Craig’s Five Point Response: A Response

1. Introduction

It has been exactly one year since I had my discussion with William Lane Craig on Capturing Christianity. Following that exchange, I wrote up my thoughts into a paper, and got it published in Mind (I posted a link to it here). This took a long time, partly because of the peer review process, and partly because the copy editing at Oxford University Press seems to be struggling over lockdown (that’s what it seemed like to me anyway). Craig was much quicker to publish his thoughts, which came out on his blog just a month after the discussion. You can read what he put here. At the time, Craig alluded to a ‘five point response’ that he had to the argument I was making. However, he didn’t get the chance to fully express those in the stream. Fortunately for us, he managed to explain them in more depth in his post.

Here I’m going to explain what each of his five points are, and respond to each of them.

2. The context

The discussion centred mainly on the argument I made with my friend Wes Morriston in our joint paper Endless and Infinite (which you can read here). The issue is whether the Hilbert’s Hotel argument, which is supposed to show that the past must have a beginning, can be used to show that the future must have an end. We gave a ‘symmetry argument’, which is just the Hilbert’s hotel argument, but ‘re-tensed’ so that it is about the future not the past.

We think the situation is perfectly symmetrical. If the past had no beginning, then the number of past events (the number of past days, if you like), will be equal to the cardinality of the natural numbers. You could assign each one a unique number, and have none left unassigned. Having this property makes it an ‘actual infinite’ for Craig; or at least, having this property makes it problematic for Craig (the ‘actual infinite’ is the problematic one for Craig). The thing is that this cardinality behaves weirdly, as it can have proper parts that are equivalent to the whole. Craig brings this out with his Hilbert’s Hotel examples, each of which involves things like there being both more guests and also the same number of guests after a new guest checks in to the hotel, etc. This is too much for Craig, who says that this shows that anything actually infinite cannot exist concretely in reality, in the same sort of way as hotels or library books. Given that there would be just as many, say, past even days as the total number of past days, the beginningless past has the problematic property that got Hilbert’s hotel into trouble. Thus the past must be finite. So his argument goes.

All we are pointing out is that this property applies to future events just as much as past ones. If the future never ends, then the number of future events (the number of future days, if you like), will be equal to the cardinality of the natural numbers. You could assign each one a unique number, and have none left unassigned. As each day passes there is the same number of days left to go as there was previously. As such the endless future is just as similar to Hilbert’s hotel as the beginningless past. There is a very obvious, at least prima facie, symmetry here. If you accept that Hilbert’s hotel is intolerably absurd, such that nothing having that property could exist, then this bars the beginningless past and the endless future equally. This is the symmetry argument in a nutshell.

But this is quite tricky if you want to hold, like Craig does, that the endless future is possible, but the beginningless past is not. At least, if you also hold that the reason to think that the beginningless past is impossible is because of these Hilbert’s hotel examples. Such a person needs to provide some kind of ‘symmetry breaker’ according to which the past and future can be treated differently with respect to Hilbert’s hotel argument.

We looked at what we took to be the various symmetry breakers that Craig has proposed in the literature, and explained why each one is insufficient. The first was his central claim, which is that the beginningless past is an actual infinite, but the endless future is merely a potential infinite. The second is that there are no future events at all; the third is that the future is pure potentialities, etc, etc. You can read it for yourself to see all the details.

I think all of Craig’s symmetry breakers obviously fail. In particular, the potential vs actual infinite is I consider to be completely dead as a response to this question. Anyway, this was the context for the discussion. Craig told me he had read the paper in advance of the discussion, so I expected these specific arguments to be addressed. Spoiler, I don’t think he read the paper very carefully. That’s the only way I can explain the following.

