Third Proposition.

“Time is composed of time-atoms,” i.e., of many parts, which on account of their short duration cannot be divided. This proposition also is a logical consequence of the first. The Mutakallemim undoubtedly saw how Aristotle proved that time, space, and locomotion are of the same nature, that is to say, they can be divided into parts which stand in the same proportion to each other: if one of them is divided, the other is divided in the same proportion. They, therefore, knew that if time were continuous and divisible ad infinitum, their assumed atom of space would of necessity likewise be divisible. Similarly, if it were supposed that space is continuous, it would necessarily follow, that the time-element, which they considered to be indivisible, could also be divided. This has been shown by Aristotle in the treatise called Acroasis. Hence they concluded that space was not continuous, but was composed of elements that could not be divided; and that time could likewise be reduced to time-elements, which were indivisible. An hour is, e.g., divided into sixty minutes, the minute into sixty seconds, the second into sixty parts, and so on; at last after ten or more successive divisions by sixty, time-elements are obtained, which are not subjected to division, and in fact are indivisible, just as is the case with space. Time would thus be an object of position and order.

The Mutakallemim did not at all understand the nature of time. This is a matter of course; for if the greatest philosophers became embarrassed when they investigated the nature of time, if some of them were altogether unable to comprehend what time really was, and if even Galenus declared time to be something divine and incomprehensible, what can be expected of those who do not regard the nature of things?

Now, mark what conclusions were drawn from these three propositions, and were accepted by the Mutakallemim as true. They held that locomotion consisted in the translation of each atom of a body from one point to the next one; accordingly the velocity of one body in motion cannot be greater than that of another body. When, nevertheless, two bodies are observed to move during the same time through different spaces, the cause of this difference is not attributed by them to the fact that the body which has moved through a larger distance had a greater velocity, but to the circumstance that motion which in ordinary language is called slow, has been interrupted by more moments of rest, while the motion which ordinarily is called quick has been interrupted by fewer moments of rest. When it is shown that the motion of an arrow, which is shot from a powerful bow, is in contradiction to their theory, they declare that in this case too the motion is interrupted by moments of rest. They believe that it is the fault of man’s senses if he believes that the arrow moves continuously, for there are many things which cannot be perceived by the senses, as they assert in the twelfth proposition. But we ask them: “Have you observed a complete revolution of a millstone? Each point in the extreme circumference of the stone describes a large circle in the very same time in which a point nearer the centre describes a small circle; the velocity of the outer circle is therefore greater than that of the inner circle. You cannot say that the motion of the latter was interrupted by more moments of rest; for the whole moving body, i.e., the millstone, is one coherent body.” They reply, “During the circular motion, the parts of the millstone separate from each other, and the moments of rest interrupting the motion of the portions nearer the centre are more than those which interrupt the motion of the outer portions.” We ask again, “How is it that the millstone, which we perceive as one body, and which cannot be easily broken, even with a hammer, resolves into its atoms when it moves, and becomes again one coherent body, returning to its previous state as soon as it comes to rest, while no one is able to notice the breaking up [of the stone]?” Again their reply is based on the twelfth proposition, which is to the effect that the perception of the senses cannot be trusted, and thus only the evidence of the intellect is admissible. Do not imagine that you have seen in the foregoing example the most absurd of the inferences which may be drawn from these three propositions: the proposition relating to the existence of a vacuum leads to more preposterous and extravagant conclusions. Nor must you suppose that the aforegoing theory concerning motion is less irrational than the proposition resulting from this theory, that the diagonal of a square is equal to one of its sides, and some of the Mutakallemim go so far as to declare that the square is not a thing of real existence. In short, the adoption of the first proposition would be tantamount to the rejection of all that has been proved in Geometry. The propositions in Geometry would, in this respect, be divided into two classes: some would be absolutely rejected; e.g., those which relate to properties of the incommensurability and the commensurability of lines and planes, to rational and irrational lines, and all other propositions contained in the tenth book of Euclid, and in similar works. Other propositions would appear to be only partially correct; e.g., the solution of the problem to divide a line into two equal parts, if the line consists of an odd number of atoms; according to the theory of the Mutakallemim such a line cannot be bisected. Furthermore, in the wellknown book of problems by the sons of Shakir are contained more than a hundred problems, all solved and practically demonstrated; but if there really were a vacuum, not one of these problems could be solved, and many of the waterworks [described in that book] could not have been constructed. The refutation of such propositions is a mere waste of time. I will now proceed to treat of the other propositions mentioned above.