A Failed Defeat: Naturalism, Reliability, and Self-Defeat

Interesting post Ted. You write,
". . . I know that I exist and that once my background knowledge is added the probability that I exist given N & E and everything else I know is close to (if not) 1.

On most forms of Bayesianism, that is going to be true (assuming that the priors for your own existence are 1, and not just nearly 1). So much the worse for those forms of Bayesianism. What Plantinga might say, I think, is that your priors are unjustified. Here are a few reasons why. The discussion concerns what we are justified in believing, given certain assumptions about naturalism. So you cannot non-circularly assume that you are antecedently certain that you exist on just the background information. If your background information in k *includes* naturalism, then (depending on how we render the Cartesian arguments, among others) your prior probability for knowing you exist *might* be low (for instance, if the Cogito is a deductive inference (as of course some deny) and therefore dependent on the use of inference rules, then if we cannot rely on any a priori knowledge of inference rules under naturalism, then the priors might be low). If k does not include either naturalism or nonnaturalism, then I think he'd urge that your priors for your own existence shouldn't be very high (but it will depend on your priors for naturalism). But his best response, I think, is that even if the priors for your own existence were 1 in the sitation you describe, it would not follow that his argument against EVO is flawed. It might still be the case that we are unreliable epistemically, but not so radically unreliable that we don't know we exist or not so radically unreliable that we don't know that 2+2 =4 or that we have hands. Something like that.

Hi Mike,

It seems that if Plantinga moves in the direction you offer he'll give the EAAN more of a skeptical spin than I took it to have (and so it'll affect not only N but ~N as well). It doesn't look very promising to argue that a high prior on my own existence is unjustified, regardless of how we construe the Cogito. If he tries to isolate the epistemic unreliability to just R (or something close to that) it still gives the argument a skeptical spin that I didn't think it originally had. I took Plantinga not to question R (full stop) but to question R given just N & E. However, if R is in the clear then the fact that R is not in the clear on a proper subset of the evidence does not show that R is irrational to accept.

Hiya Ted,
Good to see your post! I think the problem about Plantinga's not taking into account background information was raised by Fitelson and Sober in Pacific Philosophical Quarterly 79 (1998). Check out Plantinga's excellent response in Pacific Philosophical Quarterly 84 (2003).

I think what you're really worried about, however, is the conditionalization problem, raised by Merricks, Otte, and van Cleve in the Beilby anthology. (I think they're the ones that raise it.) Check out Michael Rea's response to the conditionalization problem in World Without Design, pp. 182-192.

Here's how Rea's response helps.
Plantinga thinks that S's belief that R is defeated when S has the belief that Pr(R/N&E) is low or inscrutable. Plantinga has also said early on that he doesn't ascribe to the following principle: "if S believes p and q, and S believes that P(p/q)=low, it does follows that S has a defeater for p." He doesn't hold to it for the sort of reason you gave in your opening post. (Rea's example is the belief that p: you won the free nachos lottery and q: the probability that I win the free nachos lottery is low. Merricks gives a few examples in his article.) Actually, Plantinga has argued from quite early on that he doesn't agree with this principle. (I remember him saying this in response to Carl Ginet in a 1995 PPR paper and he also talked about it, I think, in response to Keith Lehrer in the Kvanvig volume.)

Instead, Plantinga argues with analogies. If you REALLY came to believe, like Neo, that you are in the Matrix, and you believe

P(MyPerceptualBeliefsAreReliable/IamintheMatrix)=low or inscrutable

then you would have a defeater for your perceptual beliefs. Plantinga then goes on to argue that this the Matrix case is analogous to the situation the naturalist is in once he comes to form the belief that P(R/N&E) is low or inscrutable.

The weakness in Plantinga's position is that he doesn't give a general principle for when a situation is analogous to the Matrix case and when a situation is analogous to the free nachos case. Here, Michael Rea offers the principle in his book (the reference I gave above), and I think it is plausible. Rea also concludes, based on his principle, that the naturalist is in a position analogous to the Matrix person and not the freenachos person. Unfortunately, I don't have the time right now to summarize Rea's work, but I hope this points to where to look.

"I took Plantinga not to question R (full stop) but to question R given just N & E. However, if R is in the clear then the fact that R is not in the clear on a proper subset of the evidence does not show that R is irrational to accept."

