The Kalam Cosmological Argument

The ‘Kalam Cosmological Argument’ is one of the strongest of the various arguments which infer God’s existence from (variously) the existence of the universe (or cosmos), its inability to account for its own existence, or aspects of its natural order.  This is a brief introduction to the argument in its modern form, which adds recent cosmological evidences to the argument proper, which is mathematical in nature, and focuses on the problem of infinity.

The Kalam argument originated (like much of our basic algebra) with Islamic thinkers around the turn of the first millennium A.D. Probably its leading contemporary defender is Dr William Lane Craig, a philosopher and theologian who has published on cosmology. At present the most interesting question is whether Hartle-Hawking model of a universe unbounded in time and space offers an exit.

Several disclaimers should be given at the start of this page:

The Kalam argument is not about whether Christian Theism is true. If successful it merely supports the category of opinion which contains e.g. Theism and Deism, and opposes the category which contains e.g. Naturalism and Pantheism.

Secondly, much of the contemporary argument turns on issues in physics which are both complex and constantly changing. The formation of a Grand Unified Theory that will unify general relativity with quantum physics, will be necessary to understand how a universe behaves when it's compressed into a space much smaller than a tennis ball. We can reasonably expect this field to change enormously in the next century. While that is unlikely to affect the mathematical or philosophical basis of the Kalam argument, it will certainly change the physical arguments adduced in support of it, for better or worse.

In his book Not a Chance, R.C. Sproul suggests four alternative accounts of the ultimate origin or cause of the universe;  these I have borrowed and paraphrased freely:

1. Our universe is not real, but illusory — and therefore requires no origin or cause.
2. Our universe was self-caused — and therefore requires no origin or cause beyond itself.
3. Our universe is self-existent — and therefore, eternal, requiring no origin or cause.
4. Our universe was caused by some external agency (or agencies), which is (or are) self-existent (and therefore, eternal, requiring no origin or cause).

Sproul lays down a challenge for anyone to demonstrate a fifth option.

5. Graham Oppy, in reviewing Sproul’s ‘dreadful’ book, suggests that genuinely uncaused events, which Sproul considers a priori ludicrous, as most people do in day-to-day matters, are not necessarily out-of-court on the subject of origins. He notes that no contemporary cosmology knows quite what to make of natural laws before a certain point in early cosmological history, called the ‘Planck time’, leaving this option open.

Probably, three of these can be ruled out at the start: The first option, an illusory universe, seems to be a simple game of words.

• While it's possible that some illusion stops us knowing anything about reality, we could never know if that were so, simply because the illusion is so complete. So it's status as illusion or reality cannot be substantiated in any way.
• More importantly, though: To whom does the illusion appear? What real thing causes this real event to be mistaken for a real experience by real people? However real or illusory you may suppose it is, it's only as real or illusory as we ourselves are. So its status as illusion or reality is of no importance.

An argument that cannot be substantiated, and would have no importance even if it could, may reasonably be ignored.

The second option, self-causation, is a more direct impossibility. Even if we allow the possibility of time-travel, a self-caused entity will still be ontologically prior to itself. It would necessarily precede itself in a chain of cause and effect. The universe would have needed to act before it could act, to give itself existence and thus the power of action. The old maxim ex nihilo nihil fit — from nothing, nothing comes — captures the most obvious problem with this. A non-existent universe would necessarily possess no causal power.

The fifth option, that cosmological views do not exclude the possibility of an uncaused universe is potentially complicated by the complexities of quantum mechanics, and any comments on the subject must leave room for that. It nonetheless appears that something more than hypothetical possibility must be advanced here: In every other sphere of life we normally suppose that everything has some cause, and that an apparent lack of cause is just a lack of understanding. Moreover, it is one thing to suggest that during the earliest split-second of the Big Bang, natural laws do not hold (which everyone agrees) but it is not obvious that this would affect the existence itself of a universe, whatever its natural laws might be.

We are left with options (3) and (4): Either the universe or some transcendent cause is self-existent, requiring no cause. The implication being, if the universe is not eternal, then, in some sense of the word, it was created, and it depends on some external agency or agencies for its existence. Bertrand Russell, noting the dilemma, famously chose (3): At least I know the universe exists, he said. Which is fair enough, but both sides agree that the universe exists; it's not the essence of the argument.

What is wrong with the idea of an infinite length of time? The Kalam Argument presents two problems:

1. An infinite length cannot be formed by a process of adding finite segments together "as day flows into day", as an historical process would require, and
2. The existence of an infinite quantity in the first place (not merely its construction) involves intrinsic contradictions.

