Transcript

Does God Exist?

William Lane Craig vs. Quentin Smith

Southern Methodist University, Dallas, Texas, United States – March 22, 1996

William Lane Craig – Initial Arguments

A Defense of the Cosmological Argument for the Existence of God

I want to begin just by thanking the Philosophy Department for the free dinner, as well as the invitation to participate in tonight's forum!

During the last quarter century, a remarkable revolution has occurred in American philosophy. This change was so noteworthy that even the popular media observed it. In an article entitled "Modernizing the Case for God," published on April 7 of 1980, Time magazine commented,

In a quiet revolution in thought and argument that hardly anybody could have foreseen only two decades ago, God is making a comeback. Most intriguingly, this is happening, not among theologians or ordinary believers, but in the crisp intellectual circles of academic philosophers, where the consensus had long banished the Almighty from fruitful discourse.1

The article quotes Roderick Chisholm to the effect that the reason that atheism was so influential a generation ago is because the brightest philosophers were atheists. But today, Chisolm says, many of the brightest philosophers are theists, and they're using a toughminded intellectualism in defense of that theism. Premiere among this new crop of philosophers stands Alvin Plantinga of the University of Notre Dame, a sort of latterday Anselm, whom the late J. L. Mackie, perhaps one of the most prominent atheists of our day, has facetiously canonized as "St. Alvin." A few years ago, Plantinga gave a paper entitled, "Two Dozen or so Theistic Arguments," in which he laid out an impressive and very creative array of arguments for the existence of God.2 Unfortunately, the conventional wisdom that Hume and Kant put a permanent end to theistic arguments still widely persists among undergraduate students in philosophy today. This conventional wisdom is simply rooted in ignorance, and the very fact that we’re having this debate here this evening, I think, is testimony to the fact that this question is still very much a live issue today.

What I'd like to do this evening is simply to present, in outline, one particular theistic argument that I find to be a sound and persuasive argument, the socalled kalam cosmological argument. This argument not only survives the objections of Hume and Kant, but, as I shall show, both Hume and Kant actually endorsed both of the premises of the argument. So I will simply go through the outline with you, commenting on each step.

Handout: The Kalam Cosmological Argument

1. Whatever begins to exist has a cause of its existence.

2.The universe began to exist.
2.1 Argument based on the impossibility of an actual infinite:
2.11 An actual infinite cannot exist.
2.12 An infinite temporal regress of events is an actual infinite.
2.13 Therefore, an infinite temporal regress of events cannot exist.
2.2 Argument based on the impossibility of the formation of an actual infinite by successive addition:
2.21 A collection formed by successive addition cannot be actually infinite.
2.22 The temporal series of past events is a collection formed by successive addition.
2.23 Therefore, the temporal series of past events cannot be actually infinite.
2.3 Confirmation based on the expansion of the universe.
2.4 Confirmation based on the thermodynamic properties of the universe.

3. Therefore, the universe has a cause of its existence.

4. If the universe has a cause of its existence, then an uncaused, personal Creator of the universe exists, who sans creation is beginningless, changeless, immaterial, timeless, spaceless, and enormously powerful and intelligent.
4.1 Argument that the cause of the universe is a personal Creator:
4.11 The universe was brought into being either by a mechanically operating set of necessary and sufficient conditions or by a personal, free agent.
4.12 The universe could not have been brought into being by a mechanically operating set of necessary and sufficient conditions.
4.13 Therefore, the universe was brought into being by a personal, free agent.
4.2 Argument that the Creator sans creation is uncaused, beginningless, changeless, immaterial, timeless, spaceless, and enormously powerful and intelligent:
4.21 The Creator is uncaused.
4.211 An infinite temporal regress of causes cannot exist. (2.13, 2.23)
4.22 The Creator is beginningless.
4.221 Whatever is uncaused does not begin to exist. (1)
4.23 The Creator is changeless.
4.231 An infinite temporal regress of changes cannot exist. (2.13, 2.23)
4.24 The Creator is immaterial.
4.241 Whatever is material involves change on the atomic and molecular levels, but the Creator is changeless. (4.23)
4.25 The Creator is timeless.
4.251 In the complete absence of change, time does not exist, and the Creator is changeless. (4.23)
4.26 The Creator is spaceless.
4.261 Whatever is immaterial and timeless cannot be spatial, and the Creator is immaterial and timeless (4.24, 4.25)
4.27 The Creator is enormously powerful.
4.271 He brought the universe into being out of nothing. (3)
4.28 The Creator is enormously intelligent.
4.281 The initial conditions of the universe involve incomprehensible fine-tuning that points to intelligent design.

5. Therefore, an uncaused, personal Creator of the universe exists, who sans creation is "beginningless," changeless, immaterial, timeless, spaceless, and enormously powerful and intelligent.

The argument is really very simple and consists primarily of three steps. (1) Whatever begins to exist has a cause of its existence. (2) The universe began to exist. (3) Therefore, the universe has a cause of its existence. And then in premise (4) we conceptually unpack what some of the principal attributes would be of a cause of the universe's existence.

Now, with respect to premise (1), whatever begins to exist has a cause of its existence, I'm not going to say very much in defense of this premise this evening. I really don't think that it's necessary because the premise that whatever begins to exist must have a cause of its existence I think is so intuitively obvious that scarcely anybody could sincerely deny that it is false. In fact, David Hume himself agreed that this principle is true. In a letter to John Stewart dated February, 1754, Hume wrote, "But allow me to tell you that I never asserted so absurd a Proposition as that anything might arise without cause: I only maintain’d, that our Certainty of the Falshood of that Proposition proceeded neither from Intuition nor Demonstration; but from another Source."3 Hume didn't think that you could prove the causal principle, but he certainly believed in it. In fact, he thought that the denial of that principle was simply absurd. Similarly, as is well known, Kant held the principle "Every event has a cause" to be a synthetic a priori principle; that is, it's an informative proposition characterized by both universality and necessity.4 Only Kant’s implausible and perhaps incoherent restriction of the categories to phenomena alone prevented him from holding that this principle applied to reality. So, as I say, it seems to me that this first premise is intuitively obvious, and even detractors of theistic arguments such as Hume and Kant themselves admit it's true.

The more controversial premise is the second one: that the universe began to exist. And in support of this premise I present two philosophical arguments, and then two scientific confirmations of those arguments. The first philosophical argument, (2.1), is the argument based on the impossibility of an actual infinite, and it runs like this: (2.11) An actual infinite cannot exist. (2.12) An infinite temporal regress of the events is an actual infinite. (2.13) Therefore, an infinite temporal regress of events cannot exist.

Now in order to grasp this argument it's important to distinguish an actual infinite from a potential infinite. An actual infinite is a collection of things having a proper subset which has the same number of members as the original collection itself. An actual infinite is not like a potential infinite, which is a collection which is at every point in time finite but is growing toward infinity as a limit. My argument is simply that an actual infinite cannot exist. I do not deny the existence of a potential infinite.

Why do I hold to (2.11)? Well, very simply this: if you try to translate the idea of an actually infinite number of things into reality, you wind up with all sorts of absurdities and, in the end, logical contradictions. For example, what is infinity minus infinity? Well, mathematically you get selfcontradictory answers, unless you impose some wholly arbitrary rules to prevent this. This shows that infinity is just an idea in your mind, not something that exists in reality. David Hilbert, who is perhaps the greatest mathematician of this century, states, "The infinite is nowhere to be found in reality. It neither exists in nature, nor provides a legitimate basis for rational thought…. The role that remains for the infinite to play is solely that of an idea."5 So as I understand the actual infinite, it is simply a conceptual idea; it is not something that exists in reality. (2.12) says, an infinite temporal regress of events is an actual infinite. I think this is fairly obvious. If the universe never began to exist, then the number of past events is actually infinite. And therefore it follows: (2.13) that an infinite temporal regress of events cannot exist. Therefore, the temporal regress of events is finite and must have a beginning. Since the universe is not distinct from the temporal series of past events, it therefore follows that the universe began to exist.