What I think is mistaken is to assume that the priors for you existing must be high in the absence of N&E. If N&E actually does negatively affect that proposition, then the priors for your existing will depend on the priors for N&E. Given that, it *might* be true that your priors for existing are not high. Why do I say that? Not because I'm assuming any skeptical theses at all. Let Pr(E) be the prior probability of the proposition that you exist and let Pr(N) be the prior probability of naturalism. It's a theorem that Pr(E) = Pr(N)Pr(E/N) + Pr(~N)Pr(E/~N). Suppose you put the priors for naturalism pretty high, say, .8. Then of course Pr(~N) = .2. Now suppose your credence in the proposition that you exist is affected negatively (but only slightly) given that naturalism is true. Perhaps it decreases because you believe that naturalism affects your epistemic reliability even regarding your own existence. Put your credence at Pr(E/N) = .5. Finally suppose that Pr(E/~N)= 1. What are your priors for the proposition that you exist? It's Pr(E)= .6. That's not high. And the assignment of probabilities seems a very reasonable one.

Hey Andrew,

I love that you are a great reference on all topics Plantinga! I knew that you would give me some terrific references. It's nice to be in good company in thinking this is a problem for Plantinga's argument. I'll go read Branden's article in PPQ and take a look at Plantinga's response. I think my worries about conditionalization are related to my worries about background evidence (or "old evidence" since the problem is related to the problem of old evidence). Rea's lottery example is a good one. About Plantinga's analogy, I have worries about the probabilistic version of modus ponens. In the example you give suppose I believe everything Neo believes but I also rationally believe that God told me that my perceptual beliefs are reliable. In that case probabilistic modus ponens doesn't work.

Mike,

I think that's a viable response for Plantinga. What worries me is that since my prior on N is not zero, Plantinga's argument shows that everyone faces a problem re R. There's no special problem for the naturalist.

Ted,
Thanks! And really quick, that Matrix example wasn't a good one since it wasn't global skepticism (rather than just perceptual skepticism)). Plantinga's actual examples are if you came to believe that you really are under the control of an evil demon or if you take a drug called XX which renders it an inscrutable probability that most of your beliefs are false. But I've got to run!

Ted,
Okay, here's Rea's principle:

(GP) Let p be a proposition believed by S not on the basis of evidence, and let Z be the set of S's beliefs and experience. Then: S has a defeater for B(p) if, but not only if, S sees that (a) there is a belief or experience e in Z such that S's rational degree of confidence that p in light of e is not high, and (b) there is no belief or experience e* in Z such that S's rational degree of confidence that p in light of (e&e*) is high. (p. 186)

'B(p)' denotes the belief that p. Pages 186-188 is a bunch of caveats and clarifications to GP where he says things like: "I know a refinement needs to be made here or there, but that doesn't matter for the purposes of this chapter..."

Ted, I know you specifically may feel queezy about a belief without evidence, but Rea's just referring to a noninferentially justified belief. Anyway, on this principle, you have a defeater in Plantinga's skeptical scenarios (in the Brain-in-Vat case and the drug XX case) AND you have one for someone who believes in naturalism and understands EAAN, but you don't have one for the lottery case and, I think, your "I exist" case.

But please read Rea directly, because I may have misrepresented him (and I know you have a copy of the book). Interestingly, GP may be what you were looking for since GP appeals to background information.

Ted, I don't think I follow this,
"What worries me is that since my prior on N is not zero, Plantinga's argument shows that everyone faces a problem re R. There's no special problem for the naturalist."

You mean to say (no?) that everyone faces a reliability problem that places some credence in naturalism of N. Yes, that's right. But how is that a problem? Relibability worries, in varying degrees, are there for anyone who finds naturalism credible, to varying degrees. The more credible you find naturalism, the bigger the worry. But that's what we should expect, I think.

Mike, I was thinking that if the Pr(R/N&E) is low enough or inscrutable then on most reasonable assignments to Pr(N) everyone will face a problem. Since Pr(R)=Pr(N)Pr(R/N) + Pr(~N)Pr(R/~N), as long as Pr(R/N) is close to zero (or inscrutable) the product Pr(N)Pr(R/N) will be close to zero (or inscrutable). So the Pr(R) will be primarily a function of Pr(~N)Pr(R/~N). Let's suppose the Pr(~N) is .7 (which I think exorbitantly high, since it is the conjunction of an infinite number of hypotheses). And let's be exceedingly generous about Pr(R/~N), supposing it to be .7 as well. So Pr(R) will be the sum of .49 and a quantity that is either inscrutable or close to zero. Assuming I have my math right, that's a problem for everyone. In fact the situation is reminiscent of Hume's iterative probability argument (I have to consider the probability that I got the right probability, the probability that I got the right probability of getting the right probability, etc.). Since I initially don't have confidence greater than a half in R, it seems it will only diminish on reflection.

