Commentary Aristotle Posterior Analytics
And so he concludes that if the cause and the caused are taken to be simultaneous, it is necessary that they likewise be simultaneous in coming to be, in being, in having come to be, and in future coming to be.
Then, at: but what of cases (96a23), he shows how a cause which is not simultaneous with its effect is taken as the middle of demonstration.
First, in things that come to be in a direct line.
Second, in things that come to be reciprocally, at: now, we observe in Nature (96b38; [521]).
Concerning the first he does three things.
First, he states the question.
Second, he interjects something that must be known in order to solve the question, at: now, on this theory (96a27; [510]).
Third, he settles the question, at: we have also to inquire (96b1; [514]).
First, he proposes the question.
Second, he elucidates it, at: as they seem to us (96a24; [509]).
First therefore (96a23) he proposes the question, namely, whether in the case of causes which are not simultaneous with what they cause, one should say that what is caused follows upon its cause according to a continuous temporal succession, or not?
Then, at: as they seem to us (96a24) he restates the question more plainly.
For we see that some causes of things do not exist at the same time as those things: thus the cause of a “having come to be” is something prior to it, namely, a “coming to be”; and the cause of a “shall have come to be” is a “shall be coming to be”; and again the cause of a “coming to be” is a previous “has come to be.” Therefore, the question is this: Do these causes which follow one upon the other exist in a continuous span of time or not? For it is necessary that the demonstrator know this, because if there is no continuity in these causes, it will not be possible to employ an immediate principle, because between any two discontinuous now’s it is always possible to take something intermediate. Consequently, if that now during which the effect exists is not continuous with that now in which the cause exists, it will be possible to find a cause between them, and so on to infinity.
Then, at: now, on this theory (96a27) he explains something that must be understood in order to solve this question.
First, he proposes what he intends.
Second, he proves what he has proposed, at: be the time interval definite (96a32; [511]).
In regard to the first (96a27) it should be noted that just as a line is a continuous thing, but a point is an indivisible which terminates and divides the line, so the process of becoming or of being moved is something continuous, but the fact of having been moved or having come to be is something indivisible which can be taken either as terminating an entire motion or as dividing the motion, in the sense of being the end of the first part and the beginning of the second part of the motion, just as in the case of a point which divides the line. In this way, therefore, a “having come to be” is both a cause which precedes a “coming to be” of which it is the principle, and an effect following the “coming to be” of which it is the terminus.
Therefore, if we are to demonstrate, the demonstrative syllogism must proceed from a subsequent “having come to be” to a previous “coming to be.” Thus, we would say: “This has come to be; therefore that was previously coming to be.”
But because the very “having come to be” is the principle of the “coming to be” (or the things that have come to be are the cause of those that are coming to be), it follows that the former is similarly related to the things that are coming to be, namely, that one may syllogize from a subsequent “coming to be” to a prior “having come to be,” as though we were to say: “The sun is being moved to the midst of the heavens; therefore it was previously moved to a point in the east.”
But one may not syllogize from what is prior to what is later and say, for example, that because this has first come to be, it follows that what is later is coming to be or has come to be. And what is true of the relationship between coming to be and having come to be applies to what shall have come to be and what will be coming to be.
Then, at: be the time interval definite (96a32) he proves what he had said.
First, he proves his proposition with a reason based on the notion of time considered absolutely.
Second, with a reason based on the time that intervenes between a cause which is prior and an effect which is subsequent, at: and it is a further difficulty (96a39; [513]).
He says therefore first (96a32) that the reason why one may not syllogize from what is prior to what is subsequent is that the prior having been posited, it is not necessary that the subsequent follow either at some definite time or at some indefinite future time.
First, therefore, he manifests this in regard to a definite time, as in the case where we might say: “The patient has drunk the medicine; therefore he will be cured on such and such a day.” For if one could syllogize from a previous fact to something which will occur later at a definite time, it would be possible to conclude that because it is true to say that this has happened, namely, that the patient has drunk the medicine, it will also be true to say that what is subsequent has come to pass, namely, that he has been cured. But this does not follow: because it is possible to discover some time in which it is true to say that he has drunk the medicine but not yet true to say that he has been cured, say the time between the taking of the medicine and the attainment of the cure. And this is what he says, namely, that the reason why the aforesaid conclusion does not follow is because during the interim it is false to say that this has taken place, namely, that he has been cured, although the other has already taken place, namely, that he has drunk the medicine. The same reasoning holds in regard to the future. For we cannot conclude, “He is now drinking the medicine; therefore he will be cured,” referring to some definite time; because this will not be true for each subsequent period of time, namely, not in the intervening time.
Second, at: and the same argument (96a35), he proves the same point in regard to an unspecified future time, as when we might say, “He is drinking the medicine; therefore he will be cured.” For it does not follow that because this has taken place, namely, that he has drunk the medicine, that this will be, namely, that he will be cured. For it has already been established that a cause which necessarily infers its effect is simultaneous with its effect. Furthermore, the middle which is taken is homogeneous, that is, of one genus. For example, to prove that certain things have come to be in the past, one takes as the middle and cause something which has taken place in the past; likewise, for things of the future, something which is future, and for things that are in the process of coming to be, one takes that which is coming to be, and for things that exist, one takes that which exists. However, when one syllogizes, “This has taken place; therefore this will be,” the middle taken is not of one genus, but one middle is prior and the other subsequent. Therefore, having posited what is prior, the subsequent does not follow of necessity in those cases in which the effect of causes can be impeded.
Then, at: and it is a further difficulty (96a39) he presents another argument which is based on the intervening time.
And he says that just as on the part of time considered absolutely, it is obvious that one may not syllogize from what is prior to what is subsequent either according to a specified time or according to an unspecified time; so neither on the part of the intervening time is it possible to assume a specified or an unspecified time in which that which is subsequent can be concluded from what is prior. For it has already been established that during the entire intervening time it is false to say that the subsequent exists, even though that which is prior has already occurred.
Lecture 11
How a cause which is not simultaneous with its effect may be taken as a middle in demonstration
b1. We have also to inquire what it is that holds events together so that the coming-to-be now occurring in actual things follows upon a past event. It is evident, we may suggest, that a past event and a present process cannot be ‘contiguous’, for not even two past events can be ‘contiguous’. For past events are limits and atomic; so just as points are not ‘contiguous’ neither are past events, since both are indivisible. For the same reason a past event and a present process cannot be ‘contiguous’, for the process is divisible, the event indivisible. Thus the relation of present process to past event is analogous to that of line to point, since a process contains an infinity of past events. These questions, however, must receive a more explicit treatment in our general theory of change.
b12. The following must suffice as an account of the manner in which the middle would be identical with the cause on the supposition that coming-to-be is a series of consecutive events: for in the terms of such a series too the middle and major terms must form an immediate premise; e.g., we argue that, since C has occurred, therefore A occurred: and C’s occurrence was posterior, A’s prior; but C is the source of the inference because it is nearer to the present moment, and the starting-point of time is the present. We next argue that, since D has occurred, therefore C occurred. Then we conclude that, since D has occurred, therefore A must have occurred; and the cause is C, for since D has occurred C must have occurred, and since C has occurred A must previously have occurred. If we get our middle term in this way, will the series terminate in an immediate premise,