally but with their totality), and it extends beyond each of them taken separately. Thus, B is the cause of A’s inherence in the species of D: consequently A must be of wider extent than B; otherwise why should B be the cause of A’s inherence in D any more than A the cause of B’s inherence in D? Now, if A is an attribute of all the species of E, all the species of E will be united by possessing some common cause other than B: otherwise how shall we be able to say that A is predicable of all of which E is predicable, while E is not predicable of all of which A can be predicated? I mean how can there fail to be some special cause of A’s inherence in E, as there was of A’s inherence in all the species of D? Then are the species of E, too, united by possessing some common cause? This cause we must look for. Let us call it C. We conclude, then, that the same effect may have more than one cause, but not in subjects specifically identical. For instance, the cause of longevity in quadrupeds is lack of bile, in birds a dry constitution—or certainly something different.
b7. If immediate premises are not reached at once, and there is not merely one middle but several middles, that is, several causes; is the cause of the property’s inherence in the several species the middle which is proximate to the primary universal, or the middle which is proximate to the species? Clearly the cause is that nearest to each species severally in which it is manifested, for that is the cause of the subject’s falling under the universal. To illustrate formally: C is the cause of B’s inherence in D; hence C is the cause of A’s inherence in D, B of A’s inherence in C, while the cause of A’s inherence in B is B itself.
b15. As regards syllogism and demonstration, the definition of, and the conditions required to produce each of them, are now clear, and with that also the definition of, and the conditions required to produce, demonstrative knowledge, since it is the same as demonstration.
Can the cause of an identical effect. Having settled the question he raised, namely, whether upon the existence of the effect the existence of the cause follows, and conversely; the Philosopher now inquires whether unity of cause follows upon unity of effect, and conversely.
Concerning this he does two things.
First, he shows how one cause is inferred from one effect.
Second, from this he shows the sequential connection of cause and effect, at: the truth is that cause, effect, and subject (100a17; [578]).
In regard to the first he does three things.
First (100a1) he proposes the question, which is whether it happens that of the same effect there is not the same cause in all cases but different ones, or does this not occur? For it seemed to be supposed in solving the previous question that in various cases there can be various causes of one effect.
Second, at: perhaps it is impossible (100a2), he solves the question by distinguishing.
For it occurs that something is assigned as the cause of some effect in three ways: in one way, by taking the per se cause and then concluding the effect demonstratively; in another way, by taking a sign; in a third way, by taking an accident. Therefore, if one takes as cause that which is per se the middle of demonstration, there can be but one cause of one effect in all cases. And he proves this on the ground that a per se middle in demonstrations is a formality of the ultimate, that is, the definition of the major extreme, which, if it needs to be demonstrated of the subject, will be demonstrated by the definition of the subject, as we have established above. Now, it is obvious that of one thing there is one definition. Hence it is necessary that of one effect there is no cause but the one which is the middle of demonstration. However, if one does not take as the inferring cause that which is per se the middle of demonstration, but some sign or accident is used as the middle, then it does happen that of one effect several causes, as it were, are taken in diverse things, as is clear in the example given earlier. For the per se cause why something is blameworthy is that it is not according to reason. But to be excessive or defective is a sign of that which is not according to reason.
Third, at: now, it is possible to consider (100a4), he elucidates his solution by showing that the members of the division he cited are possible.
And he says that it is possible to consider both that which is the cause and that of which it is the cause, per accidens: (thus a musician is per accidens the cause of a house whose per se cause is a builder, who in turn is per accidens the cause of its being a haven for thieves, if this happens to occur in the house). Indeed, these problems even seem to be per accidens. But if cause and caused are not taken per accidens, it is required that the middle taken as cause be of the same order as the effect whose demonstration is sought. Hence if certain things are equivocal, then the common middle which is taken will also be equivocal; if they are not equivocal but agree as it were in genus, then the middle too will be common according to genus.
Thus the fact that proportionals alternate, that is, are commutatively proportional, is found univocally in many things, say in numbers and in lines, in which they have a cause which is in one sense different and in one sense the same: different, indeed, according to species, inasmuch as a line is one thing and a number another thing; but the same according to genus, inasmuch as lines as well as numbers agree in having such increments from which commutative proportion is demonstrated of them.
The other examples he gives concern equivocal things. He says that the cause of being similar is one thing in colors and another in figures, because similarity is predicated equivocally of the two. For in figures, to be similar consists in nothing more than that the sides have analogy, that is, that the sides are proportional and the angles equal. But in colors, similarity consists in the fact that they cause the same alteration in the sense, or something else of this sort.
Third, however, he says concerning things which agree according to analogy that in their case it is also required that the middle be one according to analogy, as when it was stated above that both a rainbow and an echo are reverberations.
Then, at: the truth is that cause, effect, and subject (100a17) he shows how in the light of the foregoing, causes follow one upon the other.
Concerning this he does three things.
First, he shows what sort of sequential connection there is between cause and effect.
Second, he orders this connection in a syllogistic figure, at: if an explanation in formal terms (100a30; [579]).
Third, he raises a doubt from the foregoing, at: if immediate premises (100b7; [580]).
