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The Kalam: An Overview & Defense

By Ronald Cram

William Lane Craig is famous for resurrecting and defending the Kalam Cosmological Argument (KCA). The argument appeals to both philosophical and scientific evidence for the beginning of the universe. If the Kalam is sound, it seems to prove the existence of God.

Kalam Cosmological Argument

The question is raised: Is the argument sound given our modern, scientific understanding of cosmology? In this essay I will review and examine the premises of the Kalam to see if we have good reason to affirm them as probably true. The standard form of the KCA goes as follows:

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

We can add the following steps:

4. The universe (all space, time, and matter) cannot cause itself.
5. The cause of the universe must be spaceless, timeless, immaterial, and uncaused.
6. This uncaused, immaterial and timeless cause of the universe is what everyone means by God.
7. Therefore, God exists.

The argument is valid, but are the premises true? Science uses Bayesian probability theory to assign a probability to a hypothesis. I will follow that procedure for each of the premises.

Step #1

All science is based on cause and effect relationships. Zero evidence exists that this premise is false and so this premise has never faced any serious or informed challenges. In our daily experience, objects do not pop into existence uncaused.

Scientists have proposed a number of possible causes of the Big Bang including colliding branes in string theory, false vacuum in inflationary theory, and quantum fluctuations in quantum mechanics. Each of these ideas propose a “universe generator” of some type that must exist prior to our Big Bang. Scientists recognize that the Big Bang must have a cause.

Some have attempted to claim that quantum fluctuations are uncaused, but this claim is untrue. Quantum fluctuations are caused by the energy in the vacuum. While no one can predict where quantum fluctuations will appear, the number of fluctuations within a given volume and time are quite predictable.

Others have proposed that while things within the universe need a cause to begin to exist, we have no reason to believe the universe as a whole needs a cause. This is special pleading of the most irrational type. If objects within the universe need a cause (when the atoms and molecules already exist), then it is even more true that the universe as a whole needs a cause to exist because an extra step is required (the creation of matter, energy, space and time). A Bayesian probability can be assigned to this premise of 99+%.

Step #2

This is more complicated. Stated simply, the standard cosmology is that the universe is 13.8 billion years old. This means the universe began to exist 13.8 billion years ago. While it is true that theorists are working on models for a past eternal universe, a Bayesian probability can be assigned to this premise of 98%.

For those who are not interested in cosmology, you may skip to the discussion of the third premise. For those interested in cosmology and a defense of this Bayesian probability, read on.

William Lane Craig often refers to BGV theorem in his debates with atheists. (The theorem is often misunderstood to be a singularity theorem. It is not. It is an incompleteness theorem. But it is completely compatible with the singularity theorems.) BGV theorem states that any universe which is on average expanding throughout its history cannot be eternal into the past but must have had a beginning. This is an extremely robust theorem. Within a classical spacetime, BGV theorem does not depend upon any particular energy condition (low energy, high energy) nor does it depend on any particular solution to Einstein’s equations. The fact the theorem is so robust makes it very difficult to evade. It applies to multiverse theories and cyclic universe theories. Any past eternal cosmological theory must evade BGV theorem.

In his debate with William Lane Craig, Sean Carroll referred to his paper titled “What if time really exists?” and its Quantum Eternity Theorem.

In Carroll’s post-debate reflections, he writes:

“Indeed, I quoted a stronger theorem, the “Quantum Eternity Theorem” (QET) — under conventional quantum mechanics, any universe with a non-zero energy and a time-independent Hamiltonian will necessarily last forever toward both the past and the future. For convenience I quoted my own paper as a reference, although I’m surely not the first to figure it out; it’s a fairly trivial result once you think about it.” (Click here)

The QET is not a “stronger theorem” in any sense. Most cosmologists believe our universe has zero net energy. So any model built on a non-zero energy is extremely unlikely. Also, the theorem has the requirement of “under conventional quantum mechanics.” But a beginning necessarily requires something other than conventional quantum mechanics. There’s nothing to prevent a beginning of our conventional quantum mechanics. In reality, Carroll’s QET is not at all helpful to his argument. Aron Wall provides a cosmologist’s assessment of Carroll’s claims and his use of QET (click here).

Proposed Models

Some models have been proposed than can evade BGV theorem. We will look at a few of these theories in greater detail.

A. The first of these is the Aguirre-Gratton model supported by Sean Carroll in his debate with Craig. Obviously, Carroll thinks this model is the strongest possible, the most likely to be true, or he wouldn’t have used it to support his position that the universe may be past eternal. But what is the Bayesian probability this model describes our universe?

In the Abstract of his paper “Eternal inflation and its implications,” Alan Guth writes:

“Although inflation is generically eternal into the future, it is not eternal into the past: it can be proven under reasonable assumptions that the inflating region [our universe] must be incomplete in past directions [have a beginning], so some physics other than inflation is needed to describe the past boundary of the inflating region.”

