I want to thank Quentin for his comments this evening. I've enjoyed our on–going conversation over the years in professional journals and collaborating on the book. It's been most interesting.
Now Quentin attacks both of my premises. First he accuses me, with regard to the first premise, of equivocating on the word "cause" because he thinks it must mean material cause in the one case, but in the conclusion it doesn't mean material cause. I don't think it's an equivocation at all. I'm using the word cause here simply to mean something that produces something else, and in terms of which that other thing, called the effect, can be explained. Whether it's an efficient cause or material cause is simply left out of account. So I'm not specifying in the first premise what kind of cause it has to be, but simply that there must be a cause. Now I would also say that we do have something of an analogy with creation out of nothing in our own mental ability to create thoughts in our minds, thought–worlds, fantasies. Now this is an analogy, perhaps, with God's creating the universe. Now don't misunderstand me; I'm not saying that we're all just dreams in the mind of God or something. But I think it does provide something of an analogy of the idea of creating out of nothing. And finally, I would point out that the Big Bang model of the origin of the universe, as Quentin himself said later, posits the origin of the universe without a material cause. So even in the Big Bang theory you have no material cause of the origin of the universe. But I'm maintaining that you must at least have an efficient cause to bring it into being, even if we both agree that there is no material cause. So I don't think the argument is equivocal.
Now is the premise self–evident? Well, it's rooted in the metaphysical intuition that something cannot come out of nothing. Out of nothing, nothing comes. And to me that surely is evident when you think about it. If there is absolutely nothing—no space, no time, no energy, no matter—then something cannot just come out of nothing. At least, it seems to me that the premise is far more plausible than its opposite.
Now what about the argument against the actual infinite? Here Quentin says infinity minus infinity and the paradoxes I alluded to are not self–contradictory. Well, I simply beg to disagree. It is self–contradictory. For example, infinity minus infinity: Imagine all of the natural numbers minus all of the odd numbers. What do you have left over? Infinity (all the even numbers). But now, if you take all the natural numbers and subtract all numbers greater than 4, what do you have left over? Three. So infinity minus infinity is 3. They're self–contradictory. And that is why, in transfinite arithmetic, the inverse operations of subtraction and division are prohibited: because you get self–contradictory results. Now you can slap the hand of a mathematician and say, "No, no, no! You can't do that!" But if these things really exist in reality, then there's no way to prevent that sort of thing; and these sort of absurdities and contradictions would result. When Quentin says virtually every mathematician agrees that an actually infinite number of things can exist, I think that's wrong. They may agree with the conceptual schemes of infinite set theory and so forth, but that's not the metaphysical question of whether these things actually exist in the real world. And we mustn’t underestimate the fact that although the school of what's called Intuitionism in mathematics is small, it includes some of the greatest mathematicians that have lived, people like Kroenecker and Brower. I also mentioned Hilbert and Abraham Robinson. These are some of the greatest minds in set theory and mathematics, and they're all finitists in this respect. So I think the argument is, again, a persuasive argument. Quentin did not even address my argument based on the formation of an actual infinite by successive addition. Remember: they’re independent arguments, so even if the first one doesn't work, the second one still proves that the universe had a beginning.
Now what about the Big Bang theory? He suggests Linde’s theory could provide an oscillating model that would escape the beginning of the universe. Now notice that even if this model is available, that doesn't mean that it’s more probably true than the standard Big Bang model. There's no reason to believe that it is correct, and the majority of physicists have not gone over and adopted it rather than the standard Big Bang model. But is it in fact a tenable model? Well, I talked with Andrei Grib, who is a Russian astrophysicist, one of Linde’s colleagues, and he told me at least that Linde’s model doesn't solve the thermodynamics problems that I alluded to, that, in fact, you would still have an accumulation of entropy from cycle to cycle, so that this would not solve the problem of having an infinite past. He said the only way to do it is to introduce a sort of ad hoc thermodynamic sink in between the oscillations to try to prevent the accumulation of entropy—but it was very ad hoc. In any case, wholly apart from thermodynamic problems, there’s still the observational problem: namely, there's not enough matter in the universe to close the universe and make the expansion re–contract. The evidence stubbornly continues to indicate that the universe would have to be ten times denser than what it is in order for the expansion to stop and the universe to re–contract. So the model is just observationally untenable. And finally, I don't know of any physical mechanism that would reverse a Big Crunch and make it bounce back to an expansion again. From my reading, this is physics that is completely unknown. There is no known physics that would reverse a Big Crunch to make a universe oscillate. So again, the more probable model, I think, is the Big Bang model. That's why I think that the majority of physicists continue to hold to it. So I still think that, on balance, we have good grounds for believing that the universe began to exist, and if that's the case, then, given that whatever begins to exist has a cause, there must be this transcendent Personal Cause which brought the universe into being.
That concludes the first half of the debate. Now we are going to move to the second half. If you have questions about this exchange, could you remember them and ask them afterwards? We're now going to move on to Quentin Smith's own presentation, which is "Divine Causation of the Big Bang: Is It Logically Possible?"
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