On the Ontological Status of the Big Bang Singularity

Quentin Smith is not persuaded by this line. He argues by way of a reductio that interpreting the ICS as equivalent to nothing entails (1) the denial of the truth of the Special and General Theory of Relativity, which represents spacetime as a continuum of instantaneous spatial points. Even further, if the ICS, Smith argues, were equivalent with nothing, then (2) the entire spacetime continuum would too be equivalent with nothing, and this is prima facie false. STR and GTR represent events as instantaneous spatial points having zero spatial and temporal dimension. “The difference,” Smith surmises, “between the Big Bang singularity and elements of spacetime is that the elements have four coordinates and the singularity has no coordinates; this difference is reflected in the fact that the singularity is a boundary or edge of spacetime and an event or element is a part of spacetime. Each event is a spatial point that is connected to other spatial points along the dimensions of height, width, and depth, but the initial singularity of a finite universe is a spatial point that exists in isolation. But each element of the manifold and the singularity are similar in that each is spatially and temporally pointlike.” As stated earlier, accepting the ICS as ontologically equivalent to nothing results by entailment in the prima facie false proposition that spacetime is ontologically equivalent with nothing. If 1. is true then given the high degree of plausibility assigned to GTR and STR, Craig’s contention that the singularity be ontologically equivalent with nothing should be denied. And certainly anyone half-well read in the confirmation of GTR and STR should deny the rather less plausible (in comparison) position that the ICS be equivalent with nothing.7

Smith’s arguments (1-2) would hold – should hold – did they not attend to a particularly weighty, in the bad sense of “weighty,” ontology. I, pace Smith and in accordance with Craig, do think such things as an ontological continuum do not exist. Such things as instants and points seem much rather to be mathematical fictions. This sort of position, that is, the position that says that points and instants do not exist, would undercut 1-2 such that they lose all of their power, but it might be argued “on less controversial grounds” that Smith’s argument fails. Instants of time and points of space are not themselves intervals of space and time, “but mere boundaries of intervals.” Within such an ontology it is perfectly consistent to hold that boundary points do not exist independently of the intervals they bound. Craig continues, “If instants and points exist only as boundaries of intervals, then they have no independent ontological status and so cannot subsist alone. But in the case of the initial cosmological singularity, this point-instant is said to exist independently. Therefore,” quite persuasively I think, “point-instants of the manifold can exist (as boundaries of intervals), while the singularity cannot.”8

A B-theorist would not agree with this distinction, for, under B-theoretic ontology, the singularity bounds the spacetime manifold. The A-theorist – notice how biased I am by using the for the latter and mere a for the former – would disagree with the B-theorist since he accepts temporal becoming, and since temporal becoming is predicated on a presentist ontology, the instant the ICS comes to be, all other instants would not yet exist. The ICS would thus exist alone, and supposing that instants and points exist only as boundaries of intervals and thus cannot exist alone, then the ICS would not exist; that is to say, the ICS would be ontologically equivalent to nothing. 9, 10

If the singularity were taken to be ontologically equivalent with nothing, then the universe would not have a first temporal instant, but would exist at any moment arbitrarily close to the ICS.11

The conclusion should thus be framed: given presentism, the ICS can plausibly be taken to be ontologically equivalent to nothing. Now what bearing does this have on the Kalam Cosmological Argument or the project of teologia naturalis which our blog is so very fond of? By itself, not much, but as a response to Q. Smith’s argument, very much. And this I suppose would mean it has much – well not too much, but much – bearing on the success of the KCA, and thus the project of Natural Theology (which I so cleverly referred to in its latin formulation). Watch out for the followup post that will frame this post within the context of Quentin Smith’s argument presented in Theism, Atheism, and Big Bang Cosmology, which I certainly recommend. It happens to be one of the best discussions of Kalam in print outside of The Blackwell Companion to Natural Theology (for others, see: The Kalam Cosmological Argument for God by Mark R. Nowacki). That is all. Adieu.

1. William Lane Craig and Quentin Smith, Theism, Atheism, and Big Bang Cosmology (Clarendon Paperbacks) (Oxford: Oxford University Press, USA, 1995), page 167.

2. Ibid. 120. “Furthermore, it belongs analytically to the concept of the cosmological singularity that it is not the effect of prior physical events. The definition of a singularity that is employed in singularity theorems entails that it isimpossible to extend the spacetime manifold beyond the singularity. The definition in question is based on the concept of inextendible curves, a concept that has been most completely and precisely been explicated by B.G. Schmidt. In a spacetime manifold there are timelike geodesics (paths of free falling particles), spacelike geodesics (paths of tachyons), null geodesics (paths of photons), and timelike curves with bounded acceleration (paths along which it is possible for observers to move). If one of these curves terminates after a finite proper length (or finite affine parameter in the case of null geodesics), and it is impossible to extend the spacetime manifold beyond that point (for example, because of infinite curvature), then that point, along with all adjacent terminating points, is a singularity.”