3. The Five Point Response: point one

Craig’s first point is about the ad hominem nature of the argument. Here is how he puts it on his blog:

The objection is either ad hominem or question-begging. As Alex recognized, the objection tends to be ad hominem, not in the abusive sense, but in the sense that it has force only against particular people, e.g., those who believe in personal immortality or, in the case of Andrew Loke’s formulation of the argument (see (4) below), against theists. If one tries to avoid this ad hominem feature by claiming that it’s clear that the series of future events can be infinite, then one seems to beg the question. For the objection does nothing to expose a flaw in the reasoning in support of a beginning of the series of past events. It allows that there is a sound argument against the infinitude of the past that also applies to the infinitude of the future. Without refuting this argument, it just assumes that an infinite future is possible, which begs the question against the argument.  So the objection is both question-begging and/or ad hominem

This response is itself split into two halves. The first half is everything up to “If one tries to avoid…”. He is right that there is something of an ad hominem about this discussion. The idea is that if someone advanced the Hilbert’s hotel argument as a way of showing that the past necessarily had a beginning, and also believes that the future at least could be (if not actually is) endless, then they have some explaining to do. They have to show how they are not committed to an inconsistent set of assumptions. And let it be clear, this description accurately describes Craig. So he has some explaining to do.

On the other hand, let’s also be clear about the consequences if we were to be right. What it would show would be that Craig has to figure out how to square his beliefs so that they are consistent. But there are various ways he could do that. For instance, he could do that by biting the bullet and holding that the future must come to an end. And this means that he could accept the symmetry argument without that in any way undermining the original Hilbert’s hotel argument, and the role that this plays in the Kalam. So in some sense then, the symmetry argument is not aimed at the Kalam directly. And it is only fair to be open about this. You could rationally buy the symmetry argument, and still think that Hilbert’s hotel establishes that the universe had a beginning (by biting the bullet about the future coming to an end).

But the point remains, even after we are super clear about this, that Craig in particular has to respond in some way. And he has done, in multiple places and in differing ways, and he doesn’t bite the bullet. Rather, he provides purported symmetry breakers to show how the future is not like the past with respect of the Hilbert’s hotel argument. So he is not giving up his belief in the endless future, nor the efficacy of the Hilbert’s hotel argument. And this requires some explaining.

But it being an ad hominem wasn’t itself an objection to the symmetry argument. It’s just a classification of the type of argument that it is, and not a marker that the argument is improper as such. So the first half of this response is really just signposting that the argument has this ad hominem aspect to it, but this isn’t really a response to the symmetry argument as such. It’s just a comment about it. So there’s not a lot more to say about it than that.

The second half of the quote makes the case that the symmetry argument (or at least the person making it) might themselves be guilty of begging the question at hand. He says that one could avoid it being an ad hominem by claiming that the future just could be endless. It’s like you could put the argument by saying ‘this is a problem for all those people who believe A, B and C’, and this would be ad hominem against those people. But you could avoid this by saying ‘this is a problem if A, B and C are true, and A, B and C actually are true’. In the second way of putting it, the emphasis isn’t on those people who believe certain things, but is just about how the contents of those beliefs are inconsistent. And you might want to put the argument like this if you have some prior commitment (maybe you think that it is just obvious, or perhaps highly intuitive) that the future could be endless. In that case, you might think that any theory that ends up meaning that this is impossible (like if you bite the bullet against the symmetry argument) is itself implausible, because it ends up deeming an obviously possible thing impossible.

I’m not so sure about this. Wes and Landon Hedrick seem to see it the second way; they think it is quite plausible that the future could be endless. I think that I’m unsure what I think about the possibility of the endless future. It is certainly epistemically possible – that is, consistent with what I take myself to know about the world. But then I’m quite open to my knowledge not extending very far towards possibilities like this. I’m at least as confident in the idea that we can never know whether the future is endless as I am in the proposition that it is metaphysically possible that it is endless. So I guess my own personal view is that I’m non-committal about whether it really is possible, or if it just seems to me like it is possible. Perhaps Wes and Landon agree with this as well. Either way, I don’t think I could reasonably be said to be begging the question here, because I’m not strongly committed to the possibility of the endless future; rather, I’m agnostic about it.

But that just makes me think that this first point just amounts to a statement about how the problem is particularly acute for people who hold Craig’s combination of beliefs, and an accusation that someone could (although I don’t think I do) beg the question by assuming that it is obvious that the endless future is metaphysically possible. And I honestly don’t see where an objection to anything is supposed to be found here.

4. Point two

In his second point, Craig gives a proposal for a symmetry breaker, saying “It is plausible that the past and future series of events are not perfectly symmetrical”. He goes on:

“On a tensed theory of time, according to which temporal becoming is an objective feature of reality, there are no events later than the present event and, hence, no future events. So a tensed theory of time entails that an actually infinite number of future events does not exist; indeed, the number of future events is 0.”

