I have a funny observation concerning a Level 4 Multiverse. This is precisely what David Lewis thought in his concrete conception of possible worlds. For him, * every * possible world obtained. It’s funny that some scientists are proposing precisely that (however evidentially impoverished that may be) .

“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. 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.

]]>“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.

]]>And thanks, it’s nice to be commenting here, helps sharpen my knowledge in PoR.

]]>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.

]]>As to your questions,

(1) Well if the singularity did not in fact exist or was equivalent with nothing then it would not reach a state of infinite density and curvature, for it would not exist as a thing to have such properties. This would solve the problem by removing the singularity altogether.

(2) The term “infinite” in this case is not used in the sense of a cantorian actual infinite. Otherwise, I do not know enough of the physics myself to say entirely what this means.

]]>(1) For your first response, how does equating the singularity to nothingness solve the problem of infinity? I’m afraid I don’t quite see it.

(2) So, if I understand correctly, the term infinite applied to the singularity doesn’t literally mean infinite? It just means that the numerical values are too immeasurable to have any sense of finiteness attributed to them? Just want to make sure that’s clear for me, I’m not really strong in physics.

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