J. Brian Pitts on the Kalam Cosmological Argument

I am currently doing [student] research on the Kalam Cosmological argument. A recent paper I have been looking at (and struggling with, to be honest) is Pitts, J. Brian (2007), Why the Big Bang Singularity does not Help the Kalam Cosmological Argument for Theism (http://philsci-archive.pitt.edu/archive/00003496/), which you have apparently read (?). Pitts seems to raise some technical issues which you don't appear to have addressed in the literature I have looked at so far:

1. In your arguments against actual infinites, you seem to assume that the concept of size is fully captured by the notion of cardinality. Pitts contends however that 'one might well accept the possibility of actual infinities, such as Hilbert's hotel, while denying that cardinality exhausts the notion of sameness of size', and provides evidence that contemporary physics 'implicitly denies' that it does (p.10). If that is so, might this not render much of your discourse on the absurdity of actual infinites redundant?

2. In your appeal to contemporary cosmology, Pitts also takes you to task for offering a criterion for a beginning that is 'meaningless for the Bach-Weyl theory' and 'ambiguous for scalar-tensor theories'. He appears to insist that the relevant issue at hand *is* whether or not the temporal series had a first moment / a beginning point (in the topological sense of a beginning), and that you are not at liberty to arbitrarily chop up the temporal series into equal lengths, point to the first segment and label it as the 'beginning'. Apparently you are overlooking a technical issue concerning metrics.

There are other rather technical issues that Pitts raises, but I should be grateful to hear your thoughts on these points. Of course, any other comments that you would like to make about the paper would, I am sure, be most interesting.

Thank you for your time.


Yes, Brian showed me the paper a few years ago in a pre-print version, and I've been waiting for the article to appear in print before replying. It's nice to see the attention given to the kalam argument in so prestigious a journal as the British Journal for the Philosophy of Science. James Sinclair and I shall be co-authoring and submitting a response.

I think you've actually missed the main thrust of Pitts' critique. The paper is long and somewhat rambling, so that's easy to do. Stripped of the window-dressing and extraneous material, his central points are actually familiar criticisms that offer little that is new. Let me therefore cut to the chase and reserve some additional comments for later.

Pitts' answer to the question indirectly posed in his article's title, "Why the Big Bang Singularity Does Not Help the Kalam Cosmological Argument for Theism," is two-fold: (1) if spacetime is singular, then there is no first moment time, which is a necessary condition of the universe's beginning to exist, and (2) it is likely that as yet undiscovered theories will reveal that spacetime is not singular.

I have addressed (1) in a number of places. Pitts' point is that since the initial cosmological singularity is at most a boundary point of spacetime rather than a part of spacetime, there is no first instant of the universe's existence, just as there is no smallest fraction. Therefore, even though time is finite, it cannot be said to have begun to exist.

The fallacy of this objection is Pitts' assumption that beginning to exist entails having a beginning point. Why should we think that? Plausibly, as Quentin Smith has argued, time begins to exist if and only if for any arbitrarily designated, non-zero, finite interval of time, there are only a finite number of equal intervals earlier than it; or, alternatively, time begins to exist if and only if for some non-zero, finite temporal interval there is no equal interval earlier than it ("On the Beginning of Time," Noûs 19 [1985]: 579-84). Given this intuitively plausible characterization of what it is for time to begin to exist, Pitts' case in point may be taken to provide good reason to conclude that Pitts' assumption is false.

Moreover, notice that Pitts' assumption would commit us to the reality of points. But whether space and time really are composed of an actual infinity of points, rather than simply modeled as such in general relativity, is surely a question to be settled by argument and evidence, not merely assumed, as Pitts does.

Furthermore, Pitts' own Cosmic Destroyer argument (pp. 15-16 of his article) undermines his assumption. For if beginning to exist entails having a beginning point, then, by parallel reasoning, ceasing to exist entails having an ending point. But Pitts affirms that anything falling into a black hole will cease to exist, and this despite the fact that it has no ending point of its existence (since a terminal singularity is also merely a boundary point of spacetime rather than a part of spacetime). If, then, the universe ceases to exist in the Big Crunch, parity requires that it began to exist in the Big Bang!

So we need, then, some good argument from Pitts to think that the admitted finitude of past time is not sufficient for time's having begun to exist. Here I was astonished at his answer. His reason is that the criterion I gave for time's beginning to exist is not metaphysically necessary! There are possible worlds which are governed by different laws of nature, such as the two examples you cite, and in these worlds there is no way to tell if two separate temporal intervals have the same duration or not. So in those worlds my criterion would not apply.

This argument is nutty, since I never intended nor is there any need for the criterion to be metaphysically necessary. All that matters is that it applies to the actual world. And Pitts admits that it does (at least if spacetime has an initial singularity). He says, "If the true history of the real world is characterized by such a singularity, then the world is metrically finite in age" (p. 10). Here's where it's easy to misunderstand him. All this stuff about Bach-Weyl and scalar-tensor theories has to do with other possible worlds governed by those theories rather than the actual world. But in the actual world we can compare temporal intervals with respect to their length. (For a critique of the claims of so-called metric conventionalism see my Time and the Metaphysics of Relativity, Philosophical Studies Series 84 [Dordrecht: Kluwer Academic Publishers, 2001], chap. 2.) So my criterion for time and the universe's having a beginning works just fine.

