Commentary Aristotle Posterior Analytics
b38. Now, we observe in Nature a certain kind of circular process of coming-to-be; and this is possible only if the middle and extreme terms are reciprocal, since conversion is conditioned by reciprocity in the terms of the proof. This — the convertibility of conclusions and premises — has been proved in our early chapters, and the circular process is an instance of this.
a2. In actual fact it is exemplified thus: when the earth had been moistened an exhalation was bound to rise, and when an exhalation had risen cloud was bound to form, and from the formation of cloud rain necessarily resulted and by the fall of rain the earth was necessarily moistened: but this was the starting-point, so that a circle is completed; for posit any one of the terms and another follows from it, and from that another, and from that again the first.
a8. Some occurrences are universal (for they are, or come-to-be what they are, always and in ever case); others again are not always what they are but only as a general rule: for instance, not every man can grow a beard, but it is the general rule. In the case of such connexions the middle term too must be a general rule.
a12. For if A is predicated universally of B and B of C, A too must be predicated always and in every instance of C, since to hold in every instance and always is of the nature of the universal. But we have assumed a connexion which is a general rule; consequently the middle term B must also be a general rule. So connexions which embody a general rule — that is, which exist or come to be as a general rule — will also derive from immediate basic premises.
a20. We have already explained how essential nature is set out in the terms of a demonstration, and the sense in which it is or is not demonstrable or definable.
Now, we observe in Nature. After showing how one must take the middle, which is the cause, in things that come to be in a direct line, the Philosopher now shows how one should take it in the case of things that come to be in reciprocal generation.
First, he proves his proposal.
Second, he elucidates it with examples, at: in actual fact it is exemplified (97a2; [523]).
In regard to the first it should be noted that because the circular movement of the heavens is the cause of generation in sublunar things, it is stated in On Generation II that a kind of circular reciprocity is found in generation in the sense that earth is generated from water, and water in turn from earth.
He says therefore (96b38) that since we observe a certain pattern of generation in things that are generated circularly, it is possible in these cases also to follow what has been established above, namely, to syllogize from what is subsequent, provided that the terms of the demonstration are taken in such a way that middle and extremes follow one upon the other: because in the case of things that are generated in that way, there is a kind of circular conversion in the sense that one passes from the first thing to the last thing, and then a return is made from the last to the first; although these things are not numerically but specifically the same, as is explained in On Generation II. Hence it does not follow that the same numerical thing is prior and subsequent, or is cause and effect. And this is suitable to the process of demonstrations, for, as has been established in the foregoing, whenever conclusions are converted, that is, whenever some of the premises can be syllogized from them, this is a circular demonstration. And although this is not fitting if the very same thing which was first the conclusion is later the principle of the same numerical thing (otherwise the same thing would be at once better known and less known), nevertheless if they are not entirely the same, as happens in things that are circularly generated, there is nothing unfitting.
Then, at: in actual fact it is exemplified (97a2) he uses examples to elucidate what he has said.
He says that a circular process is seen to occur in the works of nature. For if the earth is saturated with rain, it is necessary that the action of the sun release vapors from it; when these are released and borne aloft, it is necessary that clouds be formed; and after they are formed, it is necessary that rain water be formed; and when this is formed, it is necessary that in falling upon the earth it saturate it. Now, this saturation of the earth was the very thing we took as being first; however, it is not the same saturation as the one from which we first began. Thus it is clear that a cycle has been achieved in the sense that with one of them existing, another comes to be; and that other existing, still another comes to be; and that one existing, a return is made to the first, which is not numerically the same, but specifically the same.
Yet this cycle of causes cannot be found according to the order which is found in per se causes; for in per se causes it is necessary to reach some one thing which is first in each genus of causes as is proved in Metaphysics II. But the fact that water is generated from fire, and fire in turn from water, is not per se but per accidens. For being is generated per se not from actual being but from potential being, as it is stated in Physics I. Therefore, if we proceed from cause to cause in per se causes, there will not be a cycle. For we will accept as the efficient cause of the rain-soaked earth, the heat of the air which is caused by the sun, but not vice versa; but the material cause we take as water, whose matter is not vapor but the common matter of the elements.
