Lecture 10 — How something is demonstrated through a cause not simultaneous with its caused: how a cause not simultaneous with its effect is taken as middle in demonstrating

a10. The effect may be still coming to be, or its occurrence may be past or future, yet the cause will be the same as when it is actually existent—for it is the middle which is the cause—except that if the effect actually exists the cause is actually existent, if it is coming to be so is the cause, if its occurrence is past the cause is past, if future the cause is future.

a13. For example, the moon was eclipsed because the earth intervened, is becoming eclipsed because the earth is in process of intervening, will be eclipsed because the earth will intervene, is eclipsed because the earth intervenes. To take a second example: assuming that the definition of ice is solidified water, let C be water, A solidified, B the middle, which is the cause, namely total failure of heat. Then B is attributed to C, and A, solidification, to B: ice when B is occurring, has formed when B has occurred, and will form when B shall occur. This sort of cause, then, and its effect come to be simultaneously when they are in process of becoming, and exist simultaneously when they actually exist; and the same holds good when they are past and when they are future.

a23. But what of cases where they are not simultaneous? Can causes and effects different from one another form,

a24. as they seem to us to form, a continuous succession, a past effect resulting from a past cause different from itself, a future effect from a future cause different from it, and an effect which is coming-to-be from a cause different from and prior to it?

a27. Now, on this theory it is from the posterior event that we reason (and this though these later events actually have their source of origin in previous events — a fact which shows that also when the effect is coming-to-be we still reason from the posterior event), and from the event we cannot reason (we cannot argue that because an event A has occurred, therefore an event B has occurred subsequently to A but still in the past — and the same holds good if the occurrence is future) — cannot reason because,

a32. be the time interval definite or indefinite, it will never be possible to infer that because it is true to say that A occurred, therefore it is true to say that B, the subsequent event, occurred; for in the interval between the events, though A has already occurred, the latter statement will be false.

a35. And the same argument applies also to future events; that is, one cannot infer from an event which occurred in the past that a future event will occur. The reason of this is that the middle must be homogeneous, past when the extremes are past, future when they are future, coming to be when they are coming-to-be, actually existent when they are actually existent; and there cannot be a middle term homogeneous with extremes respectively past and future.

a39. And it is a further difficulty in this theory that the time interval can be neither indefinite nor definite, since during it the inference will be false.

The effect may be still coming to be. After showing how the four genera of causes are used as middles in demonstrating, the Philosopher now shows how in different cases something is demonstrated through a cause.

But there are two differences to be noted in this regard:

the first difference is whether the cause is or is not simultaneous with its effect;

the second difference is whether the cause produces its effect always or only as a general rule—this second difference will be discussed later, at: some occurrences are universal (97a8; [524]).

Concerning the first he does two things.

First, he shows how something is proved through a cause which is simultaneous with that of which it is the cause.

Second, how something is demonstrated through a cause which is not simultaneous with that of which it is the cause, at: but what of cases (96a23; [508]).

In regard to the first point it should be noted that since one is involved with the notions of prior and subsequent when he analyzes motion, so too in considering the causes of motion one must take into account that the cause and the caused are related as prior and subsequent. For it is obvious that a natural agent causes its effect by moving something.

Furthermore, just as the movable object is brought to the terminus of its motion by virtue of the entire motion, so by virtue of the first part of that motion it is brought to the second part, and so on. Hence, just as the entire motion is the cause of the subsequent state of rest, so the first part of the motion is the cause of the subsequent part, and so on.

This analysis is true whether we confine ourselves to one object which is being moved without interruption from beginning to end, or to several objects the first of which moves the second and the second the third. And although at the same time that the first mover is moving its object that object is being moved, nevertheless the object thus moved continues to act as mover even after it stops being moved. Consequently, while it is acting as mover, another object is being moved.

In this way several moveable objects are successively moved in such a way that one is the cause of the motion of another, and so on, as happens in the case of thrown objects whose motion the Philosopher explained in Physics VIII. Therefore, in this example it turns out that the cause is not simultaneous with that of which it is the cause, namely, inasmuch as the first part of the motion is the cause of the second part, or the first moved object moves the second.

But although the motion has succession in its parts, it is nevertheless simultaneous with its movent cause. For the moveable object is moved at the same time that the mover acts, inasmuch as motion is nothing else than the act existing in the moveable object from the mover, such that in virtue of that act the mover is said to move and the object is said to be moved.

Indeed, the requirement that the cause be simultaneous with what is caused must be fulfilled even more in things that are outside of motion whether we take something outside of motion to mean the terminus of the motion-as the illumination of air is simultaneous with the rising of the sun—or in the sense of something absolutely immovable, or in the sense of essential causes which are the cause of a thing’s being.

Concerning the first point, therefore, he does two things.

First, he states what he intends to establish.

Second, he clarifies this with examples, at: for example, the moon (96a13; [507]).

He says therefore first (96a10) that whenever the cause is simultaneous with its effect, it is necessary to take the same cause for the coming to be or the “having come to be” or the future existence, as is taken for the actual existence: for if the cause is simultaneous with that of which it is the cause, then just as it is necessary that when the cause exists, the effect be, so it is necessary that when the cause is coming to be, the effect be coming to be; and when the cause has come to be, the effect should have come to be; and when the cause will have been, the effect will have been.

Nor does it avail to object that when a builder is coming to be—while he is learning the art of building—the edifice is not yet being constructed: for 'builder' does not stand for the cause in act of the edifice, but for the cause in potency, or as possessed of the skill. But 'someone building' denotes the cause in act: it is this cause that must be simultaneous with that of which it is the cause, as it is stated in Physics II. There is identity in the sense that in all these cases the middle is the cause. However, this must be taken according to a due proportion, namely, so that the to be of the cause corresponds to the to be of the effect, and the coming to be of the cause to the coming to be of the effect, and the “having come to be” of the cause to the “having come to be” of the effect, and the future being of the cause to the future being of the effect.

Then, at: for example, the moon (96a13) he clarifies what he had said with two examples.

The first concerns the eclipse of the moon. For we say that there was an eclipse of the moon yesterday, because the earth was interposed between the sun and the moon yesterday; and that an eclipse of the moon is now coming to be, because such an interposition is now coming to be; and that tomorrow there will be an eclipse of the moon, because the earth will be in the middle; and that there is now an eclipse of the moon, because the earth is now interposed.

The second example concerns ice. Thus we might state what ice is and take as its definition that it is rigidly congealed water. Therefore, let C be water, that is, the minor extreme, and A be 'congealed', that is, the major extreme, and take B as the middle, that is, 'that which completely lacks heat'. For when that which is moist gives off heat it congeals; hence when it intensely gives off heat, the moist object becomes very thick and hard. Bringing this into syllogistic form, therefore, we shall say that B is in C, namely, because ice involves a complete giving up of heat; but A is in B, because that which completely lacks heat is congealed. Therefore, just as the fact that it has a deficiency of heat is the cause of ice’s being water which is completely congealed, so the cause of ice’s coming to be is that B is coming to be. And the same holds for having come to be and for future coming to be.

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]).

In regard to the first he does two things.

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.

In regard to this he does two things.

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.