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
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