“Universe,” Kalam, and Equivocation
The second premise of the Kalam Cosmological Argument states, “the universe began to exist,” where William Lane Craig defines “universe” as “the whole of material reality.” This definition is important to the Kalam argument because it serves as a linchpin for Craig to argue that the universe must be caused by something which is “uncaused, changeless, timeless, and immaterial.” In other words, if the universe isn’t the whole of material reality, then it’s possible that some other part of material reality caused it.
To be fair to Crag, his definition of the universe is traditional, but it also might be outdated. In the book The Hidden Reality (Pg. 4) physicist Brian Greene writes:
There was once a time when ‘universe’ meant ‘all there is.’ Everything. The whole shebang. The notion of more than one universe, more than one everything, would seemingly be a contradiction in terms. Yet a range of theoretical developments has gradually qualified the interpretation of ‘universe.’ The word’s meaning now depends on context. Sometimes ‘universe’ still connotes absolutely everything. Sometimes it refers only to those parts of everything that someone such as you or I could, in principle, have access to. Sometimes it’s applied to separate realms, ones that are partly or fully, temporarily or permanently, inaccessible to us; in this sense, the word relegates our universe to membership in a large, perhaps infinitely large, collection.
In A Universe from Nothing (Pg.125-126), physicist Lawrence Krauss echos the same sentiment:
Talking about many different universes can sound like an oxymoron. After all, traditionally the notion of universe has become synonymous with ‘everything that exists.’ More recently, however, universe has come to have a simpler, arguably more sensible meaning. It is now traditional to think of ‘our’ universe as comprising simply the totality of all that we can now see and all that we could ever see.
Craig, however, often cites the work of physicist Alexander Vilenkin to buttress his claim that “the whole of material reality” began to exist. So I emailed Dr. Vilenkin the following question:
Dr. Vilenkin,
Could you briefly define your use of the term “universe,” as you use it in the context of your work on the beginning of the universe? I’m just curious to know whether you use the term in the traditional sense, “all of physical reality,” or if you use it in the more modern sense of “those parts of ‘everything’ that we could, in principle, have access to.”
. His response:
Hi,
It is certainly more than what we can have access to. Regions beyond our cosmic horizon are included. But if there are other universes whose space and time are completely disconnected from ours, those are not included. So, by “universe” I mean the entire connected spacetime region.
Alex V.
So, it seems to me that there is some equivocation going on between Craig’s definition of the word “universe” and that of the physicists he uses to support his claim.
Kalam, Actual Infinites, and Set Theory
In order to establish the second premise of the Kalam Cosmological Argument (“the universe began to exist”), William Lane Craig often argues against the idea of an “actual infinite” (i.e. an infinite amount of things/moments existing in reality). To do this, Craig shows that basic arithmetic cannot make sense of infinity, therefore supposing an “actual infinite” is absurd. Philosopher Colin Howson objects:
Lane Craig uses an argument that originates with Kant to ‘establish’ that time cannot be infinite in the past and still proceed into the future, on the ground that an actual infinite cannot exist because, among other reasons, if it did it would be impossible to add to it. But this claim is vitiated by the facts that (i) in contemporary set theory it is easy to show that there exists a sequence of infinite discrete ordered sets each with a greatest but no smallest member, each set extending its predecessor by an additional largest element; and (ii) the things in the domain of any consistent theory, as set theory is thought to be, are possible existents. Adducing similar observations, the distinguished philosopher of physics Michael Redhead concludes a review of Lane Craig’s argument with the remark that it, ‘seems a total muddle’. (Objecting to God, Pg. 92-93)
In other words, Howson argues that set theory makes sense of infinity in a way that arithmetic does not. And since set theory is consistent, then it is possible that “actual infinites” do exist.
John Barrow on the Big Bang Singularity
Several months ago I wrote about the following quote which William Lane Craig very commonly uses in debates in order to bolster his Kalam Cosmological Argument:
At this singularity, space and time came into existence; literally nothing existed before the singularity, so, if the Universe originated at such a singularity, we would truly have a creation ex nihilo.