The second philosophical argument is the argument based on the impossibility of the formation of an actual infinite by successive addition. This argument is independent of the first. It's claiming that even if an actual infinite can exist, it cannot be formed by successive addition. And this argument goes this way: (2.21) A collection formed by successive addition cannot be actually infinite. (2.22) The temporal series of past events is a collection formed by successive addition. (2.23) Therefore, the temporal series of past events cannot be actually infinite. The first step in the argument, a collection formed by successive addition cannot be actually infinite, is true by the very nature of infinity. You can never get to infinity by addition because you can always add one more. Sometimes this is called the impossibility of counting to infinity, or another way it's referred to is the impossibility of traversing the infinite. Now if the past were infinite, it would be as though someone had claimed to have just finished counting down all the negative numbers ending in "0," and surely this is absurd. If you can't count to infinity, how can you count down from infinity? If you can't traverse an infinite distance by running in one direction, how can you traverse it by simply turning around and running in the opposite direction?

Indeed, the idea that the past could be actually infinite is absurd. I think this is well illustrated by the Tristram Shandy paradox of Bertrand Russell. Russell imagines Tristram Shandy, a character in a novel by Sterne, who writes his autobiography so slowly that it takes him a year to write down the events of a single day. Russell says that if Tristram Shandy were to live forever, then his autobiography would be completed because there would be an infinite number of years and an infinite number of days, so that every day would be written about. It seems to me that this conclusion is incorrect because the future is a potential infinite only. Tristram Shandy would never arrive at actual infinity. The number of days and hence the number of years of his life would always be finite but potentially increasing toward infinity as a limit. But suppose we turn this story around and imagine that Tristram Shandy has been writing from eternity past. Then the number of years and the number of days would in fact be actually infinite, and you could say that Tristram Shandy would have completed his autobiography. But if you say that Tristram Shandy would have completed his autobiography, then the question arises: Why did he finish it today rather than yesterday, or the day before, or the day before that? By any time in the past, an infinite amount of time had already elapsed, so that if Tristram Shandy would finish his autobiography given infinite time, he should have already finished at any point in the finite past. But that means that no matter how far back in the past you regress, you will never find Tristram Shandy writing, which contradicts the hypothesis that he has been writing his autobiography from eternity. And thus the notion of an infinite past, it seems to me, is absurd.

That leads to the second premise, that a temporal series of past events is a collection formed by successive addition. Again, I think this point is obvious. The series of past events is a collection which has been formed by one event occurring after another, by successive addition. But that leads to the conclusion: therefore, the series of past events cannot be actually infinite. It must be finite, and the universe must have begun to exist.

Again, this argument was agreed to by both Hume and Kant. In his Enquiry, Chapter 12, Section II, paragraph 125, Hume writes, "An infinite number of real parts of time, passing in succession, and exhausted one after another, appears so evident a contradiction, that no man whose judgment is not corrupted, instead of being improved, by the sciences, would ever be able to admit of it."6 Hume tries to elude what he calls the absurdities and contradictions of this by embracing a nominalist view of numbers and abstract objects. Now I’m very much in sympathy with that view, but clearly it does nothing to solve the problem of how a temporal series of real past events could have been formed by successive addition and yet be infinite. And, as is well known, Kant as well, in the thesis of his first antinomy concerning time, also endorses this argument. Kant writes,

If we assume that the world has no beginning in time, then up to every given moment an eternity has elapsed and there has passed away in the world an infinite series of successive states of things. Now the infinity of a series consists in the fact it can never be completed through successive synthesis. It thus follows that it is impossible for an infinite worldseries to have passed away, and that a beginning of the world is therefore a necessary condition of the world's existence.7

And it can't be emphasized enough that, according to Kant, this is an undeniable requirement of reason. Reason forces you to that conclusion, on Kant's view. Of course, he also believed that reason forced you to adopt the antithesis as well, but I think that the argument for the antithesis is simply a faulty argument. It erroneously assumes that time necessarily precedes the beginning of the universe; but on a nonNewtonian relational view of time, time begins simultaneously with the first event. So there's simply no problem about when the universe would have begun to exist in the empty time prior to the beginning of the universe. So again, it seems to me that this argument is a forceful and persuasive argument, which both Hume and Kant, in effect, concede.

Now some people are suspicious of philosophical arguments for the beginning of the universe. They want to know if there is empirical evidence for this thesis. And in fact there is. I mention in (2.3), first, the confirmation based on the expansion of the universe. According to the standard Big Bang cosmological model, the universe is not infinite in the past, but began to exist at a point in the finite past about 15 billion years ago. Not only all matter and energy, but physical space and time, were created in that event, so that there is literally nothing prior to the origin of the universe. Paul Davies, in his article, "Spacetime Singularities and Cosmology," says,

If we extrapolate this prediction to its extreme, we reach a point when all distances in the universe have shrunk to zero. An initial cosmological singularity therefore forms a past temporal extremity to the universe. We cannot continue physical reasoning, or even the concept of spacetime, through such an extremity. For this reason, most cosmologists think of the initial singularity as the beginning of the universe. On this view, the Big Bang represents the creation event; the creation not only of all the matter and energy in the universe, but also of spacetime itself.8

Now, of course, some theorists were unhappy with the notion that the universe began to exist from nothing, and alternative models have been proposed. But none of these has been tenable either empirically or philosophically. For example, the oscillating model, which says that the universe expands and contracts from eternity, is physically, observationally, and thermodynamically untenable. The vacuum fluctuation models, which hold that the universe emerged from a quantum vacuum by a fluctuation, are untenable because they predict a nonzero probability for a universe existing at every point in spacetime in the quantum vacuum, so that given an eternal quantum vacuum, all of the spacetime points would spawn universes, which would then collide and coalesce into an infinitely old universe, which contradicts observation. The quantum gravity models all depend on the use of "imaginary time" prior to 1043 second after the Big Bang; these are simply nonphysical solutions. They are nonrealistic solutions. Once you convert the numbers back to real time, the singularity reappears. So the most plausible model of the origin of the universe remains the Big Bang model, which posits a creation out of nothing. And that goes to confirm premise (2) the universe began to exist.

In the interest of time I'm going to skip over (2.4), the confirmation based on thermodynamic properties of the universe, and go right to (3. 0): Therefore, the universe has a cause of its existence.

In (4. 0), I deduce some of the principal attributes of this cause: If the universe has a cause of its existence, then an uncaused personal Creator of the universe exists, who sans creation, is beginningless, changeless, immaterial, timeless, spaceless, and enormously powerful and intelligent. Let me just focus on the argument for the personality of the Creator.

(4. 11) The universe was brought into being either by a mechanically operating set of necessary and sufficient conditions or by a personal, free agent. Either it was a free agent or it was just a mechanical physical cause. (4. 12) The universe could not have been brought into being by a mechanically operating set of necessary and sufficient conditions. Why? Because if the necessary and sufficient conditions were present from eternity, the effect would also be present from eternity. It's impossible to explain how the sufficient conditions could exist timelessly or eternally and not also have the effect equally copresent. The only way that a temporal effect could arise from an eternal cause is if the cause is a free, personal agent who is able to freely create the universe without antecedent determining conditions. And therefore it follows: (4. 13) The universe was brought into being by a personal, free agent.

And then on the rest of the page it's fairly obvious how I deduce the remainder of these attributes which form the central core of the theistic notion of God: a personal Creator, uncaused, beginningless, changeless, immaterial, timeless, spaceless, enormously powerful, and intelligent. In the words of Thomas Aquinas, this is what everybody means by God.

Quentin Smith – First Rebuttal

I think that I can agree with Bill that many of the brightest philosophers today are theists, but I recall Shakespeare’s statement that it is the fool who knows in his heart the truth, and I rely on Shakespeare to defend me in my response to Bill tonight.

