Victor Reppert recently linked to an article on the blog Saints and Sceptics (S&S), “Why Science Makes Theism Likelier than Atheism.” In this blog post, I’m going to critically assess that article.

1. What is the Evidence to be Explained?

S&S begin their article as follows:

Should we view the order of the universe, and our ability to comprehend that order, as evidence of God?

This question suggests two related but independent items of evidence to be explained:

E1. The universe is orderly.

E2. The universe contains intelligent beings able to comprehend that order.

Regarding E1, S&S don’t clarify or explain what they mean by phrases like “the order of the universe” or, elsewhere, “the high degree of order” of the universe. In order to be charitable, I’m going to “steel man” their argument by assuming they are appealing to something similar to what Christian philosopher Richard Swinburne calls the “arguments from spatial and temporal order” in his book, The Existence of God.  The argument from temporal order appeals to the fact that “there are regular successions of events, codified in laws of nature.”[1] The phrase “regular succession of events” is key; this is why, I suppose, Swinburne calls it the argument from temporal order. In contrast, the argument from spatial order appeals to the fact that, given our universe conforms to simple, formulable, scientific natural laws, “our bodies are suitable vehicles to provide us with an enormous amount of knowledge of the world and to execute an enormous variety of purposes in it.”[2] This “steel man” interpretation seems highly charitable, since E1 seems to correspond with Swinburne’s argument from temporal order, whereas E2 is very similar to Swinburne’s argument from spatial order.[3]

Accordingly, we may clarify E1 as follows.

E1′. The universe conforms to simple, formulable, scientific laws.

With the evidence to be explained sufficiently clarified, let’s unpack their argument.

2. What, Precisely, Is the Argument?

Before I can turn to the logical structure of S&S’s argument, let’s first review some notations which will make it easier to summarize the argument in a concise form.

Pr(x): the epistemic probability of any proposition x

Pr(x | y): the epistemic probability of any proposition x conditional upon y

“>!”: “is much more probable than”

“>!!”: “is much, much more probable than”

T: theism

A: atheism. A is logically equivalent to ~T.

The first premise of the argument is a simple statement of E1′:

(1) E1′ is known to be true, i.e., Pr(E1′) is close to 1.

Let’s now return to S&S:

Let’s start with atheism. From an atheistic perspective, there doesn’t seem to be any explanation for the order in the universe; it would just be a brute fact or a ‘happy accident’ as Polkinghorne puts it.

But that doesn’t seem good enough. In the absence of an explanation, we would have no reason to expect the high degree of order that we find. But does theism fare any better? To many it seems very likely that if the universe is the product of an intelligent mind, it would exhibit order.  …

So the second premise of the argument seems to be:

(2) An orderly universe is antecedently much more probable on the assumption that theism is true than on the assumption that atheism is true, i.e., Pr(E1′ | T) > Pr(E1′ | A).

The third premise is a simple statement of the evidence E2.

(3) E2 is known to be true, i.e., Pr(E2) is close to 1.

Returning to S&S:

But does theism make an intelligible universe – especially one which is governed by comprehensible laws and which can described by mathematics – any more likely? …

If our minds are the result of design we could rely on them to discover the truth. Rational rulers used laws to govern – and God was the ruler of the universe. And it would not be surprising to discover that mathematics could describe the universe if the divine mind and human minds were analogous in at least some respects. Finally if the universe is created by a good God, he would not systematically deceive us. In light of these considerations, Kepler and his fellow scientists were surely right to think that there is much more reason to expect an intelligible universe if there is a God than if there is not.

So the next premise seems to be:

(4) An intelligible universe is antecedently much more probable on the assumption that theism is true and an orderly exists than on the assumption that atheism is true and an orderly universe exists, i.e., Pr(E2 | T & E1′) > Pr(E2 | A & E1′).

Finally, S&S concludes:

And so the conclusion of their argument is:

(5) Therefore, theism is a much, much more likely explanation for the order and intelligibility of the universe than chance, i.e., Pr(T | E1′ & E2)  >!! Pr(chance | E1′ & E2).

We are now in a position to concisely state the argument in its logical form.

(1) Pr(E1′) is close to 1.

(2) Pr(E1′ | T) > Pr(E1′ | A).

(3) Pr(E2) is close to 1.

(4) Pr(E2 | T & E1′) > Pr(E2 | A & E1′).

(C) Therefore, Pr(T | E1′ & E2)  >!! Pr(chance | E1′ & E2).

