Journal of Analytic Theology, Vol. 6, May 2018
© 2018 Lydia McGrew   •  © 2018 Journal of Analytic Theology

Of Generic Gods and Generic Men:
The Limits of Armchair Philosophy of Religion

Lydia McGrew

Abstract: Thomas Crisp has attempted to revive something akin to Alvin Plantinga’s Principle of Dwindling Probabilities to argue that the historical case for the resurrection of Jesus does not make the posterior probability of the resurrection very high. I argue that Crisp’s argument fails because he is attempting to evaluate a concrete argument in an a priori manner. I show that the same moves he uses would be absurd in other contexts, as applied both to our acquaintance with human beings and to evidence for divine intervention. Crisp’s attempt to relate the evidence for a specific act of God such as the resurrection to generic theism, thereby creating skepticism about the power of the evidence, is symptomatic of a larger problem in the philosophy of religion which I dub “separationism” and which has characterized the work of both advocates of classical apologetics and philosophers of science.

1. Introduction

In Warranted Christian Belief (2000, 268–80), Alvin Plantinga uses what he calls the Principle of Dwindling Probabilities to counteract historical evidential apologetics, arguing that the probability for mere theism sets an upper boundary on the probability for the resurrection of Jesus and that the probabilities “dwindle” as we add more and more premises to bridge the gap between theism and robust Christianity.

Plantinga’s argument was subsequently refuted when it was shown that he had misconstrued the structure of the historical apologetic argument (McGrew 2004, McGrew and McGrew 2006, McGrew and McGrew 2009, 644–50). Plantinga was attempting to use the probability of theism based merely upon general background knowledge, such as that used in arguments of natural theology, to set an upper boundary on the final probability of the resurrection and Christianity. But the specific historical propositions of Christianity, such as the resurrection, should be based upon an enhanced, updated body of evidence, including specific testimonial evidence for the resurrection. The prior probability of theism, not based upon this specific evidence, in no way sets an upper boundary upon the posterior probability of Jesus’ resurrection given all available evidence. The Principle of Dwindling Probabilities as used against the historical argument for Christianity merely confused a prior probability with a posterior probability.

Thomas Crisp (2009, 190–201) has subsequently attempted to revive a modified version of the Principle of Dwindling Probabilities. Though Crisp realizes that it isn’t in general true that the prior probability of generic theism sets an upper boundary upon the probability of a more specific thesis based on additional evidence, he argues that, in the particular case of theism and the resurrection, the prior probability of theism (or something close to it) actually does set such an upper boundary. He proceeds to argue that historical evidence doesn’t, and perhaps can’t, give us a high posterior probability for the resurrection of Jesus.

Crisp’s argument fails for a number of reasons. First, a likelihood ratio that he emphasizes and argues to be inscrutable or close to 1 is arguably quite top-heavy instead, which undermines his argument. Second, it is epistemically confusing to focus on that likelihood ratio in any event and even worse to try to estimate that ratio by estimating its parts separately. Such an approach is clearly wrong in everyday cases. Consistently applied, it would make it difficult or impossible to infer that we have had contact with other agents at all. It also discourages engagement with relevant, specific data supporting concrete propositions.

Crisp’s modus operandi is symptomatic of a wider problem in the philosophy of religion that I dub “separationism”––a focus on mere theism, artificially separating mere theism from more specific theistic claims, without the recognition that minimal theism can be supported strongly and indirectly by evidence that directly supports a more specific proposition.

2. Crisp’s version of the dwindling probabilities argument

Crisp’s probabilistic argument that “we have no good reason for thinking” that the probability of Jesus’ resurrection on all evidence is “extremely high” (2009, 200) is crucially based on two points, only one of which I will respond to in any detail. The failure of his argument at either of these points is sufficient to rebut it.

The point that I will not respond to at length is Crisp’s dismissive attitude toward the arguments of pure natural theology. Of this evidence, all taken together, Crisp merely says that it is “strong but not knockdown” (199) and “good but not knockdown” (201) and illustrates by assigning a probability to minimal theism on the evidence of natural theology that “isn’t much higher than .5” (199). Since this is intended to place an upper bound upon the force of these arguments, it seems a somewhat breezy approach to the combined force of the cosmological argument (in all of its versions), teleological argument (in its various versions), the argument from consciousness, and the ontological and moral arguments.1 But this would be a long paper indeed if I undertook to show that the probability of theism on all of this other evidence is much higher than .5, so I will not attempt that here, merely noting that Crisp’s brisk statements of opinion do not constitute anything like a knock-down argument.

If, however, the evidence of natural theology (and other evidence independent of the specific evidence for the resurrection) is not sufficient to give theism a high probability, then Crisp’s other argument comes into play. Crisp argues (197) that the assertion that Jesus rose from the dead nearly entails minimal theism, since the resurrection is normally construed as a supernatural act. For purposes of streamlining and strengthening Crisp’s argument and my responses, I am going to construe the resurrection in what follows in such a way that it actually does entail mere theism––that is, I will construe the resurrection as a supernatural act. If a minimal version of theism is entailed by the resurrection, then, since the resurrection is not in turn entailed by mere theism, mere theism is a strictly logically weaker claim than the statement that the resurrection occurred. In any given probability distribution, the probability of the strictly weaker claim sets an upper bound on the probability of the strictly stronger claim. Therefore, if mere theism has a merely modest probability aside from the consideration of the specific evidence for the resurrection, and if the resurrection has a very high probability once that evidence is taken into account, the evidence for the resurrection itself must have a robust positive impact upon the probability of minimal theism.