Andrew,

I'll take a look at Rea's article. There's a problem with (GP), though. The problem seems to depend on how Rea spells out belief not based on evidence. The problem arises because a belief can be probable on a body of evidence without being probable on *most* proper subsets of the evidence. Let p be the belief that one of my 1000 friends will win the lottery. Let e be the belief that Andrew has a ticket with a .001 chance of winning. This meets condition (a) of GP. Suppose I have similar beliefs for each other 999 friends but I don't believe that all (or most) of my 1000 friends have a ticket in this lottery (I'm denying that belief is closed under entailment). In this case I don't have a defeater to my belief that one of my 1000 friends will win the lottery.

I think a similar story can be told for R. The belief that N doesn't defeat because N is probable on all my evidence, even though, when the evidence is taken individually (or in small enough groups) R is improbable on that.

Mike, let me clarify a thought in my previous remark. I said that Pr(~N) being .7 is exorbitantly high and the reason I gave wasn't a good one. I was thinking that ~N isn't the logical complement of N, but rather the hypothesis of theism. The reason I think .7 is high for that is that T is one of an infinite number of hypotheses; it's somewhat arbitrary to give it such a high prior and give other similar hypotheses a very, very low prior.

I guess I'm still not following the reasoning with the context of Plantinga's argument (I assume we are still in that context). There is no question that ~N is the logical complement of N. Of course ~N includes a large number (I doubt infinite) number of alternative hypotheses to N. But so what? One of those hypotheses--namely the theistic hypothesis--has probablity 1 for very many people. So you'll be summing lots of zero probability hypotheses to the certain theistic one. Suppose for simplicity that you are a theist. You therefore reject all alternative nonnaturalistic hypotheses. In that case you put Pr(~N) = 1 and, given your commitment to theism, you put Pr(R/~N)= 1. So your reliability is going to be established. So how do we get a problem for everyone? We don't get a problem for committed theists, and that is exactly Plantinga's point. We get a problem for people committed to naturalism, sure. We get a problem for some non-naturalists, I suppose, who are nontheists. But even that still has to be shown. In any case, we hardly get a problem for everyone.

You're right that *if* you are certain that theism is true then you won't face the problem. I was taking it for granted that it's not reasonable to assign theism such a high prior. In the context of the Plantinga argument I think this plays out in an interesting way. Suppose you assign a high value to theism but that is based on argument. You have to consider how reliable you are at coming to reasonable conclusions based on argument. And that's dependent on the value you place on R. I assume you can't use your currently high value on T to determine a high prior on R at this point. It's at this point that the EAAN affects everybody.

By the way this is how I see the dialectic developing here. Either the EAAN is another skeptical argument or it's not. If it is, then it's a problem for everybody. If not, then it's not a problem for the naturalist. Either way, there's no special problem for the naturalist.

" I assume you can't use your currently high value on T to determine a high prior on R at this point. It's at this point that the EAAN affects everybody."

I don't know. Could someone never have thought that naturalism is credible? I think so. For what it's worth, most of the theists/atheists I know were committed to theism/atheism long before they learned the arguments for it. And probably most theistic/atheistic beliefs are not evidential. Doesn't mean they're not justified/warranted, of course. Sounds like your argument might assume some form of evidentialism, but I don't know. Still it should be interesting when the probabilistic details are spelled out.

Ted,
Just to make sure, it's in Rea's book, not in an article.

I don't think your counterexample works. Notice that Rea spells out (GP) in terms of rational degree of confidence that p in light of e. So I don't think (a) is met because your rational degree of confidence that one of the tickets will win in light of your evidence (e.g. the belief that the probability that Andrew's winning is .001 and the belief that the probability that the probability that S's winning is .001 and...) is not lowered at all. Actually, in your example, not even your degree of confidence is lowered, let alone your rational degree of confidence.

Heh, responding to you right now brings back some good memories.

