Objections to the Kalam Cosmological Argument

I. Kalam Cosmological Argument

William Lane Craig formulates his argument as follows:

1. Everything that begins to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause

∴ The cause is a personal and timeless, conforming to the known definition of God.

Premise 1 rests on the ancient concept that all things that have a beginning have a cause. In premise 2, Craig states that the Big Bang singularity was the beginning of the Universe, and that the Universe therefore had a cause. He states that the cause must be singular (as opposed to an infinite series) because a true infinite temporal regress cannot exist. Justifying his summation using various arguments, from Occam’s Razor to the Fine-Tuning argument, William Lane Craig concludes that the first cause was a living agent, the Creator.

Because some Christian Apologists tautologically assume that the universe is defined as beginning at the Big Bang (which assumes the very thing they hope to prove), I’d like to clarify that I use the term “universe” to refer to any system with causal links to the current observable universe. This includes any region of spacetime preceding the Big Bang, any regions of space in different Hubble volumes, or any other physical system that has had a causal relationship with our current observable universe.

Objection 1: Actual Infinities and Set Theory

William Lane Craig uses set theory to support temporal finitude (Kalam Premise 2) by proposing to show that it is impossible to create an infinite temporal set via the successive addition of each present moment.

2.1. A collection formed by successive addition cannot be actually infinite.
2.2. The temporal series of past events is a collection formed by successive addition.
2.3. Therefore, the temporal series of past events cannot be actually infinite.

∴ 2. The Universe has a cause.

William Lane Craig suggests that if infinite time exists, then it could be divided into moments (‘events’) of a particular finite duration. All of time would be composed of an infinite collection of these events. Our present moment would constantly be added onto this collection as it occurred. Craig contends that this creates a number of “absurdities” when applied to real objects. For example, he argues that an infinite temporal series could allow for the subtraction of infinite subsets, a phenomenon he contends would be absurd if it were real. Craig also tends to use variations on Whitrow’s Tristram Shandy argument, which essentially argues that infinite time would destroy the real difference between differing rates of movement in a physical system. The end result is that Craig claims to have shown that an “actual infinite” set of real events cannot exist.

A Stanford Encyclopedia of Philosophy article detailing the contentions between Mathematicians and Craig contains a number of salient points about the metaphysical possibility of an actual infinite. Additionally, John Bell argues that Whitrow’s Tristram Shandy argument is circular. I am going to ignore these for the moment and explore Craig’s description of time a bit more.

Objection 2: Reification Fallacies and the Eternally Enduring Present

Why does Craig claim that logical absurdities can prove infinite time cannot exist? Well, it is well-established that we can deny the existence of an object/process on the basis of an absurdity or paradox that would otherwise result if such a thing existed. A good example is Einstein’s insistence that matter cannot travel faster than light because it could result in a violation of causality, a clearly absurd consequence. By creating a symbolic description of the situation and then showing that the situation leads to physically absurd or unrealizable effects, Einstein has demonstrated the impossibility of causal violations.  The point here is that there is a real precedent for believing that physically contradictory or physically paradoxical situations cannot exist in reality.

The core issue with Kalam is that it is unclear how Craig’s logical description of time “maps” to a real situation. Does Kalam assume ‘past events’ are physically real, or are they merely convenient abstractions representing particle configurations which no longer exist? The latter is argued by Presentism, a philosophical position which asserts that only the present exists. Oddly enough, Craig himself is a Presentist. For the sake of the argument, let’s grant that Presentism is true. So do past events actually exist? And if not, what does that imply for Kalam’s infinite temporal collection of past events? Luckily, Craig himself addresses this:

Now we may take it as a datum that the presentist can accurately count things that have existed but no longer exist. He knows, for example, how many U.S. presidents there have been up through the present incumbent, what day of the month it is, how many weeks it has been since his last haircut, and so forth. He knows how old his children are and can reckon how many billion years have elapsed since the Big Bang. The non-existence of such things or events is no hindrance to their being enumerated. Indeed, any obstacle here is merely epistemic, for aside from considerations of vagueness there must be a certain number of such things. So in a beginningless series of past events of equal duration, the number of past events must be infinite, for it is larger than any natural number. But then the number of past events must be ℵ0 (the first transfinite cardinal number), for ∞ (signifying a potential infinite) is not a number but an ideal limit.