Crisp argues that this robust impact of the historical evidence upon minimal theism is quite implausible. His argument is based on what he deems to be the near inscrutability (or weakness) of the likelihood ratio comparing the probability of that specific evidence given theism to the probability of that evidence given the negation of theism:



where eR is specific historical evidence taken to support the resurrection and T is minimal theism.2

The posterior probability of theism, after conditionalizing on eR together with background evidence, is higher than its prior probability just in case the above ratio is top-heavy. Moreover, the posterior probability of theism is much greater than its prior only if the above ratio is strongly top-heavy.3 It follows from all of this that, if the likelihood ratio of eR vis a vis minimal theism is inscrutable or close to 1, the posterior probability of minimal theism cannot be much greater than its prior. And, if the posterior probability of minimal theism sets an upper bound on the posterior probability of the resurrection, then, if both the prior and the posterior probability of minimal theism are merely modestly high, the posterior probability of the resurrection cannot be more than modestly high. Crisp tries to be generous, asking what would happen if one treated the allegedly “inscrutable” ratio as being as high as 2 to 1 (199). This gives him a probability of generic theism, on the evidence of the resurrection, of about .67 (assuming its prior probability was no more than .5). He points out that, even here, the final probability of the resurrection isn’t much higher than the prior probability of generic theism.

In the end, Crisp estimates that the posterior probability of theism (here he seems to mean a slightly stronger version of theism) on all evidence “falls somewhere in an interval like [.7–.9]” (201). He is thus apparently giving some sort of weight for theism to the historical evidence concerning the resurrection but does not permit us to say with any confidence that either theism or the resurrection has a very high posterior probability.

3. The evidence for the resurrection and theism

It is rather remarkable that Crisp should get this far in his argument without considering any of the specifics of the historical evidence for the resurrection. His entire allusion to that evidence consists of a short list of some propositions involved (such as the empty tomb and the disciples’ post-crucifixion experiences and martyrdoms) and a list of some authors who have made an historical argument for the resurrection. Can we really reason thus from our armchairs that specific historical evidence doesn’t have the power to make a specific occurrence more probable than some modest upper bound, without any detailed consideration of the force of that evidence itself? Something does not seem to be right with this procedure.4

I submit that Crisp’s argument begins to go wrong when he pooh-poohs the likelihood ratio



Here is his argument at that point:

So is it top-heavy? Hard to say. Minimal theism says there is some god or other, some powerful non-physical person, but tells us almost nothing about this being. Hard to see then why minimal theism should generate any expectation that we’d see something like [eR], something we’d expect not to see given the denial of minimal theism. I’d think the above ratio either inscrutable (who knows what [P(eR|T)] is) or not too far above 1 (198).5

This is less than compelling. Very often we have much better access to a ratio taken as a whole than to its separate parts, a point on which I shall have more to say later. Moreover, it is badly mistaken to imply (as Crisp appears to do here) that it is required for us to expect evidence E given some hypothesis H in order for E to favor H heavily. Because we are considering a ratio, the factor can be huge––many orders of magnitude greater on the top than on the bottom––without having a numerator that is particularly high in any absolute sense.

Oddly, Crisp has nothing to say at this point about the improbability of the evidence for the resurrection if minimal theism is false. Of course, if one thinks that the evidence for the resurrection is pretty easily explained by fraud on the part of the disciples or by hallucinations or “group storytelling” or some other such skeptical hypothesis, then perhaps the probability of that evidence would not be extremely low on ~T, just as it would not be extremely low on ~R––that is, it might be poor evidence both for the resurrection and for theism because it is well-explained in naturalistic terms. But at no point does Crisp attempt to make that argument. Moreover, those arguments––attempts to explain the evidence for the resurrection in a naturalistic fashion––are precisely what advocates of the historical argument have been at pains to answer at length. So surely Crisp cannot treat the likelihood ratio he is concerned about as inscrutable or little better than 1 by assuming that the evidence for the resurrection isn’t particularly improbable given only natural events.

The weight of his argument, instead, lies entirely on the difficulty of judging P(eR|T) all by itself. This is evident in the above quotation and also a couple of pages later when he returns to the point, discussing the arguments of Richard Swinburne:

[Swinburne] proposes that it is somewhat unlikely, though not very unlikely, we’d have the sort and strength of evidence we do for Jesus’s life and resurrection if God had incarnated himself, suggesting that the relevant probability is something in the neighborhood of .1....He then proposes that it is ‘very unlikely indeed’ we’d have that sort and strength of evidence if God hadn’t incarnated himself, suggesting a probability here of .001....Take the first probability. Swinburne has argued in various places..., plausibly to my mind, that we should expect a certain amount of divine hiddenness, a certain amount of ‘epistemic distance’ between us and God,....How much distance should we expect? Should we expect the distance on display in the sort and strength of evidence we have for Jesus’s life and resurrection? Should we expect more distance than that? Less? I have no idea. I think we have no principled way of answering such questions. Consequently, I think we have no principled way of assigning a number like .1 to the above probability, and thus no principled reason for thinking Swinburne’s ratio nearer 100:1 than, say, 2:1 or 5:1 (Crisp, 200, emphasis added).