On page 14 of the same paper Guth writes:

“If the universe can be eternal into the future, is it possible that it is also eternal into the past? Here I will describe a recent theorem [43] which shows, under plausible assumptions, that the answer to this question is no.”

According to Guth, under “reasonable assumptions” and “plausible assumptions” the BGV theorem cannot be avoided. On page 16, Guth discusses the Aguirre-Gratton model with its reversal of the arrow of time and explains that this model does evade BGV theorem. The natural conclusion is that the Aguirre-Gratton model does not have reasonable or plausible assumptions. Aguirre and Gratton have not put forward any plausible mechanisms that might cause the arrow of time to reverse and no reversal of time has ever been observed.

Remember this is the best model that Sean Carroll had to represent his view that the universe is past-eternal. A Bayesian probability that the Aguirre-Gratton model applies to our universe is <1%.

B. Cosmology from Quantum Potential Model – Because the BGV theorem applies to classical spacetimes, another way to evade the theorem is to appeal to the uncertainty of quantum mechanics. One example is the paper “Cosmology from Quantum Potential.”

However, this cosmological model has serious problems. A recent paper titled “Perturbative Instability of Cosmology from Quantum Potential” has the following Abstract:

“Apart from its debatable correctness, we examine the perturbative stability of the recently proposed cosmology from quantum potential. We find that the proposed quantum corrections invoke additional parameters which apparently introduce perturbative instability to the Universe.”

Our universe is stable. This model does not produce a universe like the one we observe. The Bayesian probability of this model being correct is less than the Aguirre-Gratton model and is <1%.

C. Emergent Universe Models – This class of models successfully evade BGV theorem. The idea is that a “cosmic egg” that exists forever until it breaks open to produce an expanding universe. Proponents of these ideas include Ellis, Barrow, Campo, Wu, and Graham.

Mithani and Vilenkin show that this class of models can collapse quantum mechanically, and therefore cannot have an eternal past.

A Bayesian probability of Emergent Universe Models being correct is <1%.


Side Note: What About Guth?weird-guth-sign

Someone may mention the photo of Alan Guth holding a sign at the Carroll/Craig debate that read [The universe is] very likely eternal but nobody knows.” Why would Guth pose holding that sign when all of his scientific papers say the universe had a beginning? Some assumed Guth was going to publish a new paper that explained his change of view, but it’s been three years and no paper has been published supporting a change in the science.

Perhaps Guth posed for that picture just as a favor to Carroll.


In order to defeat premise #2, skeptics must be able to show that a past-eternal universe is more likely than a universe of a finite age. While a number of past-eternal models have been proposed, the cosmological community has rejected all of them as highly unlikely. A Bayesian probability can be assigned to premise (2) of 98%.

Step #3

The third step of the argument is the rational conclusion of the first two premises. A Bayesian probability can be assigned to this conclusion of 98%.

Step #4

The fourth premise – “The universe cannot cause itself” – seems non-controversial. However, cosmologists (driven by their dislike of the way a beginning of the universe points to creation by God) have proposed ideas attempting to challenge this premise. Lawrence Krauss’s book, A Universe from Nothing, was one of the first of these proposals to get a wide audience. The idea, first proposed by Edward Tryon, is that the universe is a quantum fluctuation. Physicist Don Page pointed out that Krauss’s idea is not really “from nothing” because quantum fluctuations require a quantum field (which is something). Since the quantum field must exist before the Big Bang, this is not a universe from nothing at all.

Alexander Vilenkin modified Tryon’s idea referring to the origin of the universe as a “quantum nucleation” that happened before the existence of any matter, energy, time or space. In order words, the quantum nucleation happened in the absence of a quantum field. Not only is this logically incoherent as things happening before time require time, but this idea is problematic for most physicists because the theory makes an untestable claim. Scientifically untestable claims are not scientific. The probability the universe can cause itself is <1%.

Step #5

“The cause of the universe must be spaceless, timeless, immaterial, and uncaused” is mostly non-controversial. If the universe is defined as “all matter, energy, space and time” and the universe cannot create itself, then it follows that the cause of the universe must be spaceless, timeless and immaterial. Some may argue that the cause does not necessarily have to be uncaused. But if a contingent being of finite age were the creator, that being would not be the ultimate answer.

The real Creator would be the one who created the intermediate being. An infinite causal regress is a logical absurdity and has been rejected by philosophers since the time of Aristotle. A Bayesian probability can be assigned to this premise of 99%.

Step #6

“This uncaused, immaterial and timeless cause of the universe is what everyone means by God” is largely uncontroversial. A Bayesian probability can be assigned to this premise of 99%.

Step #7

“Therefore God exists” is a rational conclusion. A Bayesian probability can be assigned to this conclusion of >95%.