Bill’s basic argument is this: his first premise is: Whatever begins to exist has a cause. Second premise: The universe began to exist. And the conclusion is: The universe had a cause. Now this argument commits the fallacy of equivocation, and what that means is that the word "cause" is used in a different sense in the premise, Whatever begins to exist has a cause, than it is in the conclusion, The universe has a cause. For when we examine "things that begin to exist have causes," what we really are examining are rearrangers of preexistent materials. Anything we point to in our daily life that we say has a cause, say, a statue, is a rearrangement of, say, a slab of marble. And even a human being is a rearrangement ultimately of chemicals and atoms and quarks and so on. And so insofar as "Whatever begins to exist has a cause" has any support at all, it would have to mean "Whatever begins to exist has a rearranger of its preexistent materials." Now given that, and given the second premise, the universe began to exist, we cannot infer that universe has a rearranger of its preexistent materials, for if the universe began to exist, there are no preexistent materials, so that if "cause" has any meaning at all in the conclusion, it has to mean something that creates the materials from nothing, and we have absolutely no experience of that in any of our lives, in any of science, anywhere. It's just an idea that appears solely in theism. So I see no evidence for it based on empirical observation, scientific evidence, or anything. It seems to me a proposition of supernatural theology. So I don't think that that is an argument that a rational person should accept.

Bill Craig also says that "Whatever begins to exist as a cause" is selfevident. And he also says that "The universe has a cause" is selfevident or intuitively obvious. But that clearly is not the case. Most physicists who work in this area—Stephen Hawking and all the rest—most philosophers and just purely on my anecdotal evidence from asking students in my classes what they think—more than half usually say they don't find this selfevident. In fact, only a small proportion say they find it selfevident, and they always happen to be theists, and the other ones say either they don't know (the most common response) or that is not selfevident. They don't know whether it's true or false. It may be true or false, but they don't know. So clearly, it's not selfevident that the universe has a cause, and it is giving it much too high of a status to call it selfevident. Maybe it has some degree of possibility—that can be granted. But I think that going beyond that you need a lot more argumentation given, since there are numerous people who deny that.

Bill Craig casts aspersions upon infinity, which is a courageous undertaking for a finite being. Now he says that infinity minus infinity is selfcontradictory. But let's take an infinite number of persons and subtract Bill Craig from them. You still have an infinite number of persons. Now Bill would say that's selfcontradictory. I would say no, not only because I would still like Bill Craig around, but because I think it's not selfcontradictory. And before I explain why, I would simply note that virtually every single mathematician today, virtually every single physicist, and virtually every single philosopher believes there's nothing at all wrong with the arithmetic of infinity or applying it to the real world. There's only a tiny handful of people like Bill Craig, and Whitrow, and one or two others who actually try and find problems with it, and it’s simply not at all prevalent, not at all a standardly accepted view in contemporary thinking. It's not just sheer conformity. There are good reasons why. All of Bill Craig's arguments against infinity are based on one simple mistake. He applies the rules of finite arithmetic to infinite arithmetic, and once you do that, of course you get contradictions. Well, it's a veritable mistake to begin with, to apply the rules of finite arithmetic to infinite arithmetic. And here's one example of how this is done. Bill says we can't count one by one to infinity. Well, of course not! The definition of finite numbers is that you can count one by one. Given any finite number we can count one by one and reach it. Even if the number is ten trillion, we can imagine some idealized being who is very powerful, lives a long time; that person eventually will get to an extremely high number if he keeps counting. But if numbers are infinite, then no matter which number you count, there’s still another number, so you can't count to them. But that's a rule of finite arithmetic, and you only get a contradiction if you introduce rules of finite arithmetic to infinite ones. So I don't think those arguments are sound.

And finally, regarding the empirical evidence that the universe began to exist, it’s not nearly as strong as Bill Craig suggests. For example, one model that Bill did not mention is A. D. Linde's oscillating model. He developed a new oscillating model, not the old one that was developed in the early 1960s which the HawkingPenrose Singularity Theorem refuted. There are some technicalities there (Bill knows what I’m talking about), but the point is that A. D. Linde came up with a new theory of this, for which there's no good counterargument. I'll wax technical for a couple of sentences and give you a rough idea of what I mean. There are four forces in nature—the strong force, weak force, electromagnetic force—and there are coupling constants for each of those three forces, and we have theories of those, and they're workable. Now A. D. Linde shows that by analogy there should be a coupling constant to the gravitational force, and given that, this will solve all the problems of an oscillating universe that have ever been brought up. For example, one problem is that, if the universe oscillates, if it goes through a Big Crunch and expands again, then all the radiation from a previous cycle will accumulate in the next cycle, and as that one expands it'll get larger still because it will have more radiation from all the energy in its stars, and eventually you'll get to something that's so big it'll expand forever, and then you'll no longer have an infinite number of oscillating universes. But A. D. Linde’s theory shows that all this excess radiation from the cycle that's contracting before it hits the big bounce, when it gets near the socalled Planck era, which is about 1043 seconds, a very short time before it begins to bounce out again, all the entropy, the disorder that's built up in the previous cycle, and all the excess light and radiation that comes from the stars is lost. So in each new cycle we begin anew, the new Big Bang, and so his theory solves all the existent objections against an oscillating universe that's infinitely old, and in the literature no argument I'm aware of shows that there's no good reason to accept A. D. Linde's theory. So I think that on empirical grounds it's simply false that all the evidence points to the fact that the universe definitely began to exist 15 billion years ago.

William Lane Craig – Re-Rebuttal

I want to thank Quentin for his comments this evening. I've enjoyed our ongoing 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, thoughtworlds, 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 selfevident? 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 selfcontradictory. Well, I simply beg to disagree. It is selfcontradictory. 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 selfcontradictory. And that is why, in transfinite arithmetic, the inverse operations of subtraction and division are prohibited: because you get selfcontradictory 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 recontract. 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 recontract. 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.

Quentin Smith – Argument

Divine Causation of the Big Bang: Is It Logically Possible?

The first section of my paper is called "Introduction." Here I give some definitions. The universe is a maximal or complete space and time. It contains, say, this spacetime point here, and every point spatiotemporally connected to that point, and it contains everything—all inanimate objects and organisms—that occupies all the spacetime points. According to Big Bang cosmology, which Bill was talking about, which I'll simply assume in this article in order to deal with a certain issue of the cause of the universe if it began to exist, the universe began to exist about 15 billion years ago with the Big Bang occurring at the earliest time of t0; it's called the Big Bang singularity.

Now something is a continuing cause of the universe only if it causes each state of the universe. And something is an originating cause of the universe only if it causes the earliest state of the universe. If the universe began with the Big Bang and has no originating cause, then it has no continuing cause, since if the first state has no cause, then its false, of course, that each state has a cause.

Now my question in this paper is this: is it logically possible that the universe has an originating divine cause? Is it logically possible that there is a first state of the universe that's caused by God? I think that virtually all theists, virtually all agnostics, and even virtually all atheists today would admit this is logically possible. It seems to me, however, that this is not logically possible. And I present some arguments on behalf of this conclusion by showing that the thesis that the universe has an originating divine cause is logically inconsistent with all permissible definitions of causality. I will conclude that the cosmological and teleological arguments for a supernatural cause of the universe, traditionally understood as arguments for the existence of God, are in fact arguments for the nonexistence of God.

The second section is called "Causal Definitions and the Notion of an Originating Divine Cause." Since we are talking about the cause of the universe's beginning and not the cause of God's act of willing that the universe [would] begin, considerations of agent causality are not pertinent here. We are not examining the relationship between God, who is the agent, and his act of willing, which would be the effect, but the relation between his act of willing, which is an event, and the beginning of the universe, which is another event. Thus, definitions of agent causality referred to in the literature in the philosophy of religion are irrelevant to our discussion. We are interested only in definitions of event causality, where the cause and effect are both events.