Let us now turn to evaluating the strength of this argument. While I have many objections to this argument, let me present just four.

3. First Objection: The Argument Ignores Intrinsic Probabilities

This argument is a deductive argument about inductive probabilities. As stated, however, the argument is incomplete. It does not contain any premises regarding the prior probabilities of theism and atheism. But Bayes’ Theorem shows that posterior or final probabilities are a function of two things: prior probability and explanatory power. S&S write much about the latter, whereas they are completely silent about the former. This invalidates their argument. It’s possible that (1) – (4) could all be true and yet the conclusion, (C), still might not follow if the prior probability is extremely low.

In order to repair the argument, S&S would need to add a premise to their argument which explicitly addresses the prior probabilities of theism and atheism. Now, applying the concept of a “prior probability” to a metaphysical hypothesis like theism is tricky. It isn’t clear from S&S’s article which propositions they would include in their background information for the purpose of assessing a prior probability, and I do not know of a non-controversial way to choose such propositions. Fortunately we don’t have to solve that problem; another option is to replace “prior probability” with “intrinsic probability.” As the name implies, an intrinsic probability is the probability of a hypothesis based solely on intrinsic factors relating to its content (i.e., what it says); it has nothing to do with extrinsic factors, such as the relationship between a hypothesis and the evidence to be explained.

In an attempt to “steel man” S&S’s argument, I propose that we adopt Paul Draper’s theory of intrinsic probability, which says that the intrinsic probability of a hypothesis is determined by its scope, its modesty, and nothing else. Draper explains modesty and scope as follows.

a. Modesty: The modesty of a hypothesis is inversely proportional to its “content”—to how much it says. Hypotheses that say less—for example, because they make fewer claims or less specific claims or claims that are narrower in scope—are, other things being equal, more likely to be true than hypotheses that say more.

b. Coherence: The coherence of a hypothesis depends on how well its components fit together.

c. If we abstract from all factors extrinsic to a hypothesis, then the only thing that could affect the epistemic probability of that hypothesis is how much it says and how well what it says fits together. No other factors affecting probability could be intrinsic to the hypothesis.

Using these criteria, we’re now in a position to compare the intrinsic probabilities of theism and atheism. Before we do that, however, we need to start with the intrinsic probabilities of naturalism and supernaturalism. Here’s Draper:

4. The intrinsic probabilities of naturalism and supernaturalism

a. Naturalism is the statement that the physical world existed prior to any mental world and caused any mental world to come into existence.

b. Supernaturalism is the statement that the mental world existed prior to any physical world and caused any physical world to come into existence.

c. Otherism is the statement that both naturalism and supernaturalism are false.

d. Naturalism and supernaturalism are equally probable intrinsically because they are equally modest and coherent. Since the intrinsic epistemic probability of otherism is greater than zero, naturalism and supernaturalism are each less probable intrinsically than their denials. (So both naturalists and supernaturalists bear a burden of proof and that burden is equal.)

5. The intrinsic probabilities of theism and atheism

a. Theism is a very specific version of supernaturalism and so is many times (i.e. at least 10 times) less probable intrinsically than supernaturalism.

b. Naturalism is a specific version of atheism and so is many times less probable than atheism.

c. Thus, since naturalism and supernaturalism are equally probable intrinsically, it follows that atheism is many times more probable intrinsically than theism, which entails that atheism has a high intrinsic probability (certainly higher than .9) while theism has a very low intrinsic probability (certainly lower than .1)….

Let me introduce a bit more notation:

Pr(|x|): the intrinsic probability of any proposition x

Using that notation, we are now in a position to add the missing premise to S&S’s argument:

(5) Atheism is many times more probable intrinsically than theism, i.e., Pr(|A|) > .9 >!! Pr(|T|) < .1.

Unfortunately for S&S, however, it is far from obvious that the evidence to be explained, E1′ and E2, outweigh the very low intrinsic probability of theism. Accordingly, it’s far from obvious that the conclusion, (C), follows from premises (1)-(5).

4. Second Objection: Pr(E1′ | A) May Be Inscrutable

My second objection to S&S’s argument is that Pr(E1′ | A) may be inscrutable. If it’s inscrutable, then they can’t compare Pr(E1′ | T) to Pr(E1′ | A). Accordingly, the truth of (2) would be unknown. While I’m open to the possibility that (2) is true, I cannot figure out a way to defend it.