Whether this God is the God of the Bible or some other God is a separate question and requires additional evidence and reasoning.

Original Blog Source: http://bit.ly/2mJ8ZFg


Philosophical Arguments that the Universe had a Beginning

This is my last blog dealing with the origin of the universe as an argument for the existence of God. I’ll examine the issue of whether new physics might be discovered to enable the universe to be past eternal. I’ll offer a couple of philosophical arguments against the possibility of an eternal past. If these arguments succeed we can be confident that no scientific discoveries could ever show that the universe has existed forever. Indeed if these arguments are sound, the scientific evidence I’ve offered so far would become superfluous.

If the universe has existed forever, this would entail an actually infinite number of past events. I use the term “actually infinite” to distinguish it from a potential infinite quantity. No one doubts that the number of future events can grow without limit but this is merely a potential infinite. Any finite time in the future there would still have been a finite number of events since the current time so the infinity is just potential – it represents an unattainable limit as this article by George Ellis, a prominent cosmologist, indicates.

Is it possible for actually infinite numbers of entities to be realized in the actual world?

One of the greatest mathematicians of all-time, David Hilbert, certainly didn’t think so: “the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought.“ Georg Cantor established a mathematically rigorous way of dealing with the concept of infinity that is very useful for mathematical and scientific calculations. Although Hilbert defended Cantor’s work, he argued that infinities couldn’t exist in the actual world or they would lead to absurdities.

Some readers may be thinking that if it is mathematically possible it has to be physically possible. But not everything used in mathematics necessarily implies a direct correspondence with physical ontology (nature of being). Infinitesimals are mathematically feasible and highly useful in calculus, but modern physics holds that everything is quantized. Mathematical consistency and coherence doesn’t necessarily imply physical realization – there are abstract mathematical systems that can be constructed that are coherent but not all of them are necessarily realized anywhere in physics. In computer science we often choose between multiple mathematically equivalent but quite different ways of computing things – they can’t all correspond to physical ontology because they entail fundamentally different ways of modeling reality. Infinities that show up in physics equations are considered problematic unless and until some type of renormalization can be performed.

So if we can show that absurdities result if actual infinites exist, then we have good reasons for rejecting the possibility of an actually infinite number of past events – even if it is mathematically feasible. Here is how philosopher Peter S Williams makes this argument to a lay audience:

Suppose I ask you to loan me a certain book, but you say: ‘I don’t have it right now, but I’ll ask my friend to lend me his copy and then I’ll lend it to you.’

  • Suppose your friend says the same thing and so on…
    1. If the process of asking to borrow the book goes on forever, I’ll never get the book
    2. If I get the book, the process that led to me getting it can’t have gone on forever

Somewhere down the line of requests to borrow the book, someone had the book without having to borrow it. It’s easy to see how this analogy applies to the Kalam – if the arrival of the current event/book required infinitely many prior events, it would have never arrived. You cannot traverse an actual infinity. If the current event/book did arrive, the process that led to it couldn’t have gone on forever.

Another example of the physical impossibility of an actually infinite number of items is the following. Suppose that there is one particle of some type for every positive whole number (integer) – we can think of these as comprising a mathematical set in which we’ve numbered the particles. The number of particles is aleph null and represents a so-called countable infinity. Suppose this type of particle is not stable and thus half of the particles decay in some time interval. One could think of the number of particles in this set as now consisting of the even integers. But one can also reach a contradictory answer that the number of particles is the same as the original by proving mathematically that the number of even, positive integers is the same as the number of positive integers.

This mathematical proof is quite simply done by showing a one-to-one correspondence between the elements in the set. For every integer in the original set, there is one integer in the set of even integers (2,4,6, …) obtained by just doubling the original value. Thus, the number of particles in each set is mathematically identical even though half of the original particles underwent decay. After we wait another half-life, half of the remaining particles have now decayed so the set would consist of particles (4,8,12, …). However it can also be mathematically proven that the number of positive integers that are multiples of 4 is identical to the number of positive integers. Have the number of particles been reduced or not? We reach contradictory results – no matter how many half-lifes we wait, the number of particles is the unchanged and has been reduced as per the usual physics equation. Thus, dealing with the actually infinite in reality would violate the laws of physics.

Philosopher Alexander Pruss offers at 6 arguments in support of premise 2 of the Kalam – that there couldn’t have been an infinite number of past events. Although he thinks actual infinities might be possible in general, he doesn’t think an infinite causal chain is possible. “This strengthens the Kalaam argument by showing that the premises can be weakened: the Kalaam argument only needs the kind of causal anti-infinitism that I now cautiously accept.”

Objection: But doesn’t Christianity require that God has lived through an infinite number of events?

