Commentary Aristotle Physics
835. Then, at “since, then, it has changed” (237a25), he proves the main proposition with the following reason. Whatever has been changed was being changed in time, as we have proved. But time is divisible, and whatever is being changed in time is being changed in part of time. Therefore, it is necessary to say that what has been changed in some entire period of time was previously being changed during half of the time, and again during half of that half, and so on, because time is divisible infinitely. Therefore, it follows that what has been changed was previously being changed. Consequently, before every state of having been changed, there is a previous state of being changed.
836. Then, at “moreover, the truth” (237a28), he proves the same point with an argument based on that in respect of which a thing is changed:
first, as to motions in quantity;
second, as to other changes, at “for the same proof” (237a35; [837]).
He says first (237a28) that what was said to be common to every change from the viewpoint of time becomes clearer from the viewpoint of magnitude, for magnitude is better known than time, and magnitude is continuous, like a line, and in it, something is changed, namely, that which is according to place or according to increase and decrease. Therefore, consider something changed from C to D. Now, it cannot be said that the whole of CD is indivisible, because CD has to be part of a magnitude, just as the motion from C to D is part of a whole motion, for there is a correspondence between division of magnitude and division of motion, as we have shown. But, if an indivisible is a part of a magnitude, it follows that two indivisibles are immediate neighbors—which is impossible, as we have shown. Therefore, the whole CD cannot be an indivisible, and consequently, that which is between C and D is a magnitude and can be infinitely divided. And something is always first changed in part of a magnitude before it has been changed throughout the entire magnitude. Therefore, anything that has been changed was previously being changed, just as, before any whole magnitude, there are its parts.
837. Then, at “for the same proof” (237a35), he shows that the same point is true in those changes that do not take place in terms of a continuum, such as alteration, which is between contrary qualities, and generation and ceasing to be, which are between contradictories. And although, in those changes, the demonstration is not derived from things in which the motion is, yet it is possible to take the time in which the changes occur, and then the demonstration will proceed the same way.
Thus, in the three changes, which are alteration, generation, and ceasing to be, only the first argument holds, while in the other three—growth, decrease, and local motion—both arguments hold.
838. Then, at “so, what has changed” (237b3), he argues for the main proposition:
first, in general;
second, with special application to generation and ceasing to be, at “so it is evident” (237b9; [839]).
Thus, he first (237b3) concludes from the foregoing that everything that has been changed was previously being changed, and that everything that is being changed has previously been changed. Consequently, it is true that a state of having been changed preceded a state of being changed, and vice versa. And, so, it is clear that a first something cannot be definitely pointed to.
The reason for this is that, in motion, an indivisible is not joined to an indivisible such as to make a motion be composed of indivisibles, because, if that were the case, we could discover a first. But it is not true, for motion is infinitely divisible, just as a line is, which can be infinitely decreased by division and increased by addition opposite to the decrease, in the sense that what is taken from one is being added to another, as was shown in book 3. For it is evident that, in a line, before each part of a line, one can take a point in its midst, and before that midpoint is a part of the line, and so on to infinity. However, the line is not infinite, because no part of the line is in front of the first point of the line.
Well, the same thing is true of motion. For since each part of motion is divisible, before each part of the motion, there is in the midst of that part an indivisible that is called “having been changed,” and before that indivisible, there is a part of the motion, and so on to infinity. Yet it does not follow that the motion is infinite, for in front of the first indivisible of motion, there was no part of motion. But note that the first indivisible is not one called “having been changed,” any more than the first point of a line is a dividing point.
839. Then, at “so it is evident” (237b9), he comes to the same conclusion with reference to generation and ceasing to be. And he makes a special point of these changes, because the relation of having been changed to being changed in generation and ceasing to be is not the same as it is in other changes.
For in the others, the state of having been changed and the state of being changed occur in respect to the same thing, such as to whiteness in the case of alteration. For to be being altered is to be being changed in respect to whiteness, and to have been altered is to have been changed in regard to whiteness; and the same is true in local motion, in growth, and in decrease.
But, in generation, having been changed refers to one thing and being changed to another. For the former is based on the form, but the latter, though not based on negation of a form (which is not of itself susceptible of more and less), is based on something joined to such a negation, something that is susceptible to more and less (namely, a quality).
Therefore, to have been generated is the terminus of being altered, and the same is true of having been corrupted. And because motions get their name from the terminus to which, as we have said in the beginning of book 5, being altered has two names, since it has two termini (substantial form and quality), for it can be called “to be altered” and “to come to be and cease to be.”
And this is the sense in which coming to be and ceasing to be are substituted for being altered, because the alteration terminates at being or non-being.
And consequently, Aristotle says that what has been made was previously being made, and what is being made must necessarily have been made, provided that divisible and continuous things are involved.
And Aristotle makes that addition (as the Commentator says) in order to exclude things that indivisibly come to be without continuous motion, such as understanding and sensing, which are motions only in an analogous sense, as will be shown in De anima 3.10. But it could be that Aristotle made this addition in order to show that generation should include the entire continuous motion that precedes it.
840. But the statement what is being made has been previously made applies in different ways to different things. For some things, such as air and water, are simple and have simple generation, and in these cases, part is not generated after part, but the whole and the parts are altered and generated at once.
And it is in such that what has been made was previously being made and what is being made has been previously made, on account of the preceding alteration being continuous.
But other things are composites of unlike parts. In these cases, part is generated after part, as in an animal the heart is first generated, and in a house the foundation. In such things, what is being made was not itself previously made, but a part was.
And this is what he adds: it is not always such that what is being made has been itself previously made, but something pertaining to it has been made, as the foundation of a house.
But, since we must come to a part that is entirely being made at once, then in some part, that which is being made has been made in relation to a terminus taken in the preceding alteration; for example, in the generation of an animal, the heart has already been made, and while the heart is being generated, something else has already been made—not indeed that there has been made some part of the heart, but some alteration ordained to the generation of the heart.
And what has been said of generation is to be understood with regard to ceasing to be. For there is something infinite immediately present in what is produced in being and is corrupted, since it is continuous.
For the very coming to be and the ceasing to be are continuous. Therefore, there is no being produced in being, unless something has been previously made, and nothing has been made unless it was previously being produced in being. And the same is true of ceasing to be and having ceased to be. For a having ceased to be is always prior to a ceasing to be and a ceasing to be prior to a having ceased to be.
From this it is evident that whatever has been made was previously being made, and that all that is being made has in some way previously been made. And the reason is that every magnitude and every period of time are infinitely divisible. Consequently, in whatever period of time something comes to be, it is not coming to be in that time as in a first time, because it is always possible to find a period previous. And what we have said of generation and ceasing to be is true also of illumination, which is the termination of the local motion of the illuminating body, just as generation or ceasing to be is the terminus of an alteration.
Lecture 9. The finite and the infinite found together in magnitude, time, motion, and the mobile body
Now, since the motion of everything is in motion in time, and a greater magnitude is traversed in a longer time, it is impossible that a thing should undergo a finite motion in an infinite time, if this does not mean that the same motion or a part of it is continually repeated, but that the whole infinite time is occupied by the whole finite motion.