Craig on finitism and presentism

The kalām cosmological argument for God’s existence holds that the universe must have had a beginning.  (Not all versions of the cosmological argument make this claim.  For example, the versions I defend in my book Five Proofs of the Existence of God do not make it.)  William Lane Craig’s influential presentation of the argument defends the claim in several ways, one of which is by arguing that a beginningless universe would amount to an actual infinite, and that an actual infinite is impossible.  That judgment, in turn, is supported by appeal to examples like the Hilbert’s Hotel thought experiment, in which the idea of a hotel with an actually infinite number of rooms and guests yields a variety of bizarre consequences.

In a pair of posts from a decade ago (here and here), I explained why I don’t find this particular argument compelling.  For one thing, while the Hilbert’s Hotel scenario is certainly weird, it isn’t clear that it entails any logical contradiction.  And without that, the notion of an actual infinite has not strictly been reduced to absurdity.  The proponent of actual infinites can simply bite the bullet and hold that consequences that are oddball but nevertheless possible are only to be expected from actually infinite collections.

For another thing, it isn’t clear that a beginningless universe really does entail an actual infinite.  The idea behind Craig’s argument is that if the universe had no beginning, then an infinite series of moments (or days or years or whatever) has already passed.  This, it is claimed, amounts to an actually infinitely large collection.  But Craig is a presentist, as am I.  That is to say, we take the view that where time is concerned, only the present moment exists, which entails that past and future moments do not exist.  But if past moments do not exist, then we do not have an actual infinite.  In particular, what exists is just the present moment, rather than the present moment together with an infinite collection of past moments.  Given Craig’s own views about the nature of time, then, it is not open to him to argue against a beginningless universe on the basis of the impossibility of an actual infinite.

Others have presented similar objections, and in the second of the posts linked to above I explained why I don’t think Craig’s replies to them succeed.  But recently Craig published Volume IIb of his Systematic Philosophical Theology, devoted to topics in natural theology and Trinitarian theology.  It includes an updated treatment of the kalām cosmological argument, which revisits the issues just summarized.  Unfortunately, Craig has still not adequately addressed the problems, or so it seems to me.

Metaphysical modality

Consider first the question of how to establish that an actual infinite is impossible.  As those familiar with the debate over the kalām argument know, an actual infinite is to be contrasted with a potential infinite.  A potentially infinite collection is one that is only finitely large, but which might be added to without limit.  An actually infinite collection is one that already is infinitely large.  In volume IIb of Systematic Philosophical Theology, Craig says that whether such a thing could exist is not a matter of logical possibility or impossibility, but rather of metaphysical possibility or impossibility.  And he says that:

Since metaphysical modality is so much woollier a notion than strict logical modality, there are not the sort of clean, decisive markers of what is possible or impossible that consistency in first order logic affords for strict logical modality.  Arguments for metaphysical possibility or impossibility typically rely upon intuitions and conceivability arguments, which are obviously much less certain guides than strict logical consistency or inconsistency… [A]rguments for the metaphysical impossibility of some state of affairs will be much more subjective than arguments concerning strict logical impossibility. (p. 46)

This is doubly problematic.  On the one hand, it is a pretty damning concession, which only reinforces doubts about how much can be established via thought experiments like the Hilbert’s Hotel scenario.  On the other hand, while I’m skeptical about establishing the impossibility of a beginningless universe through arguments about metaphysical modality, the general idea of metaphysical modality is in my view not at all as woolly as Craig supposes.  Like many other contemporary analytic philosophers, he approaches the issue in a quasi-rationalist way, whereas the correct approach (I would argue) is Aristotelian.  In particular, contemporary analytic philosophers tend to start with intuitions and thought experiments; deduce from these what is possible or impossible for a thing; and then from that, in turn, determine the essence or nature of the thing.  From an Aristotelian point of view, this gets things backwards.  The right way to proceed is first to determine the nature or essence of a thing by observing how it behaves.  From this we can determine what is possible or impossible for it, and that in turn tethers any thought experiments we might entertain.  It is only if we mistakenly begin instead with intuitions and thought experiments that the notion of metaphysical modality comes to seem woolly.  (I say a lot more about this set of issues in Scholastic Metaphysics.)

In any event, while he does suggest that there may be aspects of the Hilbert’s Hotel thought experiment that involve mathematical contradictions (p. 53), he does not put much emphasis on that, relying instead on how “mind-boggling” and “wildly counterintuitive” the scenario is given the “metaphysical intuitions” many people share (p. 49).  This is pretty weak sauce.  One might as well counter that the idea that there might be some moment of time before which there was no preceding moment is itself “mind-boggling” and “wildly counterintuitive,” so that we ought to affirm that the universe had no beginning.  The point is not that this would be a good argument, but only that it isn’t obviously any worse than Craig’s own appeal to intuition. 

