One premise that almost all creationists like to adhere to is the impossibility of an infinite regression of events. Q. Smith called them anti- infinitists (1) and I liked it, so here are some responses to their…ahem…arguments

1- If an actual infinite series of events has passed then no new event can be added to the series, yet this series is being added to every day. W. Craig has given us this example of an infinite number of books in a library. Each book has been assigned an identification number. Since the number of books is infinite, all the possible identification numbers have exhausted and you cannot add any new book to the library for what ID you would assign the book to?(2)

This argument can easily be defeated by a counter example: suppose that we have an infinite number of books in a library and that we have assigned them IDs that start from (-8) down to (-infinity). Now this series of numbers is indeed infinite yet it can accommodate for 8 more books by assigning the first of those 8 an ID of (-7) and the second an ID of (-6) and so on (3).

Furthermore, if you replace (-8) with n and n was an arbitrary negative number then you could simply add whatever number of books you wish to add just by changing the value of n.

2- To have an infinite number of past events, there has to be an infinite number of temporal segments which connect every two consecutive events. If that were the case, then any arbitrary event can never arrive for it is impossible to transverse an infinite number of temporal segments otherwise the infinite would become finite, this is an impossible contradiction.(4)

No, it’s not, because the implication does not necessarily follow the assumed condition. You can have an infinite sequence of events and a finite sum of all segments connecting every two consecutive events if these segments where of decreasing length. Let me give you an example: Consider a series of events occurring at the following time instances:

{1, 1/2 , 1/4 , 1/8 , 1/16, … , 1/n} where n=1,2,3,…+

This series of events is infinite but yet the sum of its members (i.e. the time duration required to transverse it) adds up to 2.

3- W. Craig has reconstructed one of the Al-Kindi’s arguments for the impossibility of an infinite regression of events as follows:

“There are several self-evident principles: (1) two bodies of which one is not greater than the other are equal; (2) equal bodies are those where the dimensions between their limits are equal in actuality and potentiality; (3) that which is finite is not infinite; (4) when a body is added to one of two equal bodies, the one receiving the addition becomes greater than it was before and hence the greater of the two bodies; (5) when two bodies of finite magnitude are joined, the resultant body will also be of finite magnitude; (6) the smaller of two generically related things is inferior to the larger….if one has an infinite body and remove from it a body of finite magnitude, then the remainder will be either finite or infinite magnitude. If it finite, then when the body of finite magnitude that was taken from it is added back to it again, the result would have to be a finite magnitude (principle 5) which is self-contradictory… On the other hand, If it remains infinite when the finite body was removed, then when the finite body is added back to it again, the result would have to be either greater or equal to what was before the addition. Now if it’s greater than it was, then we have two infinite bodies one of which is greater than the other. The smaller is, then, inferior to the greater (principle 6) and equal to a portion of the greater but two things are equal if the dimensions between their limits are the same (principle 2). This means the smaller body and the portion to which it is equal have limits and are therefore finite. But this is self-contradictory, for the smaller body was said to be infinite. Suppose, then, on the other hand that the result is equal to what it was before the addition. This means that the two parts together make up a whole that is equal to one of its parts –which, according to the Al-kindi, is hopelessly contradictory.”(5)

Our modern understanding of infinity arose from set theory in mathematics not from fantasizing about the existence of infinitely sized bodies. In this context, the size of the set is not necessarily greater than the size of one of its parts. In fact, Dedekind [1831-1916] defined an infinite set as one having the same size as one of its proper parts, this type of infinity is often called Dedekind infinite (6).

In addition, what seems as perfectly self-evident when applied to finite bodies is not necessarily that evident or even true when applied to infinite bodies. We usually use the notion infinity to denote something without bound or limit and if this was the case then Al-kindi’s second principle is not applicable to infinite bodies as they have no limits.

Al-Kindi, as the case with almost all apologetics, is going to contradict himself when stating that he believes in the existence of unbound and limitless being that he calls God. So, to Al-Kindi, no actual infinite can exist but hey! Guess what? There is an actual infinite being! We just don’t want it to be the universe.

4- The Jewish philosopher Saadia Gaon wrote:

“…what is infinite cannot be completely traversed mentally in a fashion ascending [backward to the beginning]”(7)

Saadia, here, is concluding the impossibility of something based on failure to mentally comprehend it, which is simply wrong. For example, you cannot mentally comprehend a fourth dimension yet some physicists theorize the existence of a four dimension. In addition, it is actually perceivable to mentally transverse infinity if you have been given an infinite time to do so. To see this, imagine if you have been asked to picture the passage of four seconds in two seconds time, would you be able to accomplish that? The answer is no because you haven’t given enough time to do so, consequently, you can mentally transverse infinity if you spend an infinite amount of time doing so.

1- Q. Smith, Infinity and the Past. In: Theism, Atheism, and the Big Bang Cosmology. p. 83.
2- ibid, p. 83.
3- ibid, p. 84.
4- W. Craig, The Cosmological Argument from Plato to Leibniz. p. 63.
5- ibid, p. 62.
6- http://en.wikipedia.org/wiki/Dedekind-infinite_set
7- W. Craig, The Cosmological Argument from Plato to Leibniz. p. 128.