Aristotle, Physics. Book VI, Chapter 15


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These things being demonstrated, we say, that the impartible cannot be moved, except according to accident; as, for inatance, the body being moved, or the magnitude in which the impartible is inherent: just as if that which is in a ship should be moved by the motion of the ship, or a part by the motion of the whole. But I call that impartible, which is indivisible according to quantity: for the motions of the parts are different, according to the parts, and according to the motion of the whole. This difference also may be especially perceived in a sphere; for there will not be the same celerity of the parts which are about the centre, of those which are external, and of the whole sphere, as if there were not one motion. As we have said, therefore, the impartible may be so moved, as he who sits in a ship, is moved when the ship sails; but it cannot be moved by itself: for let it be changed from A B into B C; whether from magnitude into magnitude, or from form into form, or according to contradiction. But let the time in which it is first changed be D. It is necessary, therefore, that in the time in which it changes it should either be in A B or B C, or something of it in this, and something else of it in the other, for whatever changes, thus subsists. Something belonging to it, therefore, will not be in each of these, for it would consist of parts. But neither will something of it be in B C; for it will have been changed. But it is supposed to change: it remains, therefore, that it is in A B at the time in which it changes. Hence, it will be at rest; for to be in the same thing for any time, is to be at rest. So that the impartible cannot be moved, nor, in short, changed: for thus in one way only can its motion subsist, if time were composed from nows; since a thing would always be moved and changed in the now, so that it would never be moved, but would always have moved. But that this is impossible, has been shown before: for neither is time composed from nows, nor a line from points, nor motion from the boundaries of motion (kinēmata). And he who says this, does nothing else than assert that motion consists from impartibles; just as if he should say that time is composed from nows, or magnitude from points. Again, it is also evident, from the following considerations, that neither a point nor any other indivisible can be moved: for with respect to every thing which is moved, it is impossible that it should pass through that which is greater than itself, before it passed through that which is either equal to, or less than itself. But, if this be the case, it is evident that a point will be first moved through either that which is less, or that which is equal. Since, however, it is indivisible, it is impossible for it to be first moved through that which is less than itself. It will, therefore, pass through that which is equal to itself; so that a line will be composed from points: for the point always being moved through that which is equal to itself, will measure the whole line. If, however, this is impossible, it is also impossible for an indivisible to be moved. Farther still, if every thing that is moved, is moved in time, but nothing is moved in the now, and all time is divisible, there will be to every moveable a certain time less than that time in which it is moved through a space equal to itself: for this will be the time in which it is moved, because every thing is moved in time; and it has been before shown that all time is divisible. If, therefore, a point is moved, there will be a certain time less than that time in which the point is moved. But this is impossible: for in a less time it is necessary that it should be moved through a less space. So that the indivisible will be divisible into that which is less, just as time also into time: for, in one way, that which is impartible and indivisible may be moved, if it were possible to be moved in an indivisible now; since there is the same reason why a thing should be moved in the now, and why any thing indivsible should be moved.


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