I'll go check Rea's subsequent discussion of (GP) but I'm pretty sure that condition (a) is met in my counterexample. All (a) requires is that "there is a belief or experience e in Z such that S's rational degree of confidence that p light of e is not high". The belief is "Andrew has a lottery ticket with a .001 chance of winning" and the belief is "One of my 1000 friends will win the lottery". My rational degree of confidence in p in light of e is not high; it's .001. Furthermore there's no *individual* belief or experience e* in Z such that S's rational degree of confidence that p in light of e and e* is high (although see the technical problem below). I'm denying that my individual beliefs about my friends is closed under entailment. So, for instance, I don't believe that 1000 friends have a lottery ticket, 999 friends have a lottery ticket, etc.

As a technical problem with (GP) it implies S never has a defeater to p because p is a member of Z and S's rational degree of confidence that p in light of e and p is high.

Ted,
Okay, I think I understand your counterexample better. I think that Rea would just say that if your many beliefs about your individual friends were not closed under entailment, then you would have a defeater in that case, and I don't find that counterintuitive at all. Your counterexample involves a very abnormal human being who can't conjoin these beliefs (which most properly functioning humans could) - and given his cognitive situation in which he has all of these low rational degrees of confidence that he can't put together, it seems to me that he does have defeater. Maybe there's something I'm missing something.

We never touched on this, but I didn't see how that consideration applied to EAAN.

I don't have the book onhand, but I think Rea has a caveat for your concern about (b).

Once you get a chance to read the section in the chapter, maybe that'll help clear up some of your worries as well.

The counterexample is meant to provide a simple case of when a claim can be probable on all the evidence but not on the evidence taken individually. The relevance to the EAAN is that R may be probable on all the evidence but not probable on any sufficiently small subsets of the evidence. In this case R may still be reasonable to believe even though one can't specify how R is rationally believed, and moreover, on the evidence taken individually R is quite improbable.

Ted,
Right, the belief (in your original counterexample) would be probable in light of all the evidence, but since the person in your counterexample fails to have all of that evidence together (since belief is not closed under entailment for him), it seems that he does have a defeater (many defeaters actually) because of these individual improbabilities. I think you think that his rational degree of confidence in light of all the evidence is high, but your person simply doesn't have all the evidence that you seem to think he has since belief is not closed under entailment for him. (All the evidence would include the belief that would result if the relevant beliefs were closed under entailment. He doesn't have all of that evidence.)

Imagine a person who had a belief B and found all of these strands of evidence against B. If the person were to put all of those strands of evidence together, then he would find out that B is rational to believe. However, he fails to do this, so all he has internally are all of these strands of evidence against B. It seems that B would then have a defeater. (I mean, this is essentially your case, right?)

What Rea denies is that R is probable on all of the evidence that you have. He thinks EAAN meets the conditions of GP because there is no other belief or experience e* you have which, when conjoined to N&E, make R to be a proposition for which we have a high rational degree of confidence in light of N&E&e*. What would that belief or experience be? He thinks that there is none. This is unlike the free nachos lottery case, where there is such a proposition e* (namely, that the guy is giving you the nachos and such.)

Andrew,

There are some tricky issues here. The belief that one of my 1000 friends will win the lottery is probable on all the evidence I have, since I possess a belief of each of my friends that he has a ticket in this lottery. The question is whether it is reasonable to believe this on the evidence I have and that turns on whether you think the person needs to believe all their evidence. I think it's dubious that a body of evidence can't make reasonable a claim unless one believes the body of evidence.

Ted and Andrew, I'm going to stay out of the debate between you two on this issue, but I think it is a deep and important one. And your discussions make me proud to have been able to teach both of you before leaving Missouri!

Thanks Prof. Kvanvig! Your encouragement is well appreciated, and I appreciate having been able to have learned from you as well.

Ted,
I'm going to clarify some things. (I do this partly for my own sake so as to not get lost.)

Setting the Stage
The following are propositions:

p: one of Ted's 1000 friends will win the lottery
e1: Andrew has a lottery ticket with a .001 chance of winning
e2: Trent Dougherty has a lottery ticket with a .001 chance of winning
e3: Jon Kvanvig has a lottery ticket with a .001 chance of winning.
e4-e999: and so on.
e': A thousand of Ted's friends have a lottery ticket

We stipulate that:
1) Ted has B(p), the belief that p.
2) Ted has B(e1), the belief that e1
3) Ted has B(e2), the belief that e2
4) Ted has B(e3), the belief that e3
5) and so on.
6) Ted doesn't have B(e').

