• Can God count to infinity?


    Consider the following two premises that are accepted by several theistic philosophers:

    1. God is a being than which no greater can be conceived.
    2. An actual infinite is logically absurd.

    I contend that if one wants to accept Premise 1, then one must reject Premise 2 (along with any argument that relies on it).  Why?  Well, I think that if Premise 1 is true, then God can count to infinity. To see why, let’s suppose that Premise 1 is true.

    Now, if there was a limit to the speed at which a certain being could think or speak, then I could conceive of a greater being — one that could think or speak faster.  Therefore, since we are assuming Premise 1 is true, there is no limit to how fast God could think or speak.  So now consider the following scenario:

    • At one minute to midnight, God says “one”.
    • Half a minute later, he says “two”.
    • A quarter of a minute later, he says “three”.
    • An eighth of a minute later, he says “four”.
    • And on, and on…
    • For good measure, at midnight he says “infinity”.

    By midnight, he would have counted through all the natural numbers: 1, 2, 3, 4, 5, …… and got to infinity.  Not a single number would have been left out.  Even if God did not actually carry out such a task, the fact remains that he could do it if he wanted to.  It follows that an actual infinite (which would supposedly have been completed if someone spoke the name of all the natural numbers) is logically possible.  And this implies that Premise 2 is false.

    Category: Cosmological argumentGodHumourInfinityOntological argument


    Article by: Reasonably Faithless

    Mathematician and former Christian

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    • Stefano S.

      God counts in mysterious ways

      • ehj1919

        A contradiction of history: The nine world’s greatest rationalist, the grand theorist of quantum relativity physics, have all written extensively on their convictions as theists. On pointing this fact to Neil Godfrey his reply: “Rubbish! That a minority of scientist still cling to some form of primitive religious notions is of no significance whatsoever except to modern day relics of cave-man superstitions found among true religious believers today”.
        How does Godfrey’s statement meet blogosphere peer

        • Reasonably Faithless

          I’m not really sure what your point is, or how it relates to the post. Feel free to elaborate, or I’ll just delete it as it seems irrelevant.

          • ehj1919

            Just delete, thamks.

    • Mike Blyth

      Isn’t this a logical impossibility, or am I just falling for a day-old April Fools post? Since there is no number after which God would count “infinity” and be finished, how does this even make sense?

      • Maybe the tag “Humor” in this post could be a clue. And for a couple of minutes of blinking to the screen after reading the post, I must confess I felt as confused as you 🙂

        • brad lencioni

          Look up “supertask”, guys. It is a theoretically controversial–though logically possible– task in which an infinite number of actions is performed in a finite amount of time.

      • Reasonably Faithless

        It doesn’t matter that there was no number immediately which “infinity” was said. Each number is spoken at a certain time, and it just happens that an infinite number of numbers were spoken between any given number and infinity.

        By analogy, if time is infinitely divisible, then there is no moment “just before” midnight, but we still manage to get to midnight every day with no apparent problems!

        It might seem strange, but I think it follows logically from Premise 1 that God ought to be able to do this. So, if a Christian believes Premise 2, then I think they are forced to abandon Premise 1.

        Also, I tagged “humour” because I think it’s a funny little exercise, not because I was joking.

      • NClaw441

        The question seeks to misdescribe omniscience and/or omnipotence, as you note. I have two children, and no more. God cannot name my third child, not because He lacks the knowledge or power, but because there is no answer to that question.

    • Sonny Moonie

      It wouldn’t make any difference to anyone if some being counted to infinity. Pragmatic philosophy dismisses statements about things that can’t have any detectable effect as not about anything real. If there were a god that could do infinite numbers of steps of math problems or programs, and maybe find out some things that are supposedly unknowable that way or maybe create paradoxes, that still wouldn’t make any difference to anyone unless that god acted on that information.

      People who believe in the character called God have never provided any definition for how to tell when God is acting or not acting, except to follow the vague implications of their religious texts and leaders, which are transparently based on old superstitions about the gods, such as that God determines the weather, God determines the outcome of wars, God gives visions and dreams, if they’re true and important, otherwise they’re from evil spirits, and so on. It’s all childish, and Christianity especially revels being childish or foolish, saying it’s a stumbling block to worldly wisdom and things like that. That makes the belief system irrefutable by observation or rational thought. So it’s pointless to bring mathematics into it, like bringing a bulldozer to a pretend egg-rolling contest. They’re just going to say you crushed their pretend eggs.

