A probabilistic error in Plantinga (Reference Plantinga2011) drew my attention to some difficulties for the author's non-contingent theism, and these difficulties were the subject of Wunder (Reference Wunder2013). Unfortunately I contacted Professor Plantinga too late to incorporate his generous replies into that writing. This article aims to correct that shortcoming by summarizing my previous arguments before addressing what I take to be Plantinga's main replies to them. My conclusion will be that, with the exception of pointing out an exegetical mistake on my part, Plantinga's replies fail to undermine those earlier arguments. In particular, the Evolutionary Argument against Naturalism, when combined with theism's non-contingency, still seems to imply the necessary falsehood of theism.
Plantinga versus Draper
While taking issue with Paul Draper's evolutionary atheology, Plantinga writes ‘the probability of a contingent proposition on a necessary falsehood is 1’.Footnote 1 But this claim is false: the probability of any proposition on a necessary falsehood is undefined; conditional probabilities require that their backgrounds not be necessarily false.Footnote 2
The error is no idle typo. Plantinga's primary argument against Draper depends upon the mistake and is undercut by its correction. The uncorrected argument goes like this. First, theism is non-contingent, either necessarily true or necessarily false: Plantinga claims this is the view of most theists who have thought about such things.Footnote 3 Second, the conditional probability of evolution is much higher given naturalism than given theism: we can symbolize this claim as P(E/N) >! P(E/T). This second premise is the main premise of Draper's argument: it requires P(E/T) to be much lower than P(E/N), but by Plantinga's blunder P(E/T) will be maximal when theism is necessarily false; thus Draper's premise implies theism is not necessarily false. Given the first premise – non-contingent theism – Draper's premise ironically implies necessarily true theism.
The implication is clear: Draper's argument can succeed as atheology only by assuming theism's logical contingency; but that assumption will contradict the theistic majority about the modality of theism. As a secondary argument, Plantinga concludes that, even if Draper's premise is true, there will be multiple phenomena that are more probable given theism than given naturalism, thus providing counterevidence to Draper's premise.
Four arguments
It is important to recognize that logically necessarily true theism implies logically necessarily false naturalism. I previously argued that recognizing this fact while correcting Plantinga's probabilistic error has three devastating consequences for his probabilistic natural theology. I also used a fourth independent argument to turn the the Evolutionary Argument Against Naturalism (hereafter the EAAN) back against its creator. Allow me to summarize these arguments.
First, correcting Plantinga's probability error reveals that Draper's premise contradicts theism's non-contingency outright. Consider that the premise requires that neither theism nor naturalism be necessarily false; if either is necessarily false then one of the conditional probabilities being compared is undefined, thus falsifying the premise. Obviously this rules out theism's necessary falsehood, but it also blocks its necessary truth; for the necessary truth of theism implies the necessary falsehood of naturalism, and the necessary falsehood of naturalism (as just discussed) contradicts Draper's premise. Thus the premise prohibits not just necessarily false theism but also necessarily true theism.Footnote 4
Second, theism's non-contingency contradicts each of the probabilistic claims Plantinga uses as counterevidence against Draper. Take, for example, the claim that the conditional probability of life on earth is much higher given theism than given naturalism.Footnote 5 For the same reasons discussed earlier, this can be true only if theism and naturalism are each logically contingent: if one is necessarily true then the other is necessarily false; and the necessary falsehood of either one falsifies the claim by requiring it to compare an undefined probability. The same can be said of all the probabilistic claims Plantinga makes in this regard.
Third, the EAAN combined with theism's non-contingency entails theism's necessary falsehood. Consider the EAAN's first premise, dubbed the ‘Probability Thesis’: P(R/N & E) is low or inscrutable.Footnote 6 But if theism is necessarily true then naturalism is necessarily false, in which case P(R/N & E) cannot be low or inscrutable: it will be undefined. Only if naturalism is not necessarily false, and so only if theism is not necessarily true, can the Probability Thesis be correct. Given non-contingent theism, the truth of the Probability Thesis will entail the logically necessary falsehood of theism.
There is a final problem for Plantinga's use of the EAAN given non-contingent theism. Take X to be the metaphysics underpinning the origins story for humanity's cognitive faculties. Now consider the conditional objective probability of your having trustworthy faculties (R) against that X. The EAAN crucially presumes that if you find this probability – P(R/X) – is inscrutable, you should, if you comprehend the reasoning behind the argument, realize you have an indefeasible rationality-defeater for everything you believe.Footnote 7 Rather than dispute this presumption, observe how it can serve to turn the sceptical apologetic of the EAAN back upon Plantinga.
Let us begin with a passage from Warranted Christian Belief that addresses R's probability:
But if we are thinking of the absolute probability of R (conditioned only on necessary truths), then I can't claim . . . that P(R) is high: how would I know what proportion of the space of possible worlds is occupied by worlds in which R is true? In particular, the fact that R is true in fact is no reason for assigning it a high absolute (logical) probability.Footnote 8
So P(R) is inscrutable. But by the probability calculus, P(R/necessarily true theism) will equal P(R).Footnote 9 Therefore P(R/necessarily true theism) will be inscrutable. And this, if we are to take the EAAN's crucial presumption seriously, seems reason for the believer in necessarily true theism to contemplate his own slide into the sceptical abyss.
