We now move on to Tooley's opening statement in Knowledge of God. My entry will discuss pp. 70-108. Next week's entry will discuss the rest of the chapter, which is a detailed presentation of Tooley's version of the problem of evil.
Let me start with a brief overview of Tooley's argument in pp. 70-108. Section I, "Some Preliminary Issues," discusses a smorgasbord of issues. In it, Tooley states that he is concerned with arguing against the existence of God, conceived as an omnipotent, omniscient, and morally perfect person. He seems to think that his arguments will also establish that there is no very powerful, very knowledgeable, and morally very good person. He then argues that it is far from clear that the gods that are worshipped by historical religions can be identical with God because these gods are arguably not perfectly good. He cites a variety of standard "difficult passages" in the Bible, as well as the doctrine that hell is a place of eternal torment where many people will in fact end up. Consequently, Tooley thinks that Judaism, Islam, and Christianity all face more forceful versions of the argument from evil since they not only have to deal with the standard problem of why their god doesn't intervene to prevent evils, but they also have to deal with the fact that their religious texts describe their gods as acting in immoral ways for what we would regard as poor reasons. The following quote sums up Tooley's view about these religions: "the existence of the god of Protestant Fundamentalism, or of Roman Catholicism, or of Islam, is not something that I would welcome, for it would mean that the world, while certainly not the worst imaginable, would be very bad indeed" (to be fair, I should add that Tooley says he would welcome the existence of God in the sense of an omnipotent, omniscient, morally perfect being because the existence of such a being, "greatly increases, at the very least, the chances that the world is a very good one" (both quotes are on p. 74)). Finally, Tooley states that he will be arguing that the epistemic probability of the existence of God is low and he argues that it is better to argue about the epistemic probability of God's existence than about whether belief in God is warranted.
In section II, Tooley discusses a variety of arguments against the existence of God. The bulk of his discussion focuses on seven arguments. He presents five well-known arguments that theism is logically impossible, each of which he thinks fail. He then argues that atheism is the "default position," i.e. in the absence of evidence for the existence of God, the rational attitude to take about God's existence is atheism (as opposed to theism or agnosticism). Finally, he argues that God does not exist because there is good evidence that neurological structures are causally necessary for consciousness and thought in our world, and so there is good evidence that our world does not contain an immaterial mind. I shall discuss the latter two arguments in more detail below.
Lastly, in section III, Tooley leads into his presentation of the problem of evil by discussing some general features of the problem of evil. He states that there are four ways versions of the problem can differ: the central inference can be deductive or inductive, the premise stating the existence of evil can be abstract or concrete (i.e. it can state abstractly that evil exists or it can state more concrete facts such as that there are horrendous evils of certain kinds, or that evils are distributed in a certain way, or that a certain evil event occurred), the argument can be axiological or deontological (i.e. it can argue from the fact that a certain state of affairs is bad, or that certain actions are wrong), and the argument can be subjective or objective (i.e. it can presume moral objectivism or it can be formulated relative to a given theist's moral perspective). Tooley argues that the best version of the problem of evil will be inductive, concrete, deontological, and subjective.
The first three sections of Tooley's main contribution raise a number of interesting issues, many of which I cannot pursue in this post. I will conclude by briefly contesting three of Tooley's arguments.
A. Historical religions and the problem of evil.
Tooley thinks that historical theisms such as Judaism, Islam, and Christianity face highly forceful versions of the problem of evil from some apparently bad or wrong activities that are attributed to their gods by their own religious texts. I think that this is a very interesting issue that often gets raised in conversation but that has received little treatment (as far as I am aware) in the contemporary analytic philosophy of religion literature. Here I only want to pose a question. Granted, if one goes for theodicy one may have a more difficult time with some of these passages, but suppose one goes for a skeptical theist solution to the problem of evil. It seems that skeptical theism (if it is a viable approach at all) will just as easily avoid any potential problems of evil that arise from the contents of religious texts because even where God's motivations are revealed we can hardly expect for the text to describe God's full motivations, and so there may well be other morally relevant considerations that justify his actions of which we are unaware.
B. Atheism is the starting point
Tooley's argument seems to go as follows:
Let PGGod = there is an omniscient, omnipotent, perfectly good person, IGod = there is an omnipotent, omniscient, morally indifferent person, and PEGod = there is an omnipotent, omniscient, perfectly evil being.
1. Pr(PGGod/tautological evidence) = Pr(IGod/tautological evidence) = Pr(PEGod/tautological evidence).
2. Pr(PGGod/tautological evidence) is at most 1/3 (from premise 1).
3. If Pr(PGGod/tautological evidence) is at most 1/3, then in the absence of evidence in favor of PGGod, one ought to believe that PGGod is false.
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4. In the absence of evidence in favor of PGGod, one ought to believe that PGGod is false (from 2, 3).
Tooley then goes on to argue that, in fact, Pr(PGGod/tautological evidence) is probably a lot less than 1/3 given that Pr(there is a omnipotent, omniscient being that is morally between PGGod and IGod/tautological evidence) doesn't seem to be any lower than Pr(PGGod/tautological evidence).
Premise (3) strikes me as dubious. The best reason I can think of for accepting (3) would be:
(5) For all p, if Pr(p/tautological evidence) is at most 1/3, then in the absence of evidence in favor of p one ought to believe that not-p.
But, (5) seems false. Suppose I roll a 6-sided die behind a screen that blocks my vision of the result. The Pr(side 6 is up/tautological evidence) = at most 1/6, but it doesn't seem that I am justified in believing that the roll is not a 6. I should suspend judgment about what number comes up. Furthermore, it is quite hard to know how low Pr(p/tautological evidence) needs to be for belief that not-p to be justified in the absence of supporting evidence.
