Monday, April 25, 2022

Rowe-style inductive arguments from evil

The examples, like Rowe’s, of evils in the inductive argument from evil are chosen to make them have a certain epistemic feature F. And the claim is that P(E has F | God) < P(E has F | no God), with the background information containing the occurrence of E (i.e., the evidence isn’t that the evil has occurred, but that the evil has F). Exactly what F is differs from paper to paper, but roughly the feature is that after investigation we don’t have a plausible candidate theodicy.

But not every evil has F. If every evil had F, then the examples in the literature wouldn’t run as heavily as they do to lethal harm to children and animals. The examples used by the atheological arguers are chosen to be particularly compelling and what makes them compelling is that they have F—nobody runs an inductive argument from evil based on robber barons getting stomachaches from too much caviar, because such evils do not have F.

So there are evils that don’t have F. And then P(E has F | God) > P(E has F | no God) by Bayesianism. So checking whether an evil has F sometimes yields an argument against the existence of God (namely when the evil does have F) and sometimes yields an argument for the existence of God (when the evil doesn’t have F).

And we do not know (as far as I know, Tooley is the only one to have made a serious attempt to figure it out, and his account fails for technical reasons) what the result is once the evidence is consolidated.


Alexander R Pruss said...

Some arguments make F be such that ~F entails the existence of God. For instance, F could be: we do not know the reasons God actually has for allowing E. In that case, the atheist will not grant that there are Es that have ~F. But that seems to me to be a bad way to run the argument from evil, because we should argue from stronger evidence if we can, and the stronger evidence is that we do not know reasons that God *would have* (if we he existed) for allowing E.

Walter Van den Acker said...


But why would a robber barron having a stomach ache be more.probzble on theism?

Alexander R Pruss said...

I was thinking of the evil being the stomachache, not the robber baron's existence. :-)

Walter Van den Acker said...

So was I, so how is his stomachache more probable on theism.

Lydia McGrew said...

Alex, I think perhaps there is a probabilistic mistake here in your reasoning.

Let evidence E in the evidential PoE be

"There are evils that have property F."

If this is evidence against theism, then it's correct to say that ~E must be evidence for theism. (Though as a digression, I shd. point out that the evidences can be of vastly different magnitudes.)

But the correct statement of ~E is

A: "It is not the case that there are evils that have property F."

To say, B: "There are evils that do not have property F" is not to state ~E, nor does it follow from "E is evidence against theism" that B is evidence for theism. B is fully compatible with either E or ~E.

Alexander R Pruss said...

That there are evils that have F is quite unsurprising on theism if it's part of the background that there are lots of evils. If there are lots of evils, even if none are gratuitous, it's unsurprising that some look gratuitous. Just as, if there are lots of cats, it's unsurprising that some look like dogs.
So the evidence I am interested in is that a particular token evil E has or lacks F.

Lydia McGrew said...

But no one who is actually pressing the evidential POE is going to grant that given theism it is highly likely that there are lots of evils, much less that in that case it's likely that some will look gratuitous. (Btw, I've never seen a cat that looked like a dog, and I've seen lots of cats, so I'm not sure I would even grant your premise. But let's make it even crazier--given there are lots of cats, is it unsurprising that some look like jellyfish? elephants? airplanes?)

I take it that the person pressing the POE is arguing that some evils really *are* gratuitous, though perhaps granting that this is a fallible but highly well-supported premise, and then is taking the E to be that there are evils that are gratuitous. In which case, the negation is what I've stated--that there are no evils that are gratuitous.

The occurrence of acknowledged trivial evils--a paper cut, stubbed toe, brief tummy ache--simply doesn't seem to tell either way. In fact, I have trouble seeing how anyone could argue that the existence of trivial "evils" is evidence *for* theism. It's certainly readily compatible with there either being or not being gratuitous evils, and for that matter it's readily compatible with there either being or not being evils that *look* gratuitous.

So this just isn't a case of saying that if E is evidence against H, then ~E must be evidence for H.

And if you aren't reasoning from that probabilistic fact, I'm not seeing how you're getting so quickly to the conclusion that, "There is a token evil that lacks property F" must be evidence for theism.