We'll now look at these.

a. Infinite quantities cannot be formed by sequential addition.

Time is a sequential process, as we can illustrate by counting. An iterative argument is sufficient to demonstrate that it is not possible to count to infinity:

Given that n, m are finite numbers
repeat
    n = n + m
until n is not a finite number

The value 'n' will never reach infinity, no matter how long you run this program for, since at no point in the loop can its value be anything other than a finite number.

So, if it is not possible to form an infinite quantity by adding together finite quantities (e.g. by counting), it becomes very difficult to see how the universe could be infinitely old. It would mean that if you started counting days, going backward in time (even when normal earth-days did not yet apply), you would be unable to reach some parts of history, since they would have occurred an infinite (uncountable) length of time ago.

Two points arise from this: Firstly: If, at some point in the history of the universe, there was an infinite (uncountable) timespan between that time and the present time, how did the present time come to be?

Secondly, is the problem with the concept of infinity itself? Is there a contradiction in the idea of a number which cannot be counted to? If mathematics is ultimately based on the observation that 1 is not equal to zero, from which the idea of numbers can be constructed (by addition of non-zero units), can infinity be mathematically defined? We'll look at that next.

b. Assuming the existence of an infinite quantity leads to contradictions.

Consider the following mathematics, for any real number, n.

Since:             infinity + n = infinity
It follows that:              n = infinity - infinity

This result destroys any normal mathematical operation you put it in contact with: Since infinity minus infinity can equal 1, it can be introduced as the coefficient of any term in an equation. Since it can equal 0, it can be introduced as a term in itself. Once present, any value can be substituted for it, including positive or negative infinity.

What exactly is wrong with the working? The only faulty assumption seems to be that infinity is a ‘real’ number, and so, something to which the normal rules of addition and subtraction should apply.

The example supplied seems to be the the simplest condensation of illustrations such as ‘Hilbert's Hotel’, which demonstrate similar problems implicit in supposing infinite quantities, usually in the case of infinite sets. (A set with an infinite number of elements would possess proper subsets whose elements could be placed in a one-to-one relationship to its own elements. Do try to picture that in your mind for a moment.) Infinity, as illustrated by the case above, tends to consume and dispense normal finite numbers very freely. Reality does not (ask your bank). That's why mathematics works on it. For these reasons, it seems reasonable to deduce that infinity is, literally, not a real number.

And if infinites cannot exist in reality, then the universe cannot be infinitely large, or old. You may want to take a moment to run through this again for yourself, before we must jump into the next pressing question: Because if infinities are automatically unreal, we come to the crux of the matter:

Does this undermine Theism's God, or Atheism's universe.

Eternal, Omnipresent, Omniscient, All-powerful. God's 'infinitude' is an umbrella term covering several qualities, none of which seem to actually involve the idea of an infinite span or quantity.

God is Perfect.

This is usually qualitative, referring to his flawless being and moral excellence. Where he is described as perfect in knowledge and power it means, of course, that he has all the understanding and ability there is. But in a finite universe, these are not infinite quantities.

God is Eternal and Omnipresent.

This is due to God's transcendence of his created space-time universe, weakly analogous to a director's transcendence of the film he is making. Simply being simultaneously present (that is, aware and able to act) at every time and place in the history of a finitely old and finitely large universe does not involve the concept of an infinite timespan.

God has Infinite Power.

This is simply bad phrasing. To be able to create a finitely large universe, or to subsequently control or recreate any part of it at will, does not require infinite power. To have all possible power in a finite world does not involve the concept of an infinite quantity.

Infinity is not a word normally used to describe these qualities in the Bible. In fact, in the three main modern study bibles (NASB, NRSV and NIV), the word infinite is found just once (Psalm 147:5, NASB), and its phrasing, His understanding is infinite is translated without limit in the NIV and beyond measure in the NRSV, suggesting a poetic or an hyperbolic use of the term in this case, as would befit a Psalm.

This is a very brief list of the key results in cosmology that point to a finitely old universe. It’s brief because these points are common knowledge, and hardly in question, save by advocates of Young-Earth Creationism. In short, the astrophysical evidence for a finitely old universe is as follows:

• Galaxies in all directions are observed to be moving away from us. The is demonstrated by red shift, a kind of visual doppler effect. This indicates that the universe is expanding in all directions.
• A background of microwave radiation, which is only produced under extremely high temperatures, even by astronomical standards, is spread very evenly across the entire sky. This indicates that there was once an enormous high-energy explosion everywhere.
• The speed-of-light barrier means that light from stars takes varying amounts of time to reach us, depending on their distance from us. Telescopes, accordingly, can function like time machines for looking at events which occurred very in the past, but whose light is only reaching us now. The furthest observable astronomical bodies (quasars) are between 10 and 20 billion light years away from us. This means we are seeing them as they were that far into the past.