      • Reasonably Faithless

        Very well said!!

        I’m planning to eventually blog about the ideas you raised at the end. It was a turning point for me when I realised that “worldly wisdom” is what we rely on to evaluate everything else – only one’s chosen religion is exempt.

        Still, I think these things are worth discussing, and debunking – a lot of people respect people like William Lane Craig, and think his arguments are compelling. So I think it’s worth having good refutations available.

        EDIT: thought I should point out that I’m not bringing mathematics into it, but considering two premises that are mathematical in nature.

    • To me the concept of the greatest conceivable being is about as logical as the concept of the greatest conceivable number.

      • Reasonably Faithless

        Yes. The words “greatest conceivable number” are just as easy to say. Given any set with a way to compare its members, you can talk about the biggest member of that set, whether such a member exists or not. And here, with conceivable beings, it doesn’t even seem that there is a way to compare them, let alone ask whether a maximally great one is a coherent concept.

        • If it’s possible that there’s a greatest conceivable being, is it also possible that there’s a coolest conceivable hipster?

    • Have you ever considered this:

      If an actual infinite number of events is impossible as per the philosophical justifications of the Kalam Cosmological Argument (KCA) then isn’t it problematic that the number future events is eternal and god has knowledge of all these events? If the number of future events is infinite, and god has knowledge of all these future events (as per his all-knowing property) then wouldn’t god’s knowledge of every future event consist of an actual infinity and not a potential infinity? It seems that this would contradict the theist’s claims when justifying the KCA on philosophical grounds that an actual infinity cannot exist. They must, it seems, make an exception that god can have knowledge of an actual infinity of future events and that seems to me that actual infinities can exist.

      • Reasonably Faithless

        Yes, although Craig asserts that God’s knowledge is a grand unified whole, rather than a collection of individual pieces of knowledge. It’s quite maddening trying to argue with things like that. Because, apparently, even though God does indeed know infinitely many things, this does not somehow constitute an actual infinity. Actually, this kind of resistance to *some* things that seem clearly to be actual infinities make Craig’s arguments that things like past events being actual infinite (if infinite at all) seem very unsound.

        Wes Morriston wrote an interesting article, “Beginningless Past, Endless Future, and the Actual Infinite”, in which he draws parallels between an infinite past and future, arguing that they should be either both actual or both potential. He also constructed Hilbert-type paradoxes about the future. eg if God had ordained that an angel would praise him every day for the future, but then decided to cancel every second praise, then there would still be infinitely many praises still to be said, etc. You can get the article here:


        • The way I see it is like this. From god’s perspective, the future is an actual infinity since he can see every future event like an infinitely long film reel rolled out, and so logically this would be exactly like an actual eternal future under the B-theory of time. If god could know of every frame in this hypothetical infinitely long film reel, I don’t see why it isn’t logically possible that he could actualize every future event and create an actual infinity.

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    • kuartus

      I was hoping you would comment on Craig’s argument against an infinite past involving an immortal man counting from infinity past and finishing counting all the negative numbers today. The argument as craig presents it can be found in this article under the heading,”Second supporting argument.”:


      • Hi kuartus, thanks for your comment. I do plan to cover this argument of Craig’s one day. Actually, I think it is one of his more silly arguments. I agree that if you *start with something finite* and then add one thing at a time, you will never end up with an (actual) infinite collection (unless the additions happen quicker and quicker – eg, see my previous post here – http://www.skepticink.com/reasonablyfaithless/2013/04/02/can-god-count-to-infinity/ ). But this is not what an infinite past would involve – it would involve an infinite collection of days such that, on each of those days there had already been infinitely many prior days. But yes, more to be said another time…

        • kuartus

          Are we going to see this critique any time soon?

          • Thanks for the reminder! Life is ridiculously busy at the moment, hence my extremely low output in recent months 🙁 But, since you’ve asked, perhaps I will try and take a stab at this argument if/when I get a chance. Cheers!

            • kuartus

              I’m guessing we won’t be seeing this critique of yours then?