Lydia McGrew said...

I'm going by the fact that you said that "by Bayesianism" P(E has ∼F | God) > P(E has ∼F | no God).

So in the op you seemed to be stating this as somehow following from "Bayesianism" in some direct, clear way from the axioms of probability and something you had already said. And I'm just not seeing that at all. I really think you must have been confusing (E has ~F) with ~(E has F). A scope shift of the negation sign into the parentheses.

Alexander R Pruss said...


1. The post says that the background include that E has occurred. Given that background (or given classical logic where all names, such as E, refer), ~(E has F) is equivalent to (E has ~F).

2. You are apparently right about cats. I just googled "cat that looks like a dog", and while I got a number of feline looking dogs, I didn't get any cats that looked like dogs. But that surprised me! One would kind of expect that the world's most doglike cat would look rather doglike. But I suppose not.

3. Regarding the "many evils" thing, I was taking it as part of the background that there are many, many evils, and thinking that in the inductive argument what we want to evaluate is the additional evidence arising from those evils that appear gratuitous.

4. Some trivial evils look gratuitous and some do not. It's the gratuitousness, not the triviality, that I am interested in. We can look at it like this. Theism makes a controversial prediction: There are no gratuitous evils. Some evils appear to confirm this prediction and others appear to disconfirm it.

5. It is possible to make a direct argument on the basis of the existentially quantified claim that there are gratuitous evils. But generally, that's not what the literature starting with Rowe looks like. Most of that literature is focused on specific example evils -- a fawn burning to death, etc. -- and their apparent gratuitousness.

Lydia McGrew said...


(I'll number these responses according to your numbering in your last comment so I don't have to copy bits of them. Please excuse typos. In my current technology set-up I'm particularly typo-prone and don't always see them.)

Re #1: Not equivalent for the confirmation-theoretic purposes that you are using it, no. In fact, the way that you are using it arguably commits a confirmation-theoretic fallacy, because we are always required to conditionalize on the most specific relevant version of the evidence we possess. And the more specific evidence can point in a different direction from the evidence as described in soft focus. To see this, consider an urn model. In the set-up, there is a ball in the urn. That's given. There are three possible colors the ball could be, all equiprobable--red, white, or blue. We are given that if the ball is blue, this is evidence for H, if the ball is white, it is neither evidence for nor against H, and if the ball is red, it is evidence for ~H. From this set-up it follows that if *all we know* is that the ball is non-blue, that proposition is evidence for ~H. However, suppose that we draw the ball and find that it is white. While it is true that being white entails being non-blue, it is *not* true that the evidence of the draw of the ball supports ~H. Not everything that entails ~blue has the same confirmation-theoretical consequences as ~blue has when that is all that we know. This can be described as a failure of screening. "The ball is non-blue" does not screen off the probabilistic impact/relevance of "the ball is white" from H, even though "the ball is white" entails "the ball is non-blue."

So, no, even if "this event has the property of being an evil that appears gratuitous" is evidence against theism, it does not follow that any particular evil E, with its further-known properties, is evidence *for* theism *merely* in virtue of lacking the property of appearing gratuitous. Hence we should not simply say that if we examine an evil and find it not to be gratuitous, that is evidence for theism.

Re. #2: For real things in the real world, it isn't generally possible epistemically to tell from one's armchair whether "There are lots of As" makes it probable that "Some real As look like Bs even though they aren't." That *entirely* depends on what A and B are! (Hence my example of cats and elephants.) I don't think any skeptic should ever grant that "there are lots of evils" probabilifies that "some of them will appear gratuitous" much less what presumably you need which is "some of them will appear gratuitous even though they really aren't."

Lydia McGrew said...


Re. #5: I'm not going to claim to know what is in Rowe's mind, and maybe you are right to say that he and others aren't arguing from "There exists some gratuitous evil." But the mere fact that they're focusing on specific properties of specific events, like fawns burning in a forest, doesn't mean that they aren't doing so. If I were doing that (focusing on specific properties), I would be arguing approximately thus: Consider these specific events of a type that undeniably occur. (E.g. Conscious creatures who have done nothing wrong experience intense suffering; innocent people are corrupted by evil-doers and ruin their lives. Etc.) These appear to be instances of gratuitous evil. Therefore, it is highly probable that either these events individually or a subset of them or a conjunction of some or all of them constitutes *actual* gratuitous evil. The occurrence of actual gratuitous evil is significant evidence against the existence of a good God.