Astronomers consequently see the universe as the blast wave of an enormous explosion which they term the ‘Big Bang’, and set its date to approximately 14-20 billion years ago.

The evidence against an indefinitely self-sustaining universe is all very well-known, and you don't hear the idea defended now.

This creates a problem for any atheistic or anti-theistic system, since the most obvious fact about a finitely-old universe is that the it began to exist at some point, and the obvious question of cause arises. In a much quoted passage, Robert Jastrow, founder of NASA's Goddard Institute once wrote in God and the Astronomers --

At this moment it seems as though science will never be able to raise the curtain on the mystery of creation. For the scientist who has lived by his faith in the power of reason, the story ends like a bad dream. He has scaled the mountains of ignorance; he is about to conquer the highest peak; as he pulls himself over the final rock, he is greeted by a band of theologians who have been sitting there for centuries.

At least two main alternatives have been put forward to address this problem, the first of which has been called the ‘oscillating universe’ model. Though it is not widely believed at present, it forms useful background for the view that followed it. The essentials of the oscillating universe model are these:

• The universe does not begin at any point, but rather, (like a spring in some ways), it continues through an eternal cycle of expansions and contractions. The start of an expansion is called a 'Big Bang'; the end of a contraction is called a 'Big Crunch'. Crunch goes Bang.
• The universe must possess a 'rebound' mechanism, enabling it to escape the obvious conclusion of a Big Crunch: one supermassive black hole, and the end of the story.
• The universe must be dense enough to eventually slow its own expansion through gravity, and fall back inward to the centre. If not, the universe's final state will be dead stars falling outward forever; wonderfully poetic but entirely non-repeatable

‘Heat death’ vs. a rebound mechanism

If the universe is ultimately dense enough to re-contract, then as it does, the energy-per-unit-volume increases in a kind of reversal of the cooling that followed the Big Bang. The universe becomes a fireball, as stars so brightly burn that they explode or evaporate. Gravity tears them apart. The flaming remains will be sucked into rapidly growing black holes, which themselves will merge together, until one supermassive black hole will be coextensive with the universe. The universe will die a ‘Heat Death’ unless, somehow, the whole process rebounds into a new Big Bang.

Here lies the problem: No rebound mechanism has been suggested, let alone made plausible. Several options have been suggested to get around the finality of absorption into black holes, but none of these resemble a new 'Big Bang'. 'White holes', from which matter emerges outside a black hole as a result of the enormous distortions of space produced by its gravitational field, have been proposed, but since they require a black hole to throw out some of it's own matter, they could never deplete one entirely. Other options include the slow decay of black holes into very high-energy particles over very long periods of time, but again, this would produce nothing resembling a cycling universe. These suggestions, moreover, remain highly theoretical. Currently, there seems no way out of the problem.

The biggest question about a ‘Heat Death’ scenario, however, is this: ‘Will the universe ever contract back together?’ The alternative to Heat Death is ‘Cold Death’, and it seems more likely at the present time.

‘Cold death’ vs. contraction under gravity

If the universe is not dense enough to arrest its own expansion, it will die a 'Cold Death', as the stars burn out, and fly endlessly apart. At t = 10³⁰ years, its final state might be 90% dead stars, 9% black holes, and 1% dust and gas.

The most frequently mentioned solution to the problem of cold death is ‘dark matter’, that is, matter not accounted for by stars and other known phenomena. Various ideas have been proposed, the most interesting of which involve atomic physics, and propose that new or modified sub-atomic particles could account for the difference, but nothing conclusive has been suggested.

These points together have effectively killed off the oscillating universe model, by making new cycles impossible, and the issue of rebound a purely academic question. If the universe is expanding indefinitely, it gets harder to escape the conclusion that the Big Bang was a unique event. It has only happened once.

On top of these considerations, an oscillating universe model is still vulnerable to the Kalam argument against an infinite timespan existing in reality, and possibly to the objections based on entropy. It seems to me that entropy could be limited to each cycle, by the expected suspension of many physical laws during the initial 10^-43 seconds of the expansion cycle.

Need a section on the Hartle-Hawking (quantum gravity) model here.