So Craig maintains that under Presentism, past events are merely convenient abstractions representing configurations of matter/energy that we suppose must have existed at some point. He also maintains that the only obstacle in proving the existence of past events is only due to the epistemic limitations of the observer. But this is incorrect. Past events literally do not exist under a Presentist ontology. The obstacle is therefore ontological in nature.

This gets to the heart of the problem. Under Presentism, Time, when distilled to the most basic physical description, is merely the “smooth causal progression” of interacting matter and energy. Craig presents no obstacle to this smooth progression continuing, well, forever. And even the word “forever” fails to have meaning here…I merely mean to say that Craig provides no reason to suppose that the material progression of the universe creates any absurdities by enduring. “Past events” are simply a convenient mental abstraction, a description of either A) memories, or B) the extrapolation of information about a state of the universe other than the present, given knowledge of the present. Since Craig is erroneously basing his argument upon the idea that a collection of “past events” has some real place in the Presentist ontology, he is committing a reification fallacy.

The nature of a reification fallacy isn’t difficult to understand. Suppose that I argue “Computers perform calculations via boolean algebra using ones and zeroes…therefore ones and zeroes actually exist!”. Obviously this is incorrect; ones and zeros have no physical existence because they abstractly describe places where electrical current does or does not flow. Electrical current flows through electric circuits in a computer in such a way that we can use them to represent boolean operations. By reifying my mental model of boolean algebra, I mistakenly claimed that the abstract components of boolean algebra were real! My model about Boolean Algebra does not accurately reflect reality- it is merely a convenient linguistic description.  I couldn’t base any physically meaningful argument on the premise that ones and zeroes actually exist, and if I did, I’d have to precisely demonstrate how my conclusion follows from these purely conceptual ones and zeroes. Similarly, Craig has to show how events (and absurdities) that do not even exist in his ontology can prove that physical causal regress has some sort of finite limit. If he cannot do this, his argument fails.

To summarize, the temporal events in Craig’s temporal collection do not represent anything real. Enumerating these events involves enumerating either memories or some other abstract, stored representation of object configurations that no longer exist. So in reality, under Presentism, the present is not “added” to a past series of events, but rather flows continuously. Craig’s contention that “reaching” the present must entail successively adding each moment of the present on to a set of “past” moments is merely the imposition of a human mental model of time. Craig is reifying his own notion of temporal becoming. Because we are under no obligation to grant the physical reality of Craig’s derived temporal absurdities, we are under no obligation to entertain that time is, in reality, finite.

Objection 3: Observer Bias and the Traversal of Eternity

A closely related but somewhat distinct objection to Craig’s modeling of time can be found in critics’ charges of observer bias.

As noted above, Craig often purports to demonstrate the absurdity of infinite moments by expressing the impossibility of enumerating or traversing an infinite number of moments. Addressing both of these:

1. Traversing an infinite number of moments: As noted in objection 2, this is a absurd objection to eternity. According to Craig’s own temporal philosophy, any observer traversing time is always “stuck” in the present progression of movement. It is therefore more apt to speak of the infinite endurance of an observer rather than traversal. An apologist might tweak their argument to address this objection, claiming that an observer could not *endure* forever. But the inability of an observer to endure forever does not prove that time is infinite. It merely proves that as “time” proceeds, the probability of an observer reaching a halting state (such as death or some other form of information loss) approaches 100%.
2. Enumerating an infinite number of moments: If an observer were to try and count all past moments, he would not be able to store the infinite amount of information necessary to do so. And even if he could, he would spend a future eternity counting past eternity. But…why should that make a difference?  Modern set theory has shown that the notion of infinity is mathematically self-consistent, even if we cannot count an infinite set. So does an observer’s inability to count infinity disprove the possibility of an actual infinite collection?

This speaks to a more insidious problem: why posit an observer at all? Why is it important that an observer enumerate an infinite collection of moments, or count moments as he traverses them? Does this prove anything, other than that an observer has a finite lifespan and a finite memory capacity? There’s no “absurdity” here, other than Craig’s dependence on an observer to draw hard conclusions about what is and isn’t physically plausible. Infinite time (or any sort of associated infinite causal regress) will by definition be beyond the countability or concern of an observer. These are terrible examples on the part of Craig, because his desired physical conclusion (“time must have a finite beginning”) does not follow from the limitations of an observer.