Then, at: some occurrences are universal (97a8) he shows how one demonstrates through the cause differently in things which occur always and in things which occur as a general rule.
Concerning this he does three things.
First, he proposes what he intends.
Second, he proves what he has proposed, at: for if A is predicated (97a12; [525]).
Third, he sums up, at: we have already explained (97a20; [526]).
He says therefore first (97a8) that there are some things which come to be universally both as to time, because always, and as to subject, because in all cases; either because they maintain themselves as unchangeable things which are not subject to coming to be, or because they come to be as changeable things which always follow a uniform pattern, as in the case of heavenly movements. Again, there are other things which do not occur in the sense of always, but as a general rule. An example of this is that every human male develops a beard as a general rule, although it does not occur always. Therefore, just as in the case of things that occur always, it is necessary to take a middle which is always, so in the case of things which occur as a general rule, it is necessary to take a middle that occurs as a general rule.
Then, at: for if A is predicated (97a12) he proves that if one is to conclude to something that occurs as a general rule it is necessary to take a middle which occurs as a general rule.
For if one were to assume the opposite by taking a middle which occurs universally and always; for example, if A, which is the major extreme, is predicated universally of B, which is the middle, and B of C, which is the minor extreme, then it follows of necessity that A is predicated universally of C both as to time and as to subject, which is the same as being predicated always and of each thing. Hence, we are now saying that for something to be predicated universally is the same as being predicated of all and always. But it has been assumed that A is predicated of C as a general rule. Therefore, it is necessary that the middle, which is B, should be taken as existing as a general rule.
Thus it is obvious that certain immediate principles of things which occur as a general rule can be taken, such that those principles exist or come to be as a general rule. Yet such demonstrations do not enable one to know that what is concluded is true absolutely but only in a qualified sense, namely, that it is true in the majority of cases. And this is the way that the principles which are taken possess truth. Hence sciences of this kind fall short of sciences which deal with things absolutely necessary, so far as the certitude of demonstration is concerned.
Then, at: we have already explained (97a20) he sums up what has been said.
He says that we have now established how the 'quod quid' which is practically identical with the 'propter quid' is assigned among syllogistic terms, inasmuch as we have shown how the several genera of causes are middles of demonstration according to the respective diversities of things. We have also shown in what sense there is or is not demonstration or definition of the 'quod quid'.
Lecture 13
Characteristics which should be present in the items which constitute the definition signifying the essence of a thing
a22. So let us now discuss the method to be adopted in tracing the elements predicated as constituting the definable form.
a24. Now, of the attributes which inhere always in each several thing there are some which are wider in extent than it but not wider than its genus (by attributes of wider extent I mean all such as are universal attributes of each several subject, but in their application are not confined to that subject). While an attribute may inhere in every triad, yet also in a subject not a triad — as being inheres in triad but also in subjects not numbers at all — odd on the other hand is an attribute inhering in every triad and of wider application (inhering as it does also in pentad), but which does not extend beyond the genus of triad; for pentad is a number, but nothing outside number is odd.
a32. It is such attributes which we have to select, up to the exact point at which they are severally of wider extent than the subject but collectively coextensive with it; for this synthesis must be the substance of the thing.
a34. For example, every triad possesses the attributes number, odd, and prime in both senses, that is, not only as possessing no divisors, but also as not being a sum of numbers. This, then, is precisely what triad is, viz. a number, odd, and prime in the former and also the latter sense of the term: for these attributes taken severally apply, the first two to all odd numbers, the last to the dyad also as well as to the triad, but, taken collectively, to no other subject.
b2. Now, since we have shown above that attributes predicated as belonging to the essential nature are necessary and that universals are necessary, and since the attributes which we select as inhering in triad, or in any other subject whose attributes we select in this way, are predicated as belonging to its essential nature, triad will thus possess these attributes necessarily.