bookmark_borderHere’s One Way to Resist Naturalistic Arguments: Lack Belief that Matter Exists!

A Christian apologist writing under the pseudonym ‘InvestigativeApologetics’ stated the usual objection to atheism, namely, that it’s impossible to prove or give evidence for the non-existence of God.

The fact is that atheists who yell that “there is no evidence for God (or Christianity)” are protesting too much, so to speak, and they are, in fact, projecting the weakness of atheism onto theism. For truth be told, it is atheism, at least when in its wide and positive sense, that is the view for which there is no evidence or argumentation that could establish its position. (LINK)

I responded as follows:

Yawn. InvestigativeApologetics seems completely oblivious about the ways to establish the truth of atheism. 

LINKS: herehere

InvestigativeApologetics then doubled down on his original claim, but with a very novel justification.

Yawn all you like. I am intimately familiar both with those two links and with the various Evidential Arguments that you present at the Secular Outpost. In fact, funny enough, it was your arguments that inspired me to look into this matter and come to the conclusion that I did concerning the un-evidenced nature of atheism (when viewed broadly and positively).

Now, obviously, I cannot show this conclusion in this particular comment (although further comments may follow) and I am simultaneously–at this point in my life–beyond caring whether people are swayed by my points or not (for convincing a flesh-and-blood person is not the same as having a convincing argument). However, let me just make a few quick points:

1) First, I am not saying that we must prove that a god does not exist with certainty in order to be rational to believe that a god(s) does not exist. Rather, I am saying that the atheist cannot even show that it is more probable than not that a god does not exist…at least not without begging the question in a substantial number of ways that the theist or skeptic need not grant.

2) For example, consider all the evidential arguments that you present on the Secular Outpost in light of the Likelihood Principle (that a data/observation counts as evidence for Hypothesis 1 over Hypothesis 2 if the data/observation is more likely or expected on Hypothesis 1 than on Hypothesis 2):

The Evidential Argument from Scale (AS) – Given the kind of being described in my first comment, no specific scale of the universe would count as evidence against its existence, and all “scale types” would be equally expected on both naturalism and that form of theism. Thus, no evidential support for naturalism (and I know that you don’t fully or strongly endorse the argument from scale, but I wished to present it anyway). 

b. The Evidential Argument from the History of Science (AHS) – This argument was ripped apart in a past discussion that I remember (with Crude and CL and others, I believe…I’m sure you will disagree, but that is not surprising given that philosophy is a discipline of disagreement), and it has (at my last count) at least 10 flaws, but its worst flaw is that it assumes both that there is such a thing as “matter” and that there is such a thing as a “naturalistic” cause (or explanation), but neither of these need be accepted by the theist or skeptic, either of whom could be an immaterialist (or a-matterist) and/or an occasionalist (where God is the only true cause). So your argument rests on an assumption that need not be conceded, and hence, the argument is flawed from the start. It is also circular given that you need to deal with the objection from the occasionalist, but to do that, you cannot assume a natural cause, which is what the occasionalist denies; you would either have to disprove occasionalism or disprove the existence of any god through other means, but this, in turn, makes your argument redundant. So the argument is either redundant or begs the question. Not a good state for an argument to be in. Furthermore, even if the existence of “naturalistic” explanations was conceded, it would still be the case that if a deist non-interventionist god existed, we would expect all explanations to be naturalistic even on this type of deism, and so again, there is no evidential value in favor of naturalism or deism with this argument as naturalistic explanations would be equally likely on both worldviews.

1. InvestigativeApologetics’ comments about the AHS are confused. Theism,’ as I have defined it, is the ‘core‘ explanatory hypothesis. Sectarian doctrines like occasionalism and non-interventionism are auxiliary hypotheses, viz., theism does not entail occasionalism or non-interventionism but is compatible with both. They are at, at best, uncertain. The probability calculus specifies how we should deal with uncertain auxiliary hypotheses in a way that conforms with the pattern of probability relations specified by Bayes’ Theorem. I explain this here. What IA needs to do is provide an antecedent reason on theism for expecting that either or both of these auxiliary hypotheses are significantly more likely than their denials. Otherwise, the logically correct conclusion is to dismiss these objections as ad hoc, “just so” stories invented solely to avoid the conclusions of the arguments. “Both worldviews” might have roughly equal explanatory power, but naturalism would trump deism by virtue of having a greater intrinsic probability.
2. More important, a careful reading of my arguments will reveal that my arguments need not presuppose that material objects exist.  Supernaturalism (or “source idealism”) can be defined in a way that is neutral between dualism and idealism.  (The hypothesis that the original causes of any material objects that exist are immaterial does not entail that material objects exist.)  Similarly, naturalism or “source physicalism” can be defined in a way that is neutral between dualism and materialism.  Notice too, that even if my particular definition of supernaturalism implies the existence of material objects, that is compatible with “identity idealism”, which is far more plausible than eliminative idealism, just as identity materialism is far more plausible than eliminative materialism.  (Berkeley was an identity idealist, for example.  He believed that physical objects exist, but thought they were collections of ideas.) (I owe this point to Paul Draper.)

c. The Evidential Argument from Biological Evolution (ABE) / The Evidential Argument from Physical Minds (APM) / The Evidential Argument from Evil: The Biological Role of Pain and Pleasure (AE: APP) / The Evidential Argument from Evil: The Flourishing and Languishing of Sentient Beings (AE: AFL) / The Evidential Argument from Evil: The Self-Centeredness and Limited Altruism of Human Beings (AE: AVV) – See Point (a) – Again, none of these arguments hold any evidentiary weight against a non-interventionist god and so do not support naturalism over such a deism given that all these facts would be equally likely on naturalism or deism.

Now, to be precise, my “arguments for naturalism” are really arguments against theism, though in some sense they are of course both.

Now, you could, of course, try to claim that aspects of prior probability or modesty/coherence (from Paul Draper’s ‘Burden of Proof’ Argument, which I know you support) might make atheistic-naturalism more rational or more likely than some type of theism. But again, there are numerous problems with such maneuvers. First, prior probabilities are notoriously difficult to establish objectively, and I, on that basis alone, I would be suspicious of any argument, by an atheist, which just happens to show that atheism (or atheistic-naturalism) has a higher prior probability than theism.

IA knows very well that suspicion is not an argument. And notice that IA gives no reason to doubt that intrinsic probabilities should be determined solely by scope and coherence. Furthermore, he neglects to mention that Draper’s theory of intrinsic probability does result in the conclusion that naturalism and supernaturalism have equal intrinsic probabilities. Once that fact is taken into consideration, it becomes clear that Draper’s theory is not biased against supernaturalism. The fact that theism has a smaller intrinsic probability than supernaturalism follows directly from the definitions of supernaturalism and theism. Theism entails supernaturalism but supernaturalism does not entail theism. So the probability of theism cannot be any greater than the probability of supernaturalism but could be less. This is basic, non-controversial set theory.