There has never been a time at which God has not existed. However, if time is a physical entity that began to exist, it seems to have been something brought about by a cause outside of time. The classic theistic understanding is that God is an eternal being that exists outside of time. There is an interesting passage in the New Testament, Jude 24, that speaks of God having dominion and glory before time began. See also Titus 1:2 for another Biblical reference consistent with the understanding from modern physics that time had a beginning. As evidence of God being able to see into the future one can study Biblical prophecies of the future state of cities such as Memphis, Thebes, Babylon, Ninevah, Ashkelon and peoples such as the Philistines, Edomites, and Jews. (See this link to explore this evidence for divine inspiration of texts known to be written before the fulfillment)

It may be hard for us to grasp something that exists outside of time since we are constrained in this realm. Many scientists, however, do posit the existence of other space-time dimensions and explain how we would be unaware of these – e.g. see the book Flatland, which Hawking and Sagan point to an illustration of the possibility of unseen dimensions. Perhaps God exists in another realm or dimension of time or perhaps William Lane Craig is right in theorizing that God existed timelessly before creation and stepped into time when He created time.

Final Comments on the Implications of the Kalam

The conclusion of the Kalam is pretty modest. It doesn’t establish the existence of a particular god etc. Deism rather than theism could still be true if this is all we had to go on. The Kalam, however, is a strong refutation of naturalism – the view that nature is all there is. Most atheists hold to naturalism and if they admit that it’s false they’ve undermined the most significant traditional arguments for atheism.

A transcendent cause to the Universe possesses some properties of God such as being beyond space and time and being immaterial. It’s pretty hard to deny this as atheist scientist Lewis Wolpert discovered in his debate with William Lane Craig. Wolpert admited that the universe had a beginning saying “well we know that, nobody disputes that.” The ease with which he is willing to admit this should bother you if you’re a skeptic as it is yet another testimony to how this argument depends only upon mainstream, widely accepted science. Wolpert’s assertion that it might have been a very special computer fails miserably as one can see here.

Objection to Premise 1 of the Kalam: Doesn’t Quantum Mechanics Violate the Causal Principle?

It depends on what you mean by causality. A philosophically-informed physicist would say Quantum Mechanics (QM) doesn’t do away with causality:

“In fact, QFT[Quantum Field Theory] is constructed in such a way to explicitly preserve causality. Any QFT textbook devotes 10 pages of chapter 1 to explain why the square root of the Klein gordon equation does not make a good wave equation for a QFT – it cannot preserve causality.”

In physics, we speak of things happening based on mathematical laws. For example, two electrons are repulsed by the electromagnetic force and we can compute their path of motion. There seems to be a clear causal connection because the math is fully deterministic. In QM, the only difference is that the math is probabilistic rather than exact. No one is even sure that QM is indeterministic – Bohm’s interpretation might be right. Even if QM is non-deterministic, is it appropriate to say that things are happening without causes? We can use the Schrödinger/Dirac equation to make quite accurate probabilistic computations concerning the evolution of a system. We may not know when a particular radioactive atom will decay but we can use statistically large sets of atoms to accurately perform radiometric dating.

To be sure, there is a lot of controversy over how to interpret causation in QM (e.g., does the observer play a role?) but I don’t think QM really does away with the causal principle in the sense relied upon by the Kalam. The Kalam relies only on there being underlying reasons for things coming into being. If something happens in a manner that can be probabilistically predicted (as is always the case in QM), then it’s not a case of something being created without a cause from absolutely nothing. Things originating without causes could not be predicted even probabilistically!

Here is philosopher/Physicist David Albert on how Quantum Mechanics doesn’t explain the origin of the Universe from absolutely nothing: “The fact that some arrangements of fields happen to correspond to the existence of particles and some don’t is not a whit more mysterious than the fact that some of the possible arrangements of my fingers happen to correspond to the existence of a fist and some don’t. And the fact that particles can pop in and out of existence, over time, as those fields rearrange themselves, is not a whit more mysterious than the fact that fists can pop in and out of existence, over time, as my fingers rearrange themselves. And none of these poppings — if you look at them aright — amount to anything even remotely in the neighborhood of a creation from nothing.”

The Borde-Vilenkin-Guth theorem that I referenced in the previous blog indicates that spacetime cannot be extended into the infinite past. QM operates within spacetime so if spacetime is not eternal it is unreasonable to claim that quantum processes have been eternally in operation. Some physicists do speak of highly speculative theories of creating a universe out of the quantum vacuum but the quantum vacuum is not nothing – it’s just the lowest energy state of spacetime. It’s weird to think about spacetime not existing but such is the implication of BVG and the earlier Hawking-Penrose singularity theorems. This Scientific American article might be helpful in explaining how the Big Bang is not just describing expansion into “some imagined preexisting void.” The Big Bang is not dealing with expansion into preexisting space but the expansion of space.

For more details on the problems when some scientists speak about the Universe being created from absolutely nothing I highly recommend this blog by cosmologist Luke Barnes.