Btw, I'm sure it goes without saying (but I've been hanging out, metaphorically speaking, with New Testament scholars for a few years, and they tend to be more touchy than analytic philosophers usually are!)... This is all meant in a spirit of enjoyable give and take. Someone directed me to this blog post and there seemed to me something fishy about the arg., and I'm just trying to work out what it is. There's nothing remotely personal in it, and I hope we can run into one another again sometime.

Alexander R Pruss said...


You are right that we should use the most specific information we have. But sometimes the more specific information is something that we have no idea what to do with--we don't have any insight into the relevant conditional probabilities. For instance, in the lab you weigh a rat as part of a nutritional experiment. You get a ton of other information than the weight of the rat as part of that process: how cooperative is the rat in the weighing process, what color does the rat have, etc. But you really don't know what to do with this other data: you don't have good likelihoods for them on the hypotheses you are investigating. So in the actual practice of science, you delineate, ahead of time, which data you will measure and which data you won't, and you use that.

I'm thinking that apparent gratuitousness is a nice piece of data, because we have a direct prediction from theism that all evils are non-gratuitous. The other features of the evil besides gratuitousness or non-gratuitousness we don't know much what to do with. And our best way to guess at gratuitousness is apparent gratuitousness.

So, in theory, lots of other stuff could be taken into account. But in practice it's really hard to do that.

By the way, some cats do look very much like elephants: early cat embryos. :-)

But I take your point: maybe we can't always expect that there will be things that look other than they are. Maybe all I can do is report my priors: I would expect there to be SOME things that God would permit where I would have no idea of what justifies them, just as I would expect there to be SOME steps that a master craftsman in pretty much any discipline would do that I would have no idea what the point of them is.

Lydia McGrew said...

Alex, As I'll argue below, this is more than merely a theoretical point in this case. First, tho', I'd like to point out that even the theoretical point is important. The o.p. and even a follow-up comment seem to imply that it is a simple matter of Bayesian probability theory that, if the appearance that some evil is gratuitous is evidence against theism, the appearance that an event agreed to be an evil fails to be gratuitous (though how we should pick out *that* event while knowing nothing at first about its more specific properties is a question in itself!) must be evidence *for* theism. Yet here we are, discussing the far less straightforward issue of when and whether some more specific information is relevant to confirmation! So it is *not* a simple and direct consequence of Bayesianism, for the reason that I have stated--not everything that entails some P has the same probabilistic consequences as that which it entails. Hence, tho' "white all over" entails "non-blue all over," "white all over" may have very different probabilistic consequences than "non-blue all over." And it's quite important to avoid this mistake in reasoning, as it can lead us astray. Hence the technical point is important: "This evil does not appear to be gratuitous" may well fail to be evidence for theism, due to the evidence from which we concluded that "this evil does not appear to be gratuitous," even in a situation where "This evil appears to be gratuitous" would have been evidence against theism.

Now, to show that this is not merely theoretical: If we are to treat "appears to be gratuitous evil" as a property of an event (which I have a few metaphysical doubts about since it seem like a Cambridge property at most, but perhaps we can waive that) then "appears to be deserved" is a property and so also is "appears to be of no moral importance." But either of these entails "does not appear to be gratuitous evil." One of them, such as bad guys getting their just deserts, might be said to be loosely evidence for theism, Providence, karma, or something of the sort. We might also argue that "appears to have brought about a greater good" is a "property" that would be favorable to theism. But if a man who has done nothing to deserves it briefly stubs his toe and suffers 60 seconds of easily-endured pain and nothing worse comes of it, this is *also* a category of "does not appear to be gratuitous evil," due in this case to its triviality, and arguably it is neither evidence for nor against theism. So if we have some event in a black box labeled E for "an evil," and we don't know before we open the black box what the specifics are of the event (which frankly your set-up treats as the situation in question, since the event is said to be a specific "evil" apart from its other properties!), we may open it and find the specifics of it which turn out to be such either that it seems to be evidence for or against theism or neither for nor against. Hence the o.p. is incorrect, as far as I can tell.