Second, in all your arguments (and your priors) you begin with the assumption that materialism—in the sense of metaphysical matter actually existing—is true, but I do not concede this assumption (being an a-matterist and thus lacking a belief in the existence of matter) and so this must be proven before any one of your arguments gets off the ground and before you can even set the prior probabilities that you want. Third, modesty and coherence does not favor naturalism, but rather a type of Berkelian immaterialism, for it is that view that makes the least assumptions about reality (only thinking things exist, which we cannot deny, and is thus the most modest) while remaining coherent (and it is arguable that atheistic-naturalism even is coherent), so Draper does not help you much.

Addressed above.

Fourth, even if we grant the existence of matter, given the fact that a “material god” could exist, and given that a good case could be made that the prior probability of a “material god” existing is either just as good or better than the prior probability of straight atheistic-naturalism (for consciousness, language, life, would have a higher probability of existing given the existence of a material god than given just straight atheistic-naturalism), then, once again, your arguments run into trouble.

What is a “material god”? The word “material” tells us that such a being is composed of matter. The word “god,” I gather, is supposed to tell us that such a being has supernatural powers or abilities. The hypothesis that such a being exists is a very specific version of supernaturalism and so, like theism, has a smaller intrinsic probability than supernaturalism and naturalism. (The more a hypothesis claims, the more ways there are for that hypothesis to be false and so the lower the intrinsic probability.) So-called ‘theistic evidences’ — such as consciousness, language, life, and so forth — determine the explanatory power of the ‘material god’ hypothesis, not its intrinsic probability. Furthermore, notice that IA lists only alleged theistic evidences. It seems rather one-sided to estimate the probability of a material god existing by considering only theistic evidences, while ignoring naturalistic evidences (such as pain and suffering, evolution, nonresistant nonbelief, mind-brain dependence, and so forth). Once the evidence is fully stated, it’s doubtful that IA’s “material God” exists.

Now, I am certain that you might scoff at certain proposals that I have put forward (for example, immaterialism or occasionalism) as being not worthy of consideration. And that’s fine. But my point is this: I do not need to concede to the very assumptions which are latent in so many of the arguments that you put forward, and the moment I do not concede to those assumptions, not only do your arguments lose nearly all their force (if not all), but you actually have the burden to prove the things that you are asserting. And demonstrating such things (such as the actual existence of matter, for example) is a very difficult task to say the least. Furthermore, until and unless you do demonstrate the existence of these things you just essentially assumed, I could readily contend that you hold to them with little more than blind faith. And so these are just some of the brief reasons why, when atheistic arguments are thoroughly deconstructed, and when we realize the various underlying assumptions that they make—assumptions which we need not grant—and when we also understand that the atheist is literally denying the existence of all reasonably possible gods, which could and would include a god such as a non-interventionist one, then we can begin to understand why the atheistic position, when viewed broadly and positively, lacks any evidence for its claim. 

I’m not sure about “scoffing,” but I will say this. If the best response a person has to my arguments is to doubt or deny the existence of matter, then I’m feeling pretty good about the arguments. This must be how Christians feel when atheists use certain far-fetched objections.(“If this is the lengths they have to go to in order to deny the argument, then let them have it.”)

bookmark_borderWilliam Lane Craig on the Prior Probability of Theism and the Fine-Tuning Argument

One objection to fine-tuning arguments for God’s existence goes like this: simply showing that so-called ‘fine-tuning’ is more probable on theism than on atheism isn’t enough to show that God exists. One must also take into account the prior probability of theism.
William Lane Craig responds to this objection in a recent Q&A on his website. He begins:

Your professor’s objection will be more comprehensible if we put it into the context of the probability calculus. Let’s compare the probability of theism vs. atheism relative to the fine-tuning of the universe. Let G stand for the hypothesis that God exists and ¬G for the hypothesis that God does not exist. Let FT stand for the fine-tuning of the universe. The comparative probabilities will be computed as follows:

Now what you argued in your paper was that the third ratio favored theism. The fine-tuning of the universe is considerably more probable given God’s existence than given God’s non-existence. The evidence is therefore strongly confirmatory of theism. So far so good!
What your professor wants to say is that your argument still does not prove that God’s existence is more probable than His non-existence relative to the fine-tuning of the universe. That is the first ratio on the left-hand side of the equation. In order to show that this ratio favors theism, you also need to show that the prior probability of God’s existence is not greatly lower than the prior probability of God’s non-existence. That’s the middle ratio above. The idea here is that the greater explanatory power of a hypothesis can be offset by the enormous improbability of the hypothesis itself.

So far, so good. Craig now turns to his responses.

There are two responses you might make to this objection. First, you might deny that you were trying to prove that the first ratio favors theism. You might simply rest content with showing that the evidence we have is hugely confirmatory of theism.

Yes, a proponent of a ‘fine-tuning’ argument for God’s existence could respond that way. But then they would just be admitting that the objection is correct. That’s about as ineffective a response as possible.

Collins, for example, points out that in science we often do not have any way of estimating the prior probability of a hypothesis, and so we simply rest with arguments showing a hypothesis’ greater explanatory power. It may be that the prior probability of the hypothesis is just inscrutable.

While that may be true of some unspecified, generic hypothesis, this isn’t true of theism, atheism, or naturalism. Craig evinces no awareness of Purdue University philosopher Paul Draper’s work on intrinsic probability, which functions as a kind of prior probability and is particularly useful for ‘ultimate’ metaphysical hypotheses like theism and naturalism.

You might even point out that in order to resist your confirmatory argument on behalf of theism, it’s the atheist who has the burden of proof of showing that theism is considerably more improbable than atheism.

Again, Craig’s unawareness of Draper’s work on intrinsic probability comes back to haunt him. This challenge can be easily met. Craig needs to interact with Draper’s argument that metaphysical naturalism, which entails atheism, has an objective intrinsic probability which is greater than that of theism.

Second, you could argue that theism is not intrinsically much more improbable than atheism. For the prior probabilities Pr (G) and Pr (¬G) are not, despite appearances, computed in a vacuum. Rather these probabilities are computed relative to our background information about the world. You subtract the information about the fine-tuning of the universe from what we know about the world, and whatever is left is our background information. That information will include the evidence featured in all the other theistic arguments, such as the contingency of the universe, the beginning of the universe, the objectivity of moral values and duties, the applicability of mathematics to the physical universe, intentionality, the facts concerning the resurrection of Jesus, and so forth. I think that we should be prepared to argue that the prior probability of theism is much greater than that of atheism relative to our background information. In that way we successfully argue that theism is much more probable than atheism given the fine-tuning of the universe.

First, this reply just pushes the problem back a step. I fully support the idea of cumulative cases, but what Craig seems to forget is that all cumulative cases have to start somewhere. Whatever he wants to use as his first piece of evidence must confront the fact that theism has a lower intrinsic probability than naturalism. For example, if he wants to make the contingency of the universe his first argument, he has to confront it there.

Second, many of Craig’s arguments, including his fine-tuning argument, are textbook examples of arguments which commit the fallacy of understated evidence.