C. Immaterial minds and physical reality
Tooley's argument seems to go like this:
1. There are various ways in which mental states depend upon neurological states across humans and all animals with thought that we are aware of. Hence,
2. Neurological states are causally necessary for mental states and processes (from 1).
3. If God exists, he would be an immaterial mind whose mental processes do not depend upon neurological states.
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4. God does not exist (from 2, 3).
This arguments strikes me as extraordinarily weak, particularly in the inference from 1 to 2. Premise 1 would at best support the following claim: neurological states are causally necessary for the mental states and processes of finite, material beings that arise at least in part from material processes. But, this claim cannot be used in conjunction with 3 to get 4. Here's another way to put the point: humans and other animals are different in so many ways from God, if he existed, that regularities that hold for the former - particularly regarding correlations between mental and physical states - surely cannot be projected to hold for God as well. Here's an especially important difference: if God were to exist, he would (or at least could) be the creator of everything material and of all physical laws. And if God is the kind of being that could be the creator of physical laws, we surely cannot expect God to be subject to physical laws that hold for humans and animals.
In conclusion, although Tooley raises many interesting issues and discusses many interesting arguments, the central problems for theism that Tooley supposedly identifies in sections I-III are not genuine problems. I welcome comments on any of the arguments I have discussed as well as on any of the other arguments in sections I-III that the reader finds interesting.
Regarding Point A: Eleanore Stump has worked with this problem, in a manuscript of her future book on the problem of evil. She thinks that Christianity has a unique and powerful story to tell about why God allows evil that actually makes Christianity better suited to answer the problem of evil than "mere" theism.
I saw a manuscript in 2004 (its presumably much different now). She argues briefly, is that in traditional Christian philosophy suffering plays the role of a kind of cure for sin, constantly reminding the suffering individuals of God's work in her life. The most important thing in life for the Christian, she argues, is that man be united with God, not that he be 'happy' in the sense that most atheists like Tooley care about.
Four of her book chapters are Biblical exegesis demonstrating her points in Scripture. She has a chapter on Samson where she argues that even though his life ended in tragedy because of his previous failures, and that arguably his life wasn't a happy one, he died in unity with God.
Lately I've been reflecting on the fact that people who studying the problem of evil are primarily metaphysicians and epistemologists, not moral philosophers. For this reason, philosophers in the area have thought a lot harder about what it means to be all-knowing and all-powerful than all good. I do some moral philosophy, and my own view on this is that if the literature strays into this area things will get complicated quickly. The properly of being 'perfectly good' is really quite shockingly complex, particularly depending on your moral theory. Often atheists saddle Christians with an excessively crude, almost hedonic utilitarian theory of the good. They often think that God must be a pleasure maximizer and pain minimizer to be perfectly good. But hedonic utilitarianism is false, and obviously so.
Until we know which moral theory is true (ha!), it's going to be hard to know what it means to be perfectly good. I think we know what it means to do *something* good in *particular* situations. We often don't know what is good, though, and even more often we don't know what is *best*. So if you knew all the facts, and had to balance every possible relevant consideration against every other, then what would you choose to do? I have *no* idea, and neither does any atheist. It makes the case for the skeptical response pretty strong.
Hi Joshua,
Suppose I roll a 6-sided die behind a screen that blocks my vision of the result. The Pr(side 6 is up/tautological evidence) = at most 1/6, but it doesn't seem that I am justified in believing that the roll is not a 6.
That sounds strange. My credence for not-6 is about .83. That's pretty high. I'm not justified in believing that not-6? (to avoid lottery worries I'm comfortable saying that ~(Ex)Pr(Fx/T) = high & Pr(Ex)(Fx/T) = High). In any case, suppose my credence for God existing is .9. Should I be agnostic? Or am I justified in believing that God exists?
I find the argument of Tooley offers difficult to follow. It doesn't make much sense unless he offers an argument that the set {PGGod, IGod, PEGod} is a partition. But there are all sorts of reasons for believing it isn't. The most obvious is that goodness comes in degrees. There ought to be at the very least a denumerably infinite number Gods, each having a different degree of goodness (and maybe a continuum of Gods). So the set is clearly not exhaustive (i.e., it might be that exactly none of them exists). Nor is it obviously exclusive (i.e., it might be that more than one exists). Why couldn't there be both a PEGod and a PGGod? So the probability assignments that Tooley offers in this argument are hard to see. Given premise (1) and the fact that the set is not a partition, we could as well assign each a probability of .01 or or that matter assign each (approximately) 1 (i.e. they all exist).
Joshua,
You wrote:
It seems that skeptical theism (if it is a viable approach at all) will just as easily avoid any potential problems of evil that arise from the contents of religious texts because even where God's motivations are revealed we can hardly expect for the text to describe God's full motivations, and so there may well be other morally relevant considerations that justify his actions of which we are unaware.
Two reasons that belief in some revealed religion might face more pressing problems than belief in theism committed to no revealed religion.
First, suppose it's part of some text that once upon a time God killed every child with a flood and killed some guy's family because he was gambling with the devil but we have no evidence (apart from the text) that this is so. Advocates of the revealed religion believe there are actions that call for justification the rest of us just don't believe in. It's easier for us to believe there's a good God than it is for the folks who believe that God's deeds are revealed in this text.