Notice that I differed from your construal of "p", Ted, by making "p" denote a proposition rather than a belief. Notice also that I am letting "e1", "e2", "e3", and "e'" denote propositions and not beliefs or experiences.

The Counterexample to GP
You think that condition (a) is met because:

C) Your rational degree of confidence in p in light of e1 is low.

(It is also the case that your rational degree of confidence in p in light of e2 is low and your rational degree of confidence in p in light of e3 is low, etc., but we needn't get in to that.)

I agree that condition (a) is met since all you need is for (C) to hold.

Condition (b) is also met. This is because you don't have B(e') (as a normal human being undoubtedly would) or any other belief or experience which, when conjoined with B(e1), makes your rational degree of confidence in p high.

So according to GP, you have a defeater. And I think you have a defeater as well. I think this is very intuitive. So I don't think your scenario is a successful counterexample.

You beg to differ. In your last comment, you said you think that B(p) is not defeated. You think that B(p) can be made rational by propositions that you might not even believe. If B(p) can be made rational by propositions that you don't believe, then it turns out that you don't have a defeater after all. This would be a successful counterexample to GP. (You could also say that B(p) has defeater B(e1), but it also has a defeater-defeater e', but I think it'll be simpler to just say that B(e1) never defeats B(p) in the first place because of the presence of e'. This is more consistent with Rea's construal of the situation.)

My Response to Your Counterexample
I think there is a confusion between doxastic and propositional justification, a distinction that our mentor has stressed in many different works. As you know, doxastic justification is enjoyed by a person's belief when it is based on evidence that a believer has. (This is at least how most people construe it - most cases of doxastically justified belief will be based on evidence the believer has - Bergmann thinks that some noninferential beliefs may be doxastically justified but need not be based on anything, but that's irrelevant for this discussion.)

Propositional justification, on the other hand, can be had by a proposition that a person believes even if the person doesn't base his belief on the evidence - it may even allow that the proposition believed is probable (or evidenced by) propositions that the believer doesn't believe. (Although I think propositional justification might require that the believer at least believe the propositions which are his evidence - I'm not sure. I'll suppose the believer need not believe it.)

So as I understand you, you think that B(p) is justified by e', even though you don't believe e'. And since you are obviously not basing your belief that p on e' (since you do not even believe e'), I take it that you must be talking about propositional justification. And here is the problem. What is at stake in Rea's principle (and EAAN for that matter) is doxastic justification. And for B(p) to be doxastically justified by e', it is required that you at least have B(e') so that you can base your belief that p on your belief that e'. This is why, I think, Rea required that e* must be a belief or experience. It is the belief's justification that is at stake. And this is so not only in this counterexample, but in EAAN.

(Alternatively, you think that B(p) is justified by B(e1), B(e2), etc. And since you are not basing your belief that p on B(e1), B(e2), etc., you must be talking about propositional justification. But then we run into the same problem.)

(Btw, I'm using "rationality" and "justification" as synonyms in this discussion.)

Conclusion
So I don't think that a belief can come to have doxastic justification (or rationality) by way of evidence that the believer doesn't believe, although I think, perhaps, that the proposition believed can have propositional justification by way of evidence that the believer doesn't believe. But since what is at stake in GP (and also EAAN) is doxastic justification (or doxastic defeat), matters of propositional justification will not serve as a successful counterexample.

Thanks Jon! Your seminars and reading classes were invaluable; not to mention all your comments on my dissertation. I'm sure you can see your influence in my comments.

Andrew,

You say, "You think that B(p) can be made rational by propositions that you might not even believe." I'm not sure about that. All I've said is that B(p) is made rational by propositions I believe, the beliefs I have about each of my friends owning a lottery ticket. I've also said that I needn't believe the conjunction of those claims in order for the belief to be rational. So this isn't right: "So as I understand you, you think that B(p) is justified by e', even though you don't believe e'."

I think you may be worried about the evidential import of all these beliefs being completely oblivious to the subject, especially when the subject considers that on any individual belief the probability of p is quite small. As I understand it you want to make the evidential import explicit in belief. I don't think that's necessary. I tend to think that we have some awareness of the evidential import of a body of evidence without that being explicitly represented in belief.

Hi Ted,
Right, but I took account of that (what you said in your first paragraph) in my third to last paragraph in my last comment, which I'll highlight here:

"(Alternatively, you think that B(p) is justified by B(e1), B(e2), etc. And since you are not basing your belief that p on B(e1), B(e2), etc., you must be talking about propositional justification. But then we run into the same problem.)"

