Carroll vs. Craig (3): On Contingency

As I explained in my last posts (one, two), I’m expecting good things from the upcoming dialogue between Sean Carroll and William Lane Craig. Here, I’ll look at a species of the cosmological argument for the existence of God known as the contingency argument.

Before all that: Sean has linked to my previous post about this debate. Just to be clear, I don’t think Sean needs much advice. I’m really using these posts as an excuse to discuss Carroll’s ideas. He knows the arguments, knows the cosmology, has a clear idea about what naturalism is and how to defend it, and is an excellent public speaker. Carroll’s arguments are interesting and relevant, and Craig’s response won’t be anything as basic as “here’s a Grammar 101 lesson on using terms of negation and indefinite pronouns.”

Long post ahead. The short story: Carroll needs to make clear his objection to the Craig’s version of the principle of sufficient reason. In particular, why think that the universe is an exception (perhaps the only exception) to the general trend that things exist for a reason?

Craig’s Version of the Argument

The cosmological argument for the existence of God has been defended through the ages by a who’s who of thinkers: Plato, Aristotle, Al-Kindi, Ibn Sina, Al-Ghazali, Maimonides, Aquinas, Scotus, Spinoza, Leibnitz, … Of course, it has also been critiqued, most famously by Hume and Kant. The debate continues. Craig’s version of the contingency argument goes like this.

1. Everything that exists has an explanation of its existence (either in the necessity of its own nature or in an external cause).
2. If the universe has an explanation of its existence, that explanation is God.
3. The universe exists.

It follows from these premises that God exists (homework). Note that this argument has nothing to do with whether the universe has a beginning.

Some atheists (Lawrence Krauss in particular) object to the second premise, thinking that God is just crowbarred in, an ad hoc assumption. But premise 2 has its own argument:

4. Since the universe is the totality of space, time, matter and energy (i.e. that’s the sense of universe being used here), the cause of the universe must be spaceless, timeless, and immaterial.
5. The most plausible immaterial kind of thing that could cause a universe is a mind.
6. A spaceless, timeless, and immaterial mind that causes the universe deserves to be called God.

Premise 5, in turn, has its own argument based on the causal effeteness of abstract entities. If you want to go after premise 2, you need to deal with this argument. Krauss didn’t.

Getting slightly ahead of myself, Carroll seems to object to Premise 1. This premise is a version of the infamous Principle of Sufficient Reason (PSR). It is a mild version, applying only to things, not to all (contingent) truths. Craig argues for premise 1, or at least that the universe is not an exception to premise 1, as follows.

7. It would be arbitrary for the atheist to claim that the universe is the exception to the rule. Merely increasing the size of the object to be explained, even until it becomes the universe itself, does nothing to remove the need for some explanation of its existence.

Alexander Pruss has advanced arguments for a version of the PSR along these lines. (I’m paraphrasing, dangerously).

8. If the universe could exist without explanation, then it would be inexplicable why just anything couldn’t exist without explanation. In other words, why is only the universe an exception to premise 1?
9. Universal principles are simpler than principles that apply to an arbitrary subset. The simplest explanation of fact that contingent things typically have explanations is that all contingent things have explanations.

Carroll’s Case

Let’s consider with what Carroll’s response might be, as gleaned from this reply to an op-ed piece by Paul Davies.

“[A]t first glance, it seems plausible that there could be [an] answer to the question of why the laws of physics take the form they do. But there isn’t. At least, there isn’t any as far as we know, and there’s certainly no reason why there must be. The more mundane “why” questions make sense because they refer to objects and processes that are embedded in larger systems of cause and effect. … The universe (in the sense of “the entire natural world,” not only the physical region observable to us) isn’t like that. It’s not embedded in a bigger structure; it’s all there is. We are lulled into asking “why” questions about the universe by sloppily extending the way we think about local phenomena to the whole shebang. What kind of answers could we possibly be expecting? … [The correct possibility seems to be] that’s just how things are. There is a chain of explanations concerning things that happen in the universe, which ultimately reaches to the fundamental laws of nature and stops. This is a simple hypothesis that fits all the data; until it stops being consistent with what we know about the universe, the burden of proof is on any alternative idea for why the laws take the form they do.”

Let’s break it down. Lurking in the background of this entire discussion is this question: what makes an explanation an ultimate explanation? What is it about this explanation that makes another iteration of “and why?” out-of-bounds? Carroll’s argument seems to be:

10. Chains of explanations have to end somewhere.
11. Once we arrive at a simple explanation that fits all the data, there is nothing to be gained by going any further. Such an explanation should be considered an ultimate “stopping-point” explanation.
12. The fundamental laws of nature are just such an explanation for the physical universe.
13. Thus, we should consider the fundamental laws of nature to be the ultimate explanation of the universe.

Carroll’s formula of “simplicity + fits the data” needs a closer look.