Second, there will be some moral views on which a partial description of God's motives will suffice to show that God can't get off the hook. If you oughtn't use a person merely as a means to some end even if that end is noble, the hidden further motives that explain why God keeps poking Job in the eye with a stick needn't concern us. We know that he's using Job as a mere means to an end and that's the end of that. (Of course, if you're a sceptical theist you might just say that we don't know that the relationship between permissibility and exploitation is what Kant thought, but it seems easier to remain a sceptical theist when we know nothing of God's motives through the texts we're familiar with.)
I like the argument that Atheism is the default position.
Setting aside the issue that Mike raises about Tooley's formulation, God exists only if God has goodness to degree m (where 'm' is maximal). On any way of partitioning the state space, the probability that God has m, given that God has some degree of goodness is extremely low. It is either infinitesimal or 0. That's all that Tooley needs. And both values also avoid the issue of of whether 1/3 credence in p is sufficient for rational belief in not-p.
Hi Mike,
Since Joshua has a lot to respond to, I'll jump in. Do you at least not share the intuition about the die? Maybe another case will help pump the intuition. You hear that scientists have discovered a new sort of rock on one of the nine planets, but they won't tell you which. A friend asks you, "Which one do you think it's on?" You answer, "I don't know, but I believe that it's not on Mars!" He answers, "Why? What's your justification?" Your friend is probably expecting that you know some extra information about the scientist's research. Instead, you say, "Because the chances are 1/9!" The friend will not be satisfied; he already knew that! He will conclude that your belief is unjustified. As should we all. Intuitively, you should withhold belief, just as you should in the dice example. I'd say the same thing if there were 10 planets (to answer your question about .9).
I only lose the intuition when the number gets really high. For me, there's a big penumbra where my intuitions are just unclear. If it is .99, I don't have the intuition that the belief is unjustified.
Joshua's die argument makes good sense to me. Suppose my credence for not-6 is about .83. My credence for not-1, not-2, not-3, not-4, and not-5 must also be about .83. If a high credence alone is sufficient for justification, then I must be justified in believing that no number came up. But clearly I'm not so justified.
Perhaps Mike's comment about "lottery worries" is supposed to address this point; but what Mike is comfortable saying, I'm not comfortable interpreting. :)
Joshua's die argument makes good sense to me. Suppose my credence for not-6 is about .83. My credence for not-1, not-2, not-3, not-4, and not-5 must also be about .83. If a high credence alone is sufficient for justification, then I must be justified in believing that no number came up.
James and Andrew,
Yes, I'm aware of the lottery intuitions relating to this sort of case. My intuitions are different, as I tried to explain. What you need to address is why this does not manage the problem. I want to say this,
1. The probability is high that some number or other came up.
2. There is no number such that the probability is high that it came up.
These are perfectly consistent and reflect a scope difference in the propositions. The formal representation of (1) are and (2) are as follows, where I'm quantifying over the numbers on the die and 'Pr(Fx/T)' is the probability that x came up given tautological evidence T.
1'. Pr(Ex)(Fx/T) = High
2'. ~(Ex)Pr(Fx/T) = High
There is nothing inconsistent in these two claims. Here's another example of the same sort of pair. Assume utilitarianism is true. Three people are standing around a pond equi-distant from a child on the middle of the ice. If all three (or any two) go onto the ice, it will break and the child will fall through. The following two propositions are true.
3. There is no single person such that it is obligatory that he goes out to save the child.
4. It is obligatory that some person (or other)goes out to save the child.
Again it is a scope distinction,
3'. ~(Ex)O(Sx)
4'. O(Ex)(Sx)
The fact that someone ought to save the child DOES NOT entail that there is any single person such that he ought to save the child. Similarly, the fact that the probability is high that some number comes up DOES NOT entail that there is any number such that it is high that it comes up.
Mike,
Thanks for the explanation, I appreciate it.
I agree that your 1 and 2 are consistent; that's clear enough. What I'm questioning is the principle that if S knows p has a high a priori probability then S is justified in believing p. It is the latter that leads to the absurd conclusion that I'm justified in believing what I know to be false (in the case of the die). But it seems to me that Tooley's argument depends on that principle.
Hi James,
I'm not sure I follow you. But maybe you're denying the consistency of (1) and (2),
1. (Vx)JB(~Tx)
2. ~JB(Vx)(~Tx)
I believe the absurd consequence you're worried about is the inference from (1) to the negation of (2). But (1) and (2) are consistent. Suppose we are in a room with lots of people. One of them is taller than all of the rest, but by a fraction. I am sure that (1) can be true. (1) states,
1'. For each person in the room, I am justified in believing that he is not the tallest person in the room.
For each candidate for the tallest person, someone else has appeared taller. But (2) is true by the description of the case. (2) states,
2'. I am not justified in believing that no one is tallest person in the room.
But the same goes for the die. For each number, I'm justified in believing that it does not come up on the next toss. But I am not justified in believing that no number comes up on the next toss.
Hi Mike,
I think we may have an irresolvable clash of intuitions here. :) You say you're sure that (1) can be true. I find that (1) strikes me as highly questionable. It seems to me that in a room with lots of people of roughly the same height, for each person I ought to withhold judgement on whether or not that person is the tallest.
Moreover, I don't see the basis for this statement: "For each candidate for the tallest person, someone else has appeared taller." If two people (say) are almost exactly the same height, how can each one appear to me to be taller than the other?
In any case, my point is just this. The following epistemic principle has good intuitive support:
JB(P) & JB(Q) -> JB(P&Q)
So if I'm justified in believing that the die will be not-1, not-2, etc., then it follows that I'm justified in believing that none of the six numbers will come up.
In order to avoid absurdity, we must either deny this principle or the one in my previous comment.