Third, Craig also ignores the fact that there are other lines of evidence, independent of those related to his understated evidence, which favor naturalism over theism.

bookmark_borderWLC Denies That Anyone Has Ever Died a Sincere Seeker Without Finding God

Can anyone sincerely lack belief in God? And even if they can, can anyone sincerely lack belief in God for the rest of their lives? Many people, including nontheists but not just nontheists, think the answer to both questions is plainly “yes.” But some (many?) theists, no doubt motivated by beliefs such as divine goodness, Biblical inerrancy, and Christian particularism, deny this for the second question and possibly the first.  We’ll call people who deny a “yes” answer to the second question “sincere lifelong nontheist deniers” or “sincerity deniers” for short.
To many nontheists this denial is not only false, but offensive, for it can come across as a not-so-veiled accusation that nontheists are lying when they claim they lack belief in God or that God’s existence isn’t obvious to them. In fairness to sincerity deniers, however, we should keep in mind that ‘sincerity denial’ doesn’t have to amount to a conscious denial of a belief in God. Instead, a sincerity denier may hold that a nontheist’s nonbelief is the result of self-deception. (This was, for example, the position of the notorious Christian presuppositionalist Greg Bahnsen, among others.) A sincerity denier may also hold that, at a given time, a nontheist’s nonbelief is genuine, not the result of self-deception, but temporary. This option may be less offensive since it doesn’t require that all nontheists are resistant to theism for the entire time they are a nontheist. The idea seems to be that if a nontheist is nonresistant to belief in God, then said nontheist will eventually come to believe in God before they die.
In any case, what’s important to notice is that, regardless of the flavor of sincerity denial, the one thing all sincerity deniers seem to have in common is this. No one dies a sincere, nonresistant nonbeliever. 
Philosopher and theologian William Lane Craig is a well-known defender of Christian particularism, so it comes as no surprise that he is a sincerity denier. He reaffirmed his position in a recent answer to a question on the Q&A section of his website.  Craig not only denies that there could be a sincere, lifelong nontheist, but he also denies that there could be a sincere, lifelong theistic non-Christian (e.g., Jew, Muslim, Hindu, Buddhist, and so forth). He writes:

Therefore, if a person ultimately fails to come to faith in Christ, it is never just because of lack of evidence or because of intellectual difficulties with the faith. At root, he refuses to come because he willingly ignores and rejects the drawing of God’s Holy Spirit on his heart. Now this convicting power and drawing of the Holy Spirit may take time. It may take years in order for the unbeliever to finally come to Christ. Nevertheless, no one in the final analysis really fails to become a Christian because of lack of arguments or evidence; he fails to become a Christian because he rejects God. But anyone who does respond to the drawing of God’s Spirit with an open mind and an open heart can know with assurance that Christianity is true, because God’s Spirit will convict him that it is true.

Furthermore, he offers the following reasons for doubting the lifelong sincerity of non-Christians.

Now I don’t think we’re in a good position to say with any confidence that there is ultimate (lifelong), nonculpable unbelief, Muhammad. First, as I say, God’s drawing of a person may take time, years even, so that we can’t say of someone who is moving away from God that that’s where he’ll end up. (Read the many testimonials we receive from ex-unbelievers who for many years were moving away from God.) It is particularly the case that many Muslims go through a phase of atheism after shedding Islam before they come to Christ.
Moreover, we’re not really in a position to read a person’s heart or deepest motivations. Sin is incredibly deceitful, and we have an amazing ability to rationalize things so as to justify our behavior. Read C. S. Lewis’ provocative The Great Divorce about the self-justifying rationalizations of people in hell. If we can convince ourselves that our obstacles to faith are intellectual rather than moral or emotional that makes our unbelief respectable in our own eyes and in the eyes of others. How do you know what lies in the heart of a person who resists the drawing and conviction of the Holy Spirit until the end of his life?
Furthermore, I do think that we have good reasons for supposing that Christianity is true. First, there is the witness of the Holy Spirit. It can be an intrinsic defeater of the defeaters brought against it. Second, there are good evidences for the truth of Christianity, particularly for the historicity of the radical personal claims and resurrection of Jesus, whereby God vindicated those claims.

There are many things which could be (and have been) said in response to this sort of position. Here I’ll summarize what I think are the three most important points.
First, notice that sincerity deniers are committed to a universal generalization: there has never been (and never will be) a single sincere, lifelong nontheist. If even just one sincere, lifelong nontheist existed, exists, or will exist, then this universal generalization is false. Thus, it does Craig little good to refer to former atheists who claim that they engaged in all sorts of insincere rationalizations when they claimed to be atheists. Even if that is an accurate description for those former atheists, it doesn’t follow that it applies to all atheists or, more broadly, all nontheists.
Second, we have strong inductive evidence that this generalization is false. There are several lines of evidence which combine to create a powerful cumulative case for the existence of sincere, lifelong nontheists. Following the outstanding work of the Canadian philosopher John Schellenberg (in his recent book The Wisdom to Doubt), we may summarize this evidence as follows.
(a) The prima facie evidence of nonresistant nonbelief. In Schellenberg’s words, “in the actual world persons who do not believe that there is a God, and that in at least some of these people the absence of theistic belief is not in any way the result of their own emotional or behavioral opposition towards God or relationship with God or any of the apparent implications of such a relationship.”
(b) The prima facie evidence of former believers. To paraphrase Schellenberg, such individuals, from the perspective of theism, were on the right path when they lost belief in God. In other words, if theism is true, then such individuals already were in relationship with God and the loss of belief has terminated that.
(c) The prima facie evidence of lifelong seekers. Schellenberg describeres these individuals as people “who don’t start out in what they consider to be a relationship with God and may not even be explicitly searching for God, but who are trying to find out where they belong and, in their wanderings, are open to finding and being found by a Divine Parent–all without ever achieving their goal. These are individuals who seek but do not find.” (233)
(d) The prima facie evidence of converts to nontheistic religions. Paraphrasing Schellenberg, these are individuals who investigate other serious conceptions of the Ultimate and who turn up evidence that produces religious belief in the context of nontheistic religious communities and/or on account of nontheistic religious experiences–and the truth of atheistic claims may be seen to follow by implication. (236)
(e) The prima facie evidence of isolated nontheists. Schellenberg defines these individuals as “those who have never been in a position to resist God because they have never so much as had the idea of an all-knowing and all-powerful spiritual being who is separate from a created universe but related to it in love squarely before their minds–individuals who are entirely formed by, and unavoidably live their whole lives within, what must, if God exists, be a fundamentally misleading meaning system” (238).
Third, the fact that human beings have an “amazing ability to rationalize things” is a double-edged sword. Those of us who reject sincerity denialism — “sincerity denial” deniers? — could just as easily argue that sincerity denial itself is an example of the amazing ability to rationalize things, such as how to reconcile the existence of nontheists–not to mention the existence of theistic non-Christians–with the doctrines of God’s moral goodness and the exclusivity of salvation through Christ.
Craig concludes his answer with the website equivalent of an altar call, imploring his questioner to “Look at the work of Christian philosophers and biblical scholars, such as you will find at this [Craig’s] website.” This suggestion is fine as far as it goes, but it doesn’t go far enough. If a seeker wants to determine the truth of Christianity, Islam, or anything else, then they need to do more than just read the writings which defend those beliefs. They also need to study the work of the best critics of those beliefs.
This is simple inductive logic. If you’re going to attempt make an uncertain inference from evidence, the premises of an inductively correct argument need to embody all of the available, relevant evidence. For example, suppose you read Craig’s website and decide that God is the best explanation for both the origin of the universe and cosmic fine-tuning. Does it follow that God probably exists? No!
First, as I’ve explained in detail before, many deductive theistic arguments mask uncertainty. Consider William Lane Craig’s version of the so-called ‘fine-tuning’ argument. As I’ve argued before, even the name ‘fine-tuning argument’ is prejudicial against atheism, since the expression ‘fine-tuning’ naturally suggests a ‘fine-tuner’ ( = designer). So instead I’ll refer to this argument as the ‘life-permitting’ argument and I’ll refer to the alleged ‘fine-tuning of the universe’s initial conditions” as “the life-permitting nature of the universe’s initial conditions.” With those clarifications out of the way, then, we get the following formulation of the life-permitting argument.

