Thomas Aquinas, Commentary on Aristotle's Physics

879. After the Philosopher has shown that that which is without parts is not moved, he intends here to show that no mutation is infinite. This is contrary to Heraclitus, who held that everything is always being moved.

Concerning this he makes two points. First he shows that no mutation is infinite in its proper species. Secondly, where he says, 'But it remains . . .' (241 b 12), he shows how mutation can be infinite in time.

Concerning the first part he makes two points. First he shows that the mutations other than local motion are not infinite in species. Secondly, where he says, 'Locomotion, it is true . . .' (241 b 2), he shows that the same is true of local motion.

880. The first argument is as follows. It was said above that every mutation is from something to something. And it is clear that there are predetermined termini for mutations between contradictory opposites, that is, in generation and corruption, and for mutations between contraries, that is, in alteration and in increase and decrease. In mutations between contradictory opposites, the terminus is either an affirmation or a negation. For example, the terminus of generation is being, and the terminus of corruption is non-being.

And likewise in mutations between contraries, the contraries themselves are the termini or extremes at which such mutations are terminated. Hence, since every alteration is from a contrary to a contrary, it follows that every alteration has a terminus.

And the same must be said of increase and decrease. For the terminus of increase is completed magnitude. (By this I mean a completion in accordance with the condition of the proper nature. For the completion of magnitude that belongs to a man is different than that which belongs to a horse.) And the terminus of decrease is the total removal of such a nature from completed magnitude.

Thus it is clear that each of the above-mentioned mutations has an extreme at which it is terminated. But nothing which is terminated is infinite. Therefore none of these mutations can be infinite.

881. Next where he says, 'Locomotion, it is true . . .' (241 b 2), he begins to treat local motion.

First he shows that the argument applied to the other mutations does not apply to local motion. It was proven above that the other mutations are finite because they are terminated at a contrary or a contradictory opposite. But we cannot prove in the same way that local motion is finite. For not every local motion is between contraries in an unqualified way. For contraries are at a maximum distance from each other.

Unqualified maximum distance is found in the natural motions of the heavy and the light. For the place of fire is at a maximum distance from the centre of the earth. This is determined for such bodies in nature. Hence these mutations are between contraries in an unqualified sense. Hence in regard to these mutations it could be shown, as it was shown in regard to the other mutations, that they are not infinite.

But in violent or voluntary motions a maximum distance is not determined in an unqualified sense by definite termini. Rather the distance is determined by the purpose or by the violence of the mover, who either does not wish or is not able to move the body to a greater distance. Hence in this case there is a maximum distance only in a qualified sense, and consequently there is contrariety only in a qualified sense. Therefore it cannot be shown by means of the termini that no local motion is infinite.

882. Consequently he proves this with another argument as follows. That which cannot be cut is not cut. Now a thing is said to be impossible in many ways; that is, this could mean that something does not exist in any way, or that something can exist only with difficulty. Therefore, he indicates what he means by 'impossible' here. By 'impossible' he means that something cannot exist in any way. And that which cannot be made cannot be 'becoming' for the same reason. For example, if it is impossible for contradictories to exist simultaneously, then this cannot be 'becoming'. And for the same reason that which cannot be 'having been changed' into something cannot be 'being changed' to that. For nothing tends toward the impossible. But whatever is changed in respect to place is being changed to something. Hence it is possible for it to arrive there through motion. But the infinite cannot be crossed. Therefore nothing is moved locally through an infinity. Hence no local motion is infinite.

Thus it is universally clear that no mutation can be infinite in the sense that it is not limited by definite termini from which it has its species.

883. Next where he says, 'But it remains . . .' (241 b 12), he shows how motion can be infinite in time.

He says that it must be considered whether a motion which always remains one and the same in number can be infinite in time. There is nothing to prevent a motion which is not one in itself from enduring through an infinite time. He says this with some reservation, for he adds,'. . . it would seem that there is nothing to prevent . . .' (241 b 14). Later on he will inquire into this. He then gives an example. Let us say that after a local motion there is an alteration, and after this an increase, and after this a generation, and so forth to infinity. Such a motion might endure always for an infinite time. But this motion could not be one in number. For from such motions a numerical unity does not result, as was shown in Book V. But a motion which always remains one in number does not endure through an infinite time except in one case. For one continuous circular motion can endure through an infinite time, as will be shown in Book VIII.

Book VII