Finally, one last point that I find somewhat amusing: Pitts' insistence that beginning to exist entails having a beginning point lands him squarely in the ancient Greek paradoxes of motion concerning stopping and starting. Ancient thinkers like Parmenides argued that if an object O is at rest at time t, it is impossible for O to begin to move. For at any time t? > t, if O is in motion at t?, then there is an earlier time t* < t? at which O is already in motion. Hence, nothing can ever begin to move! If we assume the continuity of time and space, the solution to the puzzle is that O can begin to move without there being a beginning point of its motion. Pitts' demand for first instant would force upon us the absurd conclusion that nothing ever begins to move. But if we allow that beginning to move does not entail having a beginning point of motion, then, generalizing, neither should we demand that in beginning to exist the universe must have a beginning point of its existence. So much for Pitts' first objection!

His second reason why the Big Bang singularity doesn't help the kalam cosmological argument is that it's very likely that "some kind of quantum gravity will resolve the singularity into some well-defined situation that admits extrapolation to still earlier times, ad infinitum" (p. 10). So his argument is that the Big Bang singularity isn't any help because there was no Big Bang singularity!

The problem with this argument is that whether the beginning of the universe was singular or not is just irrelevant to the kalam cosmological argument. In this regard, Brian's whole project in this article is misconceived. For he evidently equates the kalam cosmological argument with what he calls "the singularity argument for theism" (p. 2). In truth, this equation is simply mistaken, since the kalam cosmological argument is committed simply to the premise that the universe began to exist.

Rather the really important question is the last phrase in the sentence quoted above: whether these quantum gravitational models will "admit extrapolation to still earlier times, ad infinitum." It is the infinity of the past that is at issue, not whether the beginning of the universe involved a singularity or not.

As a matter of fact, the initial singularity is extraordinarily difficult to get rid of. Indeed, the Borde-Guth-Vilenkin theorem of 2003 shows that any universe which has on average been in a state of cosmic expansion throughout its history must have a past boundary, regardless of what quantum theory of gravity is used to describe the initial segment (see Q & A Archive 48).

But, in any case, as I've argued elsewhere, viable non-singular models (like Stephen Hawking's model) still involve a merely finite past and therefore a beginning of time and the universe. In the forthcoming Blackwell Companion to Natural Theology Jim Sinclair surveys the gamut of current non-standard models and shows that none of them can be successfully extrapolated into the infinite past. Thus, on the evidence of contemporary cosmology we have good grounds for affirming that the universe began to exist.

Not content with the promise of quantum cosmology, Pitts goes so far as to champion the rights of unborn and, indeed, unconceived hypotheses as grounds for scepticism about the beginning of the universe: "The relevant set of competitors for GTR [General Theory of Relativity] includes the set of theories that agree with GTR on all experiments to date, whether already entertained on Earth or not" (p. 19). This is overreach. It is one thing to have good reason to think that a quantum theory of gravity will most likely resolve the singularities of the General Theory of Relativity and quite another to appeal to wholly unimagined spacetime theories which agree with all the experimental evidence to date but are non-singular. Such an appeal to ignorance would legitimate scepticism concerning any and all scientific theories. By undermining all scientific theories in general, it does nothing to undermine General Relativity in particular.

So there's really nothing here to support Pitts' claim that contemporary cosmology does nothing or little to warrant belief in the second premise of the kalam cosmological argument that the universe began to exist.

With regard to the philosophical arguments for the beginning of the universe, Pitts's incidental comments don't constitute serious criticism. Look again and you'll see that he says nothing in that paragraph about "evidence from contemporary physics." His point about cardinality and size is just a passing remark which is of no significance until he explains what other conception of size he proposes and how it would affect the absurdities of a Hilbert's Hotel, especially those involving inverse operations like subtraction.

One last point: the final sections of Pitts' paper make it very evident that his scepticism about the beginning of the universe is just as agenda-driven as the views of those "singularity-wielding theistic apologists" whom he criticizes. Pitts' paranoia about the God-of-the-gaps makes him so sceptical that he will prefer to have faith in the existence of unknown theories which have never been conceived on Earth rather than to admit that the best evidence points to a beginning of the universe. Pitts' own theological commitments thus skew his assessment of the evidence.

What makes this especially unfortunate is that "the singularity argument for theism" is in fact a misnomer. There is no such argument. What Pitts is really talking about is some supposed "singularity argument for the beginning of the universe." In places Pitts recognizes this: "The truth of the second premise, or rather, the source of warrant for the second premise, is the key question" (p. 10; cf. p. 1). But the claim that the universe began to exist is a religiously neutral statement, which can be found in virtually any textbook on astronomy and astrophysics. This is highly significant, since it implies that all of Pitts' hand-wringing about God-of-the-gaps reasoning and the impenetrability of natural theology is simply irrelevant to the argument's success and so should play no role in the discussion.