1. The life-permitting nature of the universe’s initial conditions is either the result of chance, necessity or design. (Premise)
2. It is not the result of chance or necessity. (Premise)
3. Therefore, it is the result of design. (From 1 and 2)

This argument is clearly valid, i.e., the conclusion follows from the premises. We want to know the probability of (3). The probability of (3) will depend upon the probability of (2). If we have a very weak degree of belief that (2) is true, say we think Pr(2)=0.25, then, by itself, this argument only warrants the belief Pr(3)=0.25. N.B. I’m not claiming that (2) has an exact numerical probability equal to 0.25; that value is simply an example to illustrate the point.
Second, such arguments fail to embody all of the relevant, available evidence. This is because their conclusions are stated without qualification. For example, suppose we decide to ‘inductify’ or ‘probabilify’ the conclusion of Craig’s fine-tuning argument, it becomes something like this:

3′. [probable] Therefore, it is the result of design.

The problem with this revised conclusion, however, is that it isn’t justified by the premises. It may well be the case that, by itself, the life-permitting nature of the universe’s initial conditions does make it more probable than not that the universe is designed. But that doesn’t entail that, all things considered, the total available, relevant evidence makes it more probable than not that the universe is designed. In order to defend that claim, you have to look at all of the evidence, including the evidence of evolution, biological role of pain and pleasure, nonresistant nonbelief, etc. And once you do that, it’s far from obvious that the total evidence favors theism, much less Christian theism.
So instead of 3′, what we need instead is something like:

3”. Other evidence held equal, it is probably the result of design.

The italicized words are key because the conclusion is no longer claims that the universe’s life-permitting conditions alone justifies the conclusion of design. Instead, it says, if we hold all other evidence equal–i.e., assume for the sake of argument that all other relevant evidence ‘cancels out’–then the life-permitting data justifies design inference.
As I say, 3” is a big improvement over 3′ and 3, but it comes at a cost. Craig now needs additional premises or arguments to show that the total evidence favors design. For example, he might argue:

4. Biological evolution is not more probable on no-design than on design; and
5. The problem of evil in general is some evidence against design,  but it is outweighed by the total evidence for no-design.
6. There is no other evidence against design.

But these kinds of premises are much more difficult to defend.
Third, as I’ve argued before, on the basis of Purdue University philosopher Paul Draper’s work, Craig’s appeal to cosmic fine-tuning is a textbook example of the fallacy of understated evidence. Let’s assume, for the sake of argument, that the life-permitting conditions of our universe are more likely on design than on no-design. That fact–if it is a fact–hardly exhausts what we know about the habitability of our universe. We also know that so much of our universe is hostile to life due to things such as containing vast amounts of empty space, temperatures near absolute zero, cosmic radiation, and so forth. Given that our universe is life-permitting, the fact that so much of it is hostile to life is much more probable on no-design than on design. So once all  of the evidence about cosmic life-permitting conditions has been fully stated, however, it’s far from obvious that facts about cosmic “fine-tuning” favor design over non-design.
Contrary to Craig’s special pleading, I conclude that nontheists and theists alike are amply justified in concluding, with a high degree of confidence, that there is ultimate (lifelong), nonculpable or nonresistant nonbelief. If that creates problems for historic Christian doctrines such as Christian particularism, then so much the worse for those doctrines.
Whenever I blog about the cosmic life-permitting argument, I always get at least one comment suggesting that the multiverse hypothesis is a good way to defeat that argument. My replies: “Good luck with that” and “Not according to inductive logic or probability theory.” We have little or no reason on naturalism (alone) to expect multiple universes, and the ‘independent’ evidence for a multiverse is far from conclusive. See here.

bookmark_borderStupid Atheist Meme #4: “Let’s Put an End to the Philosophy of Religion!”

Note: For the avoidance of doubt, in calling this and other memes”stupid” I’m not claiming–and don’t think–that anyone who agrees with any or all of these memes is a stupid person. 

J.L. Schellenberg has written all that needs to be said on this topic, in a combox on another site (skip down to comment #47). I think it’s worth quoting in full.

Having done philosophy of religion as an atheist for more than twenty years, I find the idea that atheistic belief should lead one to view philosophy of religion as useless or pernicious a bit out of touch with reality. Theistic work in philosophy of religion is, for cultural reasons, getting the lion’s share of attention. But this should not prevent us from noticing that the field is in fact rather well populated by non-theists. Rather, it gives us a reason to try to bring them – people like Paul Draper, Evan Fales, Steve Maitzen, Graham Oppy, Robin LePoidevin, William Rowe, and plenty of others — a lot more visibility. Those who call for an end to philosophy of religion might get some insight into just what they’re talking about (and then productively fall silent) if they consulted the work of people like these to discover why even an atheist might spend a lifetime doing philosophy of religion.

The answer is not that an atheist might spend a lifetime crawling through the minutiae of non-Christian or non-theistic religious belief systems. Here it is helpful to have formed some general conception of what philosophy of religion is about. Philosophy of religion, as I see it, involves bringing to bear on both actual and possible religious ideas and practices the resources of the rest of philosophy (ethics, epistemology, etc.) and, reciprocally, bringing to bear on the rest of philosophy the best results from philosophy of religion. If anyone thinks that the work of Christian philosophers exhausts either of these dimensions of the field, or that the most important such work has been completed if/when we recognize that there is no personal deity, they are sadly mistaken. Even if theism is false, other religious ideas – including the most fundamental (which should therefore be of greater interest to philosophers) – remain to be explored. Many of these ideas and explorations will not bring us into the embrace of some living religious tradition, but rather call for us to stretch our imaginations beyond the results of a few millenia of activity on the part of religious people.

Atheism, as I see it, therefore marks not the end of philosophy of religion but is something more like its beginning. Of course, if one is suffering from such common afflictions as the assumption that there are no real intellectual options in this realm other than traditional theism and metaphysical naturalism, or the virus that subtly turns one’s mind from a love of truth to an activist orientation, then one cannot be expected to make much sense of this. But philosophy is supposed to deliver us from such afflictions. 

(boldface mine)

It’s been suggested that our very own Keith Parsons supported this meme when he famously called the case for theism a “fraud” (see here). Two points. He quickly regretted using the word “fraud” and stated (in the combox for that post) that he wishes he had used the word “vacuous” instead as the word “fraud” implies deceit on the part of theists and he doesn’t consider theistic philosophers dishonest. Second,he confirmed in writing this morning that he does NOT think we should put an end to the philosophy of religion. With his permission, I quote his email to me.