But this is exactly one of the symmetry breakers that Wes and I addressed in the paper. It’s as if he didn’t read what we put, because his response makes no mention of it. As we pointed out, the idea that there are no future events on a tensed theory of time is ambiguous, and when disambiguating Craig himself shows why this isn’t a symmetry breaker. What I mean is that we need to distinguish between how many future events there are, and how many there will be. Fair enough, a presentist wants to deny that any non-present events exist. So for them, there are no future events. However, even a presentist wants to say that there will be future events (unless she thinks that she is at the very final moment of time, which is obviously not what someone like Craig, who thinks time doesn’t have an end, would want to say).

And as we pointed out in the paper, Craig himself makes this distinction in print. Consider the following lines:

Thus, there really are no past or future events, except in the sense that there have been certain events and there will be certain others

Craig, 2001, p. 148

It’s all good to say that for a presentist there are no future events. But if you think that there will be future events (as Craig does, look up), then the question becomes: ‘how many future events will there be, if the future is endless?’ Given the distinction, it is no good to try to claim that the answer is still ‘zero’, because that means that time is coming to an end right now, and isn’t just the innocent presentist commitment to no non-present events. So this part of the response just feels a step behind the dialectic. Craig already made this point, and we already responded to it. Craig is just repeating the point and not engaging with the response. He isn’t explaining how the disambiguation doesn’t apply, or how it does apply but the answer is still zero, or anything like that. He is just not engaging.

He goes on to develop this point, and brings up what I think is a different symmetry breaker, but which Wes and I also extensively engaged with in our paper. He says the following:

The series of events later than any event in time, including the initial cosmological singularity, is always finite and always increasing toward infinity as a limit. In other words, such a series is potentially infinite. Georg Cantor called the potential infinite “a variable finite.” If the series of future events is potentially infinite, then the series of future events is finite but endless.

This is a somewhat obscure notion, but can be made totally clear. He is saying that the ‘series of events later than any event in time’ is ‘always finite and always increasing toward infinity as a limit’. But this is just wrong. Consider a mundane case. Suppose I’m going to count from one to ten. Before I start, how many future counting events will there be? The answer is ten. Now suppose I’ve already counted five numbers. How many future counting events are there now? The answer is five. I’ve counted 1, 2, 3, 4 and 5, and I still have 6, 7, 8, 9 and 10 to go. So the amount of future counting events is might be finite, but its not increasing over time. It’s clearly decreasing.

Suppose an angel starts counting now and never stops, and that time is endless. How many numbers will she count? Well, at the start of her count she has all of the natural numbers left to count; so ℵ₀-many numbers left to count. But after she has counted, say, five numbers, she still has ℵ₀-many numbers left to count. The amount of numbers left to count is neither increasing nor decreasing, but staying exactly the same. In a very straightforward way then, when the future is endless the ‘series of events later than any event in time’ is NOT ‘always finite and always increasing toward infinity as a limit’. Rather, it is never finite, and remains the same size forever. In short, it is not a potential infinity at all, but an actual infinity.

How come Craig sees things so differently? Well, it has to do with the weird way that Craig is using the term ‘the future’. In his paper with Sinclair, he puts it like this:

For as a result of the arrow of time, the series of events later than any arbitrarily selected past event is properly to be regarded as a limit.

Craig & Sinclair, 2009, p. 116

We are looking at the ‘events later than any arbitrarily selected past event’. Why this and not just events in the future of the present? It’s because if you look at it like this, then you get something that it much more like a potential infinite (that is, always finite but ever increasing, etc). Consider the following picture, which visualises what Craig is saying:

If we think about the length of the interval marked ‘some finite amount’, then obviously it is only finitely long. Now imagine that the point marked ‘now’ slides off towards the right as time passes. Clearly, the interval between it and the arbitrarily selected past event is going to increase but never be anything other than finite. This is obviously what Craig has in mind when he says that the future is a potential infinite.

But this is where the distinction between the simple future tense and the future perfect tense comes in. Notice that the interval in question is (always) behind the now point. It marks the bit between a past event and the present. It is as if we are at the arbitrary past point and wondering how much time will have passed as of some future point. The answer to this question is that it is always finite, but ever increasing as time passes. And I totally agree that this is a potential, and not actual, infinite. Totally. But the thing that cannot be ignored is that we are not talking about the simple number of future events any more. We are talking about how many days will be past in the future. That’s super obviously not the same thing. As Wes and I put it in the paper: “…that simply isn’t an answer to the question of ‘how many events will there be?’ It is just to answer a different question”. Again, by simply repeating this line, rather than responding to the extensive critique offered in the paper, Craig just seems to be one step behind in the dialectic.

