Consider the four theses: N: Naturalism, T: Theism, R: Our doxastic faculties are reliable (in that fairly weak sense that Plantinga uses in his anti evo+nat argument), S: We exist and have doxastic faculties that seem to be reliable.
Suppose, for the sake of the argument that:
- P(R|T&S) is at least a half.
- P(R|N&S) is extremely low.
We can make the argument Moorean if we like. I know that I know empirically that I have two hands. I also know that were R false, I wouldn't know anything empirically (maybe one can get out of this by restricting R to hand-count propositions; but then one could probably argue for analogues of (1) and (2) with R thus restricted). So, I have a sound argument for R from premises that I know. Given a sound argument for R from premises that I know, and given that there premises are very few (only two) so probabilities don't peter out much, it seems that I should be able to use R as evidence, and in particular as evidence for T over N.
At least, the following seems plausible. My probability assignments should be consistent with (1) and (2). My probabilities for T and for N given R&S need to satisfy Bayes' theorem. And that constraint does mean that if I was evenly balanced between T and N before I started thinking about what R says, the scales will now be strongly tipped in favor of T.
But as I said, the argument feels fishy to me. I think one reason it does is that R just doesn't feel to me like something that it should be acceptable to use as evidence in this way. The worry is that, apart from Moorean arguments, we don't really have evidence for R, and how can we legitimately use as evidence a proposition we don't have evidence for? I am not sure how strong the worry is. Maybe it underestimates Moorean arguments.
Another(?) reason why the argument doesn't feel right to me is that it seems to me that if someone thinks about (2), she is may instead be pushed away from R rather than towards T. But perhaps then a dilemma can be set up. Either (2) is a defeater for R, in which case Plantinga's self-defeat argument is good, or else R can be used as evidence for T.
I may be missing something very simple, and may be puzzled over something unpuzzling. As I often say, I am not an epistemologist.
Alex,
My concern is that "reliable" in terms of our "doxastic faculties" is ambiguous between (at least) a couple of meanings, it might mean:
1) Our doxastic faculties are "reliable" in the relevant sense iff they are apt to produce in us a range of specific beliefs about the world which happen to be true.
or
2) Our doxastic faculties are "reliable" in the relevant sense if they apt to produce in us a range of non-specified beliefs about the world that function, whether true or false, in practically the same way as the true specified range of beliefs about the world would.
The difference? As I see it, if your argument relies on the sense of "reliable" that is given in (1) then I think that
(PN) P(R|N&S) is extremely low.
Is correct. However if the sense of "reliable" given in (2) is relevant, then I think (PN) is incorrect. Since it is arguably the case that reliability in the minimal sense given in (2) is an evolutionarily necessary feature of our doxastic faculties (our species would have long since died if we lacked it). Thus P(R*|N&S) is likely better than half, but at least half, in which case we end in a push.
Then, it seems that it should be legitimate to say, in light of (1) and (2), that R provides significant evidence for T over N.
Alex,
It's not easy to know what you mean here. Suppose we know R is true. And we know that (1) has .5 probability. Then we know that R provides no evidence at all for T. Since we put R as certain (or something close),
i. P(R/T) = P(T/R)/P(T) = .5
But then theism is half as probable on R! Of course, N might be a third as probable on R, but in any case R disconfirms theism as you set up the problem. It just disconfirms N more. It's not evidence for either.
I agree about R* (the thing in your (2)) being likely given N&S, but I was meaning R (the thing in your (1)). Likewise, Plantinga's argument concerns R.
If we're going to be justifiably confident that, say, evolution really happened (and naturalists tend to be confident about that, though maybe you think they're not justified in this confidence), then we'll need R, not just R*, I think.
Mike:
I don't think your counterargument works. P(R) in the Bayesian setting would have to be the prior probability of R. But that is much less than 1.
I was thinking of the argument in this way. Our neutral background data is S. We now want to decide between T and N. We add R to our background data. So, the relevant probabilities are the ones conditioned on S.
Then the relevant formula is:
P(T|R&S) = P(T|S) P(R|T & S)/P(R|S).
Now, P(R|S) is less than P(R|T& S). So P(T|R& S) > P(T|S). Hence, R seems to be evidence for T.
I probably have a different take on this. It seems to me that this argument supposes only two alternatives: naturalism or theism. I think this sort of argument works well as an argument against naturalism. The probability of naturalism strikes me as close to zero anyway. But non-naturalism is not theism and historically there are tons of alternative views that are neither naturalistic nor (necessarily) theistic. e.g. platonism and almost any philosophical view before the nefarious influence of Quine.
Gordon:
A fair point. These are the alternatives that my personal thinking on these matters concerns, but there are others. I think, though, everything I said in the argument, however, is compatible with there being other alternatives. The only claim I made is that theism is confirmed over naturalism.