Objection 4: “Big Bang” Singularity

William Lane Craig chooses the “Cosmological Singularity” (Big Bang) as his claim the the universe has a definite beginning. His analysis represents a laymen’s perspective of various cosmological theories, and much of his analysis is colored by his own lay intuition. He writes

Indeed, given the truth of the maxim ex nihilo nihil fit (out of nothing comes nothing), the Big Bang requires a supernatural cause. Since the initial cosmological singularity represents the terminus of all space-time trajectories, there cannot be any physical cause of the Big Bang. Rather, the cause must transcend physical space and time: it must be independent of the universe, and unimaginably powerful.

Craig supports this claim by citing a 2003 paper by Borde, Guth, and Vilenkin, which argues that cosmic inflation can only be a finite process, therefore reaching a singularity in the finite past:

Although such models were hotly debated, something of a watershed appears to have been reached in 2003, when three leading cosmologists, Arvin Borde, Alan Guth, and Alexander Vilenkin, were able to prove that any universe which has, on average, been expanding throughout its history cannot be infinite in the past but must have a past space-time boundary.

Unfortunately, Craig appears to have a serious misapprehension about the consequences of Borde, Guth, and Vilenkin’s theorem. Craig believes that the three are arguing that all of existence must have come into being ex nihilo from a singularity. There are three big problems with this:

1. The potential necessity of a singularity does not automatically imply an absolute beginning. A cosmological singularity is simply a location in spacetime where current physical models fail. In this case, the singularity is the spaciotemporal boundary of cosmic inflation, where the expansion of the current universe began. The theorem, by the authors’ own admission, says nothing other than that the universe must have begun expanding.

2. Singularities might not even exist in physical reality, since they represent the abstract mathematical artifacts of situations where physical models fail.

3. The authors suggest that a quantum fluctuation might have triggered the cosmological singularity:

What can lie beyond the boundary? Several possibilities have been discussed, one being that the boundary of the inflating region corresponds to the beginning of the Universe in a quantum nucleation event.

This contradicts Craig, who has argued that because such quantum mechanical events are not nothing, they do not represent creatio ex nihilo.

Given that Craig’s own sources so clearly contradict his physical support arguments for Kalam, we are under no obligation to seriously entertain them.

Objection 5: “Personal” Creator 

William Lane Craig, in his debate with Justin Schieber, extended his argument to deduce a personal, timeless creator. Schieber objected that if a personal God created the universe, then God must have intended to create the universe, and since intentions precede actions, God must be subject to some form of temporal causality. If God is subject to temporal causality, then He is subject to the same infinite temporal regress that Craig argues against in his Kalam argument.

Craig responded that intentions do not necessarily precede actions, but can be contemporaneous with them:

Image Credit to John Danaher

Schieber responded that intentions that seek to change a condition must, by definition, precede the attempt to change the condition. This is actually in keeping with Craig’s general intuition that causality must preside over anything to do with the physical universe. Additionally, Craig, in response, cannot make a nonphysical defense (“God is Spirit and can do anything”) without rendering his physical argument worthless, because invoking a spiritual argument to ignorance would destroy his attempts to prove theism on a rational basis.

Schieber’s Response is mapped out by John Danaher:

Image Credit to John Danaher

Closing: Further counterarguments, further issues.  

In the end, William Lane Craig offers the idea that, all things being equal, a single living creator is the simplest logical explanation. But I question, in light of continued physical evidence for material explanations, whether Occam’s Razor really favors supernaturalism over self-consistent physical models that have the power to accurately describe reality. After all,  little of the Bible, our only good independent source of supernaturalism, is self-consistent, and even less of it depicts reality in an accurate manner. I fail to see a compelling argument here.


Forthcoming Series on Apologetics

Objective: It is my intent to show that the formal arguments for the existence of God embodied in the Kalam Cosmological Argument, the Fine Tuning Argument, the Argument from Morality, and the Argument against Naturalism all fall prey to lack of empirical grounding and fallacious reasoning.

