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 constant: but are created anew whenever it pleases the Creator: their annihilation is therefore not impossible. Now I will explain to you their opinion concerning the vacuum.

SECOND PROPOSITION.

On the vacuum. The original Mutakallemim also believe that there is a vacuum. i.e., one space, or several spaces which contain nothing, which are not occupied by anything whatsoever, and which are devoid of all substance. This proposition is to them an indispensable sequel to the first. For, if the Universe were full of such atoms, how could any of them move? For it is impossible to conceive that one atom should move into another. And yet the composition, as well as the decomposition of things, can only be effected by the motion of atoms! Thus the Mutakallemim are compelled to assume a vacuum, in order that the atoms may combine, separate, and move in that vacuum which does not contain any thing or any atom.

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