Moreover, I don't see the basis for this statement: "For each candidate for the tallest person, someone else has appeared taller." If two people (say) are almost exactly the same height, how can each one appear to me to be taller than the other?
It might be that we can't resolve this. I don't find the epistemic closure principle plausible at all, for all of the reasons that have been given against it. One very compelling case against it is Stephen Maitzen's 'The Knower Paradox and Epistemic Closure' Synthese (1998).
Concerning the justification for the belief that, for each person in the room, sonmeone else in the room has appeared taller, it is very easy to see how this could arise. I see Tom and he appears taller than Sue. I then see Sue in another room, and she appears taller than Ralph. I see Tom some time later in the evening, and he appears shorter than Ralph. How? In the meantime, unknown to me, Tom has changed his shoes. If there are a hundred people in the room, it is really easy to see how evidence can mislead in this way, even when we are being careful.
James,
If I may...above you said:
In any case, my point is just this. The following epistemic principle has good intuitive support:
JB(P) & JB(Q) -> JB(P&Q)
So if I'm justified in believing that the die will be not-1, not-2, etc., then it follows that I'm justified in believing that none of the six numbers will come up.
I think the above principle may be plausible when P and Q are independent. But in the dice example, as it is with the case of God's goodness, P and Q are not independent. Whether the dice shows not-6 does, in fact, depend upon whether it shows not-5. This is because showing not-6 is equivalent to showing (1 or 2 or 3 or 4 or 5) and this disjunction is not independent of not-5 since it includes it. A plausible version of your principle will not work for the case.
But like I said above, these worries strike me to be besides the point. Assuming goodness comes in a continuum of values and that 'God exists' entails that God has exactly one degree of goodness, i.e., the maximal one, the probability that God exists given all of the possible degrees of goodness that an omnipotent and omniscient being could have is, it seems to me, 0 or infinitely close to it. That is, indeed, sufficient to justify belief that God does not exist assuming there are no independent reasons to think he does. Thus, Atheism is the default position as Tooley suggests.
Intuitively, you should withhold belief, just as you should in the dice example. I'd say the same thing if there were 10 planets (to answer your question about .9).
Andrew,
For what it's worth, I'm pretty sure we're down to 8 planets these days (Pluto has been demoted, http://www.nineplanets.org/). In any case, your recommendation to withold belief is definitely not what anyone should do. At the very least your credence for the rock being from other than Mars should be 7/8. Witholding belief is irrational. If you know that the chances are 7/8 that the rock is from other than Mars, it would be plainly irrational not to bet $1 for a 7/8 chance at $3 that the rock is from other than Mars. Your expected utility is positive. But if you suspend judgment, you won't take that bet.
Similarly, it is irrational to withold beleif in the dice example. Minimally, your credence should be 5/6 that the die did not come up 6. And your behavior (betting behavior and otherwise) should reflect that. Belief simpliciter is not sufficiently fine-grained to describe the attitudes to the die landing 6. But as I said, if we stick with the coarse grained description of my attitude to the die landing 6, my attitude is that I believe it won't. You could get me to bet that it will land 6, but it would cost you.
Thanks for the comments, everybody. Here are two (I hope helpful) comments:
1. Regarding Mike's worries that {PGGod, IGod, and PEGod} is not a partition. Tooley is fully aware that these three do not exhaust the full range of possibilities. That's why he says that the probability of each given tautological evidence is at most 1/3. Of course Tooley thinks that it is possible that no omnipotent being of any kind exists, thus the real probability will be lower. He also argues that there are an infinite number of possible beings with slightly different levels of goodness and that this will result in a decrease in the real probability of each. Lastly, he also argues that each possibility is logically incompatible with the others because he thinks it is logically impossible for there to be two omnipotent beings. Here's why, according to Tooley: "if one willed that some contingent state of affairs obtain, while the other willed that it not obtain, they could not both succeed" (p. 89).
2. I wonder if the disputes in the comments about the dice case and Andrew's planets case are due to different views about the following issue: how to map belief, suspension of judgment, and disbelief on to degrees of belief. I bet we would all agree that we should use degrees of belief in p in making bets about p, but we can all agree on that while disagreeing about whether a .83 degree of belief counts as belief or suspension of judgment.
Josh
Mike,
(Gotcha on the eight planets bit.)
In your betting case, it would not be irrational to withhold belief. It would be irrational to act in the way you say because you believe that there is a 1/8 chance that the new rock is on Mars. That proposition is something you are clearly justified in believing. But in my example, doesn't it seem obvious that the friend should not be satisfied with the guy's answer? Just try to imagine that conversation in real life. We might just be stuck at a clash of intuitions, but I'm not convinced that you don't share this intuition. (So do you have the intuition that the guy's belief that the rock wasn't found on Mars is justified?) See my response to Josh also.
Josh,
It's not obvious that we all agree that we should use degrees of belief in making bets. I think that we use our beliefs about probabilities when making bets. In our inner thinking, don't the following thoughts run through our head? "Hmm, I believe that there's a 1/4 chance that he has an Ace. But I believe that there's a 2/3 chance that it's spades. etc." That seems to be how we really think; we think about probabilities. I'm not even sure I understand what people mean when they say that they believe to .83 degrees that the die will not come up six. Some people define degrees of belief by betting behavior, but there're obvious counterexamples; consider Plantinga's case (in WCD in the first chapter on Bayesianism) of the Calvinist who will never make bets because he thinks that gambling is wrong. I think that similar counterexamples could work on other accounts. Unfortunately, I don't know the literature too well here, so I may be saying more than I should say!