– John Barrow & Frank Tipler, The Anthropic Cosmological Principle (1986), page 442
In my response (and also in a different post), I explained that it is unlikely that the universe originated with a singularity. Although the famous Hawking-Penrose theorems predict such a singularity, these theorems are known to be problematic because they are based mainly on Einstein’s general relativity and neglect quantum mechanics. Therefore, the above quote is fairly useless to anybody trying to argue that the universe was created from nothing. Interestingly, I recently discovered a book by John Barrow (the co-author of the quote), titled The Book of Nothing (2000) (amazon) in which he makes the same point. On page 289, Barrow writes
The interesting thing about the singularity that is predicted by [the Hawking-Penrose] theorems is that there is no explanation as to why it occurs. It marks the edge of the Universe in time. There is no before; no reason why the histories begin; no cause of the universe. It is a description of a true creation out of nothing.
He continues on the next page:
However, it is important to realise that they are mathematical theorems not cosmological theories. The conclusions follow by logical deduction from the assumptions. What are those assumptions and should we believe them? Unfortunately, the two central assumptions are now not regarded as likely to hold good. We expect Einstein’s equations of general relativity to be superseded by an improved theory that successfully includes the quantum effects of gravitation. … It is widely expected that this new improved theory will not contain the singular histories that charicterised Einstein’s theory, but until we have the new theory we cannot be sure.
And if this isn’t enough, Barrow goes on:
There is a more straightforward objection to the deduction of a beginning using the theorems of Penrose and Hawking. The assumption is that gravity is always an attractive force. When the theorems were first proved this was regarded as an extremely sound assumption and there was no particular reason to doubt it. But things have changed.
Barrow says that theories within particle physics as well as the theory of inflation seem to contradict this assumption, and since 1981, most physicists and cosmologists believe there to be a repulsive force within gravity. Barrow also notes that, “Indeed, the recent observations of the acceleration of the expansion of the Universe today, if correct, demonstrate there exists matter which displays gravitational repulsion.”
Barrow concludes this section on page 291 by writing, “Thus the old conclusions of the singularity theorems are no longer regarded by cosmologists as likely to be of relevance to our Universe.”
Is the Doctrine of ‘Creation from Nothing’ Absurd?
Most people are aware of the doctrine of creatio ex nihilo, which literally means “creation from nothing” – the belief that God created the universe from nothing. This doctrine is popularly held in contemporary Christian theology, and not surprisingly, William Lane Craig is an avid supporter of it.
Conversely, Craig holds to the principle ex nihilo nihil fit, “out of nothing, nothing comes,” saying that this “is as certain as anything in philosophy and that no rational person sincerely doubts it.” Furthermore, he has also claimed that “it is impossible that nothing exists.” Citing Leibniz’s view of God as a “logically necessary being,” Craig goes on to say that “there is no possible world in which nothing exists.”
The problem hardly needs to be spelled out: If it’s impossible for something to arise from nothing – and impossible for nothing to exist in the first place – then how can Craig justify the belief that God created the universe from nothing?
As far as I can tell, Craig has yet to clearly face this problem. He has written a Q&A post attempting to address it, but it’s simply nonsensical. For example, he writes, “Now is the doctrine of creatio ex nihilo absurd? No, for it doesn’t contradict [the statement ‘it is not possible for something to come from nothing.’]” Unfortunately, it plainly does seem to be contradictory.
His justification seems to be similarly nonsensical. He writes, “If something has a cause, then it doesn’t come from nothing,” and then goes onto say that God is a “creative cause” or “efficient cause” of the universe. But doesn’t this also seem to contradict the idea of creatio ex nihilo?
His only hint at a genuine solution is through his claim that God created the universe without a “material” cause. However, Craig would have to amend his statement from “out of nothing, nothing comes” to something like, “out of nothing, things can come as long as they have a creative cause.” However, I’m not sure that this latter formulation has very much intuitive force.
Stephen Hawking’s Model of Cosmic Origins*
Because it is well-accepted that the Standard Big Bang model cannot describe the origin of the universe, there have been many proposals which attempt to explain cosmic origins. One of these ideas which has garnered much discussion is Stephen Hawking’s “no-boundary proposal,” first popularly articulated in his 1988 best-seller A Brief History of Time. Hawking’s proposal is fairly easy to understand yet very difficult to imagine. He describes time as being finite but without a boundary. Just think of time as being analogous to a sphere: it has a finite amount of surface area but no “beginning” or “end.”
As Hawking and Mlodinow explain in their recent book The Grand Design (pg. 134-135),
In the early universe — when the universe was small enough to be governed by both general relativity and quantum theory — there were effectively four dimensions of space and none of time. … The realization that time can behave like another direction of space means that one can get rid of the problem of time having a beginning … when one combines the general theory of relativity with quantum theory, the question of what happened before the beginning of the universe is rendered meaningless.
