Wednesday, June 23, 2010

Is an Infinite Regress Possible?

For many arguments of natural theology, this question is simply irrelevant. However, the kalam cosmological argument (KCA) requires that universe began to exist at some finite time in the past:

1. Whatever begins to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.

In support of (2), Bonaventure reasoned that the present would not have arrived if the past were infinite. Craig summarizes this particular argument as follows [1]:

2A. The temporal series of events is a collection formed by successive addition.
2B. A collection formed by successive addition cannot be an actual infinite.
2C. Therefore the temporal series of events cannot be an actual infinite.

(2A) assumes an A-theory, or dynamic theory, of time. (The other philosophical argument that Craig defends - i.e. the impossibility of an actually infinite number of things - does not necessarily assume an A-theory of time.)

(2B) is supported by the fact that no matter how many members are added to a set, it is always and indefinitely possible to add another before arriving at infinity. Hence, any collection formed by successive addition will always be finite.

Some Objections

While Thomas Aquinas agreed that the universe began to exist, he disagreed with Bonaventure that the universe's beginning could be demonstrated by reason alone. Thomas reasoned that the universe's past, while not actually infinite, could be potentially infinite.

Thomas, I think, is technically correct. However, in order for the past to be potentially infinite, the past would also have to be growing. In other words, time would have to be moving backwards, and not forward only. Since this is contrary to experience, the objection that Thomas offers is generally not taken as a very serious threat to the KCA.

Another objection states that an infinite collection can be formed by successive addition if the collection has always been being formed. Any moment in the past is finite, so if there are infinitely-many of them, the collection as a whole will be an infinite set. This objection appears a bit fishy to me, and I don't just mean that it appears to be question-begging (e.g. the past is infinite if it is infinite). It is true that at any time in the past, there is a finite distance from that moment of time to the present. The problem is that even though each finite period of time may be traversed, it doesn't follow that the infinite set as a whole could be traversed. In short, the objection is susceptible to a composition fallacy.


Obviously, entire books can and have been written on this one argument alone. However, it seems to me that the objections put forward so far are unsuccessful. Barring any more cogent objections, it appears that it is reasonable to suppose that the universe cannot be infinitely-old on an A-theory of time.

[1] William Lane Craig, The Kalam Cosmological Argument, Wipf and Stock Publishers, 1979, p. 103. I have changed the premise numbers/letters in order to avoid confusion with the general KCA summary.


  1. As far as the past being potentially infinite goes, has anyone ever argued for this to your knowledge? It seems like a fascinating idea, and the sort of thing that would be entertained by quantum-woo sorts.

  2. The closest I've ever seen to this are (as you hint at) those who interpret quantum mechanics in such a way that there are intervals of time that move backwards. Some cite "non-local communication," in which two subatomic particles split from a single particle and are able to communicate instantaneously, regardless of distance in space and time. I'm not a scientist, though, so I cannot comment on whether such an interpretation is cogent.

    Nevertheless, the particle split itself is worth considering as a starting point of sorts.

    This is one of the reasons I prefer the Thomistic approach to natural theology. We can leave aside all of these other, albeit quite interesting questions aside, and focus on the relationship between essence and existence that requires God qua Pure Being as the ground of all existences.

    Still, these are all quite fascinating subjects. Thank you for bringing them back to my attention. :)

  3. Greetings again, in the Lord.

    I have made two posts in the same vein, my point being that infinitude is an incoherent concept in a purely physical, and thus eternally uncreated, cosmos.


    Craig's book on the kalam arg. was a great tooth-cutting experience 12 or so years ago in undergrad.

    As always, the "read my stuff to scare off obvious errors or spur new leads" proviso stands.


  4. Thanks, Codgitator, for the links. I'm glad I was able to stir up some interest in what I feel is an immensely interesting and important topic.