May 04, 2014
Some Reflections on the Sean Carroll Debate
Thank you so much again for the spirited and great debates that you participate together with cosmologists. I have to say that I find this arena of Cosmology and God to be a very good ground to keep polishing primarily because when science proves a theory or finds very good evidence of it we come closer and closer to understanding more of that vast amount of matter and energy we can observe.
In any case I wanted to ask you about the latest debate with Sean Carroll. There were some strong points made in that debate that as a layman in cosmology make me want to seek further and further what are the theoretical physicists really saying on their theories. The media is not always clear on separating the cosmologist opinion/belief vs what their theory actually says without bias. So I went ahead and looked at Sean Carroll's post debate comments, see site below:
It seems to me that the objections that make me question the way the Kalam argument works as well as what the latest theories are showing vs cosmologists own opinion are Sean's answers to:
1. First Premise of Kalam Argument (Aristotelean Causation). He digs deep onto Aristotelean analysis of causation being outdated.
2. Boltzmann Brain problem. He mentions that the BB problem helps isolate those models of multiverses that are not tenable. So what about the models that do work?
3. Fine Tuning. Sean mentions 5 points about Fine Tuning not being good argument for theism and he goes on and says that you did not respond to them. I understand that on your Q&A 49 you mentioned that the universe is fine-tuned for the existence of intelligent life is a solid fact; so I get confused with what Sean says about "he didn't offer any suggestion that we actually do know the conditions under which life can and cannot form."
Anyways, I hope you can answer this questions for me and help me advance in my pursue to understand modern cosmology, its facts and its hopes. Also, will you also make contact with Allan Guth about the BVG theorem? I find it puzzling that the first one to say you were wrong about BVG was Dr. Krauss and then we saw your e-mail exchange with Valenking proving otherwise. It would be nice to see for us viewers what your interaction would be with Allan Guth, now that Sean Carroll is claiming you are mistaken in the interpretation of the theorem.
Thank you for your questions, Jahir! I’ve refrained from commenting on the debate with Sean Carroll until I could study carefully the transcript of what was actually said by way of point and counter-point. Now that the transcription of our exchange has been completed, I feel ready to comment. Alas, however, I find that there is so much to say that I can at most respond to just the first of your questions about the causal premiss, leaving the others for another day. I was intrigued that in his blog Carroll calls this question “the most important part of the debate.” While I think that the second premiss is far more important, Carroll’s comment reveals the weight he places on his objection to the first premiss.
Time constraints precluded a discussion of the first premiss of the kalam cosmological argument in my opening speech. So all I said was:
1. If the universe began to exist, then there is a transcendent cause which brought the universe into existence.
2. The universe began to exist.
3. Therefore, there is a transcendent cause which brought the universe into existence.
. . . I take it that (1) is obviously true.
Those who know my work will notice that I did not use the typical medieval formulation of the first premise, namely,
1*. Whatever begins to exist has a cause.
Why the change? Well, some time ago my friend Chris Weaver, a grad student in philosophy, alerted me to the fact that some persons might object to (1*) because it presupposes an Aristotelian conception of causality, according to which substances stand in causal relations to one another, whereas contemporary theories of causation think of causal relations as obtaining between other entities, for example, events or states of affairs. The contemporary causal theorist would not say that God is the cause of the universe, but, for example, that God’s creating the universe is the cause of the universe’s coming into being. Now I think that the view that causal relations obtain between substances (as well as between events or states of affairs) is perfectly defensible.1 We say that God created the universe, just as Tolstoy wrote Anna Karenina or Picasso painted Guernica, which statements posit causal relations between these things. But I’m constantly engaged in honing my arguments to make them more immune to possible objections, so I re-formulated the first premiss to make it as neutral as possible with respect to one’s theory of causation. My opening speech actually includes a footnote at this point (which, of course, was not delivered orally) which reads:
(1) does not presuppose a particular analysis of the causal relation. It requires simply that the universe did not come into being uncaused. For the universe to come into being without a cause of any sort would be to come into existence from nothing, which is worse than magic.
(1) leaves it entirely open whether the transcendent cause is a substance, an event, a state of affairs, or what have you.
Notice the justification of (1): it’s obvious. In magic, the magician makes a material thing come into being without any material substratum. But if (1) is false, then the universe came into being without either a material or a productive cause, which is truly worse than magic. Anyone who denies (1) should therefore also have no problem with magic.