Anybody that read that post with any care would see that I did not state that PoR is a fraud. I said that the case for theism is a fraud. I quickly regretted the word “fraud” because it inevitably seems to imply intentional deceit. I should have said that the case for theism is vacuous. Natural theology has been given a fair hearing for centuries, and as the arguments have gotten more sophisticated, the critiques have more than kept up. PoR will always be around, it just needs to switch focus from the endless attempts to substantiate theistic arguments.
(boldface mine)

Post Edited on 11 August 2015 to add this:
The blogger known as “Ex-Apologist,” who is a nontheist with a Ph.D. in philosophy, has called the suggestion that we should put an end to the philosophy of religion “a joke.” See here.
See Also:
What is Philosophy of Religion?” by Paul Draper

bookmark_borderIndex: Draper’s Evidential Argument from Biological Evolution

The purpose of this page is to provide an index for my blog series on Paul Draper’s evidential argument against theism based on biological evolution.

  • Part 1: a summary of the argument
  • Part 2: a critical assessment of William Lane Craig’s attempt to turn the tables on Draper and argue that evolution is evidence favoring theism over naturalism.

See also:


bookmark_borderIndex: Draper’s Evidential Argument from Pain and Pleasure

The purpose of this page is to provide an index for my blog series on Paul Draper’s classic 1989 article defending an evidential argument from evil which focuses on the biological role (and apparent moral randomness) of pain and pleasure.

  • Part 1: summarizes key terminology for the argument, as well as the argument itself.
  • Part 2: summarizes the first part of Draper’s argument, which purports to show that facts about pain and pleasure are more probable on the hypothesis of indifference (HI) than on theism (T).
  • Part 3: summarizes Draper’s refutation of three theodicies which might be used to defeat the first half of his argument
  • Part 4: summarizes Draper’s own views on the evidential significance of his argument, as well as reasons for thinking it will be very difficult for theists to offset the evidence about pain and pleasure.

See also:

bookmark_borderDraper on Pain and Pleasure: Part 4

This post is part of a series on Paul Draper’s classic version of the evidential argument from evil. In the previous entry, I summarized Draper’s refutation of three theodicies which might be used as an objection to the claim that HI explains the facts about the biological role of pain and pleasure much better than T does. In this post, I’m going to review the final section of Draper’s classic 1989 article on the evidential argument from evil.
1. Darwin’s Argument from Evil
In the final section of his paper, Draper sets up an analogy between Darwin’s evidential argument against special creationism and Draper’s evidential argument against theism. It is worth quoting Draper’s remarks about Darwin’s argument in full.

“Darwin argued that his theory of the evolution of species by means of natural selection explains numerous facts (e.g., the geographical distribution of species and the existence of atrophied organs in animals) much better than the alternative hypothesis that each species of plant and animal was independently created by God. (Let us call this latter hypothesis “special creationism.”) Darwin’s results were significant partly because special creationists at Darwin’s time did not have nor were they able to obtain evidence favoring special creationism over evolution theory that outweighed or at least offset Darwin’s evidence favoring evolution theory over special creationism. For this reason, many theists, while continuing to believe in creationism, which is consistent with Darwin’s theory, rejected special creationism. And those theists who were familiar with Darwin’s arguments and yet remained special creationists did so at a cost: their belief in special creationism was no longer an epistemically rational one.”

Draper says that the significance of his evidential argument from evil is to be determined in an analogous way, viz., it depends upon whether theists have evidence favoring T over HI, evidence which could offset his evidence O favoring HI over T. (N.B. Draper points out this evidence could be propositional evidence, non-propositional evidence, or both.) If a theist confronted with his argument lacks and cannot find such offsetting evidence, Draper argues, the theist “cannot rationally continue to believe that theism is true.”
2. Prospects for Theistic Offsetting Evidence
Draper then offers four reasons for doubting the theist will be able to find such offsetting evidence. It is interesting to compare those reasons (offered in 1989) with the positions Draper has adopted later in his career.
(1) In his 1989 paper, Draper claims that it is “doubtful that it could be shown that HI is ad hoc or that T is intrinsically more probable than HI.” It is noteworthy that, long after his 1989 paper, Draper finally started developing his new theory of epistemic probability. When that theory of epistemic probability is applied to HI and T, it yields the result that the intrinsic probability of HI is significantly greater than T.
(2) Next, Draper argued in 1989 that “Traditional and contemporary arguments for theism are far from compelling.” Since 1989, Draper has gone on record as stating that several facts are evidence favoring T over naturalism (which entails HI). Indeed, he even published a paper arguing that the argument from moral agency is “in the same league” as his evidential argument from evil. But Draper also usefully identified a new fallacy of inductive reasoning he calls the “fallacy of understated evidence.” According to Draper, many (most?) evidential arguments for theism, including his own argument from moral agency, commit the fallacy of understated evidence.
(3) Draper’s third reason (in 1989) for thinking that the theist’s search for offsetting evidence will be difficult is this.

Many traditional and contemporary arguments for theism … may not solve the theist’s position even if they are sound and recognized by the theist to be so. For they at most purport to show that an omnipotent and omniscient being exists–not that the being is morally perfect.”

This point seems (to this writer) as true in 2014 as it was in 1989.
(4) Finally, Draper argues (in 1989) that religious experience doesn’t solve the problem identified in (3): “Religious experience is ambiguous with respect to the moral attributes of the creator.” Furthermore, he notes that theistic justification derived from theistic experiences is offset by atheistic justification derived from “experiences of indifference.” Not only is this yet another example of the fallacy of understated evidence, but Draper wrote an article in 1992 on the evidential value of religious experience. In that article, Draper concluded that three specific facts about religious experience favor atheism over T.

bookmark_borderDraper on Pain and Pleasure: Part 3

This post is part of a series on Paul Draper’s classic version of the evidential argument from evil. In the previous entry, I summarized Draper’s first argument, which attempts to show that certain facts about the types, quantity, and distribution of pain and pleasure (P&P) are much more probable on the hypothesis of indifference (HI) than on theism (T), and so constitute strong evidence against T and for HI. In this entry, I summarize Draper’s discussion of theistic explanations for those facts.

I apologize for the size of the text in my graphics. If you find it hard to read, you should be able to see the graphics at “full size” by clicking on them one-at-a-time in your browser window.
1. “Theodicies” and Theistic Explanations for Facts about Good and Evil
As Draper observes, “Explaining some phenomenon in terms of a statement usually involves adding other statements to that statement.” The relevance to the problem of evil is obvious: people who offer a theistic explanation for facts about good and evil add to T (the proposition that God exists) some additional statement Tn (the proposition that God must allow certain evils in order to achieve some goal).In the philosophy of religion, such additional statements are called “theodicies.” In inductive logic, additional statements of this sort are generically called ‘auxiliary hypotheses.’ In Draper’s terminology, he refers to them as “expansions.”

expansion statement: “a statement h* is an ‘expansion’ of a statement h just in case h* is known to entail h. (Notice that h* can be an expansion of h even if it is logically equivalent to h.)”