So far, point 2 merely repeats Craig’s positions without interacting with the critiques of them. Again, it’s not really a response. It’s the thing that we originally responded to, and which still stands without a response.

Craig ends this section with the following:

Consider Alex’s premise:

1. If a beginningless series of past events is impossible, then an endless series of future events is impossible.

That commits Alex to the view that there is no possible world in which the series of events has a beginning but no end. In other words, he has to say that the view that the series of events is potentially infinite is not just false but impossible. That is a radical thesis carrying a heavy burden of proof.

This premise leaves out a very important caveat. The whole point here is that if you think Hilbert’s hotel is a good argument for the past having a beginning, then the future must have an end. I don’t buy the antecedent condition here; I don’t think Hilbert’s hotel is a good argument. All I’m saying is that if you do, then you need to explain how to avoid the seemingly obvious symmetry when applying it to the future. Remember how this has an ad hominem aspect to it.

Far from me endorsing a ‘radical thesis’, I’m highlighting how Craig, and people who share his views, need to do some explaining. One way they could do that is by biting the bullet and accepting that the future comes to an end. Another way is to give up Hilbert’s hotel as applied to the past, and say that both future and past could be infinite. What they cannot do, at least without successful symmetry breaker, is maintain an asymmetrical view, where Hilbert’s hotel shows the past is finite, but not that the future is finite. I think that advocates of the Hilbert’s hotel argument (a group I’m not in) cannot maintain an asymmetrical view, because I think all the symmetry breakers fail. Again, Craig seems one step behind the debate if he thinks that I personally believe that the ontology of time has to be symmetrical. I’m making no such claim, because I don’t buy the Hilbet’s hotel argument in the first place.

5. Point 3.

Here Craig brings up an argument discussed (though not endorsed) by my friend Landon Hedrick. Here is what Craig says:

Landon Hedrick, himself no friend of the kalām cosmological argument, has offered a version of the argument for the finitude of the past that is not susceptible to the symmetry objection. It goes as follows:

(1) There cannot be a world in which an actually infinite number of things have been actualized.

(2) If the actual world is one in which the universe is past-eternal, then there is a world in which an actually infinite number of things have been actualized.

(3) Therefore, the actual world cannot be one in which the universe is past-eternal.

This version of the argument for the finitude of the past avoids any alleged parallelism with the future.

It’s strange to me to think that this argument ‘avoids any alleged parallelism with the future’. Here is an obvious re-tensing of the argument:

(1) There cannot be a world in which an actually infinite number of things will be actualized.

(2) If the actual world is one in which the universe is future-eternal, then there is a world in which an actually infinite number of things will be actualized.

(3) Therefore, the actual world cannot be one in which the universe is future-eternal.

This argument obviously has the same logical structure as the original. The reasons for thinking that the second premise are true are exactly the same in both cases. If there are an infinite number of days, either past or future, then these days constitute a set of things that is infinite each of which either will be or was actualised.

The only real place I can imagine Craig objecting is to the first premise. Here, presumably he will say that the future things are never all actualised; rather they each become actualised but the overall number of actualised future things remains finite. But now we are just back to the simple future vs future perfect thing again. I quite agree that the number of currently future events will never have been completely actualised, but that’s a future perfect thing again. It’s just the same as thinking about the interval between a random past event and the present. What matters is not this issue, but the simple question of how many events are in the future of the moving now; not how many will be between it and some random past event.

So, not only do I think there is an obvious way that this argument can be re-tensed to make it about the future, but when it is done I think it puts us right back where we started. Again, I can only think that Craig is a step behind in the dialectic here.

6. Point 4.

Here, Craig brings up Loke’s hotel room builder argument, which was also addressed at length in my paper with Wes. Craig makes the following comments:

Alex’s response to Loke involves an illicit modal operator shift. Alex thinks that if God can bring about the existence of every future room in an endless series of events, then He can bring about the existence of all of them in the present moment. This is a mistake. It does not follow from God’s ability to bring about the present existence of any particular future room that He is able to bring about the present existence of all the future rooms. So to reason is modally logically fallacious. Thus, Loke is quite justified in denying that the possibility of an endless future implies the possibility of the existence of an actually infinite number of things, as does the possibility of a beginningless past.

