LECTURE 18 (264 a 8-b 8)

HE SHOWS WITH LOGICAL ARGUMENTS THAT REFLEX MOTION IS NOT CONTINUOUS

1123. After the Philosopher has shown with proper arguments that reflex motion is not continuous, he here shows the same thing by means of common and logical arguments.

             Concerning this he makes two points. First he states his intention. Secondly, where he says, 'Everything whose motion . . .' (264 a 9), he proves his position.

             He says, therefore, first that if one wishes to approach the demonstration of the proposition rationally, that is, logically, it will be seen from the arguments which will be given that the same conclusion follows; namely, reflex motion is not continuous.

             1124. Next where he says, 'Everything whose motion . . .' (264 a 9), he proves his position. He does this first with respect to just reflex local motion, and secondly, with respect to all motion in general, where he says, 'Further, the following . . .' (264 a 21).

             The first argument is as follows. Whatever is moved continuously is moved from the beginning of its motion to that which, as an end, it arrives at through local motion. This occurs if there is no obstacle (for it could be deflected in another direction by an obstacle). He gives an example of this proposition by saying that if something arrives at B through local motion, it was moved toward B not just when it was nearby, but immediately when it began to be moved. For there is no reason why it should be moved more toward B now rather than before. And the same is true of other motions.

             If, however, it is true that reflex motion is continuous, it will be true to say that what is moved from A to C, and then is reflected to A, is moved continuously. Therefore, in the first part of the motion, from A to C, it was being moved toward the terminus of the last part, which is A. Hence, while it is being moved from A, it is being moved toward A. It follows, therefore, that it is moved simultaneously by contrary motions. For in straight motions, being moved from the same thing and to the same thing are contraries, although in circular motions these are not contraries. It is impossible, however, for a thing to be moved by contrary, simultaneous motions. Therefore, it is impossible for reflex motion to be continuous.

             1125. Next where he says, 'With this consequence . . .' (264 a 18), he brings out another inconsistency from the same thing.

             That which is being moved to A while it is being moved from A, can be moved to A only from some opposite position, C, which the mobile object had not yet reached when it began to be moved from A. It follows that it is being moved from a terminus in which it is not, and this is impossible. For a thing cannot leave a place in which it is not. Therefore, it is impossible for reflex motion to be continuous. And if this is impossible, the mobile object must rest at the turning point, namely, at C. From this it is clear that the motion is not one, for a motion which is interrupted by an intervening rest is not one.

             1126. Next where he says, 'Further, the following . . .' (264 a 21), he gives three arguments to prove the same thing universally of all motions.

             The first of these is as follows. Whatever is moved is moved by one of the species of motion designated above. Similarly, whatever is at rest must have one of the states of rest which are opposed to the above motions. For it was shown in Book V that there cannot be any motion other than those designated.

             Let us take a motion which differs from other motions in species, as whitening differs from blackening. The motion under consideration is not distinguished from other motions as one part of a motion is distinguished from the other parts of the same motion, for example, as one part of a whitening is distinct from the other parts of the same whitening. Taking one such motion as was said, it is true to say that that which is not always being moved by this motion, necessarily was previously at rest with an opposed rest. For example, that which is not always being whitened at some time was at rest with a rest opposed to whitening. But this proposition would not be true if some determinate part of the motion were taken. For it is not necessary that that which was not always being moved by this part of whitening was previously at rest with an opposed rest. For it was being whitened previously by another part of the whitening. Because of this he explicitly says, '. . . not some particular part of the whole motion . . .' (264 a 25).

             He proves the proposition in this way. When one of two privative opposites is not present, the other is present in that which is receptive of them. Now rest is a privative opposite of motion. Therefore, when motion is not present in a mobile object, it necessarily follows that rest is then present in it.

             After proving this proposition with the argument set forth above, he assumes the minor by saying that if the straight motions from A to C and from C to A are contraries, and if contrary motions cannot be simultaneous, it is clear that when the mobile object was being moved from A to C, it was not then being moved from C to A. Hence it was not always being moved by the motion from C to A. And so, according to the foregoing proposition, the mobile object must previously have been at rest with an opposed rest. For it was shown in Book V that rest in C is opposed to motion from C. Therefore it was at rest at C. Reflex motion, then, is not one and continuous, since it is interrupted by an intervening rest.

             1127. He gives the second argument where he says, 'Our next argument . . .' (264 b 1). The argument is as follows.

             Not-white is corrupted and white is generated simultaneously; and, contrarily, white is corrupted and not-white comes to be simultaneously. But if reflex motion of any genus is continuous, it will follow that continuous alteration is terminated at white, and begins to withdraw from white, and it does not rest there for any time. For otherwise, if rest intervened, it would not be continuous alteration. But, as was said, when white comes to be, not-white is corrupted, and when there is a withdrawal from white, not-white comes to be. It will follow, then, that not-white is corrupted, and not-white comes to be simultaneously. For these three occur at the same time, namely, becoming white, the corruption of not-white, and becoming not-white again, if reflex motion is continuous without an intervening rest. However it is impossible for not-white to simultaneously come to be and be corrupted. Therefore, it is impossible for reflex motion to be continuous.

             This argument, however, seems to pertain to generation and corruption. Hence he says that this argument is more proper than the previous ones, for it is more apparent that contradictories cannot be simultaneously true. Nevertheless, what is said of generation and corruption applies to all motions, since in any motion there is some kind of generation and corruption. Thus in alteration white or not-white is generated or corrupted. And the same applies to every other motion.

             1128. He gives the third argument where he says, 'Again, from the continuity . . .' (264 b 7). The argument is as follows.

             As was established in Book V, motion is not necessarily continuous because the time is continuous. For even if they succeed themselves in a continuous time, motions of different species are not continuous, but consecutive. For there must be one, common terminus of the continuous. But there cannot be one, common terminus of contraries and of things which differ in species of white and black, for example. Since, therefore, motion from A to C is contrary to motion from C to A in any genus of motion, as was shown above in Book V, it is impossible for these two motions to be continuous to each other, even if their time be continuous, with no rest intervening. It follows, therefore, that reflex motion can in no way be continuous.

             It should be noted that the arguments set forth above are called logical because they proceed from certain common principles, namely, from the property of contraries.