Now if we follow Big Bang cosmology or quantum gravity cosmology and hold that the universe and time both began to exist with the Big Bang, this rules out as impossible an originating cause according to all definitions that include temporal priority as a logically necessary condition of causation. Temporal priority, of course, means that the cause is earlier in time than the effect. The most famous definition that includes the temporal priority condition is Hume's.

This section now is called "Hume's Definition of a Cause." All, or almost all, contemporary definitions of causality are based in some way on Hume's definition in the 18th century, whether by way of repetition, modification, or reaction against Hume's definition. Hume explicitly includes temporal priority in his definition, which implies that something, c, is a cause of something, e (I'm using c throughout the paper to refer to an event that’s a cause and e to refer to the event that’s the effect), if and only if these three conditions are met: (1) c is spatially and temporally associated with e, (2) c is earlier than e (the cause is earlier than the effect), and (3) every particular like c is always conjoined with a particular like e. Given this definition of a cause, something c is a cause of the universe's beginning to exist at the earliest time only if c is earlier than the earliest time, which is an explicit logical contradiction. For all Humeantype definitions of a cause imply that the cause is earlier than the effect, which is inconsistent with the supposition that the Big Bang singularity had a cause.

Now we go to the next section, which I call "Nomological Definitions of a Cause." Nomos is a Greek word meaning the law, so these definitions are called that because they include a law of nature in any kind of causal process. So another feature of Hume’s definition, the nomological condition, which implies that a law of nature is needed in the definition of a cause, is also common to most contemporary definitions of causality. Specifically, Hume's definition belongs to the line of reductive definitions that define causality in terms of laws of nature and a set of noncausal relations between the two particulars, c and e. Now if you isolate this nomological feature and make it not merely logically necessary for causation but also logically sufficient, we have this definition: c is a cause of e if and only if there's a law of nature, called the law of nature L, that enables a statement that e occurs to be deduced from the premise that c occurs and another premise asserting the law L.

However, the nomological definition of a cause is logically inconsistent with a divine cause of the Big Bang, since God by definition is a supernatural being and his/her actions are not governed by laws of nature.

At this point, we have already ruled out virtually every existent definition of causality, since most every definition includes either the temporal priority condition or the nomological condition. In fact, most existent definitions of causality today in the philosophical literature include both conditions. So we're left with atemporal and singularist definitions of causality. Now these are very rare definitions, but we have to use them if we want to have any sort of coherent notion of God causing the Big Bang. Now an atemporal definition either makes no mention of time at all or it allows that the cause is simultaneous with the effect, in which case it would mean that God's act of causing the Big Bang is simultaneous with the existence of the Big Bang. And it's called singular, since it allows an event to cause an effect in a single case, which is obviously the case when God caused the Big Bang, without the cause of God's willing and the effect needing to instantiate some law.

Now there are so few definitions of causality in the literature that are singularist and atemporal, it's hard for us to define one. But the nearest we can get to one is David Lewis’. Lewis' definition imports counterfactual conditions, which means conditions that are contrary to the ones that in fact obtain. He's just hypothesizing about imaginary situations. David Lewis' definitions import counterfactual conditions into the definition and seems to lend itself to an atemporal and singularist instantiation. According to David Lewis, c causes e if and only if (1) c and e are events and both occur, and (2) it is the case that either if (i) c had not occurred, e would not have occurred (in other words, if the cause did not occur, the effect would not have occurred) or, as an alternative to that, (ii) if there is a causal chain linking c and e and each link d in the chain is such that if d had not occurred, then e would not have occurred. Now since there's no causal chain between the divine volition and the Big Bang, condition (ii) is inapplicable, and so we'll concentrate simply on condition (i) that c and e both occur, and if c had not occurred, e would not have occurred. This seems to be the only definition which is going to salvage the hypothesis that God might have caused the Big Bang, but we'll see whether it does or not.

There does appear to be at least one crucial instance where Lewis' counterfactual definition is not instantiated by divine willing of the Big Bang. Let c be the divine willing of the Big Bang, and let e be the Big Bang. It follows that if the effect e had not occurred, then its cause c would not have occurred. But this suggests that e is the cause of c. In other words, e here is the Big Bang and c is divine willing, so this suggests that the Big Bang caused God's willing, which, of course, is absurd. And the reason why it suggests that is that c is counterfactually dependent on e, for the very reason that I said: if the effect e had not occurred, and then its cause c would not have occurred. In this case we have, to use Lewis' words about a problem he generally notes, a "reverse causal dependence of c on e, contradicting our supposition that e did not cause c" (1). Now Lewis solves this problem, which is an effective solution for normal causes and effects, by denying the counterfactual statement that "if e had not occurred, c would not have occurred." Lewis holds that it is instead true that "c would have occurred just as it did, but would have failed to cause e."10} In other words, Lewis is saying it’s possible the cause could occur, or the event which was the cause could occur, but the effect would never have happened. However, that entails that Lewis' definition cannot be instantiated by God's willing the Big Bang, since if c had occurred, that is, if God had willed the Big Bang, then it necessarily causes e, the Big Bang, since God is omnipotent (allpowerful) and his willing is necessarily effective. It’s logically impossible for an omnipotent being to will that the Big Bang occur and yet for the Big Bang not to occur. Consequently, Lewis' definition appears to be inapplicable to the divine creation of the universe.

The next section is called "Necessary and Sufficient Conditions". We may take the simplest route and adopt one of these three definitions of a cause: The first one, which I'll call S, referring to the sufficient condition definition is: x is a cause of y if and only if x is a sufficient condition of y. The next one I call N because it's a necessary condition definition: x is a cause of y if and only if x is a necessary condition of y. And a third one combines both. I call it N&S because it includes a necessary and sufficient condition: x is a cause of y if and only if x is a necessary and sufficient condition of y.

Now could any of these three definitions apply to God? No, for the following reasons:

God's willing the Big Bang is a sufficient condition of the Big Bang, so S, that first definition about sufficient conditions, appears to be satisfied by God's creation of the Big Bang. Unfortunately, S fails as a definition of a cause, since numerous things instantiate this definition that are not causes. For example, a thermostat reading 65 degrees Fahrenheit is a sufficient condition under normal circumstances of the temperature being 65 degrees, but this reading is not a cause of the air’s temperature.

If we assume that it is necessary that the Big Bang be caused by God if it has occurred at all, then God’s willing the Big Bang will satisfy the definition N, which says that something caused something else if it's a necessary condition for its occurring. But this definition, N, is not the definition of a cause, since there are many causes that are not necessary conditions and there are many necessary conditions that are not causes. The movement of a feather on my desk is caused by my pushing the feather with my hand, but this pushing is not a necessary condition of the feather’s moving, since the feather may move by a gust of wind blowing. Further, air is a necessary condition of humans existing, but the air does not cause humans to exist.

Now the third definition that I mentioned, the one that combines both necessary and sufficient conditions, may be satisfied by God's willing the Big Bang, but this definition again is not the definition of a cause. Many causes are not both necessary and sufficient conditions of their effects. I've already mentioned many of these examples. I've mentioned that some causes of a feather's moving that are necessary conditions of it moving, and necessary conditions of humans existing are not causes of it. Then I mentioned some sufficient conditions that are not causes, such as a thermostat reading. Further, this definition is violated by probable causes, such as the radioactive decay of a uranium atom, which would seem to require a probabilistic definition of causality.

The next section is called "A Correct Formulation of Any Divine Relation to the Big Bang." There seems to be an argument that God is not the cause of the Big Bang, an argument that remains sound regardless of which definition of causality is employed. The argument is based on the simple premise, if something is a logically sufficient condition of something else, that doesn't cause it. Or to read it more formally out my paper, for any x, if x is a logically sufficient condition of y, then x is not the cause of y. For example, a body’s being in motion is a logically sufficient condition of the body’s existence. But the body’s being in motion is not the cause of the body’s existence. However, God's willing the Big Bang is a logically sufficient condition for the Big Bang, for "God wills the Big Bang and the Big Bang does not occur" are logically incompatible. The reason for this is that God is omnipotent, allpowerful, and thus his willing is always successful (of logical necessity). If an omnipotent being wills x and x does not occur, then God is not omnipotent. The omnipotent being is not omnipotent, which is a direct contradiction. Now God can do everything that is logically possible but, of course, cannot do what is logically impossible.