This passage is noteworthy for two things: Crisp moves immediately to the numerator of the likelihood ratio in question––the evidence for the resurrection given (in the context of Swinburne’s argument) God’s decision to become incarnate––and argues from divine hiddenness that it is inscrutable. He ignores the case that the denominator of the ratio is very low and any insight that the lowness of the denominator might give concerning the overall size of the ratio and goes straight for the difficulty he sees in estimating the numerator all by itself. Moreover, Crisp quite clearly assumes (as the phrase “and thus” indicates) that the only way to estimate a ratio is to estimate its parts separately, rather than accessing the approximate magnitude of the ratio (e.g., the fact that one part appears to be many orders of magnitude higher or lower than the other) as a whole. This same strategy is evident in the earlier passage concerning the ratio he is considering––the ratio showing the force of the evidence for the resurrection vis a vis generic theism.

But once again, it is not necessary to know both parts of a ratio separately in order to see that the ratio tilts one way or another and even get a sense of how strongly it tilts (McGrew 2003, 560, 564). Crisp is much too quick to throw around the word “inscrutable” and to assume that there is what one might call a “transitivity of inscrutability” principle according to which, if any one part of a mathematical expression is difficult to get a clear grip on all by itself, the entire expression must be utterly beyond our ken. In fact, there is no such principle in probability theory, and it is in many cases quite obviously false.6 I will have more to say about this point below.

I propose that we consider the claim that the denominator of the ratio––that is P(eR|~T)––is microscopically low and see what we can learn from that point. On this subject, there is evidence and to spare. To begin with, if there are no supernatural beings whatsoever, then it is overwhelmingly improbable that Jesus’ dead body would actually resuscitate by some purely natural process after being in the grave from Friday to Sunday. Not only is there no known natural process that would have that effect. We also know in modern scientific terms, in some detail, why dead bodies lying in graves stay dead given only natural processes.

At the crudest inductive level, we know quite well that dead people who lie in graves for several days not only stay dead but are known to stay dead. The vast majority of human deaths are followed by nothing remotely like the evidence for the resurrection. The dead person’s friends don’t abruptly become convinced that he has returned to life. His tomb isn’t found empty. So even considered inductively, if there are no gods in this world, if even mere theism is false, the overwhelmingly most likely thing to happen after Jesus of Nazareth dies is...nothing. No evidence for a resurrection at all.

But we can do much better than mere induction. Besides those authors with whom Crisp shows acquaintance but with whose arguments he does not interact in any detail (Wright 2003; Craig 1989; Davis 1993; Habermas 1987, and Swinburne, 2003), there is an extensive body of work with which Crisp appears to be unacquainted (some published since he wrote, some long before), showing at length and in detail that the disciples did indeed stubbornly testify to extensive, polymodal post-resurrection interactions with Jesus and that their so testifying in the socio-religious context in question is enormously improbable given nothing but natural causes. (See, e.g., Sherlock 1765, Paley 1861, Rawlinson 1860, Orr 1908, Thorburn 1910, Shaw 1920, McGrew and McGrew 2009.) These lengthy arguments, which I am not going to attempt to give here, at a minimum make a case worth considering that the probability of eR given only naturalistic explanations is almost inexpressibly low.

Given the lowness of the denominator, it is actually quite plausible that the ratio as a whole is strongly top-heavy. For if even mere theism is true, there is at least an Actor on the stage who might well have the capability of bringing about the evidence by the simple and direct means of actually raising Jesus from the dead. Moreover, Jesus claimed to be (at least) sent from God, a prophet, so raising him would not be a meaningless, trivial, or arbitrary act. (More on this point later.) Presumably it would indicate that the deity meant to endorse him, which is a distinct possibility. It would be a way for the deity to communicate with mankind. It isn’t necessary to have a specific probability of the evidence on theism to see that the existence of a deity is a game-changer as far as the probability of a miracle like the resurrection.

4. The artificiality of considering the evidence in relation to mere theism

I am quite happy to admit, even to insist, that there is something a bit strained about trying to think about the ratio on which Crisp’s attention is focused, as I have done in the last section. This unnaturalness may give rise to a feeling that one does not have a good grip upon the size of



The problem, however, lies not in some weakness in the historical case for the resurrection. Instead, it lies in the artificiality of trying to relate the evidence directly to mere theism rather than relating it to the actual topic at issue––namely, the resurrection. Why are we taking all this trouble to consider the likelihood ratio for eR in relation to minimal theism rather than, more straightforwardly, considering the likelihood ratio of eR in relation to the resurrection? It is fairly straightforward, for example, to consider that Jesus would be visible, tangible, and capable of carrying on conversations if he really physically rose from the dead; hence, his friends’ claims to have seen and talked with him at length would be more likely if he really rose from the dead than if he remained dead.

Crisp presumably would say that the reason we must consider the likelihood ratio between eR and mere theism is because that ratio has to be fairly high if mere theism has a merely modest prior but a high posterior when this evidence is taken into account. But it simply doesn’t follow from that mundane probabilistic point that it is epistemically helpful to think about that likelihood rather than the more obvious



Nor are we obligated to consider the less perspicuous



even if we think of mere theism as entailed by the resurrection. And it creates even more potential confusion to fret over the numerator of that ratio and to argue that we can’t get a strong historical case for the resurrection from eR if we don’t have a good grip on P(eR|T).

To see how artificial and misdirected this entire method is, consider an analog in our other interactions with agents and their attempts to communicate with us. One morning I open my e-mail inbox and find a message purporting to be from someone named Ante Tiric, living in Croatia, who is interested in philosophy. My correspondent asks me several philosophical questions that promise to inaugurate an interesting conversation.