You think that the disagreement is about whether .83 degrees of belief (whatever that means) counts as belief. I'd add that the disagreement is also about whether it counts as a justified belief. And here, it is intuitions about our concepts of belief and justified belief that should rule the day. And I'm not sure that Mike doesn't have the intuition that, if someone believed the die was not-6, then it would be unjustified. It seems right for someone to say, "You're not justified in believing that. You're justified in believing that it is likely that it didn't fall on 6. But you're not justified in believing that it didn't fall on 6." That seems entirely appropriate.
Probably a more important issue is whether Tooley is right that there is an infinite number of beings w/differing levels of goodness. Then the stuff about probabilities we're discussing really doesn't matter. What do you think about that?
In your betting case, it would not be irrational to withhold belief. It would be irrational to act in the way you say because you believe that there is a 1/8 chance that the new rock is on Mars. That proposition is something you are clearly justified in believing
I can't follow that. Suppose for reductio that you withhold belief. I ask you want your credence for the proposition that the rock is from Mars. Since you withold belief, you cannot ALSO SAY "oh, well, my credence is 1/8 for that proposition". If you assert your credence is 1/8, then you did not withold belief, obviously!
And it is irrational to withold belief in this case, since anyone who does so will fail to take the rational bet I note above.
Mike,
And it is irrational to withold belief in this case, since anyone who does so will fail to take the rational bet I note above
Why think that if one withholds belief, then they will fail to take the rational bet?
The person could withhold belief that the rock is not on Mars but have full belief that there is a 1/8 chance that the rock was found on Mars. They might act based on their full beliefs about the probabilities. This is what I said to Josh.
I'm guessing that people are talking past each other regarding Andrew's planetary rock case. Andrew seems to be taking "I believe that it's not on Mars" to mean, "I believe that there is no chance it's on Mars." That's the only way I can understand the claim that the friend would be unjustified. If that's what he means, then we can all agree with Andrew's judgment. (Is that what you mean, Andrew?)
I'm assuming we can also agree that the friend would be justified (hence, rational) in believing that it's highly unlikely that the rock is on Mars (given the details of the scenario). But if that's the case, then it seems that he would be justified (hence, rational) in believing that the rock is not on Mars (in a sense compatible with believing there's some chance of it being there). At the very least, we should be able to agree that it's irrational to believe contrary to the balance of your evidence (thus, to believe the rock is on Mars is irrational). But, contrary to the initial appeal of the thought experiment, and given the strength of the evidence, withholding doesn't seem to me to be rational in this case either. (An interesting implication: If you are right, Andrew, that withholding is the proper attitude to take in this case, then Feldman's version of evidentialism if false.)
Andrew,
As far as I can tell, this is just incoherent.
The person could withhold belief that the rock is not on Mars but have full belief that there is a 1/8 chance that the rock was found on Mars.
If you place a 1/8 credence in the rock being from Mars, then you have a 7/8 credence in it's negation. Otherwise you're in violation of the prob. axioms (pr(p) = 1-pr(~p)). I take such violations to be irrational, maybe you don't. So you cannot (i) withold belief that the rock is not from Mars and (ii) place 1/8 credence that the rock is from Mars and (iii) also be rational. Of course, if you don't think it's irrational to violate the probability axioms, then your views about rationality will not prevent you from assigning any proposition any probability you'd like.
Michael S,
By "S believes that it's not on Mars", I mean that S believes that it's not on Mars. Look, just go to a friend (philosopher or otherwise) outside of this debate and tell them, "suppose a new rock was found on one of the 8 planets. Suppose that's all we know. Would you believe that it's not on Mars?" They would probably say "no, I wouldn't believe that." Then ask, "do you think you would need more evidence to justifiably believe that?" They would say, "Yes". Go ahead, try it!
Mike,
I don't see how your point that if one has 1/8 credence in p, then they ought to have 7/8 credence in ~p is relevant. I'm not sure what people mean by credence (or degrees of belief, as I expressed to Josh above). But maybe it will help if I state that I see nothing inconsistent with "S believe that there is a 1/8 chance that the rock is on Mars", "S believes that there is a 7/8 chance that it is not on Mars", and "S withholds belief that the rock is on Mars." Or at least I didn't catch the argument.
Andrew,
You seem dug in. But ok, maybe one last time. You say this (my emphasis),
But maybe it will help if I state that I see nothing inconsistent with "S believe that there is a 1/8 chance that the rock is on Mars", (i) "S believes that there is a 7/8 chance that it is not on Mars", and (ii) "S withholds belief that the rock is on Mars."
To make this as explicit as possible, let's note that we are talking about the belief that some proposition is true. Which proposition is that? It's this one,
P. The rock is not from Mars.
I claim that you take two inconsistent attitudes to (P). In (i) your attitude to P is partial belief. In (ii) your attitude to P is not to believe it at all (or to withhold belief).
If you are withholding belief from P, then you are not partially believing P. Otherwise, you wind up saying things like this: I've decided to withhold payment on the defective item and also to pay most of the cost of the defective item. If you are going to pay 7/8 the cost, you did not withhold payment. To avoid saying mysterious things, you should say that you are going to withhold
some payment, not that you are going to withhold payment. And to avoid saying mysterious things in the belief case, you should say that you are withholding some belief, not that you are withholding belief.This seems like nothing more than a typo, but just to be clear, you say above at July 28, 2008 9:36 PM that (my emphasis),
The person could withhold belief that the rock is not on Mars but have full belief that there is a 1/8 chance that the rock was found on Mars.
But at July 29, 2008 4:33 PM you say that (my emphasis)
But maybe it will help if I state that I see nothing inconsistent with "S believe that there is a 1/8 chance that the rock is on Mars", (i) "S believes that there is a 7/8 chance that it is not on Mars", and (ii) "S withholds belief that the rock is on Mars."
