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all that, there is my second possibility: something like what Stephen Hawking seemed to be saying in A Brief History of Time. That is, that there is no boundary to space-time, and hence no need to appeal to God to set boundary conditions at its beginning. Or, as others have put it, as you get nearer the “bang,” ordinary notions of space and time cease to apply; there is no need to think in terms of an absolute beginning, a “singularity” where the whole of space and its contents were infinitely compressed.

      leslie

      Don’t forget that this “no boundary” idea is only a “proposal” (Hawking’s word); it isn’t implied by anything we actually know. As Hawking himself presents it, it turns on the use of what he calls “imaginary time”—which elsewhere he describes as “merely a mathematical device or trick to calculate answers about real time.” It seems funny to use a “mathematical trick” to decide such important matters as the reality or non-reality of a God.

      geoffrey

      But you don’t need to stress the idea of imaginary time; other presentations of this point have not done so. And I am told that while using “imaginary time” is indeed only a trick when one is dealing with special relativity, it becomes more serious when you get on to general relativity.

      leslie

      Ah. Perhaps I was being unfair to Hawking—or perhaps he wasn’t doing himself justice.

      myra

      If I have followed him, which is not at all certain, you can use either “real time” or “imaginary time” to describe the history of the universe. One yields a beginning, the other doesn’t. And it seems to me that if either of them does, then we have to treat the world as having a beginning. To adapt an analogy Hawking himself uses, you can go round the earth in circles indefinitely, and you can’t fall off the edge; but the earth is limited, and to someone approaching it from space there is a point where it begins.

      geoffrey

      The point is not that Hawking’s proposal is proven truth; it is simply that it is a possibility. And if it is possible, then your argument from an alleged beginning is not a proof.

      leslie

      There is of course another approach, which goes back to the Middle Ages but has been revived in recent years—the attempt to show that there must be a beginning to time, whatever physical theories may happen to be in fashion at the moment. An infinite stretch of time in the future may perhaps be possible—you don’t after all have to complete it. You never actually reach a point infinitely far in the future; it is just that whatever finite length of time you suggest lies ahead, there is more beyond it. There is no end to the time-series. But an infinite past time is another matter altogether; it implies that an infinite number of days and events has actually come to an end. And this seems impossible, literally unimaginable.

      geoffrey

      Unimaginable, maybe; but all that says is that our imaginations are limited. I can’t imagine a start to time with no moment preceding it either.

      leslie

      Perhaps I shouldn’t have used the word “unimaginable.” What we can or cannot imagine hardly matters if infinite past time is impossible anyway.

      geoffrey

      But why should it be impossible? You theists should of all people be reluctant to say this; why shouldn’t your omnipotent and eternal God have created a universe with no beginning (or end)?

      leslie

      Not even God can create an impossibility.

      geoffrey

      But either God is in time, in which case presumably he has no beginning himself, or he is not in time at all, in which case questions of ending an infinite series don’t arise; he simply creates an infinite universe which from our point of view goes back for ever. Either way, where is the impossibility?

      myra

      This seems very queer, Geoffrey. You seem to have suddenly turned theist.

      geoffrey

      Only ad hominem, to make Leslie see that an infinite past was possible after all. (As many theist philosophers have held, even when, like Maimonides or Aquinas, they thought it wasn’t actually the case.) But in any case, I do not think we need a God, whether there is a beginning or not.

      leslie

      Yet Hawking himself seems to think that if there was a beginning, there probably would have to be a God,

      geoffrey

      If he really did mean that, he was wrong. Let me explain.

      Firstly, the beginning, if there was one, was not an event. It was not in time in the way that the events that followed it were; it was the start of time. The events in a novel may follow one from the other, but the novel’s opening doesn’t. The various features of a painting have proportions one to another; the corners of the canvas don’t. If the beginning had something before it, you could perhaps treat it as an event which needed a cause (though, by the way, it would surely be a physical cause, not a divine one!); but it didn’t.

      leslie

      If you insist that causes must be events, yes; but must they? Put it another way: the beginning calls for an explanation. Why did this beginning take place?

      geoffrey

      No, it doesn’t call for an explanation: indeed, I’m not sure it could have an explanation. An explanation must include, surely, an “If A, then B” at some point. My jumping is explained by the loud explosion just before, because it is our general experience that if there is a loud noise, people jump. But the universe immediately after the singularity (if there was one) could be of almost any kind. You can’t say “If there is a Big Bang, then a universe of such-and-such a sort will emerge.” Every state of affairs that could emerge from the Bang is as likely as any other; there is no “B”—and therefore no explanation for the beginning of things.

      leslie

      Hold it there! There is no fully specific “B,” perhaps. But there could be a set of possible “Bs.” After all, there is a universe of some sort! As a matter of fact, if God created the universe, He presumably could and did specify what sort it was going to be. But even setting that aside, we have a perfectly good “if, then”: “If there is a divine act of creation, there is a universe.”

      geoffrey

      That isn’t much of an explanation, is it? We have, after all, no access to this “divine act of creation.” We have never seen such a thing; and my case is that we can’t infer it from what we have seen, either. And I’d like to make another point, please. This “Big Bang” sort of argument seems to assume that if the world did not have a beginning in time, it might after all exist without a God. That is, it could be considered as a self-sufficient whole. But exactly the same can be said of a world that does have a beginning. (and, for that matter, an end). You can treat it as a whole, and ask “Does this expanse of space-time (whether finite or infinite, bounded or unbounded) need a God?” If one form, the infinite one, and probably another, the finite but unbounded one that Hawking favors, do not require a God, then the third, the finite and bounded universe, doesn’t either.

      leslie

      But of course there is no reason to suppose that an infinite universe, or an unbounded one, could exist without a God. All the form of cosmological argument we’re looking at did was try to make it particularly obvious that this universe couldn’t. If I show you that one particular horse, or one particular kind of horse, has vestiges of other toes, I should not expect to be taken as implying that other kinds don’t.

      And in fact I distrust talk of a “self-sufficient” universe. The mere fact (if it be a fact) that the universe did not have a specific beginning a finite time ago does not mean that it has somehow become self-explanatory. In fact, people like Maimonides and Aquinas, whom you mentioned just now, argued that such a universe wasn’t self-explanatory in the least. (They were thinking of one that had no beginning in time,

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