So how does Carroll respond to (1) in his opening speech? He says,
The problem with this premise is that it is false. There’s almost no explanation or justification given for this premise in Dr. Craig’s presentation. But there’s a bigger problem with it, which is that it is not even false.
There are three separate complaints here. The second complaint is quite correct and will be rectified later in the debate, as we’ll see. The first and third complaints are self-contradictory. (1) cannot be both false and not even false. To say that (1) is not even false is to say that it is meaningless and therefore has no truth value. Although Carroll will claim that (1) has no truth value, we’ll see as things unfold that, quite to the contrary, he treats it as a meaningful and well-understood proposition which he thinks is false.
So why does he say (1) is meaningless? He explains,
The real problem is that these are not the right vocabulary words to be using when we discuss fundamental physics and cosmology. This kind of Aristotelian analysis of causation was cutting edge stuff 2,500 years ago. Today we know better. Our metaphysics must follow our physics. That’s what the word “metaphysics” means. And in modern physics, you open a quantum field theory textbook or a general relativity textbook, you will not find the words “transcendent cause” anywhere. What you find are differential equations. This reflects the fact that the way physics is known to work these days is in terms of patterns, unbreakable rules, laws of nature. Given the world at one point in time we will tell you what happens next. There is no need for any extra metaphysical baggage, like transcendent causes, on top of that. It’s precisely the wrong way to think about how the fundamental reality works.
Here we see a rejection of an “Aristotelian analysis of causation” because “Today we know better.” This seems to be precisely the objection Chris Weaver had alerted me to and which I had pre-empted. So in my following speech I responded,
To my surprise, Dr. Carroll challenges the first premise of this argument by saying it is based on outmoded Aristotelian concepts of causality. I protest - not at all! There is no analysis given of what it means to be a cause in this first premise. You can adopt your favorite theory of causation or take causation to be a conceptual primitive. All it requires is that the universe did not pop into being uncaused out of absolutely nothing.
Carroll’s allegation that the argument is based on outmoded concepts of causation is therefore groundless.
Carroll’s Rejection of a Transcendent Cause
Although Carroll appears to claim that in physics things are explained in term of laws of nature, not causes, we’ll see that he’s quite happy to admit immanent causes in the universe. In his second speech he’ll say, “when you find some event or state of affairs B today, we can very often trace it back in time to one or a couple of possible predecessor events that we therefore call the cause of that, which leads to B according to the laws of physics.” So offering explanations in terms of natural laws does not exclude there being causes and effects.
Rather what Carroll objects to is a transcendent cause—of any sort! Why? Carroll explains that in physics causal explanations are given in terms of natural laws (and, presumably, initial conditions), and so in the case of a beginning of the universe there cannot be such an explanation, since there are no prior conditions on which the laws of nature impinge.
Now to my mind all this proves is that there cannot be a physical explanation of the origin of the universe; that is to say, as we go back in time, physics stops at the beginning of the universe.2 So, of course, physics, which operates only within the universe, knows nothing of “transcendent causes.” But why couldn’t there be a meta-physical cause which transcends the universe? I think the key to Carroll’s thinking lies in his little sentence: “Our metaphysics must follow our physics.” This is an expression of epistemological naturalism. Physics leads metaphysics by the nose, and metaphysics cannot postulate entities beyond what physics requires. It goes without saying that I reject epistemological naturalism—see my debate with Alex Rosenberg for reasons why.3 Metaphysics goes beyond physics—that’s what “metaphysics” means!
Carroll goes on to advise:
The question you should be asking is, “What is the best model of the universe that science can come up with?” By a model I mean a formal mathematical system that purports to match on to what we observe. So if you want to know whether something is possible in cosmology or physics you ask, “Can I build a model?” Can I build a model where the universe had a beginning but did not have a cause? The answer is yes. It’s been done. Thirty years ago, very famously, Stephen Hawking and Jim Hartle presented the no-boundary quantum cosmology model. The point about this model is not that it’s the right model, I don’t think that we’re anywhere near the right model yet. The point is that it’s completely self-contained. It is an entire history of the universe that does not rely on anything outside. It just is like that. The demand for more than a complete and consistent model that fits the data is a relic of a pre-scientific view of the world. My claim is that if you had a perfect cosmological model that accounted for the data you would go home and declare yourself having been victorious.