I take it that in (ii) just above the missing 'not' is just a typo. That is, I take the July 28, 2008 9:36 PM version to be what you meant to say (viz., that S is withholding belief from the proposition that the rock is not from Mars) and the July 29, 2008 4:33 PM version not to be what you meant (viz., that S is withholding belief from the proposition that the rock is from Mars).
In any case, my claim that these attitudes are inconsistent assumes this. But it can also be shown to be inconsistent if you decide you meant the version in July 29, 2008 4:33 PM.
Mike,
You seem dug in to me! Yeah, I believe that that was a typo, although I do think that he ought to withhold belief in both propositions (what you are calling P and ~P).
Okay, like I said earlier (see my response to Josh), I just don't know what people mean when they talk about partial beliefs. But I'll say this: suppose S partially believes that P if S believes that . Then I don't find anything irrational about believing that there's a 7/8 chance that P and withholding belief that P. (Yes, I'm repeating myself, but maybe the next paragraph will help.)
I'm using the common sense ordinary notion of "belief", and that would translate to what you might call a "full belief". When Chisholm first gave us the expression "withholding belief", he was not talking about withholding of partial belief (where partial belief is a technically defined term). He was talking about withholding of full belief or withholding of belief (where "belief" is understood in the ordinary sense). So when you say that there is something inconsistent about partially believing that p and withholding belief that p, I see nothing inconsistent (insofar as I understand what you mean by partial belief). As far as I can understand 'partial belief', a person only partially believes that p only if they don't have full belief that p. But then it makes sense to me to say that they are withholding belief (where to withhold belief is to withhold full belief, which I think is how most epistemologists nowadays talk about 'withholding belief' (Chisholm's legacy)).
It may be the case that we're down to a semantic issue. How about this? I think we've both dug in our heels, and I don't know if we can say much more than we already have. I think that our current discussion doesn't have much to do with Tooley's overall case because Tooley doesn't think that there's a 1/3 probability that theism is correct or even a 1/8 or 1/10. He thinks it's infinitely low because there could be an infinite number of beings of higher or lower degrees of goodness. And if he's right that the chance that God exists is infinitely low (as default position), then even I'd say that that's enough for belief that God does not exist (as a default position)! I'm wondering if there's a response to that.
Darnit, another typo. In the second paragraph, it should say, "suppose S partially believes that P if S believes that there's a 7/8 chance that P."
I don't believe any of this 'I just do not understanding partial belief' talk. Other than that, I'm sure I'm losing my mind... You seem to be saying that when you withhold just 1/8 of your belief from the proposition that the rock is from Mars, you are actually withholding full belief from that proposition. One could be forgiven for finding that baffling. But tell me, when someone believes a proposition fully, are they withholding partial belief in that proposition? Is that how you would describe it? This is exactly what you're committing yourself to. It's dizzying.
Here's the problem. You are confusing Not Giving Full Belief with Withholding Full Belief. But these are clearly different. Look,
1. I did not give you the full amount I owed you.
2. I withheld the full amount I owed you.
If I owed you $10 and gave you $5, then (1) is true but (2) is false. If I owed you $10 and gave you nothing, then both (1) and (2) are true. The way you're using 'withholding full belief', it is true that if my credence for a proposition p is 1, then (3) is true, and that's just crazy.
3. I am withholding partial belief from p
Maybe we can sum things up and display the disagreement. I think I have a bead on it.
1. When you say 'S is withholding full belief in p' you mean 'S is not giving all of his credence to p'
2. When you say 'S is withholding partial belief in p' you mean 'S is not giving some credence to p.'
3. When I say 'S is withholding full belief in p' I mean 'S is not giving some credence to p'.
4. When I say 'S is withholding partial belief in p' I mean 'S is not giving all of his credence to p.'
Our quantifiers are reversed. Returning to the original question: when someone says 'I'm withholding belief in p' you think he is asserting (1) and I claim he is asserting (3). That more or less sums it up.
"I don't believe any of this 'I just do not understanding partial belief' talk. Other than that, I'm sure I'm losing my mind..."
Well, I sure hope that the latter part isn't happening. We wouldn't want one of our Prosblogion contributors to lose his mind! But I do think you should take me at my word when I say that I don't understand something. Maybe I've been unduly affected by Plantinga, who also doesn't seem to believe that there are partial beliefs (and degrees of belief in the way that Bayesians and their ilk understand them). See Warrant and Proper Function p. 8, the second big paragraph, for Plantinga's view on the matter. And I believe that many other epistemologists are in this line of thinking. In conversation with Kent Bach, he seemed to think that the idea of degrees of belief and partial beliefs didn't make sense. You either believe something or you don't, and it doesn't make sense to say that you partially believe something.
And I think that this is what Chisholm had in mind in the 2nd edition of Theory of Knowledge where he defined the technical expression "withholding belief":
“one may withhold or suspend belief–that is to say, one may refrain from believing and from disbelieving the proposition.” (p.6)
In this sentence, Chisholm is just talking about plain ol' belief (in the sense mentioned above). There is no mention of partial beliefs, and I don't think he intended talk of withholding beliefs to apply to partial beliefs. And epistemologists today are just following Chisholm's definition. You can see more discussion about withholdings here: http://philosophy.missouri.edu/show-me/?p=525.
This may explain why many of us thought it reasonable to withhold belief that the die was not a six.