With this in mind, consider’s the second part of Draper’s evidential argument from evil again.

A. O is known to be true.
B. T is not much more probable intrinsically than HI.
C. Pr(O/HI) >! Pr(O/T).
So, D. Other evidence held equal, T is probably false.

Draper argues that if a theodicy is to successfully defeat an argument from evil against theism, it must somehow undermine premise (C) by raising the value of Pr(O / T). In order to evaluate whether an expansion Tn of theism raises Pr(O / T) enough to defeat (C), Draper proposes that we use the “Weighted Average Principle” (WAP):
Pr(O / T) = Pr(O / Tn) x Pr(Tn / T) + Pr(O / ~Tn) x Pr(~Tn / T).
As Draper points out, this formula is an average because Pr(Tn / T) + Pr(~Tn / T) = 1. It is not a simple straight average, however, since those two values may not equal 1/2; that is why it is a weighted average. The higher Pr(Tn / T), the closer Pr(O / T) will be to Pr(O / Tn & T); similarly, the higher Pr(~Tn / T), the closer Pr(O / T) will be to Pr(O / T & ~Tn).
Draper states that the second part of his evidential argument from evil assumes that theodicies do not “significantly raise” Pr(O / T) and so the argument effectively treats Pr(O / T) as roughly equal with Pr(O / T & ~Tn). In order to show that this assumption is justified, he says he needs to show that Pr(O / Tn) is “not significantly greater” than Pr(O / T & ~Tn). As he puts it:

In other words, I would need to show that, independent of the observations and testimony O reports, we have little or no more reason on Tn than we have on theism ~Tn to believe that O is true.

In his 1989 article, Draper considers three theodicies:
T1: The Free Will Theodicy, version 1;
T2: The Free Will Theodicy, version 2; and
T3: The Human Ignorance Theodicy.
(Note that while the T1 – T3 notation is Draper’s, the titles of T1 – T3 are mine.)
Before we can discuss T1 and T2, we first need to define a key term:

freedom*: “An action is free* only if
(i) it is free in an incompatibilist sense–that is, in a sense incompatible with its being determined by antecedent conditions outside the agent’s control–and
(ii) if it is morally right, then at least one alternative action that is open in an incompatibilist sense to the agent is such that it would be morally wrong for the agent to perform that alternative action.”

Both T1 and T2 agree that God endows humans with freedom*. They offer contradictory explanations for the existence of pain, however. According to T1, “God permits pain in order to advance morality.” In contrast, T2 explains pain by adding to T a statement about how one of God’s goals is to “increase the responsibility humans have for their own well-being and the well-being of others and thereby increase the importance of the moral decisions humans make.”
Let’s turn to Draper’s objections to each of these expansions of T.
2. “Free Will and the Advancement of Morality”
Let T1 stand for the following expansion of T:

God exists, and one of his final ends is a favorable balance of freely* performed right actions over wrong actions.

Draper begins his response to T1 by making a very charitable concession to the theodicist. He grants, for the sake of argument, that Pr(T1 / T) is high. In order to defend (C) against T1, his strategy instead is to show that:

Pr(T1 / T) is not much greater than Pr(O / T & ~T1).

I interpret Draper’s 1989 article as offering two reasons to believe that.
First, Draper argues that T1 provides a reason we do not have on T & ~T1 to expect that “the world will contain both pain that influences humans to perfom morally right action and pain that is logically necessary for some of the right actions humans perform.” As Draper points out, “O reports the existence of pain of both these sorts,” so those predictions of T1 are confirmed.
But O also reports other facts which T1 predicts should not be true. O also reports both:
(a) that pain often influences humans to perform morally wrong actions; and
(b) that pain is logically necessary for many of the wrong actions humans perform.
Draper concludes that the combination of (a) & (b) is more surprising on the assumption that T1 is true than on the assumption that T is true and T1 is false.
Second, Draper argues that “the world does not contain a very impressive balance of right over wrong actions performed by humans and that this is due in part both to a variety of demoralizing conditions like illness, poverty, and ignorance, and to the absence of conditions that tend to promote morality.” He concludes, accordingly, that this (balance of right over wrong actions) is more surprising on the assumption that T1 is true than on the assumption that T is true and T1 is false.
3. “Free Will and Responsibility”
Let T2 stand for the following expansion of T:

T2: God exists, and one of His final ends is for humans to have the freedom* to make very important moral decisions.

Again, Draper assumes for the sake of argument that the antecedent probability of this theodicy is high, viz., Pr(T2 / T) is high. Again, his strategy is to show:

Pr(O / T2) is not >! Pr(O / T & ~T2)

Draper points out that, “assuming there is no better way,” T2 may provide us with a reason that we do not have on T & ~T2 to expect “the existence of pain for which humans are morally responsible.” But, he argues, Pr(O / T2) is not >! Pr(O / T & ~T2) since other facts O reports are even more surprising on T2 than they are on T & ~T2.
First, “Many humans are plainly not worthy of the freedom* to do serious evils.” On the assumption that T2 is true, however, we would predict that humans would only be given great responsibility when they are worthy of it.
Second, “Nor is the human race making any significant amount of moral progress.” If T2 were true, however, we would expect that humans would be “benefitted by having such responsibility.”
Third, there have been (and are) humans who had (or have) great responsibility, who have abused that responsibility, and did not have their responsibility decreased by God “until they are worthy of a second chance.” But if T2 were true, that is what we would expect.
Draper concludes, accordingly, that Pr(O / T2) is not significantly greater than Pr(O / T & ~T2).
4. The Human Ignorance Theodicy
Here is T3:

T3: God exists and has a vast amount of knowledge about good and evil and how they are related that humans do not have.

Unlike T1 and T2 where Draper granted for the sake of argument that they were antecedently very probable on T, Draper does not make such a concession for T3. It isn’t necessary. As Draper correctly states, Pr(T3 / T) = 1. This, in turn, entails that Pr(O / T) = Pr(O / T3).
But, as Draper argues, T3 fails to defeat O because

We have no more antecedent reason to expect that [God’s additional knowledge is such that he would permit any of the facts O reports to obtain], than to expect that God would have unknown reasons for preventing evil.

Observant readers will notice that the sentence just quoted just is an application of WAP to the idea that God has unknown reasons for his actions.
Furthermore, however much reason we might have on T3 to expect humans would be “unable to product a plausible theistic explanation” for the facts O reports, we have “even more reason” on  HI to expect this. Thus, T3 does not significantly raise the value of Pr(O / T).

bookmark_borderDraper on Pain and Pleasure: Part 2

This post is part of a series on Paul Draper’s classic version of the evidential argument from evil. In the previous entry, I explained Draper’s terminology and summarized the logical form of Draper’s two arguments. In this entry, I focus on Draper’s first argument, which attempts to show that known facts about the biological role of pain and pleasure are much more probable on the hypothesis of indifference than on the hypothesis of theism.
1. Background Knowledge
Like all abductive arguments, background knowledge plays a crucial role in Draper’s evidential argument from evil. Draper’s formulation suppresses reference to background knowledge, i.e., his probability notation does not explicitly contain a symbol to represent the propositions which constitute the relevant background knowledge. In the interest of clarity, however, I’m going to reformulate Draper’s argument so as to explicitly identify the role of those propositions. If we let “B” stand for our background knowledge, then Draper’s first argument may be restated as follows.

