A second proof of the same principle is not found in Saadia. It is as follows: If we imagine an actual infinite and take away a part, the remainder is less than before. Now if this remainder is still infinite, we have one infinite larger than another, which is impossible. If we say the remainder is finite, then by adding to it the finite part which was taken away, the result must be finite; but this is contrary to hypothesis, for we assumed it infinite at the start. Hence it follows that the infinite cannot have a part. But we can separate in thought out of all the generations of men from the beginning those that lived between the time of Noah and that of Moses. This will be a finite number and a part of all the men in the world. Hence, as the infinite can have no part, this shows that the whole number of men is finite, and hence that the world had a beginning. This proof is not in Saadia, but we learn from Maimonides ("Guide of the Perplexed," I, ch. 75) that it was one of the proofs used by the Mutakallimun to prove the absurdity of the belief in the eternity of the world. The third principle is that the composite is "new." This is proved simply by pointing out that the elements forming the composite are prior to it by nature, and hence the latter cannot be eternal, for nothing is prior to the eternal. This principle also is found in Saadia as the second of the four proofs in favor of creation.[113] We have now justified our assumptions and hence have proved--what? Clearly we have only proved that this _composite_ world cannot have existed _as such_ from eternity; but that it must have been composed of its elements at some point in time past, and that hence there must be a cause or agency which did the composing. But there is nothing in the principles or in the demonstration based upon them which gives us a right to go back of the composite world and say of the elements, the simple elements at the basis of all composition, viz., matter and form, that they too must have come to be in time, and hence were created out of nothing. It is only the composite that argues an act of composition and elements preceding in time and by nature the object composed of them. The simple needs not to be made, hence the question of its having made itself does not arise. It was not made at all, we may say, it just existed from eternity. The only way to solve this difficulty from Bahya's premises is by saying that if we suppose matter (or matter and form as separate entities) to have existed from eternity, we are liable to the difficulty involved in the idea of anything having traversed infinite time and reached us; though it is doubtful whether unformed matter would lend itself to the experiment of abstracting a part as in generations of men. Be this as it may, it is interesting to know that Saadia having arrived as far as Bahya in his argument was not yet satisfied that he proved creation _ex nihilo_, and added special arguments for this purpose.