Fitting the data

Do the laws of nature fit all the data? On one level, obviously yes. The fundamental laws of nature are by definition the complete description of the physical properties of the stuff of our universe. How could there be any facts about our universe that the laws miss?

Rather easily, it turns out.

• Something exists.
• This universe exists.
• This universe obeys laws.
• This universe obeys mathematical laws.
• This universe obeys these particular laws.
• There are these constants in the equations.
• The universe is described by this particular solution to the equations. (Equivalently, the universe has these particular initial / boundary conditions.)

All true. (Maybe except the one about the constants. The fundamental laws may be constant-free. It is also possible though unlikely that the fundamental equations have a unique solution. Also, I’m equating “data” and “facts” here. If Carroll means for “data” to be observable, then many of the facts above still qualify.)

If Carroll’s naturalism is true, then these facts are inexplicable. Add a “why?” at the end and you get an unanswerable question. Not just unanswered, not just awaiting a breakthrough, not just an open research question. They are non-questions. They are not explained by the laws of nature – they are too big – and so they are not explained at all.

Now, why are those facts the inexplicable ones? Why give up on those facts? Why don’t these true statements count as data, to be fit? If we have to stop somewhere, why here?

Success as an explainer doesn’t seem to excuse a fact from needing an explanation. Even if it were taken as a given that every physical observation is explained by the laws of nature (Craig believes in historical evidence for certain miracles, but ignore that for now), this does nothing to tell us whether the laws themselves need an explanation or not. That the laws of nature do a lot of explaining does nothing to tell us whether they need an explanation.

Simplicity

Consider the other half of Carroll’s formula: simplicity. This raises two questions: why simplicity? And, are ultimate physical laws really simple?

Why should the simplicity of an explanation lead us to conclude that it is an ultimate explanation? Perhaps Carroll has Occam’s razor in mind, that the simplest explanation is the most likely to be true. However, true does not equal ultimate. A simple explanation may be the most convenient, the most useful stopping point for an explanation. But why expect reality to respect convenience? After all, a deeper explanation could be a more complex explanation.

As we have dug down into the laws of physical reality, we have found simplicity, and more simplicity the further down we go. Should this lead us to expect simplicity at the bottom? Yes, I suppose. However, that simplicity is just one more feature of the ultimate laws of nature that could have an explanation. We could add

• This universe obeys simple laws.

to the list above, making yet another astonishing fact about the universe that naturalism declares inexplicable.

Put another way, we expect ultimate to imply simple, but simple doesn’t necessarily imply ultimate. Even if it did, how simple? What degree of simplicity stamps “go no further” on an explanation?

Interestingly, Carroll seems to agree with all this in another blog post. He says “[N]othing in science, logic, or philosophy provides any evidence for the claim that simple universes are “preferred” (whatever that could possibly mean). … Occam’s Razor exhorts us to stick to simple explanations. [Occam’s razor is] simply an expression of our selfish desire, not a philosophical precondition on the space of possible universes. When it comes to the actual universe, ultimately we’ll just have to take what we get.”

Carroll here is arguing that the simplicity of nothing is no reason to think that the existence of something is surprising and so demands an explanation. (I’ll have more to say about this in my next post.) It also seems to follow that the simplicity of the laws of nature is no reason to think that they are ultimate explanations.

Why inexplicable?

A theme emerges. The naturalist must convince us that, for example, the law-like behaviour of the universe is ultimately inexplicable. But how? All explanations of the universe reach the fundamental laws of nature and stop. The laws don’t explain themselves. They certainly don’t explain the existence of a universe that obeys them. The law-like behaviour of the universe is a contingent fact about reality, so mathematics and logic won’t help either. What else is there? What words are left to finish this sentence: these facts are inexplicable because … ?

The naturalist seems to have sawn off the branch he is sitting on. By ending explanations of facts about the universe at the fundamental laws of nature, he has no way of justifying naturalism. Naturalism doesn’t follow from the laws of nature, and so it doesn’t follow at all. The question “why believe naturalism?” seems destined to be added to the pile marked unanswerable. Naturalism is, by its own standards, unjustifiable.

Science in a Theocracy

Carroll argues further for the laws of nature as the stopping point for explanations:

The laws exist however they exist, and it’s our job to figure that out, not to insist ahead of time that nature’s innermost workings conform to our predilections. … [We should] simply accept [the universe] for what it is.”

This passage tries paint a picture of the theologian dictating science to the scientist. But it need not be this way. We are entitled – expected, even – to ask what hypotheses are aided or assailed by what we know. The theologian can claim that what science has revealed about the universe points to a creator, without this creating a feedback loop in which theology starts making scientific claims.

As a specific example, suppose the theologian believes that the law-like nature of the universe supports the hypothesis of an intelligent creator of those laws. This is not a claim “ahead of time” about “nature’s innermost workings”. It is a claim from nature’s innermost workings to an explanation of those workings. The theologian need not tell the scientist what those laws must be. When it comes to the universe, science must accept what it gets. But that doesn’t mean that we can’t ask questions about how we got what we have.

