For scientific materialists the materialism comes first; the science comes thereafter. We might more accurately term them “materialists employing science.” And if materialism is true, then some materialistic theory of evolution has to be true simply as a matter of logical deduction, regardless of the evidence. That theory will necessarily be at least roughly like neo-Darwinism, in that it will have to involve some combination of random changes and law-like processes capable of producing complicated organisms . . .

Phillip Johnson

Johnson’s observation came to mind when I read HeKS comment to a prior post. That comment recasts Johnson’s observation in terms of Bayesian priors. It would be cumbersome to put everything in block quotes. All that follows is HeKS:

“If the probability that mind is responsible for some effect is preemptively set at zero for methodological purposes and only one naturalistic explanation, in its rough outline, is logically possible, then is the probability that the naturalistic explanation is correct actually 1? And does it necessarily remain 1 in spite of what the evidence may tell us?”

I’m not looking for a formula to make a calculation. I’m asking a philosophical question about the effect of presupposition when you are trying to explain some effect where two causes seem logically possible, but the one that is actually known to be causally adequate is ruled out by an a priori philosophical or methodological presupposition.

That said…

p(theory) = [p(theory|naturalism) * p(naturalism) ] + [p(theory|not-naturalism) * p(not-naturalism)]

On Methodological Naturalism (MN), it seems this would be:

P(theory) = [P(theory|naturalism) * 1] + [P(theory|not-naturalism) * 0]

Without knowing the value of P(theory|naturalism) (or, the probability that the theory is true given naturalism is true), we can’t give a final probability percentage. We can, however, recognize that [P(theory|not-naturalism) * P(not-naturalism)] = 0.

On MN, it doesn’t matter what the probability is that the theory is true given naturalism is false, because the probability of naturalism being false is already determined to be 0.

of course, if a naturalistic theory explains data well then it makes p(naturalism) higher:

where

p(observations|naturalism) is p(observations|theory) (or perhaps summed over all naturalistic theories that might explain the observation)

Wouldn’t that be…

p(naturalism|observations) = p(observations|naturalism) * P(naturalism) / [p(observations|naturalism) * p(naturalism)] + [p(observations|not-naturalism) * p(not-naturalism)]

…or am I missing something?

In any case, the problem here is that on MN, P(naturalism) = 1

Methodological Naturalism is the methodological implementation of a philosophical presupposition, not the conclusion of a Bayesian probability calculation. But if we incorporate MN into a Bayesian calculation for the probability that the ‘only viable naturalistic theory’ (ovnt) for some effect is correct, the result is entirely predictable.

P(ovnt) = [P(ovnt|naturalism) * P(naturalism)] + [P(ovnt|not-naturalism) * P(not-naturalism)]

Becomes…

P(ovnt) = [1 * 1] + [x * 0]

[Given naturalism is true (i.e. P(naturalism) = 1), the probability that the only viable naturalistic theory is true is, by logical necessity, 1 (i.e. P(ovnt|naturalism) = 1). Meanwhile the probability that the theory would be true on not-naturalism is ultimately irrelevant because the probability of not-naturalism is 0]

So, this becomes…

P(ovnt) = 1 + 0

Becomes…

P(ovnt) = 1

It doesn’t seem to me that this is the kind of scenario that Bayes Theorem was intended for.

On MN, if we find a singularly viable naturalistic theory to explain something, a Bayesian calculation that takes MN into account will always reveal to us with 100% certainty that the theory is correct.

You obviously get the exact same result if you replace ‘only viable naturalistic theory’ (ovnt) with ‘some naturalistic theory’ (snt). We get certain conclusions we can hold with certainty without the need for any supporting evidence at all. We only need to deduce them from the principle of Methodological Naturalism.

For example, on MN, what is the probability that the Origin of Life came about through purely naturalistic causes without any role played by a mind? Simple. The probability is 1. On MN we can know this with complete certainty even if we never figure out how it could possibly happen.

I’m no expert in Bayesian analysis, but this seems philosophically problematic to me.