But your last paragraph added something. My worry is that a belief can be justified by my other beliefs even if I am not aware of their evidential import. Perhaps you can base B(p) on B(e1), B(e2), etc. and A, where A is an awareness of some sort, that makes high S's rational degree of confidence in p in light of A (and B(e1)&B(e2)...). But if this is what you are saying, then you don't meet condition (b). There is an experience e* (i.e., A&B(e1)&B(e2)...) that makes my rational degree of confidence in p in light of e* high.

Recall that Rea is okay with saying that e* can be an experience or a belief. So long as this awareness you are talking about is experienced by the believer, that is enough. But then your scenario is no longer a counterexample.

Hey Andrew,

I won't be able to blog this week because I have orientation all week.

Two quick thoughts that I'll follow up on later if you want. First, go read Kvanvig on coherentism and the basing relation. That should help to answer your worry about the first thing. Second, if you allow Rea to understand the notion of experience as any non-doxastic awareness of evidential import then you're right that my CE doesn't work. That's not a typical way of understanding experience, though.

Ted,
The first worry is interesting, but isn't a big worry. I do remember reading Kvanvig's work on INUS conditions, but I'd have to go back and give it a more careful read.

What is more important for this discussion, however, (let's not lose sight of the main issue!) is that GP gives us a plausible principle that allows us to say that the naturalist has a defeater and the lottery ticket guy doesn't. This is because, as it is, the naturalist doesn't have an experience which, when conjoined with N&E, makes it such that the naturalist has a high rational degree of confidence in p in light of that experience and N&E. Furthermore, if we allow the experiences clause in (b) to allow nondoxastic awareness (in order to block your counterexample =) ), GP still maintains its plausibility and keeps the naturalist with his defeater. More specifically, I doubt there is any sort of nondoxastic awareness A, plus any number of other beliefs or experiences that the naturalist has, which when conjoined with N&E, make the naturalist have a high rational degree of confidence in R. (This is of course granting that the naturalist's rational degree of confidence in R in light of N&E is itself low, which has been assumed at the outset and is itself an interesting debate.)

Enjoy your orientation! Just followup when you can!

Andrew,

I think it's dubious that experience should be equated with any sort of non-doxastic awareness of evidential import. Think, for instance, of the awareness of our own experiences; sometimes we are aware of their evidential import, other times we are not so aware. That aside, though, suppose we understand "experience" very broadly and try to apply GP to EAAN. The application will have to invoke the additional premise that,

(+) the naturalist lacks any experience, e*, such that Pr(R/N&E&e*) is sufficiently high.

As I understand it e* is the body of evidence the Naturalist has, so Pr(R/N&E&e*) is equivalent to Pr(R/e*). Now, if Plantinga's argument is non-skeptical then on the body of evidence most people have, e`, the Pr(R/e`) is sufficiently high. I think that the difference between e* and e` is not sufficient to make a difference to the Pr(R). So, the Pr(R/e*) is sufficiently high on the non-skeptical intepretation of EAAN.

Ted,
As I understand you, you begged the question. You say, "I think that the difference between e* and e` is not sufficient to make a difference to the Pr(R)" But e* includes N&E, and so Plantinga and Rea would think that there is loads of difference between P(R/e*) (they'll think it's low or inscrutable) and P(R/e`) (which they will think is high, provided that it doesn't include N&E or even just N).

Maybe this will get at the issue. What belief or experience does e* include such that P(R/N&E) is low or inscrutable, but P(R/N&E&e*) is high? Is it supposed to be evidence for naturalism? But if you've already granted that P(R/N&E) is low or inscrutable, then I don't see how that evidence would increase P(R/N&E) at all. So I wonder what it is about e* that is supposed to increase the probability.

Andrew,

Nope, I didn't beg the question. (By the way, what are the N&S conditions for begging the question? And for that matter, how exactly is begging the question a bad making property of arguments?) I can fill out the argument for claim you highlighted, which I'll do in a bit. First, though, part of my point is that the Naturalist needn't specify which individual items in their body of evidence makes R probable; it will suffice that R is probable on all their evidence. It is, of course, very difficult to specify exactly how R is made probable by certain bodies of evidence. As I understand the EAAN that's not the challenge. If it were then the argument would need to show that Pr(R/e`) is sufficiently high and the fact that Pr(R/T) is high doesn't show that Pr(R/e`) is high (where again e` is the body of evidence held by most folks).

