Aristotle starts his argument about the impossibility of the infinite motion with the statement: “Everything that is in motion must be moved by something”. Let’s consider that there is something that is not moved by something. It has the source of its motion in itself. Then, let’s imagine this thing at rest. Aristotle supposes that if something is at rest, it is because a part of it is not in motion. For instance, ABC is a whole that is in motion. It is not moved by anything external to itself. However, if BC is not in motion, AB will be at rest. Thus, ABC cannot be in motion in its own right and primarily for if a part of it is not in motion the whole must be at rest. Consequently, everything that is in motion is moved by something other than itself.

If everything that is in motion must be moved by something, then that again is moved by something that is in motion, and so on continually. Let’s take the series to be infinite. For instance, D is moved by C, C by B, B by A, and so on. In this infinite series, we may still take the motion of each as numerically one. Every motion that is numerically one proceeds from something numerically one which in turn proceeds from something numerically one and so on. So, every single motion is not infinite in respect of its extreme points. If the motion of a numerically one is finite, then the time of every single motion will also be finite. Since every single motion and each of the others are simultaneous, the whole series of the motion must occupy the same time as a single motion, that is finite. However, we consider the series of motions to be infinite. So, the motion will be infinite in a finite time, which is impossible.

 The argument still does not prove that in a finite time there may not be an infinite motion. Let’s take that each thing accomplishes its own motion without being in contact with each other. So, it is possible in many things being in a motion simultaneously in a finite time. Nevertheless, we take an infinite series where things form a unity. The things moved and the movers are in contact with each other and all the things are in motion simultaneously. In this case, an infinite motion cannot pass through in a finite time. Thus, the series must come to an end. Since it cannot go on to infinity, there must be some first mover and a first moved.  

Bibliography:

  • Aristotle, Physics Book IV, Chapter 8 in The Scientific Background to Modern Philosophy, Selected Readings, Edited by Michael R. Matthews, Hackett Publishing Company, Indianapolis/Cambidge, 1989.