Now, let’s suppose, to make the case more interesting, that before receiving this communication I was so ignorant of geography that I had never even heard of Croatia. This is my first encounter, as far as I know, with any Croatian. Ex hypothesi, I have very little idea how interested Croatians are in philosophy. And I have no independent evidence on the question of how likely any Croatian would be to want to make personal contact with me. How much “Croatian hiddenness” should I expect? I have no idea. Certainly there is nothing about “minimal Croatianism” that generates any expectation of my receiving the e-mail. A good argument could be made that, in the extremely loose sense of “inscrutable” that Crisp employs, P(eA|C) is “inscrutable,” where eA is “The evidence seeming to indicate that I have received an e-mail from Ante Tiric” and C is “minimal Croatianism”––namely, the proposition that some Croatian or other exists. Now, if we define “Ante Tiric” by a Russellian definite description that includes, inter alia, his being a Croatian, then the richer proposition A entails C (minimal Croatianism), but not vice versa. So the probability of minimal Croatianism is necessarily higher in any distribution than the probability of the complex thesis that Ante exists and wrote me an e-mail. Moreover, since I was previously ignorant of the existence of Croatia, the prior probability of minimal Croatianism was low. So if the posterior probability of A––that Ante exists and wrote me an e-mail––were very high on the basis of the e-mail, this would have to mean that eA had a strongly top-heavy Bayes factor vis a vis minimal Croatianism, that is, that



was quite top-heavy. But alas, I have very little idea of the value of P(eA|C). Applying Crisp’s method concerning the specific evidence for the resurrection to this situation, I should pay little attention to



that is, the ratio representing the strength of the evidence of the e-mail for A, which is the more obvious proposition to which to relate eA. Instead I should focus narrowly on the difficult-to-assess probability that I would receive this type of e-mail if some Croatian or other exists. Having thrown up my hands in despair, due to my inability to give that probability any definite value, I should declare that the value of the e-mail evidence for minimal Croatianism is “inscrutable” or perhaps close to 1––that is, forceless. Hence, I should conclude, the posterior probability of minimal Croatianism can’t be much higher than its prior probability, which was low. Hence, the posterior probability of A isn’t very high on the basis of this e-mail either. Perhaps I shouldn’t bother responding at all.

That reasoning, of course, is quite absurd. We routinely and rationally move in daily life directly to the conclusion that particular agents exist and are communicating with us, on the basis of complex data suggesting as much, without giving a moment’s thought to the relationship of that data to a more minimal proposition entailed by the salient specific hypothesis. No one needs to stop to worry about the relationship of a given (apparent) encounter with a friend to the proposition, “Some other minds exist.” If I meet my first Irishman at a bar, I don’t need to bother about the fact that I could not previously have assessed the probability that his accent would sound like that or that he would have spoken thus, or that I would have met such a person there at all, if Irishmen in general exist. We are capable of rational “first contact” with a type of agent that we have never encountered before, and this means that we rationally relate evidence directly to complex propositions about particular persons even if we would have had little idea of the probability of our evidence given that some person or other of that type exists. The evidence that this specific agent has acted in the world is simultaneously evidence for both the richer and the stripped-down claims.

No doubt, in the Ante e-mail situation, if I were forced to stop and think about it, I could make a stab at an argument that



is top-heavy, along lines similar to the argument about the evidence for the resurrection in the previous section. If no Croatians exist at all, then the probability is very low that I would get an e-mail purporting to be from a fictional country. Even a spammer would presumably choose a real country to refer to. What possible motive would my correspondent have to say that he is from Croatia if no Croatians whatsoever exist? Whereas if some Croatian or other exists, there is at least the possibility that I will receive e-mail from one of them, which in turn would explain my evidence very easily. This gives us some grip on the ratio taken as a whole even if we have little grip on its numerator by itself. I could do something similar for a given apparent encounter with a friend and the existence of other minds and for the existence of Irishmen and the meeting in the pub. But there is still that sense of strain in thinking in that way, and it is psychologically easier to see that the ratio favoring the existence and activity of a particular Croatian, friend, or Irishman is top-heavy than to contemplate a ratio relating the evidence to a more abstract proposition.

The connection to the argument for the resurrection is fairly obvious. There is no more reason to require the evidentialist to give a specific value to P(eR|T)––the probability of our particular evidence for the resurrection on minimal theism––as a condition of showing that the posterior probability of R is high than to require me to give a value to P(eA|C)––the probability of my e-mail given minimal Croatianism––as a condition of concluding with high confidence that Ante exists and has e-mailed me. The mere fact that we can distill out of the probability calculus a mathematical expression that must have a particular shape if an argument is strong does not mean that we have to have clear access to all of the separate mathematical parts of that expression in order to see the force of the argument. This is as true in the philosophy of religion as it is anywhere else. Our evidence that directly supports the existence and activity of a specific God who raised Jesus from the dead can very strongly support that proposition even if we don’t know how to assess the probability of that evidence given only that some God or other exists. There is no rationale whatsoever for holding the epistemically clearer argument hostage to an abstract question that is bound to be more difficult to get a grip on.

5. Separationism: A broader error in the philosophy of religion

Crisp’s confusions are symptomatic of a broader confusion in the philosophy of religion which I will dub “separationism.” Separationism is the idea that we are epistemically obligated to separate the question of the existence of God (in some sense of “God”) from claims of particular divine acts in the world and evaluate these propositions independently.

There are, roughly, two varieties of separationism. The first kind of separationism concerns the prior probability of generic theism. On this view, arguments from evidence for particular acts of God (such as eR) cannot support their conclusions unless generic theism already has, on independent grounds, a probability that meets some threshold k. Hence, an atheist or agnostic is never rationally obligated to think of putative evidence for particular miracles as challenging to his view, since his prior probability for generic theism is below k.