This is not to say that we cannot talk intelligibly about God and his relation to the Big Bang. We can say that a mental event in God's mind is a logically sufficient condition of the Big Bang's occurrence. And that's what we should say rather than that God causes the Big Bang. We can say that there's a certain relation, R, in which God stands to the property F, F being the property of being the Big Bang, such that by virtue of God's standing in this relation R (the reason I call it R is because we may not know what that relation is; maybe it's the relation of God trying to will the Big Bang to be instantiated), to the property of being the Big Bang, it is logically necessary that the property or characteristic of being a Big Bang is instantiated and therefore that there is a Big Bang.

Now my conclusion, which puts an interesting twist on all this, is this: the argument of this paper might seem at first glance to tell us more about the nature of God than about theism vs. atheism. "God cannot cause the Big Bang" does not entail that "God does not exist" or that "The Big Bang is not logically necessitated by God," but it does entail that we cannot define God as the cause of the Big Bang or the universe. Nonetheless, there are implications for the debate between theism and atheism, namely, that arguments from the necessary truth, a priori truth, or empirical truth of some causal principle cannot be a relevant premise from which to deduce or induce that the Big Bang is the logical consequence of God's standing in this relation, R (which is some relationship, it’s not the causal relationship—we don't know what is) to the property of being a Big Bang. Consider, for example, the argument that Bill brought up in his talk, the argument also that I responded to. The argument is this: (1) Everything that begins to exist has a cause. (2) The universe begins to exist. (3) Therefore, the universe has a cause. That argument fails to support the thesis that God exists or is the cause of the universe's beginning to exist. Indeed, this very argument entails that the universe's existence is not a consequence of any act on the part of God, since God could not have caused the universe to exist. Nor can any inductive argument, based on the fact that every observed event has a cause, be used to support the thesis that the Big Bang is a result of a divine act, since this inductive argument would instead support a thesis incompatible with theism: namely, the Big Bang has a cause. Indeed, any inductive evidence for the thesis that all events have a cause is by that very fact evidence against the existence of God, or at least against the hypothesis that the Big Bang is a consequence of standing in some relationship to a deity. Indeed, it seems now that all the various cosmological and teleological arguments for the existence of God are in fact arguments for God's nonexistence, since these arguments are arguments for the thesis that the universe has a cause. For example, one version of the teleological argument is this: (1) Artifacts are caused to exist by intelligent beings. This is a cup, it's an artifact, it was caused by an intelligent being with some purpose in mind. (2) The universe resembles an artifact. (3) Therefore, it's probable that the universe was caused to exist by some intelligent being or beings, with some purpose in mind. If this argument is an adequate argument from analogy, then God probably does not exist, since God is not a cause, but a logically sufficient condition of the universe's existence. Since the cosmological and teleological arguments have standardly been thought to be the strongest arguments for God's existence, and since they support atheism rather than theism (which is rather odd, since traditionally atheists have said, "Well, here's a problem of evil; therefore, God doesn't exist," and then their next move is to go through all the theistic arguments—the cosmological, the teleological, the ontological, and all that—and then try and refute them all). What I'm doing is saying, "O. K., let's grant all the theistic arguments are sound. Grant all the cosmological arguments are sound. Grant Bill's argument is sound. Grant the teleological argument is sound. What does that prove?" I'm arguing that they prove that God doesn't exist because their conclusion has got a God who causes the beginning of the universe. So it seems now that the case for theism is very weak indeed. Indeed, it seems hard to imagine how one could ever inductively or deductively establish, or let alone find selfevident, that the Big Bang has a logically sufficient condition of its occurrence, which it would have to if God in some sense brought it about. Perhaps there are somewhat plausible arguments that the Big Bang had a cause, but there are no existent arguments, at least that I'm aware of, that the Big Bang has a logically sufficient condition of its existence. This suggests that the belief in the existence of God is considerably less reasonable than even the most cautious theologians have standardly supposed.

William Lane Craig – Rebuttal

Quentin Smith has presented us with a wideranging and very erudite argument to the effect that it's logically impossible for the universe to have a divine originating cause. In the end, however, I must confess myself to be unmoved by the argument. Well, why is this? Smith's argument goes like this:

(1) If the claim that God caused the Big Bang cannot be analyzed in terms of extant definitions of causality, then God cannot have caused the Big Bang.

(2) The claim that God caused the Big Bang cannot be analyzed in terms of extant definitions of causality.

(3) Therefore, God cannot have caused the Big Bang.

Is this a sound and persuasive argument? Well, I think not.

Consider premise (1) If the claim that God caused the Big Bang cannot be analyzed in terms of extant definitions of causality, then God cannot have caused the Big Bang. I see no reason to think that this premise is true. In general, arguments to the effect that some intuitively intelligible notion can't be analyzed in terms of certain philosophical theories should make us suspect the adequacy of those theories rather than reject the common sense notion. The idea that God caused the universe is intuitively intelligible. A cause is, loosely speaking, something which produces something else and in terms of which the thing that is produced can be explained. This notion certainly applies to God's causing the universe. If God's causing the universe cannot be analyzed in terms of current philosophical definitions of causality, then so much the worse for those theories! This only shows that the definitions need to be revised. Indeed, the standard procedure in terms of which proposed definitions of causality are assessed is typically to propose some counterexamples in terms of intuitively plausible cases of causation and then show how the definition fails to accommodate these new cases. In the same way, if God's causing the universe cannot be accommodated by current philosophical definitions of causality, then that plausibly constitutes a counterexample to the definition, which shows that it's inadequate as a general metaphysical analysis of the causal relation, however adequate it might be for scientific purposes. Moreover, there's no reason to believe that we have arrived at the final and correct analysis of causation. In fact, as I'll point out in a minute, there's good reason to believe quite the opposite. The point that I'm making , I think, is especially plausible when you recall that the philosophers who drafted the definitions quoted by Quentin were exclusively concerned with natural causes, even physical causes. They weren’t even considering such recondite examples as divine causation of the origin of the universe. It's hardly surprising, therefore, that their theories should fail to capture this notion. So I see no reason to think premise (1) is true and good reasons for thinking that it is false.

Now what about premise (2), The claim that God caused the Big Bang cannot be analyzed in terms of extant definitions of causality? As it stands, premise (2) is clearly false, and Quentin himself, in effect, admits that it is false. For in his discussion of the analysis of causation in terms of necessary and sufficient conditions, he does not deny that God's willing the universe or the Big Bang is a case that satisfies the definitions proposed. On the contrary, he explicitly states that it does satisfy the proposed definitions. Rather he attacks the adequacy of the definitions themselves. Now that puts an entirely different light on the matter! What Smith is really defending is

(2) The claim that God caused the Big Bang cannot be analyzed in terms of any adequate extant definitions of causality.

But premise (2) is extremely problematic, for it is, I think, generally acknowledged that there is no adequate extant definition of causality to date. The very proliferation of different definitions which were only partially surveyed by Quentin in his talk testifies to the uncertainty and the dissatisfaction which exists in the philosophical community today with proposed analyses of the causal relation. Thus the expression in (2) "adequate definitions of causality" may well be a nonreferring expression, so that (2) cannot be true.