Craig’s main criticism of this proposal focuses on the way in which Hawking converts the time dimension to a fourth spacial dimension using imaginary numbers. As Craig explained in a recent Reasonable Faith podcast,
Now, the interesting thing about this is that Hawking was able to achieve this result only by using imaginary numbers for the time variable. Now, imaginary numbers are numbers which are the products of the square root of negative one. Now, there’s no real number that is the square root of a negative number … And the problem is that although these are useful tools in computations, nobody has any idea what it would mean to talk about imaginary time anymore than talking about the imaginary volume of this room … The use of imaginary numbers is just a mathematical device to make the equations easier to solve … when you reconvert to real numbers in [Hawking’s] model, presto, the singularity reappears.
Craig then goes on to claim outright that imaginary time “has no physical significance.”
Now, it should first be pointed out that imaginary numbers aren’t any more “imaginary” than most real numbers. As mathematicians John Conway and Richard Guy write, imaginary numbers “turn out to be invaluable in many applications of mathematics to engineering, physics, and almost every other science. Moreover, these numbers obey all the rules which you already know for ‘real’ numbers” (The Book of Numbers, pg. 212).
Conway and Guy go on to explain that irrational numbers (which are a subset of “real” numbers) , such as √2 or pi, don’t truly exist in the physical sense, yet these numbers certainly go a long way in helping us to understand reality. A similar conclusion can be drawn about negative numbers. For example, does negative money make sense in the real world? Well, “negative dollars” certainly don’t exist, but they still go a long way in helping us to describe the (very real) concept of debt.
So, can imaginary numbers be used to describe the concept of time in the very early universe? Luckily, this is discussed at length in A Brief History of Time (pg. 139).
If the universe really is in such a quantum state, there would be no singularities in the history of the universe in imaginary time. … In real time, the universe has a beginning and end at singularities that form a boundary to space-time and at which the laws of science break down. But in imaginary time, there are no singularities or boundaries. So maybe what we call imaginary time is really more basic, and what we call real time is just an idea that we invent to help us describe what we think the universe is like.
Hawking then suggests that asking the question “which is real” might be irrelevant, “It is simply a matter of which is the more useful description.”
While I personally have no idea whether “imaginary time” exists or not, it seems to me that any honest person will admit that it’s at least an intriguing idea. Craig, on the other hand, seems to reject the idea of “imaginary time” outright.
*Note: This post is an edited version of my post on the Tuesday Afternoon blog.
Alexander Vilenkin’s Model of Cosmic Origins
Alexander Vilenkin’s “tunneling from literally nothing” model (pdf of 1982 paper; pdf of 1988 paper) for the origin of the universe is brought up frequently in both scientific and religious arenas: In the context of science, the model is just plain interesting. And in the context of religion, it has an unique parallel to the doctrine of creation ex nihilo – the belief that God created the universe from nothing – a doctrine to which William Lane Craig subscribes (and, incidentally, is part of his Kalam Cosmological Argument).
In a nutshell, Vilenkin’s model is a variation on Edward Tryon’s “vacuum fluctuation” model, but instead of the universe appearing within a background of space, the universe appears from an empty geometry (i.e. “nothing”). As Vilenkin’s colleague Alan Guth explains,
Putting [general relativity and quantum mechanics] together, one can imagine that the universe started in the total empty geometry – absolute nothingness – and then made a quantum tunneling transition to a nonempty state. Calculations show that a universe created this way would typically be subatomic in size, but that is no problem . . . Vilenkin was able to invoke inflation to enlarge the universe to its current size.
The Inflationary Universe (1997), Page 275
But perhaps calling this creation from “absolute nothingness” is a bit confusing. As Guth points out, Vilenkin’s “absolute nothingness” is “mathematically well-defined, and can be used as a starting point for theories of creation” (Pg. 273). In fact, Vilenkin himself seems to dislike the terminology.
[T]he state of “nothing” cannot be identified with absolute nothingness. The tunneling is described by the laws of quantum mechanics, and thus “nothing” should be subject to these laws. The laws of physics must have existed, even though there was no universe.
– Alexander Vilenkin in his book Many Worlds in One (2006), Page 181
In Craig’s review essay of Vilenkin’s book, he responds to this statement by arguing that “If these laws are truly descriptive, then obviously it cannot be true that ‘there was no universe.'” However, I think this is simply a misunderstanding on Craig’s part. Craig seems to think of the word “universe” as being synonymous with “all of physical reality,” but if Vilenkin’s “nothingness” is simply an empty geometry (as described by general relativity), then it is certainly plausible that this “nothing” behaves in a way which can be described by quantum mechanical laws.