A statement of this brand of separationism comes from J.L. Mackie, referring to the attempt to use miracles as an argument for theism, presented to an atheist or agnostic.

Here one party to the debate is initially...agnostic, and does not yet concede that there is a supernatural power at all. From this point of view the intrinsic improbability of a genuine very great, and one or other of the alternative explanations in our fork will always be much more likely – that is, either that the alleged event is not miraculous, or that it did not occur....

      This entails that it is pretty well impossible that reported miracles should provide a worthwhile argument for theism addressed to those who are initially inclined to atheism or even to agnosticism.... Not only are such reports unable to carry any rational conviction on their own, but also they are unable even to contribute independently to the kind of accumulation or battery of arguments referred to in the Introduction. To this extent Hume is right.... (Mackie 1982, 27, emphasis added)

Mackie is not merely making a psychological or sociological point. It is clear that he considers his point to be normative: The atheist or agnostic is, according to Mackie, justified in dismissing the putative evidence for a miracle because the existence of a supernatural power does not, he believes, have a prior probability of at least k.

Nor does this type of statement of prior separationism come only from atheist philosophers. It can also be found in Christian philosophers and theologians. Here is the Thomist Edward Feser, sounding surprisingly similar to Mackie:

A sophisticated naturalist supposes that he has good reason to think events like resurrections just can’t happen, and good reason to think the body of religious teaching associated with this particular resurrection story is a priori implausible.  So unless this set of general background assumptions is first undermined, he will understandably think himself perfectly justified in shrugging his shoulders and dismissing even the strongest evidence for the Resurrection as just one of several odd pieces of data we find here and there in history –– a curiosity perhaps, but not something that could by itself undermine what he takes to be an otherwise well–established naturalism. (Feser 2014, emphasis added)

Feser’s point, in context, is that arguments from natural theology (which he deems to be very strong) must precede any argument from miracles, where the “must” appears to be an epistemic and normative matter rather than merely a matter of sociological usefulness.

Similarly, a trio of Protestant theologians make a strongly separationist statement.

Natural theology shows that there is a God. If there is a God, miracles are possible. If a God exists who created the world and operates it, there can be no doubting that He can modify His modus operandi. On the other hand, if we did not know that there is a God, we would have to step into an irrational view of the operation of nature by chance....[M]iracles cannot prove God. God, as a matter of fact, alone can prove miracles. That is, only on the prior evidence that God exists is a miracle even possible (Sproul, Lindsley, Gerstner 1984, 146).

Probabilistically speaking, this sort of separationism is flatly inaccurate. Evidence supporting all parts of the complex proposition that, say, God raised Jesus from the dead is ipso facto evidence supporting the proposition that there is some God or other, and there is nothing about the prior improbability of the existence of some God or other that limits the force of evidence for a particular God. A prior improbability does not create a limitation on the extent to which some subsequent piece of data can support the previously improbable proposition. One may think that the evidence for the resurrection isn’t all that strong. That’s as may be, and can be decided only by examining it. But the evidence tending to show that a particular God has acted in some particular circumstance doesn’t become rationally weak simply because one doesn’t already believe in any deity.

One can see this point schematically in the odds form of Bayes’s Theorem:

The first expression is the ratio of the prior probabilities––say, the probability of theism and the negation of theism. The second is the ratio of the likelihoods––the probability of the evidence given the hypothesis over the probability of the evidence given its negation. The ratio after the equals sign is the ratio of the posterior probabilities––the probability of the hypothesis given the evidence over the probability of its negation given the evidence. No matter how large the first ratio is (the ratio of the priors), the ratio of the likelihoods could, in principle, be large enough to overcome it.

This probabilistic point––that any non-zero prior improbability can in principle be overcome by evidence for the proposition––has been explained in detail by John Earman in his examination of the failure of Humean objections to miracles (Earman 2000, McGrew and McGrew 2009, 637–44), so I will not belabor it here. W.E. Gladstone’s remark is apt:

For the present let it suffice to bear in mind that there is no limit to the strength of working, as distinguished from abstract, certainty, to which probable evidence may not lead us along its gently ascending paths (Gladstone 1896, 349).

The prevalence of separationism at the level of the priors indicates a great oddity in the philosophy of religion. The very existence of the arguments of natural theology seems to have led to demands placed on those arguments that handicap all other kinds of arguments. Hence, if the arguments of natural theology are not “made first,” and if they are not sufficient to bring the prior probability of generic theism up to at least k, then, we are told, arguments for more particular versions of theism would be forceless. Surely this is very strange. If anything, the arguments of natural theology should be a bonus for the theist. In what other area do we even purport to have purely a priori or metaphysical arguments showing the existence of some kind of thing, totally independent from arguments for a particular entity of that kind? No one thinks that we have purely a priori or metaphysical arguments (based only, say, on the minimal claim that something exists) that some Croatians or other must exist, that some planets or other must exist, or that some other minds or other must exist. In all of these instances we are forced to make do with more particular arguments. We justifiedly believe that some Croatians exist if we appear to have contact with some particular Croatians. We believe that some planets or other exist by encountering evidence for specific planets. And we see that other minds exist by way of our evidence that our parents and friends exist. If we did have metaphysical, armchair arguments for these types of things, that would fine, but it would be epistemically highly confused to insist that such arguments must be strong enough to make the general proposition probable all by themselves, independent of the more specific evidence. It might be easier for me to believe that I have received a letter from a specific Croatian if I have already seen Croatia on a map, but this doesn’t produce an epistemic principle that only Croatia can prove Croatians or that I would be perfectly justified in shrugging off the letter as a fake without first seeing the country on a map.