But now replace N by ~T in the argument. Then maybe it's not the case that we get "extremely low" in (2), but we still get "pretty low". After all, with ~T the options include N, various theological views involving evil deities, good deities, neutral deities, Platonism (on which we really don't have much reason to be confident of our empirical knowledge, which is what R concerns), etc. Some of these make R probable, and some make R improbable. Arguably, none, or at least very few, of them make R significantly more probable than T makes R. So, the argument still incrementally confirms T over ~T.
That is, if the argument works. But when I said that the argument seems fishy to me, I wasn't being coy. I really meant it. And I really would like someone to either lay my worries about the piscine odor to rest, or to explain how the worries are justified.
Let me be a little bit more explicit. Let J be the claim that there is intelligent life, and let M be the laws of nature and initial conditions of the universe. If it could be established that:
(1a) P(J|T&M) is at least 1/2
and
(2a) P(J|N&M) is extremely low,
then it would be very plausible to say that J is strong evidence in favor of T and against N. That would be a good argument. But if we put R in place of J, the probability stuff seems to be exactly the same, but to me the argument reeks of non-tetrapod chordates with life-long gills and no non-fin limbs. And the reason for the olfactory sensation seems to have nothing to do with the question whether there are alternatives other than N, technical problems with the probabilities, etc. Am I alone?
Now, P(R|S) is less than P(R|T& S). . .
How can that be? You say,
Now, as a matter of fact both you and I believe R. Or so I shall also assume.
Presumably that means that we know R (or give R a very high credence) given our background data. I'm not sure what else it could mean. You are not asserting here, of course, that we know R on theism and our background info. And this is exactly what I had in mind with the simplified version that replaces P(R|S) with P(R). So, it makes no difference to my point whether we complicate the formula a little or not. The only way to avoid this problem is to drop the assumption that we know (or give high credence to) our cognitive faculties are reliable on S. But the fact is that we do know, right now, prior to any commitment to theism or naturalism, that our cognitive faculties are reliable. Plantinga too, for what it's worth, makes that assumption. You don't want the argument to assume skepticism or agnosticism, I'm sure.
Mike:
I think this is just the problem of old evidence. Sure, if p is a proposition affirming the precession of the perihelion of Mercury, we believe p, indeed with epistemic probability close to 1. But it still makes sense to see p as evidence for relativity theory. To do that, we need to move to a set of background knowledge independent of our belief in p, and ask how surprising p is relative to that reduced set of background knowledge. How exactly one does this is, I understand, a really hard question. But I take it to be doable.
Nice thoughts here Alexander...here's an extra.
You might reconsider A.P. Taylors second understanding of R. There are evolutionary reasons for why that second account of R might be easier to account for; however, those reasons assume that the contents of our beliefs can influence our behaviors. If not, belief content is invisible to the hand of natural selection. Naturalism does not seem to render it at all likely that belief content influences behavior. To illustrate, if an opera singer's voice breaks glass then this occurs due to the physical properties of her vocalization, not the content of the lyric she sang. On a naturalist view, behaviors result from the physical/chemical activity of the brain, not the belief contents that are somehow associated with that activity.
Just thought you might wanna consider that since R in Taylor's second sense is harder to deny. And(PN) is true on either reading I think.
Mr. Nunley:
I think that on the best naturalistic theories, there will be a connection between behavior and belief content because beliefs will be defined in a way that makes them depend in part on behavioral tendencies (I am thinking here of Lewis-style Ramsey-sentence based causal theories). If so, then APT's second notion of reliability will be pretty cheaply available to the naturalist.
In the end, I think these theories fail, because the only sense that the naturalists can make of the normativity in them is either statistical, and that's surely no good, or evolutionary, and that in fact doesn't work. But that's a different argument.
"Either (2) is a defeater for R, in which case Plantinga's self-defeat argument is good, or else R can be used as evidence for T."
This is nice, Alex. Seems much more promising than Plantinga's line. I think R can be used as evidence for T. It should be thrown into the mix, by all means...
Troy:
You find the Plantinga argument fishy but this one seems more promising. I find this argument fishy but the Plantinga one seems more promising. :-) Interesting how people differ. (I think a part of this is that I am one of the few people who are attracted to Descartes' project...)
Alex, what you have constructed here is just a variant of an argument Plantinga considers and rejects on pp. 229-230 of "Warranted Christian Belief". There, Plantinga introduces a proposition B, standing in for "our background information", which plays the exact functional role as your S. He then examines the formula
P(N|R&B) = P(N|B) P(R|N&B)/P(R|B)
which is of course just the "naturalist" version of your P(T|R&S) = P(T|S) P(R|T&S)/P(R|S). His intention is to prove that P(N|R&B) is low on the premise that P(R|N&B) is low (your assumption (2)), but his own belief that P(R|B) is "very high" leads him to conclude that "I can't sensibly claim that P(R|N&B) is low" [p. 229].