He says therefore first (100a17) that the type of connection found between cause and caused and the subject in which that caused inheres is such that if one were to take in a particular case that of which the cause is sought, it will be in more than the cause or subject.
Thus, to have its exterior angles equal to four right angles belongs to every triangle for a single reason, namely, because its three exterior angles added to its three interior angles are equal to six right angles. Therefore, since the three interior angles are equal to two right angles, it follows that the three exterior angles are equal to four right angles. However, a rhombus also has four exterior angles equal to four right angles, but for another reason. For its exterior angles plus its interior angles equal eight right angles, but the four interior angles of a rhombus are equal to four right angles; therefore, the four exterior angles are equal to four right angles.
Therefore, to have its exterior angles equal to four right angles extends to more things than either triangle or rhombus does; but if the latter are taken together, they are equal to the former. For all figures which agree in having their exterior angles equal to four right angles must similarly agree as to their middle, which is the cause of being equal to four right angles. And he proves this, as in the previous case, on the ground that the middle is the definition of the major extreme. And this is why all sciences come to be in virtue of a definition.
He proves this also with an example from natural things. For the fact that its leaves fall follows on being a vine, but it extends to more, because it is true of several other things; it also follows upon being a fig tree, and extends to more. But it does not extend to more than the sum total of things in which it is found, but it is equal to their sum. Therefore, if someone desires to discover what is the first middle in relation to all, it will be the definition of the fact that the leaves fall: and this definition will be the first middle in respect to the others, since all the others are such. And again, some other middle will be discovered for this, say that the sap hardens by drying, or something of that sort. Hence, if it be asked what it is to have leaves fall off, we will say that it is nothing more than the seminal sap hardening at a point of contact, that is, where the leaf meets a branch.
Then, at: if an explanation in formal terms (100a30) he arranges the mode of the aforesaid connection in syllogistic form.
He says that if the sequence of cause and caused be sought, it can be assigned in the following way according to the figures of syllogisms. Thus let A be in every B, and B in all things that are D, but in things additional to D. Then B will inhere universally in the things contained under D, inasmuch as that is said to inhere universally which is not converted. But a primary universal is one such that each of the inferiors contained under it is not converted with it, but all of them taken together are converted with the first universal and exceed each of those which are contained under it. Thus, therefore, the cause of the fact that A inheres in the things contained under D is B. Therefore, it is required that A extend to more things than B does. If this were not so but they were equal, then why should B be the cause of inferring that A is in D, any more than A be the cause of inferring that B is in D? For either of two convertible things can be concluded from the other. Suppose, furthermore, that A is predicated of all things in which E inheres, but is not convertible. Then it will be necessary to say that all the things contained under E form one thing, which is diverse from B. For if E were not diverse from B, how could it be true to say that A inheres in every B and not vice versa, since A is only in E and in B? And so it would follow, if E and B were not diverse, that A would not be in more than E. Therefore, suppose that A is in more things than D and than E. Then why could not a cause be found explaining why it is in all things which are in D? And this cause is B. But we must still inquire whether all the things contained under E have one cause. Let C be that cause. Thus, therefore, he concludes that a same thing turns out to have several causes, but not in the same subject according to species. Thus the cause of that which is A is both B and C; but B is the cause that A is found in the things contained under D, while C is the cause that A is found in the things contained under E. And he gives an example from natural things. Let the fact of being long-lived be taken as A; quadrupeds as D; to have no bile, that is, in superfluity (which is the cause of long life in quadrupeds) as B;
birds as E; and to be dry, or something of that sort, which is the cause of long life, or something of that sort in birds, as C.
Then, at: if immediate premises (100b7) he raises a problem occasioned by the foregoing.
For it was stated above that one does not straightway from the beginning arrive at something atomic, that is, at the indivisible, in which is found that whose cause is being sought. But straightway many and indistinct things are found in which that one thing occurs; furthermore, there is not one middle through which this one thing can be demonstrated of all, and the causes are several. The doubt therefore is whether, if some cause is to be taken of these several middles, it is to be taken on the side of the primary universal, say on the side of A, or on the side of the singulars, that is, of those which are less common, as E and D were taken above, that is, quadrupeds and birds?
And he answers this by saying that it is always required to take the middles which are nearer the subject, in which the cause of that common caused thing is searched for: and it is necessary to proceed thus until one reaches that which is immediate to the common caused thing. And he assigns a reason for this, namely, because that which is on the part of what is contained under something common is the cause of its being under this common thing; just as is the case if D is under B, and if C is the cause of D having B in it. And from this it further follows that C is the cause of A’s being in D, and that B is the cause of A’s being in C. But A is in B in virtue of itself and immediately.
Finally (100b15), he summarizes what has been said in the entire teaching of the Analytics.
He says that it is clear from all that has been stated—both in the book of the Prior and in this book of the Posterior—concerning the syllogism and concerning demonstration, both what each is and how each is formed. Furthermore, in regard to demonstrative science it is also clear how it comes to exist in us. For this pertains to the same thing, because demonstration is a syllogism causing scientific knowledge, as has been established above.