Plantinga replies
Professor Plantinga has very kindly responded to these arguments via e-mail. I will summarize his replies and argue that they do not obviously mitigate the serious problems pointed out here.
Arguments one and two
Curiously, Plantinga's initial reason for the mistaken probability claim was that contradictions imply everything.Footnote 10 He was quick to grasp his mistake, and so I assume he now agrees that Draper's main premise contradicts not just necessarily false but also necessarily true theism. Plantinga cannot have his ironic conclusion that Draper's premise combined with non-contingent theism (non-trivially) implies necessarily true theism.
But my second argument, concerning Plantinga's probabilistic counterevidence against Draper's premise, was based on my misunderstanding of the text. Plantinga explained that in the context of making those claims he had been granting theism's contingency, directing me to the text immediately prior to the introduction of those claims: ‘Draper is of course assuming that theism is contingent; hence his argument won't be relevant if theism is noncontingent. But let's set this limitation aside and look at his interesting argument.’Footnote 11
I had not originally taken this passage to be a clear statement that in what follows theism's contingency is being granted for the sake of argument. Given Plantinga's authorial clarification my second argument seems somewhat deflated, reduced to observing that claims made on the hypothesis of theism's contingency are committed to that hypothesis.Footnote 12 Still, there is some new information for Plantinga here: correcting his mistake reveals that he cannot endorse these claims, while maintaining non-contingent theism, and still rightly profess to hold a logically consistent world-view.
Arguments three and four
The remaining arguments of my earlier paper concerned the combination of non-contingent theism with the premises of the EAAN. Plantinga's main reply here was to concede that the problems I observed did indeed arise when the probabilities in question were objective, but to suggest that the probabilities at work in the EAAN should now be read as epistemic probabilities: epistemic probability, says Plantinga, can disregard the probability calculus.Footnote 13 Therefore the Probability Thesis needn't contradict logically true theism: even if naturalism is necessarily false, P(R/N&E), read epistemically, needn't be undefined. Similarly, Plantinga thinks the conditional epistemic probability P(R/necessarily true theism) is quite high for himself despite the inscrutability of P(R) taken logically; they needn't equal one another, as my effort to turn the tables on him requires, since the former is an epistemic, not objective, probability.
Despite the initial appearance of a reasonable reply, this concession of Plantinga's has significant consequences for the EAAN as it has been defended since its creation over twenty years ago. Every major published version of the argument, of those addressing the distinction between objective and epistemic probabilities, has (thus far) been explicitly presented in terms of objective probability.Footnote 14 While Plantinga frequently suggests the argument can also be construed epistemically, he neither does so himself in those sources nor clarifies how this alternate construal is to be carried out. So Plantinga's concession concerning objective probabilities entails that the EAAN, as it has been defended from its inception until now, has been for all those years a proof of atheism for advocates of logically non-contingent theism.
Obviously this is a bold claim for me to make, so let us see what Plantinga himself says about which sort of probability he has in mind for the EAAN. First up: the original 1991 publication of the argument, ‘An evolutionary argument against naturalism’.Footnote 15 The abstract mentions only objective probability:
Consider the objective conditional probability of our cognitive faculties' being reliable, given that they have arisen by way of the mechanisms sanctioned by contemporary evolutionary theory and given philosophical or metaphysical naturalism, according to which there is no such person as God. I argue that the reasonable attitude to take with respect to this probability is either to estimate it as low or to be agnostic with respect to it.Footnote 16
The next relevant passage also mentions only objective probability: ‘Perhaps Darwin and Churchland mean to propose that a certain objective conditional probability is relatively low . . .’.Footnote 17 The final reference to the matter appears in an endnote specifically addressing the sort of probability being used by the argument:
We could think of this probability in two ways: as a conditional epistemic probability, or as a conditional objective probability. Either will serve for my argument, but I should think the better way to think of it would be as objective probability; for in this sort of context epistemic probability, presumably, would follow known (or conjectured) objective probability.Footnote 18
Moving forward two years to Warrant and Proper Function, Plantinga recycles the just-quoted endnote, nearly verbatim, as a footnote.Footnote 19 There are additional references to objective and statistical probability further in the relevant chapter of the text,Footnote 20 but no more references to epistemic probability. Again, the message is clear: where this argument is concerned, objective probability is preferable to epistemic probability.