Why think Pr(E1′ | A) is inscrutable? In the context of E1′, A is a catch-all hypothesis. A is logically equivalent to A conjoined with all possible explanations for temporal order in the universe apart from theism.[4] For example:

A1: A is true, and the explanation for temporal order in the universe is naturalistic explanation #1.

A2: A is true, and the explanation for temporal order in the universe is naturalistic explanation #2.

…

An: A is true, and the explanation for temporal order in the universe is naturalistic explanation #n.

That’s a lot of potential explanations. Accordingly, this constitutes a prima facie reason to be skeptical of the claim that Pr(E1′ | A) can be known well enough to support a comparative claim such as (2). The only way to reject this prima facie reason would be to identify some intrinsic feature of A which either ruled out a naturalistic explanation for E1′ or which made such an explanation antecedently less likely than it would be on T. Is there such a reason?

Let’s reconsider part of what S&S write in support of (2):

From an atheistic perspective, there doesn’t seem to be any explanation for the order in the universe; it would just be a brute fact or a ‘happy accident’ as Polkinghorne puts it.

By “brute fact,” I assume that S&S mean “a fact which has no explanation.” By “happy accident,” I assume that Polkinghorne means due to chance. But “brute fact” and “happy accident” hardly constitute an exhaustive set of the possibilities. Let me add just one more to the list: factual necessity. Metaphysical naturalism (as defined in the Draper quote, above) is antecedently very probable on the assumption that atheism is true. If metaphysical naturalism is true, then it seems highly plausible that physical reality — whether that consists of just our universe or a multiverse — is factually necessary.  If physical reality is factually necessary, it seems highly plausible that temporal order could also be factually necessary. But if temporal order is factually necessary, then it is just factually necessary and there is nothing for atheism to explain.

Admittedly, the hypothesis, “our universe and its laws are factually necessary,” is highly speculative and not known to be true. But, to paraphrase a point once made by CalTech physicist Sean Carroll, theists like S&S are the ones proposing bizarre thought experiments involving the fundamental laws of nature. So we have to consider such speculative possibilities due to the very nature of the topic and the argument. In any case, this much is clear: S&S give no evidence of having even considered, much less addressed, such a possibility.

5. Third Objection: The Conclusion Confuses Atheism with Chance

My third objection is closely related to my point about factual necessity.

The conclusion of the argument does not follow from the premises because the conclusion compares theism to chance, not theism to atheism. But, as we’ve just seen, atheism functions as a catch-all hypothesis. Atheism is compatible with the proposition, “The universe and its temporal order are factually necessary.” N.B. That proposition denies that the order of the universe is due to chance. And S&S provide no reason to think that chance is antecedently much more probable on atheism than factual necessity.

6. Fourth Objection: The Argument Commits the Fallacy of Understated Evidence

As is the case with E1′, I’m open to the possibility that E2, either by itself or when conjoined with E1′, is evidence favoring theism over atheism.[5] In other words, I’m open to the idea that (4) is true. I don’t think S&S have successfully shown this, however. Rather than pursue that objection here, however, I’ll leave that as an exercise for interested readers. Instead, I want to pursue a different objection: even if (4) were true, it would commit the fallacy of understated evidence.

Let’s suppose, for the sake of argument, that the intelligibility of the universe really is evidence favoring theism over atheism. Given that the universe is intelligible, the fact that so much of it is intelligible without appealing to supernatural agency is much more probable on naturalism than on theism. (I’ve defended this argument at length elsewhere, so I will refer interested readers to that defense.) Since naturalism entails atheism, it follows that this evidence favoring atheism over theism.

The upshot is this: even if the intelligibility of the universe is evidence favoring theism, there is other, more specific evidence relating to its intelligibility which favors naturalism (and hence atheism) over theism. It’s far from obvious that the former outweighs the latter.

7. Conclusion

As we’ve seen, there are four good objections to S&S’s claim that science makes theism more likely than atheism. I conclude, then, that S&S’s argument is not successful.

Notes

[1] Richard Swinburne, The Existence of God (second ed., New York: Oxford University Press, 2004), p. 153.

[2] Swinburne 2004, p. 154.

[3] The main or only difference between Swinburne’s argument from spatial order and S&S’s E2 is that the former also appeals to our ability “to execute an enormous variety of purposes” in the world, whereas the latter does not.

[4] Herman Phillipse, God in the Age of Science? A Critique of Religious Reason (New York: Oxford University Press, 2012), 258.

[5] For what it’s worth, I think E2 is much more promising than E1′ as a potential source of theistic evidence.