Your own argument suffers from a similar defect - quite apart from the fact that, as Mike has already noted, your conclusion P(T|R&S) > P(T|S) does not follow from your premises (1) and (2) but requires the additional assumption that P(R|S) is less than P(R|T&S). Now what exactly do the probabilities P(R|S), P(R|T&S) and P(R|N&S) you introduce here represent? They are not objective probabilities, unless you can specify the relevant sample space and an objective measure on that sample space (which I seriously doubt). So perhaps they are epistemic probabilities. As Plantinga defines epistemic probabilities on pages 162-163 of "Warrant and Proper Function", they contain an "objective component" (which we have just discounted) and a "normative component", of which Plantinga writes:
"In asking after the normative component of such a probability judgement, we are asking what someone of 'sound understanding', someone whose rational faculties are functioning properly, would believe..." ["Warrant and Proper Function", p. 163]
In accordance with this, Plantinga quite reasonably concludes that both P(R|B) and P(R|N&B) are very high, if not 1. And the same goes a fortiori for your conditioning proposition S = "We exist and have doxastic faculties that seem to be reliable". For how could someone whose rational faculties, by prescription, are functioning properly, not believe that there is a high likelihood they are functioning properly when they seem to be functioning properly? It follows that we should expect that P(R|S) is very high, conceivably 1, which makes it a very difficult task for you to argue that P(R|S) is less than P(R|T& S) or that P(T|R&S) > P(T|S) [as unsurprising evidence (R) lends little or no weight to a hypothesis (T)]. And furthermore, we should expect P(R|N&S) to also be high, contrary to your assumption (2). Plantinga would certainly seem to agree with this assessment.
Now perhaps you have an alternative theory of epistemic probabilities. I would be interested to see it. But Plantinga's rationality condition was not inserted into his definition of epistemic probability by accident. It is an attempt (ultimately unsuccessful) to argue his way out of the circle of subjectivity that plagues all versions of epistemic probability: epistemic probabilities are those believed by rational people, and rational people are those whose epistemic probabilities are always (or almost always) right.
1. Whether I need the assumption "P(R|S) is less than P(R|T&S)" depends on how the conclusion "R provides significant evidence for T over N" is read. It is possible that a piece of evidence provides evidence for H1 over H2 in some appropriate sense (e.g., in the sense that when we condition on the disjunction of H1 and H2, the probability of H1 will go up given this evidence), while overall providing evidence against H1 and H2, but more against H2 than against H1.
2. I wonder now how these remarks of Plantinga's are consistent with his evolutionary argument. Maybe the issue is the B--in the evolutionary argument, he reduces the background information available. One needs to do a similar reduction in this argument.
I don't have answers to the foundational questions about probability. I guess that if we throw into S the laws and the initial conditions of our universe, we can then try to make the probabilities be objective (in the naturalism case, grounded just in the laws and initial conditions; in the theism case, grounded in laws and initial conditions, combined with the behavior propensities of a perfect being).
Of course, it would be nice if we had a probability measure on the collection of all worlds. We don't. But I think that for purposes of getting intuitions about what is evidence for what, we can use toy cases where there are such probability measures. Perhaps we take a range of laws and a range of constants in the laws, and distribute uniformly. That will give us a toy model in which these probabilities work. If (1) and (2) hold in that toy model, and if R then provides evidence for T over N, then we can say that, intuitively, R would provide evidence for T over N even outside the toy model.
Granted, solving these problems of objective probability is hard. But I think one can proceed intuitively in the absence of a solution. The inductive problem of evil for its intuitive plausibility requires the possibility of proceeding intuitively in these matters, of being able to ask the question whether the evils of this world would be more likely on T or on ~T. Of course, we're quite certain about the existence of the evils of this world. So if B is our background, P(evils|T&B)=1. But, nonetheless, there is a plausibility the idea that the evils of this world are the sort of thing that, in principle, could be evidence for or, especially, against the existence of God. Imagine a world where the evils are even greater, where they are arranged in such a way that they never actually contribute to anybody's soul-building, and where there is very good reason to think that nobody actually has libertarian free will. It is fairly plausible that, unless the deductive arguments from evil to the existence of God work, this would be evidence against the existence of God. But making this statement precise would have the same sample-space problems that the argument I offered does.
This isn't very satisfactory, I grant.
1. My point was simply that "P(R|S) is less than P(R|T&S)" does not follow from your premises (1) and (2) and seems to beg your (strong) conclusion that P(T|R&S) > P(T|S). If you want to move to the weaker conclusion that P(T|R&S) > P(N|R&S) given (1) and (2) and the assumption of equal a priori probabilities P(T|S) and P(N|S), then this has already been done (absent the S) by Plantinga on p. 230 of "Warrant and Proper Function".