Disclaimer: As a person who doesn’t set stock by blind faith, I still say that there are elements of faith in God which cannot be formally debunked. Arguments from personal divine revelation, for example, represent highly subjective, anecdotal experiences that make few formal claims and therefore do not lend themselves to formal critique. Whereof one does not know, thereof one must be silent. The Divine Simulation argument may also represent an acceptable basis for supporting theism.

A Preliminary Note on Ontological Arguments

Many apologists attempt to prove the existence of divine beings or divine influence using Ontological Arguments. Ontological arguments are intended to draw an a priori inference about the existence of a real-world entity. These are typically constructed by taking a few basic premises believed to be true about the state of the world and using them to logically infer that a real-world entity must or must not exist.

Truth and validity are two different properties of a logical argument, and in practice, correct ontological arguments only demonstrate their own validity. This is because ontological arguments typically cannot demonstrate that there is no situation under which their conclusion could be untrue. In other words, valid ontological conclusions must be warranted in order to be convincing. It is because of this issue that ontological arguments are often not even addressed by philosophers- they are viewed as uninteresting exercises in world-building, not undeniable arguments which warrant addressing.

An ontological argument for the existence of God often takes the form of an explanation. Typically, the goal of the arguer is to make the case that a particular characteristic about the world can only be explained by invoking God. The arguer must show that God is absolutely warranted, and that no other possible explanation is warranted.

Few ontological arguments for divinity are “pure” ontological arguments. Most include significant a posterioribacked reasoning in order to disprove other possible explanations in favor of leaving God as the sole warranted explanation. Unfortunately, many such arguers either misapprehend modern scientific explanations or commit fallacies in the process.

“Moral” Rebellion and Religious Fundamentalism

An interesting thought that has always struck me about framing the world in terms of good and evil is that “black and white” moral perspectives constrain the moralizer into viewing all individuals (and their decisions!) as essentially partisan. The most obvious problem with this ideology manifests itself when a moral or ethical issue is composed of more than just two dimensions.  More precisely, a black-and-white moralizer cannot perform accurate moral reasoning about actions that may not instantly conform to stereotypically “good” or “evil” motivations. Also true is that most fundamentalist religious sects are required by their doctrine to observe this moral worldview…that’s incredibly obvious to anyone who has ever beat their heads against the philosophical brick wall of fundamentalism.

The big deal is that this “moral framing” problem makes people despise religious fundamentalism. At the core of this strong dislike lies the fact that fundamentalist ideologies leave no room for legitimate doubt in core doctrine. Modern evangelical Christianity, for example, stresses that “doubting is natural”… but only if you eventually see the light of denominational orthodoxy.

The fundamentalist perspective is that doubters, agnostics, atheists, and members of other religions must be choosing to rebel against God, because if they weren’t choosing rebellion, then only one of two other possibilities could explain their disbelief:

A) The doubters/disbelievers were somehow forced to reject belief in God.

B) The doubters/disbelievers have legitimate reasons to disbelieve in God.

Option A violates the (very popular) doctrine of free will, so relatively few religious adherents would think that an unbeliever could be “forced” to doubt. We can therefore rule out option A as a religious rationale for disbelief. Likewise, very few modern religious adherents would opt to favor option B, because if there existed legitimate reasons to doubt the truth of core doctrine, then any reasonable God would have to grant a reprieve to any unbeliever that had legitimate reasons to disbelieve. Obviously such reprieves would run against specific criteria that scripture lays out as being necessary for salvation. So we can also rule out option B as a religious rationale for disbelief, which leaves willful rebellion as the only explanation for disbelief that Abrahamic fundamentalists are willing to accept.

Do you see what this means? In their eyes, significant doubt or disbelief is ultimately unreasonable, the result of a rebellious “spiritual adolescence”.  They won’t ever admit, as a matter of doctrine, that legitimate reasons for disbelief exist, because if legitimate reasons did exist, it would essentially make their religion one of many optional paths to salvation. And that’s a no-no for the sort of authoritarian mindset that thrives in the certainty and discipline created by strict religious doctrine. To fundamentalists, all people either willfully trust God or willfully reject God- there is no middle ground. And that’s just one of the many reasons why it dangerous to allow the religious to pidgeonhole anyone into adhering to their monochromatic view of the world.


