Common Objections to Kalam: Part 5: Absurdity of Actual Infinities and God’s Infinitude

Here is another very common objection to the Kalam Cosmological Argument. I’ve noticed it used by some commentators on youtube as well as a good friend on Facebook. Here’s the objection:

If the Kalam Cosmological Argument entails that actual infinities are impossible, and God is infinite (as many Christians tend to say), then it is impossible for God to exist. The question is whether the term “infinite” is being used univocally. Is the kind of infinity that the Kalam renders impossible the kind of infinity that God allegedly possesses?

I do not think so. Consider what kind of infinity the Kalam calls impossible: the kind that is composed of discreet parts––the kind that is composite. Does anyone think that God has an infinite number of parts?––that God has goodness, kindness, rationality, and an endless array of other properties? The answer is very clearly no.

Those that endorse Divine Simplicity will unabashedly deny God’s composite nature. They will say that God is not composed of any physical or metaphysics parts. God is simply what he is, without division, without distinction, and without opposition.

But those that say that God is composite need not feel threatened by this objection either: on their view, God does not have an infinite number of parts.

What then do we mean when we say that God is infinite? William Lane Craig has called God’s infinity a qualitative and not quantitive kind of thing.[1] That is certainly right, but it is not very illuminating. I cannot cite any one scholar on this, so take what I will say here with some measure of skepticism: I suspect that calling God infinite is just to say that God is without limit. God is not a created being, which is finite in both its duration of existence and its quality of existence. The creature is limited to some space: God is not limited to some space. The creature is limited in focus: God is not limited in focus. The list goes on and on. God is not limited. God is the unlimited One. This talk of limit and unlimit is probably a more precise, if even still vague, way of referring to whatever we mean when we say God is “infinite.” It would be very interesting to see a blog post devoted to outlining the different approaches to this Divine description.

The Kalam is still safe––at least from this objection.


  • I would love to have a class taught by WLC. I just finished Time and Eternity a couple days ago. I’d love to read more on the subject…especially more elaboration on God’s relationship to creation via time.

    Nice note on the distinction between qualitative and quantitative infinitude, by the way.

  • It seems that you largely copied this response from Dr. Craig’s website, right? In any case, I think the arguments presented here are sound. I apologize for the following for being off topic, but I would like to ask you guys about my objection concerning the applicability of Hilbert’s Hotel to the past.

    The goal of Hilbert’s hotel is to show that the actual infinite is absurd *in actuality*. Notice that the absurdities that occur in this thought experiment only occur when you move guests around.

    If you want an actual infinite set of past events to be absurd, you must be able to get the absurdities. Aka, you must be able to move around temporal events for an actual infinite of past events to be impossible. However, I posit that moving around temporal events is metaphysically impossible. Because moving around temporal events is *in actuality* impossible, the concerns raised by hilbert’s hotel are not applicable to the past.

    Dr. Craig responds to this by claiming that the mere fact that you can move these events around conceptually proves that the past is absurd (he said this in his podcast about his debate with Wes Morriston on the Kalam). The problem is that this only gets you to an absurdity *conceptually*, not in actuality–the latter being the goal of bringing up Hilbert’s hotel in the first place.


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