3. Ibid. 167.

4. Ibid. 171.

5. Ibid. 226.

6. Ibid. 260.

7. Ibid. 245.

8. Ibid. 259-260.

9. Ibid. 260. Craig further adds, “It seems very difficult to reconcile the A-theory of time with the view that instants are not mere boundary points, but subsist as independent intervals of zero duration. “Not only does this raise the ancient puzzle of how the present moment can be an interval of zero temporal duration, given that past and future are ontologically unreal, but the notion that the present is a solitary instant also seems to post insuperable problems for the reality of temporal becoming, since instants have no immediate successors, so that one after another cannot elapse….”

10. Ibid. 260.

11. Ibid. 260.

3 comments

  • July 18, 2011 at 8:38 pm // Reply

    Did you happen to write this in response to my question from your Common Objections post? I would certainly be flattered if a question of mine merited an entirely new post in response. Ha ha!

    I just need (once more) a bit of clarification: instances of time and points of space are not intervals of space and time but boundaries of intervals. My question is: what exactly is an interval? I feel like knowing that might clear a few things up. Also, could you give an explanation as to how boundaries are dependant on the intervals that they bind? Thanks.

  • “The question of the ontological status of this mathematical core involves not whether the math is sound, but whether what the mathematics describes as a boundary to the spacetime continuum is ontologically equivalent to nothing.”
    “I, pace Smith and in accordance with Craig, do think such things as an ontological continuum do not exist. Such things as instants and points seem much rather to be mathematical fictions.”

    Sounds a bit like Buckminster Fuller: “Science has made no experimental finding of any phenomena that can be described as solid, or as continuous, or as a straight surface plane, or as a straight line, or as infinite anything.”

    “Instants of time and points of space are not themselves intervals of space and time, “but mere boundaries of intervals.” Within such an ontology it is perfectly consistent to hold that boundary points do not exist independently of the intervals they bound. Craig continues, “If instants and points exist only as boundaries of intervals, then they have no independent ontological status and so cannot subsist alone. But in the case of the initial cosmological singularity, this point-instant is said to exist independently. Therefore,” quite persuasively I think, “point-instants of the manifold can exist (as boundaries of intervals), while the singularity cannot.””

    Points and instances, whatever they are, do indeed seem meaningless, without definition, in fact “nothing”, unless they exist theoretically as frameworks for a “something”, like distance or time. So it seems that points help to define theoretically, but cannot be defined themselves.

  • Alex,

    “Did you happen to write this in response to my question from your Common Objections post? I would certainly be flattered if a question of mine merited an entirely new post in response. Ha ha!”

    No, unfortunately I did not. :P I had been planning to write on this since I picked up and read Theism, Atheism, and Big Bang Cosmology. The want to write on such a bewildering topic is due in part to my own interest in the initial cosmological singularity and in another part to a discussion I had with an Atheist some time ago. That discussion inspired the post in a loose sense, for in truth it had very little to do with this topic per se. Nonetheless, I think it’s been quite profitable and will fit well into my next post.

    I just need (once more) a bit of clarification: instances of time and points of space are not intervals of space and time but boundaries of intervals. My question is: what exactly is an interval? I feel like knowing that might clear a few things up. Also, could you give an explanation as to how boundaries are dependant on the intervals that they bind? Thanks.

    Since I am no mathematician, not even a lousy one, I’ll instead stick to a real world example and you’ll have to do the business of lining that up with the math. On second thought, Matthew will hopefully pop in and say something mathematical; he is our resident mathematician for a reason. Okay, so here we go: think of a blank sheet of paper with two dots any nonzero finite distance away from each other. And then think of a line drawn between these two points. An interval would be the line connecting these two points. Now within an A-theoretic ontology that accepts the existence of bounded instants and points, that is, instants and points bounded by intervals, yet denies the independent existence of instants not bounded by intervals, the singularity would exist independently for a solitary instant and thus would not exist at all. I’m persuaded myself to not think such things as points, intervals and all that exist apart from their mathematical characterizations. I do suppose I’m a bit of a fictionalist about those sorts of things.

    I do want to add that Quentin Smith now, or last I heard, agrees with Craig that the singularity is ontologically equivalent to nothing.

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