Okay, the title of my post is a little misleading. A more accurate, but less catchy, title for my post would be, “Confessions of a Skeptic of the Multiverse Objection to the Fine-Tuning Argument.” Whew! Just trying saying that five times fast!

On a serious note, I’ve mentioned before that I am not convinced by appeals to the multiverse hypothesis to probabilistic versions of the fine-tuning argument (FTA). In this post, I will try to explain why.

Informal Critique of the Multiverse Objection

According to the multiverse objection (M), a ‘fine-tuned’ universe is just as probable on naturalism as on theism since, for all we know, there could be multiple (or even infinite) universes. Since the physical laws in each of these universes are random, there is bound to be at least one, if not many, life-permitting universes; we just happen to live in a life-permitting universe.

The problem with M is that, in the absence of any independent evidence for a multiverse, the multiverse hypothesis is ad hoc. On the assumption that naturalism is true, we have little or no antecedent reason to expect a multiverse to exist. Therefore, unless or until physicists or cosmologists discover evidence that a multiverse actually exists, the multiverse is a weak objection to probabilistic versions of the FTA.

Formal Critique of the Multiverse Objection

Consider the following formulation of FTA.

Abbreviations

>!: much greater than
F: the universe is fine-tuned for life
T: theism
N: naturalism

Argument Formulated

(1) F is known to be true.
(2) Pr(F | T) >! Pr(F | N).
(3) N is not intrinsically much more probable than T.
(4) Other evidence held equal, Pr(T) > Pr(N).

The Multiverse Objection

According to the multiverse objection (M), (2) is false because, for all we know, there could be multiple (or even infinite) universes. Since the physical laws in each of these universes are random, there is bound to be at least one, if not many, life-permitting universe. We just happen to live in a life-permitting universe.

At first glance, M seems irrelevant to the above formulation of FTA, since (2) compares the antecedent probability of F on theism to the antecedent probability of F on naturalism, not naturalism conjoined with an auxiliary hypothesis about the multiverse. So how could M be relevant to (2)?

Those of you who have read my other recent postings can probably predict what I’m going to write next. Using the probability calculus, we can measure the effect that an auxiliary hypothesis like M has on Pr(F/N). In order to assess the evidential significance of an auxiliary hypothesis like M, we would simply need to consider a weighted average, as follows:

This formula is an average because Pr(M/N) + Pr(~M/N) = 1. It is not a simple straight average, however, since those two values may not equal 1/2.

The weighted average formula above gives us some insight into what would need to be the case in order for M to be a good defeater for the FTA. I assume we all agree that the second half of the right-hand side of that equation, Pr(~M/N) x Pr(F/~M&N;), is not going to be useful for deriving a high value for Pr(F/N). (Otherwise, there would be no need to introduce M in the first place!)

So we’re stuck with the first half of the right-hand side: Pr(M/N) x Pr(F/M&N;). In order for M to be a good defeater of the FTA, then, Pr(M/N) x Pr(F/M&N;) needs to be high, the higher the better. The problem, however, is that we have little or no reason to believe that Pr(M/N) is high, i.e., we have little or no reason on naturalism (alone) to expect multiple universes. If Pr(M/N) is not high, then there is no reason to believe that Pr(F/N), as a weighted average of Pr(M/N) and Pr(~M/N), is high. So, unless there is independent evidence for M–i.e., evidence that is independent of the evidence for F–it appears that using M as a defeater against FTA fails and fails miserably.