There exists an interesting contradiction that I’ve recently seen emerging in the world of religious debate.  If I were to formulate the core evangelical position as a proposition, it would look something like this:

A god who would let us prove his existence would be an idol, but individuals ought to believe in God because evidence exists for both God’s existence and God’s involvement in the universe.

So which is it? This conversion tactic is obviously contradictory. On one hand, proving God with evidence is declared a fruitless exercise that fails to convey “true” trust and thus is largely irrelevant to salvation. On the other hand, it is thought that people ought to believe in the scant evidence for God’s existence (because then, I suppose, they can be saved), and that those who don’t are irrational.

A post addressing the debate itself is forthcoming.

Belief and Choice

There is a certain sort of ideology which views belief as a fully conscious choice. That is to say, there are those who believe that a person could potentially wake up one morning and make the fully conscious choice to believe that elephants can fly (should it suit their fancy to believe such a thing). Belief, in this view, is as much a choice as deciding what clothes to wear.

I’ll leave the whole “free will vs. determinism” debate at the door; it complicates the terminology, and in this scenario we’re only talking about whether belief is a conscious mechanism. That is to say, we’re talking about whether the act of believing in information presented by another person is a simple decision. 

Take a moment, and try to believe something for which you have no precedent to believe.  You could try my earlier elephant example, or you could come up with something else. Either way, it must be something that does not already exist within your worldview. Can you do it? Is it easy? Or do you still know, on some level, why it doesn’t mesh with your reality?

When I used the words “your reality”, I am not, of course, embracing some sort of subjectivist New Age philosophy. I believe that objective reality exists, even if not all aspects of reality are easily comprehensible. When I say “your reality”, I’m talking about your internal model of the way the world works. I’m talking about the way you rationalize and support the things you believe. You might rationalize your attraction to the ground by invoking the well-documented concept of gravity. You probably base your views about personal success on the priorities you have developed over the course of your life. You support your religious beliefs (if you have them) with religious education and personal experiences.

All of this represents a large, complex intellectual infrastructure which composes and supports your view of the world. Lack the intellectual infrastructure necessary to believe in something, and you’ll find that it is very difficult to convince yourself to “just believe”. Conversely, if you possess the intellectual infrastructure supporting a particular belief, you’ll find that it is very difficult to simply throw that belief away. It is for these reasons that altering a deeply-entrenched belief is often a long, arduous, and only partially-voluntary process.

Example: 9/11 Truther Conspiracies. What sorts of things would you already need to believe if you wanted to believe in a 9/11 conspiracy? Well, first, you would need to believe that the government, for all of its bureaucratic incompetence, is capable of planning an attack on America in perfect secrecy. You’d need to disbelieve the overwhelming evidence that radical Islamists and political dissidents perpetrated the attack. You’d need to believe that the government was capable of perfectly coordinating its response to make it appear that they were just as surprised  as we were. You’d need to believe that the extensive evidence in the 9/11 Commission Report, written and reviewed by hundreds of independent experts, was fake. Do you see what it takes to believe such a thing? Your entire worldview must be very well-coordinated,  while simultaneously ignoring all opposing evidence.

Belief is not a trivial act. It’s act that requires an entire complementary worldview. People don’t believe (or disbelieve) ideas because they want to; they believe (or disbelieve) ideas on the basis of having (or not having) the intellectual infrastructure necessary to support the ideas. Certainly it is true that emotions and personal preferences play into belief, but liking or disliking an idea tends to only manifest as confirmation bias. That is to say, the like or dislike of an idea tends to make it easier to cement acceptance of an already-believed notion, deny an already-disbelieved notion, or seed doubt in a shaky belief. Preference alone does not change belief. It simply makes you more (or less) amenable to belief.

No doubt that the religious would like to believe that we could all choose belief in their respective religions if we just made the choice to accept their god(s). No doubt that conspiracy theorists would like the believe that the evidence is all obvious, man, you just have to accept it and draw the obvious conclusion! No doubt that scientists would like the believe that scientific concepts are universally (and easily) acceptable notions, for the same reasons as the conspiracy theorist. But none of this true. Until we all understand the psychological complexity of belief, we won’t be able to properly persuade others about controversial issues (or understand why they refuse to believe) without a great deal of frustration and argument.