(1′) Pr(O1/HI & B) >! Pr(O1/T & B)
(2′) Pr(O2/HI & O1 & B) > Pr(O2/T & O1 & B)
(3′) Pr(O3/HI & O1 & O2 & B) >! Pr(O3/T & O1 & O2 & B)
(4′) Therefore, Pr(O/HI & B) >! Pr(O/T & B). (from 1, 2, and 3)

As I interpret him, the following propositions constitute the relevant background knowledge B.
B1: Pain and pleasure, if they exist, have intrinsic moral value.
B2: A physical universe–which operates according to natural laws, is intelligible, and which supports the possibility of intelligent life–exists.
B3: Living things, including sentient beings, exist on Earth. These sentient beings include, but are not limited to, human beings.
B4: Some (Earthly) sentient beings are not moral agents but are biologically very similar to embodied moral agents.
B5: Humans are goal-directed organic systems, composed of parts that systematically contribute to the biological goals of these systems.
2. Draper’s Defense of Premise (1′): Pr(O1 / HI & B) !> Pr(O1 / T & B)
B5 gives us some antecedent reason to expect that pain and pleasure (P&P), if they exist, will also systematically contribute to those goals, just as O1 reports. But, as B1 reports, notice that, unlike other parts of organic systems, P&P have intrinsic moral value: “pain is intrinsically bad and pleasure is intrinsic good.” This difference (hereafter, “moral difference”) between P&P and other organic systems is crucial to Draper’s argument.
First. consider HI. On HI & B, Draper argues this moral difference gives us no reason at all to be surprised by O1. HI entails that, if P&P exist, then they are not the result of “malevolent or benevolent” supernatural persons. Therefore, on HI, the moral difference between P&P and other parts of organic systems provides no reason whatsoever to predict that P&P “will not play the same biological role that other parts of organic systems play.” In other words, blind nature is indifferent to moral value.
Second, consider T. On T & B, Draper argues this moral difference does gives us good reason to predict that O1 is false. T entails that, if P&P exist, God is responsible for their existence. Since God is morally perfect, He would have good reasons for producing pleasure even if it is never biologically useful, and He would not permit pain unless He had, not just a biological reason, but also a morally sufficient reason to do so. Furthermore, since God is omnipotent and omniscient, He could create goal-directed organic systems (including humans) without biologically useful P&P. So T entails both:
(a) that “God does not need biologically useful P&P to produce human goal-directed organic systems;” and
(b) “that, if human P&P exist, then God has good moral reasons for producing them, reasons that … might be inconsistent with P&P contributing to the biological goals of those systems.”
Thus, we have much less antecedent reason on T & B than on HI & B “to be surprised if it turned out that human P&P differed from other parts of organic systems by not systematically contributing to the biological goals of those systems.” In other words, Pr(O1 / HI & B) !> Pr(O1 / T & B).
3. Draper’s Defense of Premise (2′): Pr(O2 / HI & O1 & B) > Pr(O2 / T & O1 & B)
Here is Draper on O2:

O2 reports the observations and testimony reported by O about sentient beings that are not moral agents (e.g., young human children and nonhuman animals) experiencing pain or pleasure that we know to be biologically useful.

Draper’s defense of (2′) is based upon the insight of B4. For the convenience of the reader, I’ll state it again:
B4: Some (Earthly) sentient beings are not moral agents but are biologically very similar to embodied moral agents.
Since O1 implies that moral agents experience biologically useful P&P, HI & O1 & B makes it likely that some sentient beings that are not moral agents will also experience biologically useful P&P. But the corresponding, parallel claim about T is not true: T & O1 & B do not make O2 just as likely HI & O1 & B do. Given T & O1, “we have reasons to believe that God permits the pain O1 reports because it plays some sort of (presently indiscernible) moral role in the lives of the humans that experience it. But the pain O2 reports cannot play such a role, since the subjects of it [hereafter, ‘moral patients’] are not moral agents.”
The distinction between moral agents and moral patients isn’t relevant to Pr(O2 / HI & O1 & B), but it is relevant to Pr(O1 / T & O1 & B). This distinction gives us some reason on T & O1 & B to expect that “the good reasons God has for permitting moral agents to experience pain and pleasure do not apply to moral patients.” This, in turn, gives us some reason to believe that God will not permit such beings to experience pain.
4. Draper’s Defense of Premise (3′): Pr(O3 / HI & O1 & O2 & B) !> Pr(O3 / T & O1 & & O2 & B)
Finally, let’s turn to (3′). Let’s begin by quoting what Draper has to say about O3 and then introduce some more terminology. Here is Draper on O3:

O3 reports facts about sentient beings experiencing pain or pleasure that we do not know to be biologically useful. This includes much pain and pleasure that we know to be biologically gratuitous, as well as some that is not known to be useful and is also not known to be gratuitous.

And here is the terminology.

pathological P&P: P&P that results from the failure of some organic system to function properly, i.e., pain caused by terminal cancer.
biologically appropriate P&P: P&P that occurs in a situation which is such that it is biologically useful that pain or pleasure is felt in situations of that sort.
biologically gratuitous P&P: P&P that occurs in a situation which is such that it is biologically useful that pain or pleasure is felt in situations of this sort, i.e., pain felt by a person killed in a fire is not biologically useful, but it is biologically appropriate because it is biologically useful that humans feel pain when they come in contact with fire.

Let’s move onto Draper’s defense of (3′). He offers a two-part argument in support.
First, he argues, we have much more reason to expect sentient beings, especially nonhuman animals, to be happy given T & O1 & O2 & B than given HI & O1 & O2 & B. Why? We find that many humans and animals experience prolonged and intense suffering and a much greater number are far from happy. Also, we have more reason on T & O1 & O2 & B than on HI & O1 & O2 & B to expect a close connection between moral goods and biologically gratuitous P&P. But we discover no such connection.
Second, Draper observes that we have much more reason on HI & O1 & O2 & B than on T & O1 & O2 & B to believe that the fundamental role of pain and pleasure is biological and that biologically gratuitous P&P is “a biological accident resulting from nature’s or an indifferent creator’s failure to ‘fine tune’ organic systems.” This is supported by O3: much of the P&P reported by O3 is “either pathological or biologically appropriate, while very little is known to be both non-pathological and biologically inappropriate.” “This is exactly what we would expect if P&P are fundamentally biological rather than moral phenomena.”


5. The Deduction of (4′) from (1′) – (3′)
I have saved this section for last since it is uncontroversial. Why is it uncontroversial? Because if (1′) – (3′) are true, (4′) has to be true. This is easier to see graphically, so I’ll start with a graphic and then prove the result.