I do not say any of this to indicate that I think the arguments of natural theology weak. Indeed, in an earlier section I suggested that Crisp is overly dismissive of them. They may be extremely strong. But something is very wrong if the mere fact that theologians and philosophers do argue for and against generic theism causes us to say that natural theology arguments must be strong or else arguments for more particular versions of theism can have no place, are forceless, or could not possibly have enough force to support theism. It is difficult to avoid the sense that the artificiality of philosophy of religion and the prominent place of natural theology within the discipline has led to the development of misguided principles about the nature of evidence in this area, principles that have no justification and would obviously be absurd in other contexts.

A similar point arises when one considers the other version of separationism––separationism concerning the likelihoods. Crisp’s argument falls into this category. Separationism concerning the likelihoods consists of the demand that we know separately the probability that God, if he existed, would do something before we can be justified in attributing a specific outcome to divine action. Crisp’s exclusive focus on P(eR|T) and his insistence that the evidence for the resurrection can’t do much if we don’t know P(eR|T) exemplify this kind of separationism. But Crisp is not alone in this error. Philosopher of science Elliott Sober demands that we know independently what goals God would have if he existed in order to be justified in attributing some action to God. Speaking in the context of the debate over evolution and design, Sober asserts,

The problem is that the design hypothesis confers a probability on the observation only when it is supplemented with further assumptions about what the designer’s goals and abilities would be if he existed....There are as many likelihoods as there are suppositions concerning the goals and abilities of the putative designer. Which of these, or which class of these, should we take seriously?

      It is no good answering this question by assuming that the eye was built by an intelligent designer and then inferring that the designer must have wanted to give the eye features F1 ... Fn and must have had the ability to do so since, after all, these are the features we observe. For one thing, this pattern of argument is question–begging. One needs independent evidence as to what the designer’s plans and abilities would be if he existed. One can’t obtain this evidence by assuming the design hypothesis is true....

      This objection to the design argument is...continuous with the precepts of “negative theology,” which holds that God is so different from us and the world we already know about that it is impossible for us to have much of a grasp of what his characteristics are....We are imagine a designer who is radically different from the human craftsmen we know about. But if this designer is so different, why are we so sure that this being would build the vertebrate eye in the form in which we find it? (Sober 2004, 10–11)

As we saw when discussing Crisp’s similar argument, the requirement of “independent evidence as to what the [agent’s] desires and abilities would be if he existed” is completely foreign to our normal and apparently rational means of coming to know other agents.7 If someone I have never met before introduces himself to me at a party, I do not need independent evidence as to what his goals would be if he existed in order to regard his speaking to me as evidence that he exists and desires to communicate with me. I would not even have developed a concept of that person had we never met, so of course I don’t have any prior idea of how likely he would be to approach me at a party if he existed. Nor is there anything question-begging about this inference. I rationally infer both that this person exists and that he wishes to communicate with me from the evidence of his (apparently) approaching me and speaking.

Sober’s idea seems to be that God is different from all ordinary agents and hence that these commonsense analogies do not apply. (This objection is similar to Crisp’s reference to divine “epistemic distance.”) Since the kind of inference Sober envisages is comparative, he implies that the action of a God much unlike ourselves cannot participate in a contest with other hypotheses because we have no independent idea about what God would or would not do.8 In the context of the design argument, Sober goes so far as to say that the argument about the design of creatures will come to have “practical meaning” only in the future when it is “stripped of its theological trappings” by humans’ acquisition of the ability to build living creatures from non-living matter. Then it will be possible to argue about intelligent design concerning just those living entities around us that could have been made by human beings, but only because in that context it will have “nothing to do with whether God exists.” (Sober 2004, 23) In other words, an argument that some action was performed by an agent can be reasonably made only when we already know that any agent who could have been involved was much like ourselves. Hence, in principle, no agent-action argument can be made when the agent in question would be a deity.

This argument, however, seems to require that all theists consider only the existence of a God who is unable to reveal himself to mankind by signs in the world. Consider some putative evidence of divine communication eD, where D stands for “a divine being has attempted to communicate with human beings.” Sober’s argument seems to imply that



will be no better than 1 so long as we are invited to imagine a God radically different from ourselves. But why assume that the ways in which God is radically different from ourselves render that ratio no better than 1 for any eD? Surely the person making the theistic argument need not assume a God who is so much different from ourselves that we could never be rationally justified in thinking that a given action is his act. Indeed, to demand that of the theist seems like a form of question-begging in and of itself––that is, question-begging against the hypothesis that a God exists who does reveal himself by acts in the world (see L. McGrew 2013).

Consider the following propositions:


1)    If God exists, he is (by definition) personal.

2)    If God exists, he is (by definition) capable of acting in the world miraculously.

3)    If a personal God exists, it is not ridiculous to imagine that he might wish to communicate with man, either to convey the fact that he exists or to convey substantive truths about himself.

4)    If God exists, he is (by definition) wise and hence knows that he cannot communicate with man except by events or facts that man is able to recognize as salient––standing out from all of the rest of the events in the world. If he wishes to convey substantive semantic content, he knows that he must do so in a way that man can understand.