Here Carroll rightly says that physics can (in principle, at least) craft a model of the universe in which the state of the universe at any time t has a complete physical description. Such a model is “self-contained” in the sense that does not include supernatural interventions in the universe (miracles) at any time t. But Carroll takes it be self-contained in a more radical sense, namely, the universe does not have a transcendent cause that brings it into being. He thinks that the Hartle-Hawking model represents a universe which is uncaused in that sense.
In my second speech I replied,
Dr. Carroll says on the Hartle-Hawking model the universe is uncaused. Not at all! The universe comes into being on such a model, and there is nothing in the theory that would explain why that universe exists rather than not. The model may be self-contained; but that is perfectly consistent with my argument. I am not arguing for some kind of interventionist deity, but rather, why does the universe exist? Why did it come into being at all?
Notice here that I am quite willing to admit, for the sake of argument, that the universe is self-contained in the sense that there are no supernatural interventions at any time t. As a purely physical model, the Hartle-Hawking model says absolutely nothing about whether there is a transcendent cause of the universe’s coming into being. How could it? As Carroll himself repeatedly emphasizes, such causes are not contemplated in a physical theory and so are neither affirmed nor denied. So the question remains, why did the universe come into being? Apart from a metaphysical, transcendent cause, you’re stuck with the universe’s popping into being uncaused, and, as I said, if that’s the price of non-theism, then the non-theist is welcome to it.
So how does Carroll respond? He replies, “I claim that a consistent, complete model that fits the data accounts for what we see in the world is a success. There’s no right that we have to demand more than that, and I believe that Dr. Craig’s response was, ‘Yes, there is!’ I don’t think this counts as a very good response.” This is an uncharitable rendering of my response! My claim has been precisely that “a consistent complete model that fits the data” will involve a beginning of the universe. It is beginningless models that are inconsistent or fail to fit the data. As for the right to demand more than that, such a right is grounded in the absurdity of the universe’s coming into being from nothing.
Carroll now proceeds to explain why we shouldn’t be worried about the universe’s beginning to exist without a cause:
It’s a very difficult thing because the universe is different than our everyday experience. That doesn’t sound like a surprising statement but we really need to take it to heart. To look at a modern cosmological model and say, “Yes, but what was the cause?” is like looking at someone taking pictures with an iPhone and saying, “But where does the film go?” It’s not that the answer is difficult or inscrutable; it’s completely the wrong question to be asking. In fact it’s a little technical, most of my second talk here, but I think it’s worth getting it right. Why should we expect that there are causes or explanations or a reason why in the universe in which we live? It’s because the physical world inside of which we’re embedded has two important features. There are unbreakable patterns, laws of physics—things don’t just happen, they obey the laws—and there is an arrow of time stretching from the past to the future. The entropy was lower in the past and increases towards the future. Therefore, when you find some event or state of affairs B today, we can very often trace it back in time to one or a couple of possible predecessor events that we therefore call the cause of that, which leads to B according to the laws of physics. But crucially, both of these features of the universe that allow us to speak the language of causes and effects are completely absent when we talk about the universe as a whole. We don’t think that our universe is part of a bigger ensemble that obeys laws. Even if it’s part of the multiverse, the multiverse is not part of a bigger ensemble that obeys laws. Therefore, nothing gives us the right to demand some kind of external cause.
Look what’s going on here: Carroll identifies two features of the universe (natural laws and a direction of time) that, he thinks, make it appropriate to demand causes of immanent events but which do not apply to the universe’s beginning to exist. Therefore the universe’s beginning is exempt from the causal principle. This argument is a non sequitur. (That is to say, it is logically invalid.) For this argument to pass muster, Carroll would need to show that these two features are not only sufficient but necessary conditions of the demand for causal explanation. He doesn’t do either. Indeed, if something can’t come into being uncaused at an embedded moment of time, how could it come into being without a cause if that moment were the first moment of time? If something that can be explained by natural laws requires a cause of its coming into being, how would that exempt something which admittedly cannot be explained in terms of natural laws? Carroll’s view seems unintelligible.