I'm inclined to agree with you that on theism there could well be some events that we wrongly take to be gratuitous evil, but bringing in our experience with master craftsmen, etc., is doing something quite a bit different than "given that there are many evils, some of them are likely to appear gratuitous." Rather, it's arguing for a particular likelihood given a particular concept of God.

Alexander R Pruss said...


'if a man who has done nothing to deserves it briefly stubs his toe and suffers 60 seconds of easily-endured pain and nothing worse comes of it, this is *also* a category of "does not appear to be gratuitous evil," due in this case to its triviality':

It's not that clear that this is in the category of "does not appear to be gratuitous evil". An evil is gratuitous iff an omniscient and omnipotent being would have had sufficient moral reason not to prevent it. Triviality is not by itself a sufficient moral reason not to prevent an evil. (Suppose there is a heavy object on the floor of a room, and you've seen five out of five people walking into the room stubbing their toes on it. You expect one more person to walk in. If you put a chair in front of the object, it'll prevent that person from stubbing their toe. The effort to put in the chair is even more trivial than the unpleasantness of the stubbing, so you should put in the chair.)

Maybe, though, you are thinking this: if an evil is trivial, it takes a very small reason to justify permitting it, and we cannot have much confidence that God wouldn't have such a reason not to prevent it. So if the evil is trivial, it won't be the case that it appears gratuitous (though it also won't appear non-gratuitous). Is that what you're thinking?

All that said, I think what I was imagining is something like this. You have a block box labeled "evil". You get to ask an honest human expert who was able to examine the contents of the box: "Does the thing in the box appear gratuitous?" And then we look at the evidence coming from the answer.

Now, you are quite right that in practice there is other evidence available. There can be evils that don't positively appear gratuitous but nonetheless could be some evidence against the existence of God: the toe-stubbing could be like that (on my suggested way to make the case work). Conversely, there can be evils that appear gratuitous but are evidence for the existence of God. Suppose a Roman guard observed the resurrection of Jesus but then lied about it. Let E = the Roman guard lied that he didn't see Jesus resurrected. It could be that E appears gratuitous. However, E may nonetheless be evidence for theism, because E entails that the guard thought that he saw Jesus resurrected, and that could add more evidence to theism than the apparent gratuitousness of E adds to atheism.

But whatever other evidence may or may not be available, it is worth examining what the evidential impact of the appearance of gratuitousness _by itself_ is.

Now let's come back to the probability that some evil would look gratuitous, and let me see if I can improve my argument. Take a billion items, and suppose that humans are supposed to judge if one of the items has some property H. Suppose that a part of the background is that determining that an item has H is not trivial and determining that an item has non-H is also not trivial. Then, absent further evidence, we would expect at least one error of judgment, regardless of whether all the items have H, none of the items have H, or some but not all the items have H.

But determining an evil to be gratuitous is non-trivial and determining an evil to be non-gratuitous is non-trivial. So, absent further evidence, given billions of evils (a typical person suffers and/or perpetrates at least one evil per day, I assume), we would expect some cases of erroneous judgment, even if all evils are non-gratuitous. Hence, even if all evils are non-gratuitous, we would expect some cases where humans judge an evil gratuitous, and hence the evil appears gratuitous to them.

(This is assuming that standard facts about human error-proneness are in the background. One might think that these facts are themselves evidence against theism. Examining the import of that evidence is a separate task.)

So, I agree with you that we can't JUST use the number of cases by itself. We need some kind of non-triviality constraint.

Lydia McGrew said...


As I understand your most recent comment, you are taking "appears non-gratuitous" to be something to the effect that we somehow have a very strong intuition that everyone (or almost everyone?) will agree with that the evil is not gratuitous. Your example in the o.p. was of a robber baron getting a tummy ache from eating too much caviar. My guess is that you were clueing there to the aptness of the tummy ache to the crimes that enabled him to eat too much caviar, coupled with the fact that a tummy ache isn't that bad. (So it's not like he's getting tortured to death.) Poetic justice. Hence you assume that everyone will agree that that is non-gratuitous.