These quite modest consequences of the hypothesis that a personal, wise, powerful God exists (which is still a fairly minimal T) are quite enough to give us reason to believe that there is some eD such that



is significantly greater than 1, without knowing what P(eD|T) is as a separate quantity and without knowing detailed information about God’s goals. If this is all that is meant by having “independent evidence as to what [God’s] plans and abilities would be if he existed,” the demand is fairly easily satisfied. The eD might be, for example, apparent miracles associated with a putative prophet or messenger from God. It might be an audible voice, speaking in a language the hearer understands. Or it might be what appears to be real, detailed teleology, similar to what we know agents otherwise produce (see L. McGrew 2004), in some aspect or aspects of the physical world.

Taken with strict consistency, the argument that God is too much unlike ourselves to participate in a comparative inference to the best explanation because of the absence of independently justified auxiliary assumptions would make it impossible to count as evidence even something quite radical. If stars, viewed from planet Earth, spelled out, “Repent and turn to Yahweh” in English, Mandarin, and Latin, we would have to admit that we did not know independently that God, if he existed, would choose to reveal himself in this way. Sober’s complaint about the eye would apply just as well (or as poorly) to this scenario. The hypothesis that God designed the stars to form these words “confers a probability on the observation only when it is supplemented with further assumptions about what the designer’s goals and abilities would be if he existed.” But “there are as many likelihoods as there are suppositions concerning the goals and abilities of the putative designer. Which of these, or which class of these, should we take seriously?” The same argument could be made if each cell individually were inscribed with the words “Made by Yahweh” in a recognizable human language. Indeed, the more specific we make the scenarios, the more we have to admit that we don’t have independent knowledge that God would desire to carry them out. But that doesn’t prevent us from recognizing scenarios that would be evidence for God’s action. This seems like a reductio of the demand for independent justification concerning what specific action God would take if he existed.

Nor does one need to use entirely hypothetical examples for such a reductio; we can also use biblical examples. What if you were personally present and heard what sounded like a voice from the sky endorsing Jesus at his baptism? What if you were able to check out the facts surrounding the alleged resurrection of Lazarus? What if you saw the Red Sea part or the fire fall from heaven on Elijah’s altar? In none of these cases do we have any clear idea of P(eD|T), nor independent knowledge of the “goals and abilities” that a generic God would have if he existed, pertaining to these specific events, yet it seems absurd to say that such evidence would not support the conclusion that God had intervened. This type of reductio applies to Crisp’s argument as well, for it is highly dubious to say a priori that the posterior probability of divine action in these cases could not be high merely because we cannot get a grip on the probability of the specific evidence given generic theism.

I am not arguing, aside from concrete evidence, that God certainly would want to reveal himself if he exists. My claim is more modest.9 It is merely that we should not block the course of inquiry by setting P(eD|T) so low for all eD (putative evidence of divine communication) as to make it impossible for there to be good evidence favoring the conclusion that God has specially acted in the world.

Consider again the mundane case of the e-mail from Ante Tiric. Suppose that the probability that a Croatian will wish to contact me if any Croatian exists is zero. In that case, I could never receive any evidence that would raise the probability that some Croatian has deliberately made contact with me. But even if the probability is not set so low as zero, if it is set as low as or lower than the probability that I will receive what purports to be communication from a Croatian if there are no Croatians, the effect is the same: I can never receive evidence of communication from a Croatian. Such an extreme probabilistic assumption seems entirely unmotivated and closed-minded.

On any reasonable approach, I could receive evidence significantly raising the probability that a Croatian is attempting to contact me and could even draw that conclusion. As discussed in the previous section, the Bayes factor showing the force of the evidence for the hypothesis that a specific person has sent me an e-mail might be much easier to grasp clearly than the Bayes factor concerning Croatians in general. The fact that the latter (the Bayes factor for generic Croatianism) is quite top-heavy may be clearer in hindsight, on the basis of considerations that allow me to see that the Bayes factor for a specific putative contact with a specific Croatian is top-heavy. Similarly, if we do not artificially set the probability that God would want to reveal himself if he existed so low as to make it impossible for us to recognize any divine communication, we are free to look at the Bayes factor ratio for some particular E, such as the evidence for the resurrection of Jesus or the evidence of intelligent design in nature, and ask, on the basis of all the specifics of the situation, whether it is strongly favorable to that particular conclusion.

There could, of course, be reason to think that God would not make use of some alleged means of communication. Suppose that we include benevolence in a particular version of theism. Then if it turns out that a supposed prophet is cheating people out of their money, we have reason against God’s acting to endorse that person’s message. If the event in question would unambiguously and directly encourage a person in wrong or irrational behavior, such as murder or compulsive gambling, we are probably justified in assuming that a benevolent God would not intervene to bring it about. Aside from benevolence, an action that would be pointless or trivial, such as rearranging the chairs in someone’s living room, with no context that would make this significant as divine communication or as a sign, will not count as an eD that has a top-heavy Bayes factor, since there is little or no greater reason to think that God would rearrange the chairs than to think that some finite person did so.

The mention of triviality brings us to a slightly different objection––namely, that God’s involvement in all matters in the world eliminates our ability to attribute any outcome to God more than any other. On this view, the most trivial events or arrangements of matter, such as the particular arrangement of water droplets on a window in a rainstorm, would be (if God existed) as much the result of divine action as a man’s resurrection from the dead; therefore, there is nothing that makes a resurrection from the dead stand out as attributable to God. We might call this the Gilbert and Sullivan objection: If everybody’s somebody, then no one’s anybody. If everything is an act of God, then no event in the world is salient qua act of God. Gregory Dawes articulates this objection in terms of a poltergeist who is responsible for everything that happens in a room.