2. I agree that there seems to be a tension between Plantinga's remarks about the "Preliminary Argument" in WPF and his "Main Argument" against naturalism. It is difficult to see how he can reconcile a high value of P(R|N&B) with a low value of P(R|N).
In its original form the "Preliminary Argument" assumed no background information (i.e. B was absent), but it relied on the presumption that P(R) was high, and Plantinga was eventually forced to withdraw this claim in the face of criticism from Fitelson and Sober. I suspect your argument would confront a similar problem if you replaced P(R|S) with P(R), as you would need to argue that P(R) is low (or at least not too high). As Plantinga quite rightly states: "I can't claim (as I did) that P(R) is high: how would I know what proportion of the space of possible worlds is occupied by worlds in which R is true?" [WPF, p. 229]. The same goes for any determinate value of P(R).
Your suggestion that we estimate probabilities by averaging over a set of toy models embodying a range of laws and a range of constants is interesting, but I suspect even this would be hopelessly complicated. We have enough trouble trying to make hard predictions (or retrodictions) about life, intelligence, consciousness etc. given just one set of laws and one set of constants.
And the problem with "intuitions" is that they are highly subjective. The intuitions of theists are quite different from the intuitions of naturalists. And in the matter of estimating P(R|N&S) it is the intuitions of naturalists that are relevant, for, if we follow Plantinga's definition of epistemic probabilities, this probability is nothing but the rational naturalist's perceived likelihood that his or her own faculties are reliable.
I also agree that a probabilistic version of the argument from evil would share all the same problems of any other argument that relies on intuitive or epistemic probabilities.
It's an interesting sociological question how naturalists would estimate P(R|N&S). I myself don't have much of an intuition about that estimate. I was interested more in the hypothetical--if we grant that this probability is low, what follows?
I'm kind of a naturalist (I'm not afraid of normativity like most are) and I find this and Plantinga's argument very interesting but I feel like I'm missing something. Doesn't the naturalist just have to be an externalist about mental content to get out of "2. P(R|N&S) is extremely low"?
Maybe. That was one of my first reactions to Plantiga's argument, too.
But here are two thoughts that suggest that the externalist answer may not be as easy.
1. Externalism can come in a moderate and a radical variety. In a radical variety, even if some standard sense-data sceptical hypothesis (e.g., brain in a vat being fed data from a computer) is true, nonetheless most of the victim's empirical beliefs can still be true. Thus, the victim has a thought that is neurally the same as our thought "There exist horses", but her thought actually means that the computer program feeding her sense impressions satisfies certain conditions. On a moderate variety, if some standard sense-data sceptical hypothesis were true, most of the victim's empirical beliefs would be false. Radical content externalism is implausible--it is plausible that we would be deceived if we were brains in a vat (one can vary the radical content externalism: maybe we would be deceived if we were individually put in a vat, but not if we were all in a vat and grew up--that might give the content externalist a way out). But on moderate content externalism, it is not clear that one gets out of (2). I am not saying one doesn't--just that more work is needed.
2. How would the content externalism work for mathematical and logical knowledge? (It might be true, I guess, that one could be really bad at math and P(R|N&S) could be high, but the argument could be run with the reliability of mathematical and logical knowledge.) Is the external stuff, in this case, the Platonic and causally inefficacious realm of mathematics? Again, I am not saying this is insoluble--but there is some work to be done.
Thank you for your reply.
Yeah, I think Davidson and Rorty were the only ones that bought into the radical externalism you describe, but personally I'm still on the fence about its plausibility. I think it's fair to say, though, that even if our vat-belief that p is true, our belief that our belief that p is true would be false (since, presumably, I believe that I believe that I'm *actually* seeing horses). So, self-knowledge seems to go out the window and we're radically self-deceived rather than just plain deceived. So, I agree it's implausible, if that is right.
Is the thought concerning moderate externalism and (2) this: that (a) moderate externalism admits the possibility of false belief about our environment, and (b) since I would behave the same way whether or not I was in the vat-world or the real world, that (c) the truth of the content doesn't matter since evolution acts solely on behavior?
I would question (b). Would I behave the same? It seems to me that I wouldn't behave the same at least given a plausible story about how content causes action. Perhaps I have misunderstood you though.
With regards to logico-mathematical knowledge, I'm at a loss and have been for a while. All I can do is maybe hint at a weak analytic/synthetic distinction or some kind of constructivism. Lakoff and Nunez recently (2001) wrote a nice book called "Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being" offering a kind of neo-conceptualist/constructivist account. Like you said, though, much more work needs to be done.
I'm wrong about (b). I wouldn't act differently since the content would be the same; though false in one case, true in the other.