Al-Kindī proved the impossibility of the existence of an actual infinite body by asserting that bodies are quantitative objects, and then by proving that any quantitative thing could not have infinity in actuality.
Time and motion are quantitative; thus, it is impossible for both to be infinite in actuality. Therefore, they are finite and time has a beginning.
Let us now follow al-Kindī’s proof that motion and time are finite:
If there is a body, then there must of necessity either be motion or not be motion. If there is a body and there was no motion, then either there would be no motion at all, or it would not be, though it would be possible for it to be. If there were no motion at all, then motion would not be an existent. However, since a body exists, motion is an existent, and this is an impossible contradiction and it is not possible for there to be no motion at all, if a body exists. If, furthermore, when there is an existing body, it is possible that there is existing motion, then motion necessarily exists in some bodies, for what is possible is that which exists in some possessors of its substance; as the (art of) writing which may be affirmed as a possibility for Muḥammad, though it is not in him in actuality, since it does exist in some human substance, i.e., in another man. Motion, therefore, necessarily exists in some bodies, and exists in a simple body, existing necessarily in a simple body; accordingly a body exists and motion exists.
Now it has been said that there may not be motion when a body exists. Accordingly, there will be motion when body exists, and there will not be motion when body exists, and this is an absurdity and an impossible contradiction, and it is not possible for there to be a body and not motion; thus, when there is a body there is motion necessarily.
Al-Kindī, before presenting his arguments, starts by offering a few premises and conclusions of previous mathematical demonstrations that are clear. These demonstrations need no further proof:
- The actual body of the universe is finite, and it is quantitatively finite.
- Things that are predicated of a finite object are necessarily finite, such as place, time, motion, and quantity.
- If there is motion, there is of necessity, a body. (We will return to this statement later, when we see how al-Kindī proves it.)
- Motion is not only spatial (from place to place), but may also be of different kinds, such as change (internal motion—chemical or biological), alteration, and the change of an object’s substance (generation or corruption).
- Every change or motion counts from the duration of the body; thus, every change and motion is temporal.
- It is not necessary for the whole to be in motion to say that the whole body moves. The motion of some of the parts (and the possibility of other parts moving) is enough of an indication that the whole exists in motion.
Now let us go back to the section on al-Kindī’s natural philosophy to examine and reconstruct his argument on motion. He says that
- The existence of a body has one of these two possibilities: It exists with motion, or, it exists without motion.
- Al-Kindī thinks that if a body exists, then it must, of necessity, exist with motion. The movement from nonexistence to existence is motion.
- Now, if we take the second possibility and claim that a body exists without motion, then we have to clarify further:
Either there would be no motion at all; or it would not be, though it would be possible for it to be. Al-Kindī disproves the premise that there would be no motion at all.
- If a body exists and there is no motion at all, then that means that motion does not exist.
- However, since a body exists, motion is an existent too. (According to premise number 2, motion is one of the things predicated of the finite body.)
- Therefore, to say that there is a body (an actual existent body) with no motion at all is an impossible contradiction. (According to premise number 4, motion is of many different kinds.)
- Therefore, it is impossible for a body to exist and be without motion at all.
The very concept of an actual, finite, existing body means, by definition, an object with motion. For example, a wooden chair came into existence by the act of a carpenter who made it out of various material things; it came into existence through motion. The coming into being itself is motion.
A newborn baby (as an actual finite being) came into existence in a process (motion) of being born and growing up, and thus existence (coming into being), by definition, is motion.
Al-Kindī disproves the premise that motion would not be, though it would be possible for it to be.
- If we claim that a body exists with the possibility of being in motion or not being in motion, then, its motion is possible to be and not to be.
- Al-Kindī says: “when there is an existing body, it is possible that there is existing motion, then motion necessarily exists in some bodies.”
- However, “that which is possible is that which exists in some possessors of its substance.” For example, “writing may be affirmed as a possibility for Muḥammad, though it is not in him in actuality, since it does exist in some human substance, i.e., in another man.”
- Motion, therefore, necessarily exists in some bodies, and exists in the whole body.
- Therefore, motion exists necessarily in the whole body; accordingly, a body exists and motion exists.
- Therefore, it is impossible for a body to exist and motion not to exist.
- Therefore, as al-Kindī says, “when there is a body there is motion necessarily.”
This last conclusion will be added to premise number 3 in the section entitled “Premises supporting al-Kindī’s arguments.” Thus, number 3 will read as a modified premise-proof statement of the simultaneous existence of matter and motion as follows:
If there is motion, there is of necessity a body, and when there is a body there is motion necessarily.
Remember that al-Kindī is not only trying to prove that an actual finite quantitative body necessarily has a finite motion; he is also trying to prove that matter and motion simultaneously coexist.
Al-Kindī did not stop at the previous proof; he went further to raise certain difficulties regarding matter and motion. He says “It is sometimes assumed that it is possible for the body of the universe to have been at rest originally, to have the possibility to move, and then to have moved.”
Al-Kindī thinks that this opinion is necessarily false. His argument is that if the body of the universe was at rest originally and then moved, then either (A) the body of the universe would have to be generated from nothing, or (B) it is eternal.
Al-Kindī disproves A, that the universe is generated from nothing, in the following eight arguments:
To study the logical steps of these arguments, please see Dr. Al-Allaf’s book:
The Essential Ideas of Muslim Philosophers, 2006.
 Al-Kindī, Al-Kindī’s metaphysics (trans. Ivry), p. 71.
 Ibid., p. 71.
 Ibid., pp. 71–72.