Gregory Gruszecki
11/14/13
1st Essay on Craig/Morriston

An Understanding of Infinite Past In Morristons’ paper on the Kalam Cosmological Argument, he demonstrates that Craig argues against the idea that there can be an infinite past. He argues against this by using the Kalam Cosmological Argument to support his ideas. The Kalam argument is stated as “(1.) Everything that begins to exist has a cause of its existence. (2.) The universe began to exist. (3.) Therefore, the universe has a cause of its existence.” (Pg. 132) His argument is trying to demonstrate that the cause of the universe must be eternal, and that an eternal cause of something that begins to exist could only be a person. I will argue in my paper that Craig’s argument although entertaining, is not sound, and that both of his arguments against an infinite past are not effective. Craig begins his argument by asking us to imagine a library that contains an infinite amount of books. He explains that this library would be extremely strange because it cannot become any larger or smaller if one takes out or puts a book back. A person could add or subtract an infinite amount of books to this library and it would not become any larger or smaller. This does indeed seem like a very strange library. A reason for this peculiarity is because the library is put in a one-to-one correspondence with the prior set of books and the current set of books. Here Craig is using the Principle of Correspondence (PC) to show this peculiarity. This principle states that if two sets can be placed in a one-to-one correspondence, they must have the same number of elements. He believes that this scenario is absurd. This example can be shown more easily by the use of a number line. If we have a set of natural numbers and a set of real numbers, there would be more numbers on the real number line than on the natural number line. These numbers do not match up to make a one to one correspondence. He argues that this is the same problem with the infinite library. Craig also uses Euclid’s maxim (EM) to solidify his argument. Euclid’s maxim simply states that a whole is greater than any of its parts. With these two definitions Craig believes he can show that there are no actually infinite sets because these two definitions are only true for finite sets. This may just be a miss-interpretation of the definitions on Craig’s part. Although Craig used (PC) correctly, (EM) does not seem to be used correctly. Morriston in this paper states, “Euclid’s maxim about wholes and parts says nothing about the number of elements in a set.”(PG.133) This interpretation seems undeniably true and strikes a blow in Craig’s argument. Euclid’s maxim is more inclined to show that a set must be greater than a mere part of itself. The mere part would simply be called a subset of the latter set. This is an important point by Morriston because it shows that even an infinite set must be greater than any of its’ proper subsets or parts. In this sense the greater set contains all numbers in the lesser set, plus some that the lesser does not contain at all. This brings about a problem in Craig’s first argument against infinity. This is because it does not infringe on the principle that a whole can be greater than its’ parts. In order for Craig to even begin to argue his theory he needs to alter his definition of (EM). Morriston explains that he needs to change it to (EM*). (EM*) would state that a set must have a greater number of elements than any of its proper subsets. I still do not agree that (EM*) can show that there is no such thing as an infinite set. Craig’s theory can easily be disproved by showing the correlation between finite pieces of land with infinitely divisible parts. If a particular person marks out their land as 1 acre by 1 acre in a perfect square, it would be possible to divide those acres up into pieces for an infinite amount of time. We would ultimately end up with an infinite amount of divisible