By now it should be clear that Carroll’s claim is, not that premiss (1) is meaningless, but that it is false. In fact, he later admits in response to Question 11: “I completely can conceive of a universe that was brought into existence by God who was omnipotent and so forth and for whatever reason God has chosen to be completely invisible and the universe runs by purely naturalistic principles.” This is to agree with what I say in response to that same question: “The arguments that I've offered tonight are consistent with the universe’s being self-contained in the way that Dr. Carroll described. So that needn't be an issue of debate between us.” Carroll thinks that there could be a cause of a self-contained universe’s beginning to exist but that there need not be such a cause. The universe can just begin to exist uncaused. In response to Question 13 he will later say,
I do not think that if the universe has a first moment in time that means there is any sort of eternal or preexisting conditions or rules or laws or anything like that. It simply means that our best and maybe the correct description of the cosmos is one that had a first moment in time. The question is, can that be self-contained in the sense that I'm using it, which is that if I write down the equations and the conditions and so forth that describe the universe with an earliest moment, am I done? Are there questions that I might have about that universe that cannot be answered by that formalism?
In my view, you’re far from done. For the biggest question still remains unaddressed: why did the universe come into being?
Justification of the Causal Premiss
So in my third speech I provide my justification for the causal premiss which Carroll had complained was missing from my opening presentation:
Honestly, I am quite astonished that he would think that the universe can literally pop into being out of nothing. Let me just give three arguments for why there must be a cause.
First of all, it seems to me a metaphysical first principle that being doesn’t come from non-being. Things don’t just pop into existence from literally nothing. Nothingness has no properties, no potentialities. It is not anything. So it seems to me inconceivable metaphysically to think the universe can come into being from nothing.
Secondly, if the universe could come into being from nothing, then why is it that only universes can pop into being out of nothing? Why not bicycles and Beethoven and root beer? What makes nothingness so discriminatory? If universes could pop into being out of nothing, then anything and everything should pop into being out of nothing. Since it doesn’t, that suggests that things that come into being have causes.
Finally, all the empirical evidence we have supports the truth of the causal principle. When Dr. Carroll says, “The universe is different than our experience,” this is really committing what Alexander Pruss calls the taxi-cab fallacy, that is to say, you go with the causal principle until you reach your desired goal and then you think you can just dismiss it like a hack because you don’t want there to be a cause of your entity, the universe. But if the universe came into existence, if the universe is not eternal, then surely it would need to have a cause. In fact, to deny this is unscientific because the whole project of contemporary cosmogony is to try to find what is the cause of the universe! So on his principle, it would be a science-stopper and would destroy his very field of expertise.
My first argument above makes it clear that I think that metaphysics is an independent discipline. There are obvious first principles that we must come to terms with.
My second argument comes from the great Oxford philosopher A. N. Prior. I find it an incredibly powerful argument. Since nothingness cannot constrain anything, if the universe can come into being without a cause, then it is inexplicable why anything and everything does not do so. Why didn’t a Chevron gas station or an Eskimo village pop into being instead of our universe? No reason can be given. Not only is this the case with respect to absolute beginnings, but also for things immanent in the universe. You can’t say that the laws of nature or the arrow of time prevent things’ popping into being uncaused, precisely for the reason that they are uncaused. There are no causal conditions governing their coming into being. So you can’t confine them just to the beginning of time and the universe.
Finally, the third reason is meant to appeal to scientific naturalists like Carroll. Here I try respond to Carroll’s attempt to subvert the inductive argument by exempting the universe from the causal principle. I claim that his attempt to exempt the universe is arbitrary and would be a science-stopper, since cosmogony tries precisely to give a causal explanation of the universe’s origin. Here I could have been clearer that I see no reason to think that the two features mentioned by Carroll are essential to the need for causal explanation. Rather I maintain that a sufficient condition for demanding a causal explanation is that something begin to exist, and that condition is met in the case of the universe. Fortunately, in response to Question 1 from the audience I expressed myself more clearly:
So it seems to me that this is a difference without a difference. I would say that the condition that applies to the universe that makes the causal principle relevant would be its beginning to exist. If a horse begins to exist, there's got to be a cause for that. If a building begins to exist, there's got to be a cause for that. Similarly if the universe begins to exist, there needs to be a cause for that. And in that respect the conditions for the causal principle do apply.
This seems to me quite correct. Being embedded in time or admitting of a natural explanation are not necessary conditions of requiring a causal explanation. Rather a sufficient condition for requiring a causal explanation is beginning to exist.
