Alvin Plantinga‘s ‘evolutionary argument against naturalism‘ (EAAN) goes like this:

1. If humans were created by natural selection, and also not under the guidance of a creator (‘naturalism’), then (for various reasons he gives) the probability that their beliefs are accurate is low.
2. Therefore believing in natural selection and naturalism should lead a reasonable person to abandon these beliefs (among others). i.e. belief in naturalism and natural selection is self defeating.
3. Therefore a reasonable person should not believe in naturalism and natural selection.
4. Naturalism is generally taken to imply natural selection, so a reasonable person should not believe in naturalism.

This has been attacked from many directions. I agree with others that what I have called point 1 is dubious. However even on accepting it, it seems to me the argument fails.

Let us break down the space of possibilities under consideration into:

• A: N&T: naturalism and true beliefs
• B: N&F: naturalism and false beliefs
• C: G&T: God and true beliefs

The EAAN says conditional on N, B is more likely than A, and infers from this that one cannot believe in either A or B, since both are included in N.

But there is no obvious reason to lump A and B together. Why not lump B and C together? Suppose we believe ‘natural selection has not produced true beliefs in us’. Then either natural selection has produced false beliefs, or God has produced true beliefs. If we don’t assign very high credence to the latter relative to the former, then we have a version of the EAAN that contradicts its earlier incarnation: ‘natural selection has not produced true beliefs in us’ is self-defeating. So we must believe that natural selection has produced true beliefs in us*.

What if we do assign a very high credence to C over B? It seems we can just break C up into smaller parts, and defeat them one at a time. B is more likely than C&D, where D = “I roll 1 on my n sided dice”, for some value of n. So consider the belief “B or C&D”. This is self-defeating. As it would seem “B or C&E” is, where E is “I roll 2 on my n sided dice”. And so on.

By this reasoning, if there is any possible world that is self-defeating, pretty much any other possible world can be sucked into the defeat. This depends a bit on the details about how unlikely reliable beliefs must be for belief in that situation to be self-defeating, and how the space can be broken up. But generally, this reasoning allows the self-defeatingness of any state of affairs to contaminate any other state of affairs that can be placed in disjunction with it, and that can be broken into states of affairs not much more probable than it.

It seems to me that any reasoning with this property must be faulty. So I suggest probabilistic self-defeat arguments of this form can’t work in general.

It could be that Plantinga means to make a stronger argument, for instance ‘there is no set of beliefs consistent with naturalism under which one’s beliefs have high probability’, but this seems like quite a hard argument to make. I could place a high probability on A for instance.

It could also be that Plantinga means to use further assumptions that make a distinction between grouping A and B together and grouping B and C together. One possibility is that it is important that N is a cause of T or F, but this seems both ad-hoc and possible to get around. At any rate, Plantinga doesn’t seem to articulate further assumptions in the account of his argument that I read, so his argument seems unlikely to be correct as it stands, all other criticisms aside.

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*Note that if you wanted to turn the argument against creationism, it seems you could also just expand the space to include creators who don’t produce true beliefs, and  depending on probabilities, use this to defeat the belief in a creator, including one who does produce true beliefs.