Here is the proof:
Pr(O / h) = P(O1 & O2 & O3 / h) [logical equivalence]
By the chain rule, we know that Pr(O / h) = Pr(O1 / h) x Pr(O2 / O1 & h) x Pr(O3 / O2 & O1 & h). But, just for fun, let’s derive the chain result anyway.
Let X = O2 & O3 and let Y = O1
Pr(O / h) = Pr(X & Y/ h) [definition of X and Y]
Pr(O / h) = Pr(X / Y & h) x Pr(Y / h) [product rule]
Pr(O / h) = Pr(X / O1 & h) x Pr(O1 / h) [definition of Y]
Pr(O / h) = Pr(O2 & O3 / O1 & h) x Pr(O1 / h) [ definition of X]
Let D = O3 and E = O2
Pr(O / h) = Pr(E & D / O1 & h) x Pr(O1 / h) [definition of D and E]
Pr(O / h) = Pr(D / E & O1 & h) x Pr (E / O1 & h) x Pr(O1 / h) [definition of conditional probability]
Pr(O / h) = Pr (O3 / O2 & O1 & h) x Pr(O2 / O1 & h) x Pr(O1 / h) [definition of D and E]
Pr(O / h) = Pr(O1 / h) x Pr(O2 / O1 & h) x Pr(O3 / O2 & O1 & h)
Using this application of the chain rule, we get:
Pr(O/HI) = Pr(O1/HI) x Pr(O2/O1 & HI) x Pr(O3/O1 & O2 & HI)
Pr(O/T) = Pr(O1/T) x Pr(O2/O1 & T) x Pr(O3/O1 & O2 & T)
At this point it follows axiomatically that Pr(O / HI) >! Pr (O / T) just in case the ratio of each multiplicand on the right-hand side of the equation is greater than one and at least one of those ratios is much greater than one. That is exactly what (1′) – (3′) show:

  • (1′) shows that the first multiplicand for HI is much greater than the first multiplicand for T;
  • (2′) shows that the second multiplicand for HI is greater than the second multiplicand for T; and
  • (3′) shows that the third multiplicand for HI is much greater than the third multiplicand for T.

Thus, if (1′) – (3′) are true, (4′) must be true: Pr(O / HI) must be much greater than Pr(O / T).

bookmark_borderDraper on Pain and Pleasure: Part One

The academic journal Nous published an article by Paul Draper in 1989 on the evidential argument from evil. (The article used to be available online for free but is now only available behind a paywall at JSTOR.) The article is now widely regarded as a ‘classic’ in the contemporary literature on the problem of evil; it has been republished in numerous anthologies and readers.
In this part, I’ll summarize the terminology he uses and provide a basic overview of the argument’s logical structure or form. Note that, unless otherwise indicated, all quotations inside quotation marks (“) are quotations of Draper’s article.
1. Terminology, Symbols, and Key Concepts
Before we begin, we need to be clear on how Draper uses the key terminology in his argument.

hypothesis: a proposition which we do not know with certainty to be true or false
theism (T): the hypothesis that “there exists an omnipotent, omniscient, and morally perfect person who created the Universe.”
hypothesis of indifference (HI): the proposition that neither the nature nor the condition of sentient beings on earth results from benevolent or malevolent actions performed by supernatural persons.” Note that HI is logically consistent with both supernaturalism and naturalism. Furthermore, note that HI is logically incompatible with T.
goal-directed: “a system S is ‘goal-directed’ just in case some property G that S has exhibited or will exhibit, a broad range of potential environmental changes are such that:
(i) if they occurred at a time when S is exhibiting G and no compensating changes took place in the parts of S, then S would cease to exhibit G and never exhibit G again,
(ii) if they occurred at t a time when S is exhibiting G, then compensating changes would take place in the parts of S, resulting in either S’s continuing to exhibit G or in S’s exhibiting G once again.”
biological goals: “the goals to which organic systems are directed.”
biologically useful: “a part of some goal-directed organic system S is ‘biologically useful’ just in case:
(i) it causally contributes to one of S’s biological goals (or to one of the biological goals of some other goal-directed organic system of which it is a part), and
(ii) its doing so is not biologically accidental.”
biologically gratuitous: pain and pleasure that is not biologically useful.
O: a statement about “the kinds, amounts, and distribution of pain and pleasure in the world.” O is the conjunction (combination) of the following statements:
O1: a statement about facts about “moral agents experiencing pain or pleasure that we know to be biologically useful;”
O2: a statement about facts about “sentient beings that are not moral agents experiencing pain or pleasure that we know to be biologically useful;” and
O3: a statement about facts about “sentient beings experiencing pain or pleasure that we do not know to be biologically useful.”
“>!”: much greater than
epistemic probability: “Relative to K, p is epistemically more probable than Q, where K is an epistemic situation and p and q are propositions, just in case any fully rational person in K would have a higher degree of belief in p than in q.” Note that epistemic probabilities can “vary from person to person and from time to time, since different persons can be in different epistemic situations at the same time and the same person can be in different epistemic situations at different times.”
Pr(x): the epistemic probability of X.
Pr(x | y): the epistemic probability of x conditional upon y, viz., the epistemic probability that proposition X is true, on the assumption that proposition y is true.

2. The Argument’s Logical Structure 
Draper’s 1989 classic article really has two arguments, which I will summarize in reverse order. The second argument is his evidential argument from evil. That argument is the argument where he argues that the biological role of pain and pleasure is prima facie evidence against theism. Draper did not explicitly state the logical form of his argument in his 1989 article, but he did in a later article. He states the argument as follows.

A. O is known to be true.
B. T is not much more probable intrinsically than HI.
C. Pr(O/HI) >! Pr(O/T).
So, D. Other evidence held equal, T is probably false.

Note that while the above argument implies that we have a good prima facie reason to believe that T is probably false (since T and HI are incompatible), it does not imply that we have a good prima facie reason to believe that HI is true (since T and HI are not jointly exhaustive and so both could be improbable). So the argument from the biological role of pain and pleasure could be more accurately described as an argument against T than as an argument for HI, though of course in some sense it is both.
Let’s turn, then, to Draper’s first argument. Draper’s first argument, which was the focus of his 1989 article, is his argument for the truth of C. Since O is logically equivalent to O1 & O2 & O3, Draper observes that we can use the chain rule to measure the evidential impact of O upon any generic hypothesis h:
Pr(O/h) = Pr(O1 & O2 & O3/h)= Pr(O1/h) x Pr(O2/O1 & h) x Pr(O3/O1 & O2 & h)
By substituting h with “HI” and “T” we get the following statements, respectively:
(a) Pr(O/HI) = Pr(O1/HI) x Pr(O2/O1 & HI) x Pr(O3/O1 & O2 & HI)
(b) Pr(O/T) = Pr(O1/T) x Pr(O2/O1 & T) x Pr(O3/O1 & O2 & T)
Draper’s strategy for showing that Pr(O / HI) is much greater than Pr(O / T) is to show that “each of the multiplicands” on the right-hand side of (a) is “either greater or much greater than the corresponding multiplicand” of (b). Thus, his first argument goes like this.

(1) Pr(O1/HI) >! Pr(O1/T)
(2) Pr(O2/HI & O1) > Pr(O2/T & O1)
(3) Pr(O3/HI & O1 & O2) >! Pr(O3/T & O1 & O2)
(4) Therefore, Pr(O/HI) >! Pr(O/T). (from 1, 2, and 3)

Obviously, to make both arguments in any way compelling, Draper needs to support the premises of both arguments. We’ll look at the support for those premises in future posts.