To illustrate this point, let me go back to Swinburne’s poltergeist scenario, modifying it a little. Let’s posit the existence of a poltergeist who is responsible for both the existence and the behavior of every object in the room. We can then ask, “Why did the inkwell fly across the room?” On this scenario, it would be true that “the poltergeist did it.” But this proposition lacks empirical content. It constitutes nothing more than the beginning of an answer to our question. For if the inkwell had simply fallen to the floor, the same answer could be given. And if the inkwell had not moved at all, the poltergeist would also be responsible, for he would have chosen to maintain it in existence in its current position....[The existence of the poltergeist] alone would not constitute an adequate explanation, since it would not single out the event to be explained from any other event. (Dawes 2009, 45)

But why should someone arguing for a miracle or divine revelation be forced to assume that God is involved in the same sense in all events in the world? Surely this is rather a strong and dubious view of divine causation. Given that God might want to reveal himself to man, given that such revelation would not be a trivial or unworthy undertaking, and given that man would need to be able to recognize a revelatory act as special, we ought to be open to the possibility that special divine action will look different from God’s “background” activity in the world, whatever we call that. To make that general divine involvement so central as to rule out the possibility of recognizable, salient special divine action is deliberately designed poor theology, a kind of a priori deism, guaranteed to close the mind to any attempted divine sign or communication.

Separationism, then, is unjustified for the likelihoods as well as for the priors. There is no good argument for demanding separate evidence, independent of the eD in question, that shows how likely some outcome would be if God exists or that God’s goals would favor that outcome. If the skeptic (or anti-evidentialist) wishes to argue that the eD in question is definitely something God would not do to reveal himself or that for some other reason it does not probabilistically favor the hypothesis of special divine action, he will need to argue that on the basis of the specifics. A general allusion to divine mysteriousness or to the differences between God and his creatures will not do the job.

6. Conclusion

Divine transcendence is no small matter, and I do not at all mean to dismiss or scoff at the notion that God is very much unlike his creatures. But if the theistic hypothesis is taken by definition to refer to a God so distant, so mysterious, so much unlike ourselves that it is in principle impossible for him to reveal himself to rational creatures, something has gone wrong. At that point we are justified in considering instead the explanatory prospects of a God who is capable of interacting with and willing to interact with his creation in recognizable ways.

Crisp’s somewhat idiosyncratic attempt to revive something that resembles Plantinga’s Principle of Dwindling Probabilities thus provides an entrance into a broader problem of a priori objections to empirical theistic inferences.

In all these instances I propose as a rule of thumb the following: If a philosopher or theologian is arguing that a paradigmatically empirical or historical question is decidable by paradigmatically un-empirical methods, check his assumptions. The chances are high that an artificial and unjustifiable rule is being imposed upon the inference. Once such a rule is made explicit, it should be abandoned, permitting the evidence to speak for itself.




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1 Not to mention such “extras” (which would be separate from the specific evidence for the resurrection) as the argument from fulfilled prophecy.

2 I am silently changing Crisp’s notation to my own. He uses R for the detailed historical evidence for the resurrection (197) and C for the proposition that the resurrection occurred (194), taking this notation from Warranted Christian Belief (Plantinga 2000) and the subsequent debate between Plantinga and McGrew (McGrew 2004, Plantinga 2006, McGrew and McGrew 2006).

3 The converse of the second sentence does not hold. It is possible for the likelihood ratio to be very top-heavy while the difference between the prior and the posterior is fairly small. This happens, for example, when the prior probability is already quite high so that there is little “space” for it to increase even when additional, strongly favorable evidence is taken into account. Crisp, however, denies that the prior probability of theism is very high.

4 Crisp is open about the a priori nature of his argument, and he does not seem to see anything odd about it. After listing several writers who have argued that Jesus rose from the dead, Crisp says that their arguments don’t show the probability of the resurrection “anywhere near 1” and says, “Here’s why” (197). He then launches into a discussion, using the Theorem on Total Probability, of the points I am responding to (197–200). So he apparently thinks that he can tell that empirical arguments for an event don’t make the probability of the event very high, merely by the armchair method of noting difficulties with relating the evidence to some more minimal proposition.

5 Here again I am changing Crisp’s notation to my own.

6 There is also a distinction to be maintained, which Crisp does not maintain, between in-principle inscrutability and mere difficulty seeing some probability. The former is better understood as the meaninglessness of a probability expression. For example, one could argue that there is, literally, no such thing as the probability of a single ticket’s winning an infinite lottery. Crisp’s use of “inscrutable” is far looser and hence more readily answered.

7 Elsewhere Sober asserts that the need for independently justified auxiliary assumptions is normative in scientific practice. Auxiliary assumptions, he says, must be independently justified (2004, 13); one must have independent reason to believe that they “are true” (1999, 54, 57). But the issue of distributing blame for an anomalous outcome between a main hypothesis and auxiliary hypotheses, and the sharpness of the distinction itself, is understandably controversial in the philosophy of science (see, for example, Strevens 2001 and Dorling 1982). Such a clear distinction cannot be taken as a given in the philosophy of religion and especially should not be assumed to apply to explanations concerning the actions of personal beings.

8 Gregory Dawes (2009, 141) makes a similar argument from divine mysteriousness.

9 In this regard my claims here are similar to but even more minimal than the arguments of Swinburne in The Resurrection of God Incarnate (2003), Chapter 2.


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