Philosophers are prone to express confusion over perfectly coherent ideas. In this case, too, I don't believe it is genuine confusion, unless I'm supposed to believe that Richard Jeffrey, Brian Skyrms, Howard Sobel, David Lewis, Isaac Levi, Ed McClennen, Ellery Eells, Allan Gibbard, Robert Stalnaker, William Harper, Peter Gardenfors and a host of other top philosophers just completely confused about partial belief. My guess is that they aren't. To get a better idea of what partial belief is, I'd recommend a copy of Jeffrey's The Logic of Decision or Eells, Rational Decision and Causality.
Mike - You've stacked your deck with formalist who of course think that things like degrees of belief and partial belief straight forward matters, which is cool because it lets them do all kinds of interesting models. However, I'm not sure that these notions are so well accepted among mainstream epistemologists, though I could be mistaken.
Hi Matt,
I took the question to be whether the concept of partial belief is sensible. But it's as well-defined as any concept in philosophy and it's not a purely technical notion. Were it purely technical--answering to nothing in ordinary usage--it wouldn't be useful in discussion of rational belief and action. But it's very useful. As I noted, it's pretty common among philosophers to affect confusion over perfecly coherent ideas. I take as evidence of the coherence of partial belief that all of these top-of-the-line philosophers (and there are many more than I bothered to name) who find it perfectly sensible. It leaves me unmoved by claims not to understand partial belief.
"I took the question to be whether the concept of partial belief is sensible."
Let's not forget the question of how we should understand "withhold belief". I think that most mainstream epistemologists, influenced by Chisholm, take this expression to refer to withholding full belief. Actually, I very rarely hear the sort of people who talk about partial/degreesof belief talk about withholding. (I'd be interested, Mike, if you know of any that do.) The sort of people who talk about withholdings tend to be people who think that there's just a trichotomy of doxastic attitudes towards a proposition: belief, disbelief, withholding. These people (BonJour, Conee, Feldman, Goldman, Alston, Plantinga, Sosa, Chisholm, Fumerton, Lehrer, Audi, Klein) tend not to talk about degrees and partial beliefs.
Anyway, if we understand withholding belief as withholding full belief, there's the question of whether we should withhold belief that the die is not six. I (and James and Joshua) think that we should. And I think that Mike might agree. Do you? Furthermore, Tooley's argument that there's only a 1/3 probability that God exists should move us to think that we should withhold belief.
Lastly, though, none of this really matters for Tooley's main argument, right? I mean, if he's right that there is an infinite number of levels of goodness, then it doesn't matter that we should withhold belief that the die is not six. His argument for atheism as default position would then be successful.
Andrew,
"Lastly, though, none of this really matters for Tooley's main argument, right? I mean, if he's right that there is an infinite number of levels of goodness, then it doesn't matter that we should withhold belief that the die is not six. His argument for atheism as default position would then be successful."
I've been watching this claim, and I don't really follow the leap from 'infinite number of levels of goodness' to 'atheism'. The argument seems to be that a 'real God' be maximally powerful, knowledgeable, and good. Anything less would not be God. And since there's an infinite variety of possible beings of varying levels of (at least, limited to in this argument) good, yet only one 'maximally' good, the odds in the absence of evidence speak against the existence of the single maximally good being, and therefore against God.
But that seems flawed on a number of levels, even if we put evidence claims aside with regards to revealed religion(s). First and foremost, it seems more likely to establish bare deism as the 'default position', since the question doesn't deal with the existence of a creator/'ultimate' being but rather the nature of said being.
I can think of other objections based around conceptualizing goodness at the level of God, but the deism objection is the one I'm most concerned with.
Anyway, if we understand withholding belief as withholding full belief, there's the question of whether we should withhold belief that the die is not six. I (and James and Joshua) think that we should. And I think that Mike might agree. Do you?
Let p = the die does not land six. If what you mean by 'withholding full belief in p' is not putting credence 1 in the proposition p, then yes, I'd agree. In this case 'not withholding full belief in p' means putting credence 1 in p. So I would disagree that you should, in this sense, 'not withhold full belief in p'. That amounts to saying that if the credence in a proposition should be 5/6, then you shouldn't put credence 1. Almost too obvious to say, right?
But if what is meant by 'withholding full belief in p' is putting credence 0 in p, then I'd disagree. But in this case 'not putting full belief in p' is putting a credence greater than 0 in p. I agree that, in this sense, you should not withhold belief in p.
But if I wanted to be precise, I'd say your credence for the die not coming up six should be 5/6. And your credence for God not existing should be 2/3 (assuming Tooley is right). And your behavior, inferences, willingness to wager, and so on should reflect exactly these credences.
Hi Mike,
It seems to me that the concept of partial belief could be quite useful in decision theory without it literally describing a genuine feature of believers. The concept of a hole is useful in many ways but that doesn't automatically imply that holes are real things or substances. The concept of a hole is useful because it somehow picks out useful properties of things even though it doesn't literally refer to holes (because holes aren't really things, or so I think). Perhaps, then, "partial belief" picks out not a literal kind of belief, but something like a level of confidence in a proposition. Those who think that the notion of partial belief doesn't make sense surely must be able to make sense of "level of confidence." My confidence level in "2+2=4" is a lot higher than my confidence level in "internalism about justification is true" even though I believe both.
But, is level of confidence really just degree of belief? Well, I also have a hard time putting my finger on the notion of degree of belief, so I doubt level of confidence reduces to degree of belief. Here's a theory that keeps them distinct: one can either believe, disbelieve, or suspend judgment about a proposition and one can have a level of confidence about a proposition. One's level of confidence is simply another belief about the probability of the truth of a proposition. Such a theory can take full advantage of decision theory because decision theory makes use of levels of confidence.