But let's assume that the definitions surveyed by Smith are adequate. The fact is that God's causing the universe does satisfy at least some of these definitions, so that (2) is false. Take David Lewis' analysis of causation, for example: According to Lewis, c causes e if and only if c and e are both events, and both occur, and if c had not occurred e would not have occurred. Now God's willing the Big Bang clearly satisfies this definition. God's willing and a Big Bang are both events which occur, and if God's willing had not occurred, the Big Bang would not have occurred. No problem! But, Quentin rejoins, if the Big Bang had not occurred, God's willing would not have occurred. So is the Big Bang the cause of God's willing? Well, obviously not; but what this calls into question is the adequacy of Lewis' analysis, not whether divine causation satisfies it. Lewis remedies the problem by stipulating that if e had not occurred, c would still have occurred, a remedy that won't work for divine causation. Actually, Lewis' remedy won't work for many natural causes either, since in some cases the counterfactual, "if e had not occurred, c would not have occurred" is true. So what Lewis' definition provides is not a definition of "c causes e," but rather it is a definition of "c and e are causally related," and it fails to specify the direction of causation. But here the theist, you see, faces no problem because it is metaphysically impossible for God's willing to have an external cause. There is no possible world in which the Big Bang causes God's willing or God's volition. Therefore, given Lewis' definition of "c and e are causally related" and the impossibility of the Big Bang causing God's willing, it follows that God's willing causes the Big Bang, and thus divine causation satisfies Lewis' definition of causality.

Or, again, if we hold with Isaac Newton, Richard Swinburne, Nicholas Wolterstorff, and others that God exists prior to the Big Bang in a metaphysical time, then there's no objection to adopting an analysis of causality which involves the component of temporal priority of cause to effect. God would be temporarily prior to the Big Bang. So it seems to me that the premise (2) fares no better than premise (1). Both premise (1) and premise (2) are false, and therefore the argument against divine causation of the universe is unsound.

Quentin Smith – Re-Rebuttal

One of Bill’s points was that simply my saying that no existent philosophical definition of causality can be applied to God and the Big Bang is not a strong argument because there is very little agreement about what is an existent and correct definition of causality. And, of course, that's true for any single philosophical theory, any subject. Philosophy is the area where the socalled experts disagree with one another, and once they start agreeing, then the whole subject matter stops being philosophy and becomes a science. It's like linguistics used to be philosophy in the nineteenth century; then the experts started agreeing with each other, and they got shoved off and became a science. So philosophers are at the task where all the socalled experts disagree with each other, and all the nonexperts disagree with the experts and with each other, and the only things they can agree upon is that other philosophers aren’t any good! They can’t agree why they are needed. So I don't think this is any unique case about the fact that there's no one accepted definition of causality.

But there is something in common to every single definition of causality I gave that all philosophers agree upon (one might make exceptions for one or two or three theists maybe). So virtually all philosophers agree upon this. In all these definitions the cause is something, usually an event, that does not logically entail the event that's the effect. Take what every philosopher says, the sun shines on the stone, and the effect is the stone becoming warm, and I say, O.K., that's a law of nature, but can we derive that just from pure logic? Is it a logical contradiction to say the sun shines on the stone, and the stone does not become warm? No. To have a logical contradiction, you have to say something like: the sun shines on the stone, and the sun does not shine on the stone. So all these definitions of causality, even though they differ in a number of respects, all agree in this very fundamental point, that the cause is not logically sufficient for the occurrence of the effect. And that's precisely how they all differ from the relationship of God to the Big Bang. And, of course, if Craig wanted to rest his argument just there (which he doesn't, but if he did), we'd have to ask Craig for some definition of causality, preferably one that applies both to God and to things in the world, and then clearly we’re no longer talking about causality, or at least some definition of causality that applies to God and not to the world. And in that case we’re in grave danger because we're not quite sure what causality means anymore at all. For theists say God caused the Big Bang, but this is different from anything we normally mean when we talk about things’ causing. We mean something else, and we’re quite unclear what the something else means, and you can question whether words are being used meaningfully. They just metaphors, really. And it's not clear what's behind the metaphors.

But Craig goes beyond that. He doesn’t leave this argument right there. Craig wanted to say that Lewis' definition of causality applies to God and the Big Bang. But I confess that I did not follow that argument very well because I couldn't see how Lewis' definition was satisfied by God and the Big Bang at all. For there's a part of David Lewis' definition that, if some event c is going to cause some even e, then Lewis holds that if the event e had not occurred (which would be the Big Bang), then c (God’s willing) would not have occurred. And that does not apply to the case of God and the Big Bang. Lewis holds that, in this case, if e had not occurred (the Big Bang had not occurred), then c (God's willing) would have occurred just as it did, but have failed to cause e (the Big Bang). But that's inconsistent with the notion of theism, which implies that if God's willing occurs, it is a logically sufficient condition of the Big Bang.

O.K., I have some more time. Let me see. Remind me of some more arguments you brought up, Bill.

Craig: Newton, Swinburne, Wolterstorff’s view that God exists temporally prior the Big Bang….

Smith: O.K., that's a good argument. In that case, in the case of conflict between science and religion, that's one part of a response. But holding that there was time before the Big Bang is in direct contradiction to the HawkingPenrose Singularity Theorems, which entail that time began at the Big Bang singularity. So we have to reject physical cosmology. We have to reject Einstein’s General Theory of Relativity and Big Bang cosmology in order to accept those positions. And then we’re on a different debating ground. We’re no longer talking about whether "God exists" is consistent with contemporary science. By that one statement we’re rejecting contemporary science, which, in the form of Big Bang cosmology and General Relativity, holds that time began with the Big Bang singularity. But even if you suppose there was a time before the Big Bang, that does nothing to solve the problem, and I assume Bill brought that up because that shows that God could meet one condition of being a cause, that God's act of willing the Big Bang is temporally prior to the effect, which would be the Big Bang. But still that doesn't address the main issue, the crucial issue is that God's willing the Big Bang is a logically sufficient condition of the Big Bang. And once we have that condition, then that violates every existent definition of causality. Craig might respond and admit that it does and say, "Well, maybe all these existent definitions are false." But then he seems to be introducing his own sense to the word cause. It seems to be analogous to this: he could say, "Well, all the existent definitions of causality are false. Let’s redefine causality so that it allows that God's being a logically sufficient condition of the Big Bang counts as a cause." Well, that seems to me just a case of changing the meaning of the words in order to save the theory. Suppose I’m a theist, and someone says, "Well, I just proved to you that God does exist because of the problem of evil." And I say, "Well, you’re all wrong because what God means [tape unintelligible] so all your arguments are invalid." When I think my simply changing the meaning that all philosophers, scientists, and everybody else means by cause, changing that meaning is not going to rescue the theory that God caused the Big Bang.

Question and Answer

Alastair Norcross, Moderator

I’m going to open the floor up for questions now, and as this event is specifically aimed at students, I would very much like to encourage questions from students. They don’t have to be good questions, just questions.

Questioner: First question: this is a question for Dr. Smith. It seems that a part of your critique of sufficient conditions presupposes that there are other sufficient conditions [tape unintelligible] we’re talking about Big Bang cosmology, and there are no other sufficient conditions other than God—how could that analogy apply?

Smith: In that part of the paper I was trying to argue it cannot be a definition of causality that applies to any instances in the world for the reason you mentioned, and you want to wonder how that reason that I gave, why it can't define causality in the world, applies to God. It is not that particular reason that shows that God cannot satisfy that definition of causality. The reason goes back to the one main reason, that God’s action is a logically sufficient condition, whereas the sufficient condition of this pen flying in the air is my throwing it in the air, but it's not a logically sufficient condition; it's merely sufficient given the initial conditions going on right now in the universe and given our contingent laws of nature. But that's not a logically sufficient condition. There is no logical contradiction in saying, "I threw the pen up in the air, and it just stayed in my hand." That doesn't contradict any law of logic. To contradict a law of logic, you have to say something like I threw the pen up in the air and I did not throw it up in the air." So does that answer your question?

Questioner: If God is the only possible cause, then isn’t it logically sufficient?

Smith: I would say that God isn’t possibly a cause at all. I would say there are many possible causes of the universe's beginning to exist, depending on how you define the universe. But I don't think it's possible that God can cause anything. God may be, assuming there are no other problems with the notion of God (and there are numerous other problems). But God would have to be the logically sufficient condition of other things that you would normally want to say that God caused.