Back to the claim you highlighted--"I think that the difference between e* and e` is not sufficient to make a difference to the Pr(R)". I'm fine with allowing that to reflect a natural judgment, but here's an argument for it. Suppose a certain claim p is sufficiently probable on a body of evidence E (it's much greater than .5). Then, that body of evidence E can undergo small changes by subtraction or addition and p will still be sufficiently probable on that revised body of E* (which is E subtracting or adding r). (It's much easier to write this with formal notation but the notation gets messed up in html).

To illustrate let

p = one of my 1000 friends will win the lottery.
E = my body of evidence consisting of all the individual beliefs about my friends owning a lottery ticket.
r = Melnyk owns a ticket.

Pr(p/E) is much greater than . 5. Pr(p/(E-r)) is much greater than .5. This illustrates how a body of evidence can undergo small changes by subtraction or addition without the evidential import of the body of evidence changing with respect to p. This supports the general claim that small changes by addition and subtraction don't affect the evidential import of a body of evidence. {*There are sorities worries here, but perhaps the principle can be formulated in terms of justification where justification requires a margin of error.}

Applied to the EAAN it works like this: Plantinga claims that Pr(R/E & T) is much greater than .5 (where E is the body of evidence held by an unreflective person and T is the theistic claim). By the above principle, Pr(R/E) is much greater than .5. The body of evidence, E, is closely similar to the body of evidence, E*, held by the unreflective Naturalist. The difference between E and E* is small enough such that the principle above applies (you can get from E to E* by a series of small changes by addition or subtraction.). So, Pr(R/E*) is sufficiently high. One more application of the above principle gets the claim that Pr(R/(E*&N)) is sufficiently high.

Ted,
I guess the disagreement would be about the last step you made in the last sentence. It seems to me that that rational degree of confidence one has in R in light of E*&N is not high, but low. This is for the reasons I gave in my previous comment. If one has already granted that one's rational degree of confidence in R in light of N&Evolution is a low degree of rational confidence for the naturalist, then it seems that one's rational degree of confidence in R in light of N&Evolution&E* also has the same low degree. (I am just writing 'Evolution' instead of 'E' since you used 'E' for background evidence, which could result in confusion.) It seems that an application of your principle only works if it is the sort of background evidence that is not very important or only changes one's rational degree of confidence by a little bit (as in your example), but adding N to your background evidence can make one's rational degree of confidence in R take a nose-dive. The reason I asked what belief or experience e* could make it the case that one's rational degree of confidence in R in light of N&Evolution&e* is high was because I wanted some reason for thinking that that value would be high. I see now that you meant those other considerations (which you just emphasized in your previous comment) to be reason to think that that value is high. But it still seems to me that you are just assuming that it will be high, and that's the point I meant to get at when I said that you were begging the question.

(Whether you were actually begging the question and whether it's a bad-making property of arguments is not of consequence with respect to this discussion. I'm happy to drop what I said about it.)

So I'm not convinced by the line of reasoning you just gave (but perhaps I'm misunderstanding something), but so what reason is there to think that one's rational degree of confidence in R in light of N&Evolution&E* is high?

Btw, Plantinga thinks that P(R) is high even without any evidence for R. He thinks that any evidence one tries to muster up to support R will inevitably be epistemically circular. I agree with him. I'm not sure if this matters, but I'm also not sure if you know this.

(Also, did you get a chance to read the Rea chapter? Did it clear anything up? You'll notice that I switched back to the language of "rational degrees of confidence", even though I mistakenly didn't in my last comment. It might not be of consequence whether we talk about it in terms of probabilities or not, but Rea did talk about the issue in terms of rational degrees of confidence for a reason, and you can see why in the book.)

Andrew,

Imagine that, two philosophers disagreeing! I'll send you the paper when I write it. Thanks for all the great questions; you've made the transition from post to paper a lot easier. I think we have two basic disagreements. One, on the import of the lottery example I gave, and two on whether any individual belief can create a significant evidential difference in a body of evidence. I don't think that the introduction of N to the body of evidence most folks have makes a significant difference to the rational degree of confidence one should have in R.

Ted,
Yeah! If you write a paper on this, I'd like to take a look at it. Definitely make sure you look at those references I gave earlier on in the post as well if you're writing a paper on it. Blessings!