The Alternative?

I’m not sure what Carroll means by “the burden of proof is on any alternative idea for why the laws take the form they do”. Let’s be clear about this. Naturalism is not an idea for why the laws take the form they do. We are not comparing Explanation A with Explanation B. We are comparing “there is an explanation” with “there is no explanation”.

This threatens to derail the ordinary process by which theories are evaluated. Given some theory T, we want to know the probability that it is true, given everything we know. This is known as the posterior probability of T.

Not being handed posteriors from the clouds, we use probability identities to break them into manageable pieces. One of those pieces is the likelihood – the probability of the evidence given the theory. When evaluating naturalism, we need to be able to discuss quantities like “the probability that the laws of nature take the form they do, given that naturalism is true”. Roughly, p(laws | naturalism). Comparing this to p(laws | theism) allows us to assess the relative merits of the two theories.

If explanations concerning things that happen in the universe ultimately reach the fundamental laws of nature and stop, then this could imply one of two things. Either,

a) p(laws | naturalism) is undefined, since the laws have no explanation. We can calculate probabilities with the laws, but not the probability of the laws. In this case, assessing the merits of naturalism seems impossible, since we cannot reason about the probability that it is true¹.

b) p(laws | naturalism) is “uninformed”, so to speak. Since there is nothing beyond the laws to inform us of what those laws might be, naturalism gives us no reason to prefer any particular form of the laws of nature. Naturalism gives the same result as no information at all. In which case, the “burden of proof” isn’t much of a burden at all. Naturalism represents the baseline, maximal ignorance, the lowest likelihood a theory could have without being prejudiced against our laws of nature. Any theory that would lead us to expect our universe, or a class of universes that includes ours, must do better than naturalism, at least in terms of the likelihood.

Carroll challenges theists to produce “a compelling argument to that effect … that God provides a better explanation (for whatever reason) than a purely materialist picture, not an a priori insistence that a purely materialist picture is unsatisfying”. Craig’s argument is that the materialist exemption of the universe from the PSR is arbitrary and inconsistent, rather than unsatisfying. But, regardless, it seems the low likelihood of our universe given naturalism gives plenty of scope for the theist to meet Carroll’s challenge. Any feature of our universe that would be preferred by God (e.g. free moral agents that inhabit law-like environments) is a reason that God provides a better explanation than materialism. [It is odd that he says this shortly after quoting Swinburne, because this is exactly what Swinburne argues in “The Existence of God” (required reading!).]

Note the flip side. Any feature of our universe that would not be preferred by God (e.g. evil) is a reason that God provides a worse explanation than materialism. Thus, the problem of evil is very relevant to this discussion.

Other issues that could arise

• Is a necessary being a coherent concept? Swinburne doesn’t think so, and so doesn’t think Leibniz’s (and Craig’s) argument succeeds. (What is Swinburne’s argument? Is it a good argument?)
• What is the prior probability of theism vs naturalism? In particular, is God too complex to be an ultimate explanation? Can a mind be fundamental? Can a mind be immaterial? If I can infer from “things with which I am familiar need explanations” to “everything needs an explanation”, can I not also infer from “minds with which I am familiar require a material brain” to “all minds require a material brain”?
• Where are we getting our ideas about what sort of universes God would or wouldn’t prefer? If we have no idea what might be the intentions of God, then theism too would be uninformative about why the laws and the universe take the forms they do, giving it no advantage over naturalism. Swinburne argues that God’s reasons are moral reasons, so any moral knowledge we have gives some information on the intentions of a perfect moral agent.

Conclusion

I think both sides face a substantial burden of proof. Carroll claims that, perhaps uniquely, the the universe and its laws need no explanation. That is one mother of a philosophical claim. Scientists see a few theoretical curves match up with data points and have the nerve to announce that, if you’ll just turn to Chapter 1 of my textbook, Equations (1) – (3), you’ll find the fundamental principles of all reality. No further explanation needed. All deeper questions are meaningless.

Craig faces the Principle of Sufficient Reason. Even his milder version leaps the chasm from the physical to the metaphysical, from the familiar to the fundamental. What is the degree-of-difficulty of that stunt? If the fundamental laws of nature simple and powerful, why not stop there? He must also defend the idea that an immaterial, necessarily-existing, all-powerful, free, benevolent God is a suitable stopping point for explanations, and in particular that it is not disqualified by being too complex.

As I said, this should be interesting.

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Footnote 1: This will depend on one’s view of probabilities. I’m an objective Bayesian. Probabilities characterise states of knowledge. So I can still ask: if all I knew were naturalism (and, say, tautological truths like maths and logic), how plausible would it be that a universe obeying these particular natural laws would exist?