But Craig has claimed that usage of the word “nothingness” is both “philosophically naive” and “misleading” when used in similar contexts, so presumably Craig wouldn’t consider Vilenkin’s model to be akin to creation ex nihilo. Perhaps this is why Craig continues to defend the standard Big Bang model (unfortunately, that really doesn’t describe creation ex nihilo either).
Are Vacuum Fluctuation Models Dead?
In 1973, a new model for the origin of the universe was born when physicist Edward Tryon published a paper (pdf) asking the question, “Is the Universe a Vacuum Fluctuation?” This model suggests that the universe as a whole is something like a long-lived virtual particle; a random (and extremely large) fluctuation of energy in the quantum vacuum. And although William Lane Craig refers to Tryons proposal as a “bizarre speculation,” it sparked a buzz for the better part of a decade with many physicists proposing different variants on the model (Ex. 1, Ex. 2, Ex. 3).
The problem with all the above models is that they presuppose a background space from which our universe arose. But where did this background space come from? It could have begun in the past – an unsatisfying answer which only pushes back our question of origins another step – or we could say that it is simply eternal. Craig, however, doesn’t like this second answer and raises two objections:
Within any finite interval of time there is a positive probability of such a fluctuation occurring at any point in space. Thus, given infinite past time, universes will eventually be spawned at every point in the primordial vacuum, and, as they expand, they will begin to collide and coalesce with one another. Thus, given infinite past time, we should by now be observing an infinitely old universe, not a relatively young one.
The second objection, that we should be observing an infinitely old universe, seems easily answered by the anthropic principle – an infinitely old universe would have infinite entropy where observers cannot exist. However, the first objection does make sense – given an infinite past of this meta-space, there should be universe-sized fluctuations occurring all over (i.e. our universe should be colliding with other universes, but we don’t see that).
Craig then drives his objections home by quoting physicist Christopher Isham:
According to Isham this problem proved to be “fairly lethal” to Vacuum Fluctuation Models; hence, these models were “jettisoned twenty years ago” and “nothing much” has been done with them since.
The citation for these fragmented quotes points to a 1990 paper by Isham titled “Space, Time, and Quantum Cosmology,” which I have been completely unable to locate in any book or journal – and according to Google Scholar, this paper has only ever been cited by Craig and various other religious apologists.
Luckily, I was able to find two other papers by Isham which were on the same subject: “Creation of the Universe as a Quantum Process” (1988) published in the book Physics, Philosophy, and Theology and “Quantum Theories of the Creation of the Universe” (1993) published in the book Quantum Cosmology and the Laws of Nature – both of these papers are highly critical of Tryon’s proposal.
. . . Except there is one variation of Tryon’s model which are immune to both Craig’s and Isham’s criticisms: Alexander Vilenkin’s model (pdf). This model, unlike the others, does not propose any sort of background space. Rather, Vilenkin suggests that the universe was a quantum tunneling event “from nothing” – though not “absolutely nothing” (this will be discussed further in a future post). In fact, Isham writes in his 1993 paper that, “a scheme like Vilenkin’s might have some approximate validity.” Although, Isham cautiously goes on to say that we won’t know for sure until the theories of quantum mechanics and general relativity are unified.
So, are vacuum fluctuation models dead? Well, Tryon’s model has some serious problems – there’s no doubt about it. On the other hand, Vilenkin’s variation on Tryon’s theme is still alive and kicking.
On a final note, I’d like to quote a bit of Isham’s 1993 paper (page 50) which seems relevant to this discussion (though you’ll never see Craig using it):
A variety of reactions is generated by the idea that the universe may be temporally finite . . . For example, a rather naive reaction is to posit a God who performs creation at the precise point where the theory breaks down but who is such that the subsequent development of the universe is described exactly by the existing theoretical structure. The invocation of such a Deistic creator is psychologically understandable even if it cannot be justified logically.
Bad Advice for Informal Debates
I was reading William Lane Craig’s Q&A post #170 in which the question was, in a nutshell, How can I successfully debate my non-believing co-workers – who claim that Christianity is stupid – when I don’t have enough time to study apologetics?