However, as you see even from the toe-stubbing incident, this is not always a simple matter. I would argue that pretty much everyone would agree that a good man stubbing his toe and suffering no more than 60 seconds of typical toe-stubbing pain is not gratuitous simply because of the intuition that it is of such little moral weight that God doesn't need a reason not to intervene. Perhaps on the well-known principle embodied in the saying of Horace, "Let not a god intervene unless there be a knot worthy of a god's untying."

I think it's safe to say that Rowe would be unlikely to use an innocent man's non-damaging toe stubbing as an example for his evidential POE. Your whole point in the o.p. concerns the properties of evils in Rowe-style arguments, and these seem to focus on particularly bad things happening to innocent conscious being.

In any event, the very fact that we can disagree about whether or not the toe stubbing has the property of "appears to be non-gratuitous" shows that the particulars matter and that evils don't divide neatly between "appears clearly to be gratuitous" and "appears clearly to be non-gratuitous." There's a third category (and maybe a fourth category too, depending on how we carve it up) that includes cases where reasonable person A will think it fails to be gratuitous and reasonable person B will think that it is. If we take Rowe-style cases (babies dying in horrible pain, fawns burning to death in the woods) to be "clearly appears to be gratuitous," then we can agree that those are interesting in themselves and studying cases that have that property is interesting in itself.

But please remember that your o.p. gave the strong impression that you were considering "appears gratuitous" and "appears not gratuitous" to constitute a partition of evils, so that any evil that does not appear to be gratuitous automatically appears to be non-gratuitous, so that "by Bayesianism" we can find confirmation of theism from every evil that fails to appear gratuitous a la "fawn burning in the forest." Our conversation here has shown that it is no such simple matter. It isn't as though every evil that isn't like a baby dying in horrible pain is automatically like a bad guy getting his just deserts or serving a higher good and therefore something that we can see to be plausible confirmation of theism. Even your "honest human witness" who looks in the black box may give you a "no" answer to "does the evil in the box appear to be gratuitous" and then, if you say, "Oh, good, then it's evidence for theism" he may well demur, due to the fact that there are more relevant categories than "appears to be gratuitous [hence is prima facie evidence against theism]" and "fails to appear gratuitous [hence is prima facie evidence for theism]." I just have to stress that this is a simplistic way of looking at it and definitely doesn't drop out of the probability axioms.

Lydia McGrew said...

I think by non-trivial concerning judgements, what you're intending to build in is something like "not easy." So if a judgement is not trivially easy to make for some type of being, then we'd expect some errors by that type of being over a long run of making such judgements. That's obviously true if for no other reason than that you're building the difficulty and hence the probability of error into the model from the beginning. So if two animals really do look similar from a certain distance, then if people are trying to distinguish them over and over from that distance they are bound to make some errors doing so over the long run. That's fine, and granted.

But notice that *this* argument now simply *confirms* the point I'm making about the larger argument, which is that evils don't come merely in two varieties--really looks gratuitous and hence is evidence against theism" and "really looks non-gratuitous and hence is evidence for theism." If you are going to say that it's hard to make that judgement, then it seems that you should add a middle category at least, "Does not appear to be evidence for or against theism." Rather as if a person saw an animal from a sufficient distance and said that, *at that distance and in that lighting*, he would not say that it looked like a racoon rather than a woodchuck.

Alexander R Pruss said...


I have tried to avoid language like "Does not appear to be gratuitous", because in English it is ambiguous between "Not (Appears to be gratuitous)" and "Appears to be non-gratuitous". My original argument concerned "Not (Appears to be gratuitous)".

I wouldn't take the Horace line uncritically. Maybe, though, we can say that a regularity theodicy easily handles very minor evils: the fact that preventing these evils would disturb the regularity of nature gives God a sufficient moral reason not to prevent them, given the value of the regularity of nature.