Next up is Plantinga's ‘Introduction’ to Beilby (Reference Beilby2002). There Plantinga makes a by-now-standard comment about Churchland (Reference Churchland1987): ‘[p]erhaps Churchland's claim can be understood as the suggestion that the objective probability that our cognitive faculties are reliable, given naturalism and given that we have been cobbled together by the processes to which contemporary evolutionary theory calls our attention, is low.’Footnote 21 Beilby himself renders the argument in terms of objective conditional probability; Evan Fales and Richard Otte, contributors to Beilby's volume, also seem explicitly to see the argument this way.Footnote 22 Plantinga corrects none of them. Of all Beilby's cohorts, only William Alston wonders whether the argument might operate on something other than straightforwardly objective probability, but Plantinga's response to Alston at the end of the volume ignores this issue.Footnote 23
The two most recent major presentations of the argument are contained in Plantinga & Tooley (Reference Plantinga and Tooley2008) and Plantinga (Reference Plantinga2011). Concerning the matter at hand, both sources use nigh-identical text:
The probability we are thinking of here is objective, not the personalist's subjective probability, and also not epistemic probability. (Of course there will be a connection between objective and epistemic probability, perhaps a connection in the neighborhood of Miller's principle; presumably epistemic probability will in some way follow known objective probability.)Footnote 24
Both also include the following in a footnote: ‘It's worth noting that the argument can also be conducted in terms of epistemic probability, although I don't have space here to show how.’
Clearly, Plantinga has preferred to cast the EAAN in terms of objective rather than epistemic probability. But Plantinga cannot consistently advocate the objective version of the argument without committing himself to necessarily false theism. Worse still, even when he grants the argument can be construed in terms of either sort of probability, he routinely claims the epistemic probabilities will, in this case, presumably follow known (or conjectured) objective probability.Footnote 25 But as we have just seen, the advocate of non-contingent theism following objective probability in this case should conclude that theism is logically necessarily false. So it is not at all clear how eschewing objective probabilities and shifting exclusively to epistemic probabilities can save the EAAN for Plantinga.
Where my final table-turning argument is concerned, some naturalists might feel tempted to hard-heartedness. Plantinga has repeatedly presented the EAAN in terms of objective probability: finding that the conditional objective probability P(R/the metaphysics behind one's cognitive origins story) is inscrutable (or low) was supposedly epistemically disastrous. A very stubborn naturalist might suggest that Plantinga, by the consequences of his own prior reasoning, must now take his own medicine. Trying to avoid the problem by replacing objective with epistemic probability begs the question against the defeater which is based on objective probabilities, much like the naturalist's appeal to science (or anything else for that matter) is alleged by Plantinga to beg the question against the EAAN; the move should therefore be blocked for the same reason.Footnote 26
Suppose we are not hard-hearted and allow that the probabilities behind the EAAN can be shifted completely and unproblematically from objective to epistemic. But surely more must be done than simply replacing ‘objective’ with ‘epistemic’ in all the relevant sentences; otherwise Plantinga's clear preference for objective probabilities, and his claim to lack the space to show how to cast the argument epistemically, makes little sense. Since Plantinga has not yet done the work, it is hard to know exactly how the revised argument will look. But it does seem clear that the argument's many appeals to Bayes' Theorem and the probability calculus will need reconsidering: if the revised EAAN is to avoid the same consequence suffered by the objective version of the argument, it cannot use an epistemic probability that conforms to the probability calculus.
But it is not at all clear what sort of epistemic probability that would be. Epistemic probability is much less well understood than objective probability. Plantinga himself judges none of the three main accounts of epistemic probability to be successful, good, decent, or even satisfactory.Footnote 27 Even his own account, though suggested to be ‘the sober truth’ by the subtitle of its chapter, is admitted to be only an outline of ‘the basic idea, making little more than a gesture or two in the direction of a complete and satisfying theory’.Footnote 28 The naturalist taking the EAAN seriously may well ask for something better than this to support that argument's extremely ambitious conclusion.
And even if Plantinga does use his own theory of epistemic probability, there is good reason to doubt that it can escape the probability calculus which accompanies objective probability. He insists epistemic probability is two-faced: one face is objective and thereby bound to the probability calculus; the second face is epistemic/normative, and so it is this component of his account that would have to violate the probability calculus if the new epistemic version of the EAAN is to evade my objection.Footnote 29 But Plantinga thinks this latter component is best interpreted as warrant,Footnote 30 and that one of the necessary conditions of a belief possessing warrant is ‘that the objective probability of a belief's being true, given that it is produced by cognitive faculties functioning in accord with the relevant module of the design plan, is high’.Footnote 31 If this is the ‘sober truth’ of the matter, it seems doubtful that converting the EAAN into an argument of epistemic probabilities is going to help Plantinga avoid the problems that plague the objective probability version of the argument.
Conclusion
In light of my analysis there remains a serious tension between Plantinga's advocacy of logically non-contingent theism on the one hand, and the probabilistic claims he is prone to make on behalf of theism, against naturalism, on the other. The retreat to epistemic probability may seem to provide a tempting escape hatch, but much more work must be done to show how this form of probability can support claims that Plantinga was rather clearly originally making with an entirely different sort of probability in mind.Footnote 32