Here is the first part of Craig’s answer:
One easy thing that we can all do is learn to ask questions. Greg Koukl recommends asking two questions of non-believers:
1. What do you mean by that?
2. What reasons do you have to think that?
It’s amazing how these two disarmingly simple questions can tie people in knots!
Yikes! I thought the first piece of advice would be don’t debate religion with your co-workers. Seriously, you don’t want to be alienated at work (especially if you need the money). So, unless you know your co-workers well enough, either ignore the discussion going on about religion or ask them politely to leave you out of the conversation.
And since the questioner stated that he didn’t know much about Christian apologetics or philosophy (and he is too busy to study it), I thought the second piece of advice would be don’t debate religion if you don’t know what you’re talking about. This goes for theists and atheists alike. If the person you’re debating does know what they’re talking about, then chances are quite high that you’ll look stupid (and this guy’s goal was to show that Christianity is not stupid).
Furthermore, the two questions Craig suggests asking are not very hard to answer. For example, a person might quote the well-known meme, “Christianity is the belief that a cosmic Jewish zombie who was his own father can make you live forever if you symbolically eat his flesh and telepathically tell him you accept him as your master.” That certainly does paint Christianity in a fairly silly light.
…Of course, I’m not advocating that people use this sort of argument. It’d probably be extremely unproductive, but it pales in comparison to Craig’s further advice; throw them off on a book, appeal to authority, and then strawman (to be fair, Craig never uses those words but it’s definitely what he describes).
His final piece of advice is the only genuinely good one: study up on the atheist-theist debate. …Well, actually, Craig suggests that he “memorize the premisses [sic] of the theistic arguments so that you can share them at the drop of a hat.” But let’s give him the benefit of the doubt.
Can a Singularity Be Described as “Nothing?”
According to the Standard Big Bang model, the universe began in the form of a singularity – a point of infinite density and infinitesimal (zero) volume. And although there are problems with extrapolating the Standard model this far back, William Lane Craig seems willing to ignore them so that he can continue claiming that the universe came “from nothing and by nothing.”
But how does the Standard model allow him to make this claim? Well, a singularity’s property of having “zero volume” is pretty easy to square away with the idea of “nothing,” but as for the singularity’s “infinite density,” Craig has a completely different explanation:
This event that marked the beginning of the universe becomes all the more amazing when one reflects on the fact that a state of “infinite density” is synonymous to “nothing.” There can be no object that possesses infinite density, for if it had any size at all it could still be even more dense.
– W.L. Craig, “The Existence of God and the Beginning of the Universe” (first published 1991; updated 2002).
If you’re finding yourself thinking, “…uh …what!?” after reading that then you’re not alone. This is an extremely sloppy piece of work, and it’s hard to imagine that Craig, a man with two PhDs, could have seriously written such a thing. Here are three problems with this argument:
#1: Craig writes, “…if [the singularity] had any size at all…” but the singularity predicted by the Standard model doesn’t have any size at all. So to put it bluntly, this means that Craig’s justification doesn’t even apply to the proper situation.
#2: Craig writes “There can be no object that possesses infinite density,” but the singularity is defined as a state of infinite density. So, even if his justification for this claim made sense, all it proves is that singularities, as they are defined by physics and mathematics, cannot exist. And because the Standard model predicts this singularity, it only means that the standard model is incorrect in this regard (which is probably true).
#3: Craig is claiming that “‘infinite density’ is synonymous with ‘nothing,”” but he only attempts to demonstrate that a state of “infinite density” is impossible. It simply doesn’t follow. As the philosopher Wes Morriston pointed out,
No one would suppose that it follows from the fact that there can be no round squares, that “round square” is synonymous with “nothing.” But neither should anyone suppose it follows from the fact (assuming it is a fact) that there can be no infinitely dense objects, that “infinite density” is synonymous with “nothing.”
To compound the confusion, Craig goes on to quote Fred Hoyle saying that the universe, according to the Standard Big Bang model, was shrunk down to “nothing at all.” But as I’ve elaborated upon in a previous post, Hoyle was only talking in terms of volume – he didn’t even mention density.
Furthermore, in the glossary to The Inflationary Universe (amazon), theoretical physicist Alan Guth notes that a singularity should also have an infinite pressure and an infinite temperature. How does Craig explain these properties as being “synonymous with nothing?” As far as I’ve looked, he never does, but I can assume that his explanation would be as ridiculous as the one he gives for infinite density.
Debunking William Lane Craig 