Questioner: Prof. Craig, I guess I’d like to hear [tape unintelligible] this comes up in two places in your two independent arguments. In (2. 11), that an actual infinite can’t exist, and again it would be in (2. 21) the collection formed by successive addition cannot…. Let me concentrate on (2. 1) about the successive addition problem. I think the kinds of reasons you give for (2. 1)—address the confusion—let me see if I can—you can't count to zero or a negative infinity because you can't traverse an infinity going that direction any more than you can going in a positive direction, and that shows that it can't [tape unintelligible] now I think what that turns on is that you can't have a starting premise anyway and traverse from negative infinity to zero. But, of course, people that think that there was no beginning are not worried about….

Craig: Right.

Questioner: And so the analogy in the positive direction is that I would say, "Of course you can count from zero to infinity"… if an infinite amount time passes, then in fact I think that you can probably—it would be logically possible to count to infinity in a finite amount of time, provided you just speed up your numbering….

Craig: Yes, supertasks, as they're called.

Questioner: I don't see a logical problem with that....

Craig: Well, remember, I'm not talking about there being a logical problem there, but a metaphysical problem. And I do think that both supertasks and the counting to infinity are logically, or metaphysically rather, impossible, because trying to count to infinity only generates a potential infinite, and it's impossible to turn a potential infinite into an actual infinite by addition. No matter how many items of a potential infinite you have, adding one more you'll never get to infinity. One way to see this is that the infinite has no immediate predecessor. The first transfinite number, À 0, has no immediate predecessor, so there's no way to get to it by addition. And speeding up isn't going to do it either. I would say that those socalled supertasks are really metaphysically absurd. There isn't any way to jump from the series of events in the supertask to the state of completion in a continuous way. Now with respect to never beginning but finishing, that to me is even more intuitively implausible and problematic than starting and never ending. Never beginning but finishing, to me, is just very difficult to even conceive of, and it does run into this Tristram Shandy paradox. If you could do that—never begin but finish—then why didn't you finish yesterday, or the day before that, because you’d have had just as much time by then. Why would there be anything left to do yesterday? Why wouldn't you already be done? If you would be finished by today, it seems to me that you would already have finished yesterday or the day before, and hence there wouldn’t be any point in the finite past at which you would be finishing your task.

Questioner: I have a question for Professor Craig. It seems important to your discussion that God be timeless, but not eternal. I'm wondering how you talk about God's willing if God is supposed to be timeless.

Craig: Oh, I don't think that willing is a change in another itself. I can well imagine that God would have an eternal, unchanging, free determination to do something….

Questioner: That's eternal?

Craig: Well, in the sense of timeless—or either way actually! I can imagine an eternal (in the sense of everlasting), unchanging, free determination of a will to do something, say, to sustain something in existence. Imagine, say, a flautist blowing on a flute for eternity and never changing the intention to blow. I could well imagine that there would be an intention of the will that would be an unchanging free intention or volition. So I don't see....

Questioner: Something in existence can be like that [tape unintelligible]

Craig: Well, now that's a different question, and here I’ve finessed this a little bit in (4. 0), where I say a Creator of the universe exists who, sans creation, is "beginningless," changeless, immaterial, timeless, spaceless, etc. My own view is that once the Creator creates the Big Bang and the first event occurs, then, in fact, God enters into time and is temporal from the beginning of time subsequently, so that while there is no time prior to the Big Bang or the creation event, God is, in fact, temporally related to the universe at, and subsequent to, the moment of creation.

Questioner: And the willing of the Big Bang—when did that occur?

Craig: Well, I would say that God had a timeless intention to create a Big Bang, but in terms of the actual causal exercise of His power, the actual volition, "Let there be…!" that would occur simultaneously with the Big Bang singularity.

Questioner: This is a question for Professor Smith, and it has to do with whether or not we should say that a cause is a logically sufficient condition. I suppose that's true, but that doesn't mean that, for example, scientists, in offering natural explanations of phenomena, don't avail themselves, say, of complex causes that might collectively be logically sufficient for the event that's being explained. For example, if I cited a cause together with a law of nature and said that this cause always brings about such and such an effect under certain conditions, and I would include another cause that says those conditions obtain—which is to say there are no counteracting causes coming in from the outside obstructing the production of the effect—, I mean, I have cited a logically sufficient condition for the occurrence of the effect, and scientists have availed themselves of these kind of explanations all the time. So I guess I'm not too worried about the status of what was sufficient conditions [tape unintelligible]

Smith: O. K., the problem there is, unlike the case of theism, the scientists needed empirical evidence to establish both the premises stating the laws in the deduction, and they needed empirical evidence to establish the whole set of initial conditions. And since they need to be empirically established, that means they are not only not necessarily true, but the probability of their being true is not one hundred percent, even though it might be 99.9 percent. And by virtue of that, the very premises of the argument are not themselves true, strictly true. The accurate way to state the argument would be that it is probably true to such and such a degree that a law of nature L holds. It is probably true to such and such a degree that these initial conditions held. Therefore, it’s probably true that the effect occurred. Now I don't think that is a logically sufficient condition of the effect. I think that's quite different than the case with theism.

Questioner: Well, there are two issues, of course. The question, first of all, is whether or not the explanation it is [tape unintelligible] a logically sufficient condition [tape unintelligible] over the occurrence of the effect. And then there's the question whether the explanation is true or not. And my point is, simply, that it is standard scientific procedure in many cases to explain an event in terms of logically sufficient conditions, which will typically involve, not just a single cause, but more than one cause. And I would agree with you, of course, that the cause may not be known to be true with certainty, but I didn't think that was your objection to the notion of logically sufficient condition of the cause of the explanation.

Smith: O. K., we have to get into a lot of issues like [tape unintelligible] causes, and we need those to make it logically sufficient; and to make it logically sufficient, we have to have had almost a vacuous one, saying that any other interfering condition that might not make this entailment go through is absent, and, given that, we can derive the conclusion.

Questioner: But you don't think scientists use [tape unintelligible] causes.

Smith: Oh, oh, they do, they do! I think the real issue is, of course, I think you're right about the structure, naturally, at least of a deterministic explanation, not a probabilistic one. But the question is, do causes in the actual world, are they themselves logically sufficient conditions of their effects, and I think that is a different issue than the actual form of the scientific explanation, even there are [tape unintelligible] causes, which would say, "No, there are interfering factors," and so on. And the causes in the world, they require some empirical evidence as to their existence, and they require empirical evidence as to whether the laws they instantiate really obtain, and they require empirical evidence that there are no interfering conditions, and so on. And there's no evidence in any given case that all those things obtain. So there's no evidence of any given case in the universe, in fact there can be no evidence. We have to have an omniscient mind to know that with the [tape unintelligible] causes, and no interfering conditions, that really obtains. So I think it's in principle impossible for scientists to know that in the world there is something that is a logically sufficient cause of something else. You know, I think that is an excellent question, because the real strong force of your question is that in the form of deductive scientific explanations, taken at face value, we have a law premise, we have the initial conditions premise, and the conclusion logically follows with the effect that that occurs, and that seems to be a case of a logically sufficient cause. So, I think, that seems to me that is the best line of attack there is against the theory I’m presenting; but I think the way I responded to it is the way I did about then, "O. K., let’s look in the world, not just at the form of the laws." In that case, we don’t get logically sufficient conditions.

Questioner: Dr. Craig, your first premise [tape unintelligible] you’re employing a rather intuitively [tape unintelligible] why something comes from nothing because they believe this is nothing [tape unintelligible] the Big Bang, so we seem to be denying premise (1), and it sounds like it ought to [tape unintelligible]

Craig: That's exactly the problem. You see, it lies outside the domain of physics, and that's why I think that it's not idiocy, it’s simply not a scientific question as to what caused the Big Bang, unless you’re postulating alternative models to the standard model.