I think at the end you make a rather interesting point that does affect my post significantly. If the witness observing the contents of the box instead of giving us a binary "appears gratuitous" / "not (appears gratuitous)" gives us a ternary judgment "appears gratuitous" / "appears non-gratuitous" / "neither appears gratuitous nor appears non-gratuitous", then things are different. Intuitively, "appears gratuitous" is evidence against theism, "appears non-gratuitous" is evidence for theism, and "neither appears gratuitous nor appears non-gratuitous" is either neutral or weaker evidence against theism.

It's still true that even on the ternary approach nobody has done a credible job consolidating all the evidence. My vague intuition is that "neither" outnumbers "appears gratuitous" which in turn outnumbers "appears non-gratuitous". But since we don't really have good numbers for the conditional probabilities of all three on theism/atheism, I don't know what that adds up to on the whole.

Another way of thinking about this is to replace the witness's judgment with "I can't think of any plausible theodicy" / "I can think of a plausible theodicy". Then it sounds more like the binary way of thinking about it is appropriate, but even so, in practice, there will be a richer set of options: "I can think of three higly pausible theodicies", "I can think of one barely plausible theodicy", "I can't think of any theodicy that's close to being plausible". But maybe we have clearer likelihoods for the binary cases than for the richer ones and we should go for the binary ones.

There are difficult questions for Bayesianism in the vicinity: What should we do when we cannot conditionalize on our total evidence because we don't have the relevant likelihoods? Should we conditionalize on the largest available set of evidence for which we do have the likelihoods? Or should we just give up and not conditionalize at all?

Lydia McGrew said...

" My original argument concerned "Not (Appears to be gratuitous)"."

Yes, that's how I took it originally. Which is why I've been pushing all along the point that that is a fairly broad category which, arguably, includes things (maybe even many things) that appear intuitively to be neither evidence for nor against theism.

What I said about the witness looking into the box is just another way of saying what I've been saying all along. It's a way of getting past the strangeness of the whole black-box approach and trying to get closer to what I think is the true epistemic state, in which we are confronted not with events designated with total vagueness as "evils" and then simply told baldly that they either do or don't appear to someone else to be gratuitous but rather are confronted with concrete envisaged events or event-types which we then intuitively judge as to whether they seem like gratuitous evils or not. After all, Rowe uses concrete examples! He doesn't just say, "Take my word for it that I've looked at some actual evils and I'm here to tell you that they look like gratuitous evil to me, never mind the particulars of what this would be like." Which would then be countered by some Christian philosopher saying, "Well, *I've* looked at a *lot* of other evils and they appear to me to be the result of a wise and just Providence, never mind what the particulars are, so there." That would never make a philosophical debate! Which is why the whole "witness looking into a black box" thing is super-odd as an approach. My suggestion of a witness that gives you one of three judgements was another attempt to make it somewhat less artificial in order to bring home what I've been saying all along is a problem with the o.p.--namely, that not every evil that fails to appear to be gratuitous is ipso facto evidence against theism, and that I can think of quite a few examples thereof.

Your last questions are of course big ones. It seems to me a good deal easier in empirical cases, since then we hope to be able to gather more empirical evidence to flesh out our likelihoods. But one point I would make: It isn't always necessary to have separate P(E|H) and P(E|~H) in order to access P(E|H)/P(E|~H). Tim and I have both pointed out that an estimate of the ratio is often more accessible than the separate likelihoods. For example, if I get an e-mail from a new person that gives me some sort of Russellian definite description for him (e.g., a name, an interest or question he has for me) and that appears to come from a real individual, it is *much* easier to see (IMO) that this e-mail is much more probable given that such an individual exists than given that no such individual exists than it is to estimate separately what the probability of the e-mail would be if he existed and what the probability would be if he didn't exist.

How exactly that applies to the evidential POE I'm not sure, but I think it has lots of applications in design arguments.

Lydia McGrew said...

What I get for not proofreading before I hit publish:

Should be, "not every evil that fails to appear to be gratuitous is ipso facto evidence *for* theism, and that I can think of quite a few examples thereof."

Alexander R Pruss said...


It's a good point that the Bayes' ratio can get a decent estimate even when the numerator and denominator can't. I'll need to think about that.

Thanks for all the great comments. You've made me realize that this is a lot more complicated than I thought.

Lydia McGrew said...

Thanks, it's been a lot of fun!