In conclusion, it looks like the disbeliever in degrees of belief can still make perfect sense of why decision theory is useful, via the notion of levels of confidence, understood in the way I have suggested or perhaps in some other similar way. But, then, the usefulness of decision theory is neutral with regard to the coherence of the notion of degrees of belief. All that's left to do, then, is to ask people if they can make sense of the notion of degrees of belief, and if they claim to, to ask them what it is that they have in mind when they think of degrees of belief. It may well turn out that all they have in mind is something like level of confidence, understood as I have suggested. If so, then there is no real dispute between those who claim to understand the notion of degrees of belief and those who don't.
How does that sound?
Josh
One's level of confidence is simply another belief about the probability of the truth of a proposition. Such a theory can take full advantage of decision theory because decision theory makes use of levels of confidence.
This seems to make no space for subjectivists about probability. I agree that there is such a thing as chance or the propensity of objects to behave in certain ways. But I deny that probability is in general objective. When I talk about my credence for p, I have in mind my subjective probability that p, or better my degree of belief that p. My subjective probability (i.e., my degree of belief) should reflect the chances that p in cases where that matters (this is just what the Principal Principle requires). But there are lots of cases where my degree of belief that a proposition is true has nothing to do with objective chance (my degree of belief that the Red Sox win another world series, for instance). In any case, my confidence about p, is not in general a belief about the probability of p. The credence I put in p IS in many cases the probability of p from my point of view, given my evidence and my estimations. It is not a belief about what the probability of p happens to be. It is not as though I believe there is some objective probability we could discover concerning whether Berkeley's idealism is more likely to be correct than Hegel's. I don't think there is any such thing. But I can give you the degree to which I think Berkeley and Hegel are right. And when someone disagrees, we are definitely not arguing about the exact objective probability. So, at least as I see it, we need something like objective chance, but we need degrees of belief too. Of course someone might insist on calling degrees of belief, degrees of schmelief. There's nothing to say at that level of discussion, or (maybe better) further discussion has diminishing marginal utility.
One's level of confidence is simply another belief about the probability of the truth of a proposition. Such a theory can take full advantage of decision theory because decision theory makes use of levels of confidence.
Joshua,
I don't want to pile on, but I'd be interested to know what you (or others) made of the following objection this view: there's simply no appropriate content to ascribe to a normal person that would allow us to identify this person's levels of confidence in the truth of some hypothesis with categorical beliefs about probabilities.
I wish this sort of view could be right as it would make life much easier, but what is it that you think an ordinary person is thinking about when they say that they are more confident that, say, content externalism is true than they are that motivational internalism is true or not very confident that McCain will run a clean campaign?
Anyway, rather than get bogged down in this debate about the relationship between belief understood as an all or nothing affair and belief understood in terms of degrees, presumably Tooley could just say that the crucial point is this: those of you who wish to follow Andrew's line nevertheless have to concede that the default attitude is that it's unlikely that God exists. If you want to say that the atheist goes beyond this, so be it. Tooley thinks he's shown that at the very least (setting aside issues of the semantics of 'belief' and 'atheist'), the theist faces an uphill battle as the default rational attitude to take is that it's much more likely that the atheist is right. So, shouldn't we focus on the question as to whether this much is right?
there's simply no appropriate content to ascribe to a normal person that would allow us to identify this person's levels of confidence in the truth of some hypothesis with categorical beliefs about probabilities.
I'm not sure if this goes to your question, Clayton, but there are ways to identify a person's degree of belief (Joshua's 'degree of confidence') from the person's preferences. Maybe the most famous way is from Frank Ramsey. To give an example, take some ethically neutral proposition P. This is a proposition whose truth you are indifferent about (you don't prefer P to ~P and you don't prefer ~P to P). Now suppose you prefer A to B. If you are indifferent between the gamble (1)[A if P; B if ~P] and the gamble (2) [B if P;A if ~P], then your degree of belief in P is .5. If you thought P had a higher probability than .5, you'd prefer the first gamble. If you thought it was lower, you'd prefer the second gamble. So you can arrive at a person's degree of belief that P from the person's preferences over P, A and B. It's more complicated for beliefs that are not ethically neutral, but it's in principle the same method.
Hey Mike,
I'm not sure I formulated the question in quite the way I should have, but I think it's one thing to say that S's degrees of belief ought to be constrained by their preferences or that ascriptions to S of degrees of belief ought to be constrained by descriptions of S's preferences, but it's another to say that S is _thinking about_ these preferences when S forms these beliefs about probabilities that Josh is appealing to in his answer to you. And that's what worried me about his response to you. I do think it makes sense to say that my having such and such degree of confidence in h is _really_ just my having certain preferences. I don't think it seems right to add to this account that I cannot have such degrees of confidence unless I have beliefs about my preferences. It's that identification of degree of belief with categorical belief in propositions about preferences that strikes me as problematic, if that makes sense.
Clayton, you write,
It's that identification of degree of belief with categorical belief in propositions about preferences that strikes me as problematic, if that makes sense.
No, I think that's right. (1) and (2) are not equivalent (where I take (2) as a categorical belief statement of the sort you mention),
1. My credence for p is .5.
2. I believe that the probability of p is .5.
(2) is a belief about the probability of a proposition. (1) is not a belief about the probability of a proposition. It's rather the assertion that p has (subjective) probability .5. It makes sense to reply to (2) this way: I think you're wrong, the probability is .6. But it makes no sense to reply that way to (1), since your assertion that the subjective probability of p is .6 does not conflict with what is asserted in (1). In any case, these are my reasons for not identifying propositions like (1) with those like (2).