Questioner: [tape unintelligible]

Craig: They don't, they don't, they simply don't address one. Robert Jastrow, for example, in his little book entitled, God and the Astronomers, points out that the scientists’ pursuit of the past ends at the moment of creation. The question of what brought this into being is a metaphysical question, which science doesn't address, unless science attempts to provide some alternative model to the standard model. So I think it's quite remarkable that the standard paradigm for Big Bang cosmology would be something that posits the origin of the universe from nothing. But where the universe came from wouldn't be a question that would be scientific in nature. That's a metaphysical question outside the domain of physics.

Questioner: [tape unintelligible] they seem to be content to let it rest....

Craig: As scientists; but when they take off their white coats and go out of the laboratory, I think you find a great deal of speculation and metaphysical theorizing going on. I mean, some of the most interesting literature in the flourishing dialogue between science and religion today is by people who are physicists who want to speculate philosophically on these issues. And I think when they take off their lab coats, they are very interested in wondering why the universe exists and where it came from.

Smith: Could I respond to that as well? I'm not sure it's quite true that physicists have to take off their, so to speak, white coats to address these larger issues of where the universe came from and so on. In fact, many of them, Stephen Hawking, James Hartle, [tape unintelligible] and numerous others have said it is part of current physical cosmology to ask the questions, "Where did the universe come from, why does it exist, why is it the way it is, what explains all its features, why is there something rather than nothing?" and all these great questions that used to be called the great metaphysical questions. And philosophers gave up on them in the era of logical positivism, and they’ve revived only recently in the 1970s among philosophers of religion. And philosophers of science have ignored them, but the physicists themselves have since the 1980s begun to address them again and have been coming up with attempts at answers, and that's precisely what the most famous theory, Hartle and Hawking’s Wave Function of the Universe is. It attempts to explain why our universe exists, and why any universe exists at all, and why the universe has the structures it does. So I think that it’s a part of science—it's not a part of philosophy—it’s a part of science, and philosophers can help, and the way they answer that question is through interaction with the mathematical results and the observational evidence gathered by the physicists like Hawking and [tape unintelligible] and so on, and the philosophers attempting to interpret their results. So I think it's not really that divide between physics and metaphysics that Bill suggests.

Questioner: I have a twopart question for Professor Craig. First part: are there an infinite number of truths in number theory?

Craig: I don't conceive of abstract objects or number theory or things of this sort as being Platonic in nature. So if you're asking me what they are, I would say, no.

Questioner: No, I'm asking [tape unintelligible] metaphysical underpinnings. Are there or are there not an infinite number of true statements...

Craig: I don’t know how to answer that question, putting aside the metaphysical aspects of it, because, I mean, if you are leading where it seems to me you’re leading, you're saying are there an infinite number of things; namely, these truths or something.

Questioner: Right, and.…

Craig: And what I'm trying to say is that I don't conceive of these Platonistically, and so I don't think there are an infinite number of these things. My sympathies would be more with Hume, when, as I quoted, he would try to avoid these by some sort of conceptualism or nominalism or something of that sort. So I don't think there are an infinite number of these sorts of truths.

Questioner: But if there are an infinite number of truths [tape unintelligible] in other words [tape unintelligible] I mean some of these windy truths that required the atomic entities, they would just require [tape unintelligible]

Craig: You see, the question is, is there that truth itself—does it exist? That's a sort of abstract object. That's the question we’re raising, and I'm saying, no, I don't think there are these sorts of ideal or abstract entities existing out there somehow in an ideal space. I don't even understand, in a sense, what such things are, or what they would be. So I want to hold to some kind of conceptualism or nominalism of some sort, which I would probably put a theistic spin on. I think my view would probably be some sort of view similar to Thomas Aquinas’s, which reduces these things to a simple intuition in the mind of God, which human knowers would fractionalize into separate propositions and truths and properties and things of that sort.

Questioner: Well, to put it slightly differently: is God omniscient?

Craig: Yes.

Questioner: And he knows everything there is to know?

Craig: Yes.

Questioner: And half anything is [tape unintelligible] that?

Craig: Well, again, on a Thomistic model, God’s knowledge is not propositional in character. It's a simple intuition of the truth, which human beings, in order to conceptualize, break into propositions. So that I would say, on a Thomistic sort of model, the number of propositions is potentially infinite, but there aren’t such things, they don't exist, outside the mind of God, and they don't exist as distinct ideas in the mind of God. So it's a different kind of metaphysic than Platonism, which is in the Thomistic tradition, which is what I would accept wholly apart from this argument that I've given tonight. I'm just so antiPlatonistic in my orientation that I prefer some kind of conceptualism.

Questioner: I have a question for Dr. Smith. There's some strange worry about this idea that God's omnipotence can’t cause anything .…

Smith: The definition of God's omnipotence is that God can do everything that is logically possible. But if it belongs to the logical definition of a cause that a cause cannot be a logically sufficient condition of its effect, then it would follow that God cannot cause something because then God would be doing something that it is logically impossible to do. And the reason why God's omnipotence prevents him from causing something is that it belongs to the very nature of the cause that it is not a logically sufficient condition of its effect, and God, because he is allpowerful, that just implies by definition that whatever he attempts to do automatically happens, necessarily happens, logically happens. There's a contradiction if it doesn't happen.

Questioner: So that is the definition of omnipotent: that if you will something, then his willing it causes that thing to happen. O. K. , so now he wills something. Just because his omnipotence creates this, the thing happens. I don't see that that makes his willing it logically sufficient of the thing’s happening….

Smith: O. K., it’s logically sufficient because that means that we can derive a contradiction from the supposition that God wills something, for example, that this microphone will fall over, and that it didn't happen. Because if God is allpowerful, then anything that God wills is going to happen as a matter of logic. And so if God wills this microphone falls over and it doesn't, then we have the contradiction that a being who wills something, and everything that being wills necessarily happens just the way that being wants it to, that being willed the microphone to fall over, and it didn't happen just the way he wanted to. Now that would be a logical contradiction. So that's why there's a contradiction to think that God who is omnipotent can cause something.

Craig: It seems to me that this argument is questionbegging. You're just simply defining omnipotence away, in a sense, by saying that there cannot be infallible causes. And, if there is an omnipotent being, that's simply incorrect. It seems the whole thing is just questionbegging. You’re just sort of "ruling out" the idea of an omnipotent being by definition.

Smith: No, actually I'm giving a clear and accurate definition of an omnipotent being. I'm doing a service to theists by helping them have a better definition of God, and the way I’m doing that is by clarifying this relation, that theists have called causation, between God and the world, and I'm saying, "Well, let's examine that to help out the theists on this score. Examine it very closely and we find out it's not really causation after all. It's a different relation called "God being the logically sufficient condition of the thing happening." So I’m really just giving a clearer and more accurate definition of what God is. So I’m not trying to—that's what an omnipotent being is, so it certainly would be the last thing I ever want to do to argue that an omnipotent being doesn't exist. I just want to help the theists to clarify the theistic position.

Notes

1 "Modernizing the Case for God," Time (April 7, 1980), pp. 6566.

2 Alvin Plantinga, "Two Dozen (or so) Theistic Arguments," 33rd Annual Philosophy Conference, Wheaton College, October 2324, 1986.

3 David Hume to John Stewart, February, 1754, in The Letters of David Hume, ed. J. Y. T. Greig (Oxford: Clarendon Press, 1932), 1: 187.

4 Immanuel Kant, Critique of Pure Reason, A 189 / B 232; A 196 / B 241.

5 David Hilbert, "On the Infinite," in Philosophy of Mathematics, ed. Paul Benacerraf and Hilary Putnam (Englewood Cliffs, N.J.: PrenticeHall, 1964), p. 151.

6 David Hume, Enquiry concerning Human Understanding, 12.II. 125.

7 Kant, Critique, A 426 / B 454.

8 P. C. W. Davies, "Spacetime Singularities in Cosmology," in The Study of Time III, ed. J. T. Fraser (Berlin: Springer Verlag, 1978), pp. 7879.

9 David Lewis, Philosophical Papers (New York: Oxford University Press, 1983), 2: 170.

10 Ibid.