Again, this seems to be clear evidence that Craig isn’t tracking the dialectic clearly. It is true that in the paper we said: “If an omnipotent God had completely unrestricted power, then he would have the ability to make a HH appear all in one go.” (p. 15). However, we went on to discuss what the consequences are for the argument when the theist insists that “God has the ability do anything metaphysically possible, but nothing metaphysically impossible” (p. 16). Given the metaphysical impossibility of Hilbert’s hotel (granted for the sake of the argument), this restriction on omnipotence has the precise consequence that “for each natural number n, it is possible that God made a hotel with n many rooms in total”, but not “it is possible that God made a hotel so big that there is a hotel room for every natural number n” (p. 16).

Basically, we made precisely the distinction that Craig drew. We are saying: assume that God could make any natural number of hotel rooms in one go, but not infinitely many. It is strange to think that you could carefully read our paper, and the response to Loke, and think that we are arguing with the assumption that because God could make any number of hotel rooms, that he could make infinitely many. I don’t know how to have been more clear about the assumptions we were working with, and how we were presuming the restricted omnipotence that blocks the idea of God making Hilbert’s hotel all in one go. Needless to say, Craig is clearly wrong in his charge here. He doesn’t begin to engage properly with the response to Loke, and so is far too premature to say that Loke is justified in making his argument.

7. Point 5.

Finally, Craig brings up “Alexander Pruss’ version of the argument for the finitude of the past”, by which he means the grim reaper paradox. Now, it might be true that there is no temporal mirror of the GRP. Perhaps. Cohen’s paper ‘Endless Future: A Persistent Thorn in the Kalam Cosmological Argument’ presents a version of this, and I developed a similar one in my post on the Dry Eternity Paradox (which I keep meaning to write up properly). So I don’t accept that it is obvious that no temporal mirror version of this argument could be made to show that the future must have an end. I think it is basically an open question, and that the various responses and counter responses have not been explored enough in the literature.

But, as Craig noted in point 1, and as I have been explicit about here, the symmetry argument wasn’t ever supposed to show that there is no successful argument for the beginning of the universe. It is not even required to defend the thesis that any such argument can be mirrored into an argument for the finitude of the future. Rather, the thought is just that the Hilbert’s hotel argument does apply to both past and future equally. Let’s suppose the GRP is asymmetrical in a way that Hilbert’s hotel is not. What would the significance of this be for the symmetry argument? It seems to me nothing. The GRP isn’t another version of the Hilbert’s hotel argument (and Pruss isn’t an advocate of the Hilbert’s hotel argument). So it would just be that an independent argument supports the second premise of the Kalam. This is basically irrelevant when it comes to assessing the merits of the symmetry argument, which is all about whether there is a symmetry breaker with respect to the Hilbert’s hotel argument to prevent it being applied to the future.

At this point, Craig’s appeal to the GRP seems like he is just appealing to another argument than the Hilbert’s hotel argument altogether. And that is fine, I’m happy to talk about the GRP instead of Hilbert’s hotel, but changing topic isn’t a response to the symmetry argument.

8. Conclusion.

I have no beef with Craig. In fact, I enjoy engaging with his published philosophy, even if I am critical of it. I wouldn’t engage with it if I thought it was low-tier material. He isn’t an idiot, nor do I think he is in bad faith (as it were). But I genuinely struggle to see how he carefully read the paper, or internalised the responses we gave to his arguments, given the contents of this five point response. The things he brings up are basically irrelevant (the ad hominem classification, or the comments about the GRP), or are just behind the discussion (as with his gesture to the asymmetry of time on the dynamic theory, or Loke’s theory). I genuinely think he skim read the paper and thought to himself “oh, this stuff again; I’ve already seen this sort of thing before” and didn’t pause to engage with it deeply. Otherwise it is hard to explain how his responses here are so superficial.

Perhaps one day he will spend some time going through it in more detail, or perhaps someone else will take up the challenge to defend him from the critiques. But his five point response really does nothing to advance the dialectic.