In his final speech Carroll responds to these points:
He said he was astonished that I refused to accept the fact that things need causes to happen. To which I could only quote David Lewis, “I do not know how to refute an incredulous stare.” I tried to give the reason why the causation analysis that we use for objects within the universe does not apply to the universe but that more or less whizzed on by. Dr. Craig gets a lot of mileage out of the presumed nuttiness of things just popping into existence. “Why don’t bicycles just pop into existence?” Again, I tried to explain what makes the universe different but more importantly the phrase “popping into existence” is not the right one to use when you’re talking about the universe. It sounds as if it’s something that happens in time but that’s not the right way to do it because there’s no before the beginning, if there’s a beginning. The correct thing to say is there was a first moment of time. When you say it that way it doesn’t sound so implausible. The question is, is there a model in which that’s true? Do the equations of the model hang together? Does the model fit the data? And we have plausibly positive answers to all of those.
Actually, David Lewis considered the incredulous stare to be a very powerful way to respond to a philosophical position! Some things are just unbelievable. That the universe should come into being from nothing is one of those, in my opinion.
Carroll then alludes to his two aforementioned, allegedly necessary conditions for demanding a causal explanation, to which I have given my response above.
Finally, he objects to the language of “popping into existence” because it seems to presuppose a prior time during which the thing in question did not exist, a condition which is inapplicable in the case of the beginning of time itself. He thinks that it doesn’t sound so implausible to say instead that there was a first moment of time. Right; but the whole point of philosophical analysis is to unpack such locutions and to expose their implications, which may turn out to be quite implausible. I’ll say more on this in a moment. Note that I give affirmative answers to the three questions he poses: yes, there are models with a beginning of time; yes, the equations of such models hang together; and yes, the models fit the data! Therefore, we have good reason to believe that the universe began to exist, which is the second premise of the kalam cosmological argument.
Philosophy of Time
The question, then, is whether it is more plausible that there is a transcendent cause which brought the universe into being or the universe began to exist uncaused from nothing. During this entire debate, I tried hard to avoid appealing to philosophical arguments, so as to remain squarely in Carroll’s field of specialization. But now a huge philosophical issue that had been lurking just beneath the surface finally breaks into view in response to Question 8. Picking up on Carroll’s complaint about the locution of “popping into existence,” I explain,
I do want to take this opportunity to highlight for you a very significant difference between Sean and myself that is a philosophical difference that has tremendous impact upon this whole debate. And that has to do with this idea of “popping into existence.” If I'm not mistaken, Dr. Carroll holds to what is called a tenseless theory of time. That is to say, past, present, and future events are all equally real. Temporal becoming is merely a subjective illusion of human consciousness. There is nothing privileged about the present, ontologically speaking. I hold to quite a different view of time. I think that temporal becoming is a real and objective feature of the universe. The future doesn't in any sense exist; things really do come into being and go out of being. And that's why I use the language of popping into existence. Not because I illicitly presuppose time prior to the origin of the universe, but because I believe in a tensed theory of time which affirms the objectivity of temporal becoming. And on that view the beginning of the universe does not just tenselessly exist. The universe comes into being, and surely that requires a cause. Now this is not just an unfounded metaphysical assumption on my part. I've written two books on this in which I defend the tensed theory of time, giving arguments for it and answering objections against it, and then I attack the tenseless theory of time, giving arguments against it and answering arguments for it. But this is a huge metaphysical assumption that underlies this debate and divides us.4
This philosophical question is vitally important to the debate over the causal premiss. On Carroll’s view the universe begins to exist at the Big Bang only in the sense that a yardstick begins to exist at the first inch. That is to say, it has a front edge, so to speak, but it really does not come into being. But on my view the universe comes into being at the first moment of its existence. The tensed theory of time is my trump card for defending the causal premiss. If Carroll’s denial of the causal principle is to have any credibility he must argue for a tenseless theory of time. That is a philosophical debate in which I am happy to engage, but also a debate for another day.
Let’s sum up this portion of the debate. The causal premiss
1. If the universe began to exist, then there is a transcendent cause which brought the universe into existence.
does not presuppose any particular analysis of the causal relation but was deliberately formulated to be as neutral as possible in that regard. So Carroll’s charge that it assumes an Aristotelian concept of causation (the tenability of which remains moot) is vacuous.
