Commentary Aristotle Posterior Analytics
b23. for since, as we said, no two events are ‘contiguous’, will a fresh middle term always intervene because there is an infinity of middles? No: though no two events are ‘contiguous’, yet we must start from a premise consisting of a middle and the present event as major.
b25. The like is true of future events too, since if it is true to say that D will exist, it must be a prior truth to say that A will exist, and the cause of this conclusion is C; for if D will exist, C will exist prior to D, and if C will exist, A will exist prior to it. And here too the same infinite divisibility might be urged, since future events are not ‘contiguous’. But here too an immediate basic premise must be assumed.
b31. And in the world of fact this is so: if a house has been built, then blocks must have been quarried and shaped. The reason is that a house having been built necessitates a foundation having been laid, and if a foundation has been laid blocks must have been shaped beforehand. Again, if a house will be built, blocks will similarly be shaped beforehand; and proof is through the middle in the same way, for the foundation will exist before the house.
We have also to inquire what it is. After stating the question whether in things that do not come to be simultaneously the subsequent according to temporal continuity follows the prior, and after interjecting something necessary, namely, that one may not syllogize from what is prior to what is subsequent, the Philosopher now undertakes to settle the question he raised.
Concerning this he does two things.
First, he shows how coming to be and having come to be are related according to continuity of time.
Second, he proves his proposal, at: the following must suffice (96b12; [516]).
He says therefore first (96b1), that in order to prove the proposal it is necessary to investigate what it is that joins or forms a continuity between a “having come to be” and a “coming to be,” so that one might follow the other without interruption. In regard to this he says first of all that it is obvious that a “coming to be” is not had, that is, is not consecutive to a “having come to be.”
(Those things are said to be consecutive which have no member of their genus between them; for example, two soldiers in a line or two clerics in their choir stalls. Had, however, adds the notion of contact to that which is consequent, as it is stated in Physics V).
Thus, therefore, he is saying that a “coming to be” cannot be consecutive or contiguous to a “having come to be.” Then he proves this, because not even a “having come to be” is contiguous in the sense of consecutive to any other “having come to be”: for two instances of “having come to be” are related in the way that two indivisible boundaries of time are related, or as two points in a line. Hence just as two points are not consecutive to one another, so neither are two instances of “having come to be”: for the points and the instances of “having come to be” exist as indivisibles, and such things are not consecutive in their continua, as is proved in Physics VI. And since two instances of “having come to be” are not consecutive, it is therefore obvious that a “coming to be” and a “having come to be” are not consecutive. For a “coming to be” is something divisible, just as a “being moved” is; but a “having come to be” is something indivisible, just as a point is. Therefore, as the line is to the point, so the “coming to be” is to the “having come to be.” For there is an infinitude of “having come to be’s,” just as there is potentially an infinitude of points in a line.
And this is the cause why it is impossible to take two points that are consecutive in a line, namely, because between any two points there is still another point to be taken; likewise, between any two “having come to be’s” there is another to be taken. Hence two “having come to be’s” are not consecutive. Furthermore, because a “having come to be” is the terminus of a “coming to be,” it follows that not even a “coming to be” is consecutive to a “having come to be”; otherwise two “having come to be’s” would be consecutive. Rather a “coming to be” is terminated immediately at a “having come to be,” as a line is terminated at a point. This matter is treated at greater length in the analysis of motion, that is, in Physics VI.
Then (96b12) he shows in the light of the foregoing how the effect can be taken as being immediate or mediate to the cause in cases where they are not simultaneous.
First, he proves his proposal.
Second, he elucidates it with examples, at: and in the world of fact (96b31; [520]).
Concerning the first he does two things.
First, he shows his proposal in regard to the past.
Second, in future things, at: the like is true of future events (96b25; [519]).
Concerning the first he does two things.
First, he shows his proposal.
Second, he excludes an objection, at: for since, as we said (96b23; [518]).