In response to Graham Oppy’s suggestion that the advocate of a beginningless universe could simply bite the bullet and accept the strange consequences that follow from an actual infinite, Craig objects that this “does nothing to prove that the envisioned situations are not absurd” but merely notes what we have to accept if there could be actual infinites (p. 52).  That’s true, but it misses the point.  Craig is the one making the bold assertion that an actual infinite is impossible, and drawing momentous and controversial conclusions from this assertion.  The burden of proof is on him to show that such a thing really is impossible, not on Oppy to show that it isn’t.

Simultaneous actual infinites

Following Alexander Pruss, Craig draws a distinction between full finitism and causal finitism (p. 47).  Full finitism denies the possibility of actual infinites of any kind.  Causal finitism, more modestly, denies only that there could be an actually infinite sequence of causally connected objects or events.  Craig’s approach has been to defend the kalām cosmological argument by appealing to full finitism, but Pruss suggests that a better course is to appeal to causal finitism.

For present purposes, I put to one side the questions of whether causal finitism is true and can successfully be deployed to rule out a beginningless universe, because Craig continues to defend the full finitist approach.  Here is where presentism poses a difficulty for him.  As Pruss notes, if the full finitist accepts the presentist view that only the present moment exists, then the only actual infinites he can rule out are infinitely large collections of things existing simultaneously at the present moment.  But that is not what the hypothesis of a beginningless universe entails.  It posits an infinite series of past moments, but these moments do not exist at present.  The present moment alone, and not an infinite collection of moments, is what now exists.  Thus does Pruss recommend appealing to causal finitism rather than full finitism in order to rule out a beginningless universe.

Craig thinks this is unnecessary.  To be sure, he acknowledges that:

[I]t has been said that on presentism, past events no more exist than future events, so that the number of past events is no greater than the number of future events, even if the series of past events is beginningless.  That is true. (p. 59)

He notes that Aristotle and Aquinas were presentists, and for that reason they concluded that the series of past events is not an actual infinite, even if it had no beginning (p. 71).  But he thinks they were mistaken to draw that inference.  He writes:

Now we may take it as a datum that the presentist can accurately count things that have existed but no longer exist.  He knows, for example, how many US Presidents there have been, what day of the month it is, how many shots Oswald squeezed off, and so forth.  He knows how old his children are and can reckon how many billions of years have elapsed since the Big Bang.  The non-existence of such things or events is no hindrance to their being enumerated.  (p. 72)

But there are two problems with this.  First, if it is meant to support the claim that a beginningless series of past events amounts to an actual infinite, then it is a non sequitur.  We can enumerate the superheroes that appear in the Marvel movies, but that doesn’t entail that we’ve enumerated a collection of actual things, because those characters are not actual but fictional.  Similarly, the fact that we can enumerate past events does not entail that what we are enumerating is a collection of actual things (whether finitely or infinitely large).  On the contrary, we are enumerating things that used to be actual but no longer are.

The second problem is this.  In the Hilbert’s Hotel paradox, it seems that what is doing the work is the supposition that there are, simultaneously, an infinite number of rooms and an infinite number of guests.  That’s what generates the oddball consequences.  These consequences would not follow if we imagined instead that at any particular moment, there were only finitely many rooms or guests (with infinity entering the picture only with respect to the duration of the hotel’s existence, or with the number of guests who have successively arrived and checked out over the course of the past). 

By Craig’s own admission, though, a beginningless universe doesn’t entail an actually infinite collection of simultaneously existing objects or events.  So, while Craig is correct to hold that we can enumerate things that no longer exist, it is not clear how that is relevant to the point at issue, even if we were to concede that the series of past events amounts to an actual infinite of some kind.  The Hilbert’s Hotel paradox shows at most only that an actually infinite collection of simultaneously existing things is problematic (if it really shows even that).  It does not show that an actually infinite collection of no longer existing things is problematic.  Again, Craig’s argument appears to be a non sequitur.

I conclude that Craig has not solved the problems facing his version of the kalām cosmological argument that I raised in those articles from a decade ago.  (For interested readers, I discuss presentism and the philosophy of time more generally at length in Aristotle’s Revenge, and in most of the posts listed below.)

Related reading:

A difficulty for Craig’s kalām cosmological argument?

Yeah, but is it actually actually infinite?

Review of Craig’s God Over All

Craig, conventionalism, and voluntarism

Vallicella on the truthmaker objection against presentism

Vallicella on existence-entailing relations and presentism

Aristotelians ought to be presentists

More on presentism and truthmakers

Cundy on relativity and the A-theory of time

Craig contra the truthmaker objection to presentism

Presentism and analogical language

Koons on time and relative actuality