(1) is also consistent, as Carroll comes to admit, with the universe’s being self-contained in the sense that a complete physical description of the universe can be given at any time t. So Carroll’s repudiation of a transcendent cause on the basis of the completeness of physics is gratuitous.
I have offered three arguments in support of (1). First, it is grounded by an obvious metaphysical first principle that something cannot come into being from nothing. If Carroll’s naturalism requires him to flout this principle, then his view, being worse than magic, heartily deserves the incredulous stare. In the end, however, Carroll, by adopting a tenseless theory of time according to which beginning-to-exist does not imply coming-into-being, does not, in fact, flout this first principle. Given this first principle, a tensed theory of time is sufficient for (1). The question then for Carroll becomes two-fold: (i) what justification can he offer for a tenseless theory of time, and (ii) is (1) true even on a tenseless theory, that is, is a tensed theory of time merely a sufficient, but not a necessary, condition for (1)? Those questions remain to be addressed.
Second, if something can come into being without a cause, then it becomes inexplicable why anything and everything does not do so. Carroll might try to avoid this argument by appealing once again to a tenseless theory of time. But it is not evident that this argument will not also work even on a tenseless theory. One may simply re-phrase it to remove any reference to temporal becoming: if something can begin to exist without a cause, then it becomes inexplicable why anything and everything does not do so.
Third, we have overwhelming inductive evidence in support of (1). Carroll’s attempt to subvert this inductive inference by pointing out that two features of immanent events, namely, their being temporally embedded and explicable in terms of natural law, do not apply in the case of the universe’s beginning to exist fails to show that these features are necessary conditions of the requirement of causal explanation. Indeed, it is unintelligible why being located at a first moment of time and being naturally inexplicable would enable an event to occur without a cause. A common condition shared by both immanent events and an initial cosmic event is beginning to exist, and it is this commonly shared condition that is plausibly sufficient for the need of causal explanation. Hence, the inductive inference goes through.
So we have good grounds for affirming (1), whereas Carroll’s proffered defeaters of (1) are either inconclusive or outright failures.
Next stop: premiss (2)!
1. See, e.g., Alfred Freddoso’s defense of medieval conceptions of causation in his Introduction to Francisco Suarez, On Creation, Conservation, and Concurrence, trans. by Alfred J. Freddoso (South Bend, Ind.: St. Augustine's Press, 2002). Freddoso argues persuasively that Suarez’s analysis of causation compares very favorably to contemporary theories.
2. In fact, I actually appeal to physics’ impotency in this regard as one argument for the personhood of the cause of the universe. As I explain in Reasonable Faith,
“First, as Richard Swinburne points out, there are two types of causal explanation: scientific explanations in terms of laws and initial conditions and personal explanations in terms of agents and their volitions (The Existence of God, rev. ed. [Oxford: Clarendon Press, 1991], pp. 32-48). For example, if I come into the kitchen and find the kettle boiling and I ask Jan, “Why is the kettle boiling?” she might answer, “The heat of the flame is being conducted via the copper bottom of the kettle to the water, increasing the kinetic energy of the water molecules, such that they vibrate so violently that they break the surface tension of the water and are thrown off in the form of steam.” Or she might say, “I put it on to make a cup of tea. Would you like some?” The first provides a scientific explanation, the second a personal explanation. Each is a perfectly legitimate form of explanation; indeed, in certain contexts it would be wholly inappropriate to give one rather than the other. Now a first state of the universe cannot have a scientific explanation, since there is nothing before it, and therefore it cannot be accounted for in terms of laws operating on initial conditions. It can only be accounted for in terms of an agent and his volitions, a personal explanation.”
3. See William Lane Craig and Alex Rosenberg, Is Faith in God Reasonable? Debates in Philosophy, Science, and Rhetoric, ed. Paul Gould and Corey Miller, with Responses by Robert Kaita, Victor Stenger, Paul Moser, Theodore Drange, Timothy McGrew, Michael Ruse, Martin Medhurst, and Clarke Rountree, Routledge Studies in the Philosophy of Religion (London: Routledge, 2014).
4. See William Lane Craig, The Tensed Theory of Time: A Critical Examination, Synthese Library 293 (Dordrecht: Kluwer Academic Publishers, 2000) and William Lane Craig, The Tenseless Theory of Time: A Critical Examination, Synthese Library 294 (Dordrecht: Kluwer Academic Publishers, 2000).