He says, therefore first (96b12) that from what has been established it is possible to gather how a cause which is taken as a middle in demonstration may be consecutive to that which is in the process of becoming or of being generated: because even in these demonstrations which syllogize about things that are in a “coming to be,” it is necessary to admit a middle and a first which are immediate, as when we conclude that A has come to be because C has come to be, so long, namely, as C has come to be subsequently and A previously.
For example, if we should say, “He has been cured; therefore he drank the medicine”: for the syllogism would not follow if we began with what is prior, as we have established above; but C is taken as a principle, although it is later in coming to be, owing to the fact that it is closer to the present now than A. But the present now is a principle of time because according to it the past and future are distinguished; hence it is necessary to take the present now as the principle for making known the succession of time. For in the realm of the past, something is more subsequent in becoming the closer it is to the present now.
Therefore, just as C is taken as the principle of syllogizing, since it is more subsequent in coming to be than A and closer to the present now, so we may take D as nearer to the present now than C, and conclude that if D has come to be, C came to be previously: for example, if he performs the tasks of a healthy man, then previous to that he was cured.
Therefore, we can conclude that if D has come to pass, it is necessary that A have previously come to pass; and we take as cause that which was in the interim, namely, C. For D having come to be, it is necessary that C previously have come to be; and C having come to be, it is necessary that A have previously come to be.
Therefore, D having come to be, it is necessary that A have previously come to be. For example, if this person now accomplishes the tasks of a healthy man, it follows that previously he had been cured; and if he has been cured, it is necessary that previously he have drunk the medicine.
Therefore, by always taking a middle in this way, for example, something else between C and A, as C was taken as middle between D and A, one will come to rest somewhere at something immediate.
Then, at: for since, as we said (96b23) he presents an objection.
For someone can say that some thing immediate will never be reached, but it will always be necessary to take something between two “having come to be’s” on the ground that in every instance of coming to be there is an infinitude of “having come to be’s,” since one “having come to be” is not consecutive to another, as has been said.
But he excludes this objection because although there is an infinitude of “having come to be’s” in one case of coming to be, nevertheless it is necessary to begin at some middle, namely, from a now as from something first: for it has been established that that which is subsequent is a principle of syllogizing. But in relation to all things that have come to be in the past, the latest is the present now; hence it is necessary to take the present now as the first and immediate principle. However, any other “having come to be” is taken as a mediate principle.
Then, at: the like is true of future events (96b25) he shows the same for future things.
He says that as the case was in that which has come to be, so it is in that which will have come to be: because if it is true that D will be, it is necessary that it previously be verified that A exists; and the cause of this will be taken to be C, which falls as middle between D and A. For if D will be, it is necessary that prior to it C will be, and if C will be, it is necessary that prior to it A will be. In this case, likewise, the objection concerning the infinite division of the future into instants, or of motion into moments can be lodged: because, as in the case of past things, so also in future things, the indivisibles are not consecutive.
Nevertheless here too, something must be taken as an immediate principle, as was done in things which came to be in the past. For although one cannot take two consecutive “having come to be’s” either in the past or in the future, nevertheless something terminal can be the closer it is to the present now; but the converse is true in regard to the one taken in both, and this will be taken as the immediate principle.
Then, at: and in the world of fact (96b31) he elucidates what he had said with examples.
He says that the manner of arguing employed above can be considered in regard to human works. Thus, let us take the “having come to be” of a house as something terminal; from this it is concluded, as something first, that it is necessary that the stones have previously been cut; and we shall take as middle the laying of the foundation: because if the house has been constructed, it is necessary that previously the foundation has been laid; and if the foundation has been laid, it is necessary first that the stones have been cut. And what was taken in regard to the past must also be taken in regard to the future: for example, if a house will exist, it is necessary that first the cutting of the stones will occur, and that this be demonstrated through some middle, which is the laying of the foundation.
Lecture 12
How in things that come to be reciprocally, a cause which is not simultaneous with the effect is taken as middle in a demonstration; how one demonstrates through cause differently, in things that occur always and in things that occur as a general rule