Monday, September 05, 2011
The Global Warming Wager
Metacrock here points out the Pascalian character of the argument for global warming, and then shows that you can't accept global warming argument while at the same time also accepting atheist anti-wager polemics. He also has some useful things to say about the Wager as a tiebreaker for those otherwise undecided about God.
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Uh, I think the equivalence is a bit mistaken. Pascal's wager is both unsound and invalid.
Also, Pascal did not `invent probability'. He was back there all right, but really now...
The poster appears to think that there's some inconsistency in accepting decision-theoretic arguments about wise strategy while rejecting Pascal's wager. Color me unimpressed. One could create a decision-theoretic argument for Christian belief, but (1) you have to ensure the completeness of the decision matrix, and (2) you have to spell out (finite) utilities and specific probabilities for which the argument is valid.
I question whether Pascal's Wager was ever meant to be so rigorous a claim, complete with assertions of 'infinite' payoff. Could be, but something doesn't seem right bout that claim. And even if it was, I think the wager can remain reasonable if reformulated, or that close variations of it can go through that result in atheism - certainly popular atheism - being skunked.
Of course, then people can and will argue about that ad nauseum. But there's philosophy for you.
Addendum: Yes, I know Pascal himself talked about infinite payoffs, but I'm not sure what he was aiming for there is adequately represented in criticisms like these. Either way, etc.
Crude,
If you're interested in variations on the `infinite payoffs' case, Alan Hájek is the man to consult. He wrote the SEP entry, and he comments on the Wager in several other articles. I agree with him that (hitherto seen) reformulations have not succeeded.
If one wants to be rigorous about it, one needs to figure out a way to ascribe finite utilities (avoiding paradoxes which come with stipulating a `maximum' utility). Further, one has to work with a more comprehensive truth table. Then, and only then, will one be able to argue for a best strategy, which should itself be checked for dependencies, i.e. effects of adopting the strategy on the probabilities of the outcomes. After all of this, if you are successful, you might be able to say something like, "above this probability, one should attempt to arrive at Christian belief."
I see little hope for a convincing such method, as it requires getting atheists to accept (strongly Christianity-favoring) odds on differing theological claims, among other things.
Jesse,
If one wants to be rigorous about it,
Who wants to be rigorous about it? As I said, you can spin off into objections and counter-replies ad nauseum in either direction.
But I think the more down to earth and basic reasoning has some persuasive power that places one in a situation where theism or general religious belief is arguably preferable to atheism. I notice in your criticism you allude to there being more options than Christianity and therefore no strategy results - but (and you were quick there, so I'm not treating your response as thorough) that seems wrong. Let's expand the list to Christianity, Islam, Hinduism and atheism. Let's further assume that if I choose one religion and another religion is 'correct', then a negative result comes to pass. Let's say it's the case for all three religions. You may not, on that basis alone, have a strategy for choosing any of the religions over the other. You are left, however, with any of the three being preferable to atheism. That's strategy enough.
I see little hope for a convincing such method, as it requires getting atheists to accept (strongly Christianity-favoring) odds on differing theological claims, among other things.
Not really. Rather, I don't think the only aim of the Wager is 'So become a Christian right now' - I see it as a pretty good argument (framed as it is in a very practical way) against atheism, not necessarily for Christianity specifically. And that's where I think the effectiveness of the wager really comes into play - on, at least a certain level, dislodging a person from a content or committed atheism to a more favorable approach and consideration of theism broadly, and on approaching religion generally with a (say, from the religious perspective) better attitude.
Of course, if the standard is 'getting a completely committed atheist to give up their atheism', then to hell with it. But I think that's a bogus standard anyway.
Crude,
But I think the more down to earth and basic reasoning has some persuasive power that places one in a situation where theism or general religious belief is arguably preferable to atheism.
Yes, invalid reasoning has persuasive power. If you want to convince me, an atheist, that I should value Christians deliberately using fallacious arguments for purposes of propaganda, I wish you luck.
Let's expand the list to Christianity, Islam, Hinduism and atheism. Let's further assume that if I choose one religion and another religion is 'correct', then a negative result comes to pass. Let's say it's the case for all three religions. You may not, on that basis alone, have a strategy for choosing any of the religions over the other. You are left, however, with any of the three being preferable to atheism. That's strategy enough.
Actually no. In the case of infinite utilities, the same problems result here as they do in the simpler matrix. If you employ finite utilities, you also must explain why the "atheist's wager", which allows for other theologies (e.g. a God which condemns all believers to Hell and sends atheists to heaven) and ascribes them lower probability. Even now, we're not being comprehensive enough, as we still have the possible case that strategy effects outcomes.
Not really. Rather, I don't think the only aim of the Wager is 'So become a Christian right now' - I see it as a pretty good argument (framed as it is in a very practical way) against atheism, not necessarily for Christianity specifically.
I don't say that's the intended conclusion of the Wager as well, as you'd know if you'd read my post.
And that's where I think the effectiveness of the wager really comes into play - on, at least a certain level, dislodging a person from a content or committed atheism to a more favorable approach and consideration of theism broadly, and on approaching religion generally with a (say, from the religious perspective) better attitude.
I'm not sure how the religious perspective will afford a `better attitude'. But this is obviously completely different from the conclusions of the Wager. On such grounds, one could defend the OTF as `simply inviting believers to inspect their faith', as many defenders of the same have.
Of course, if the standard is 'getting a completely committed atheist to give up their atheism', then to hell with it. But I think that's a bogus standard anyway.
The Wager is only intended to apply to those who ascribe non-zero probability to Christianity. That's another issue. The big issue here is not `complete commitment'; I would be interested in a convincing Wager that has any valid capacity to convince. But again, such a Wager depends completely on getting the target atheist to ascribe high probabilities to a wide range of theological commitments while having a suitably high confidence in Christianity.
It's not going to put anybody on the fence that isn't already there, or put them on that path.
Jesse,
Yes, invalid reasoning has persuasive power. If you want to convince me, an atheist, that I should value Christians deliberately using fallacious arguments for purposes of propaganda, I wish you luck.
Yes yes, you're adorable. I didn't say that, and you know I didn't. If you have to stoop to this out of the gates, it doesn't bode well for you. ;)
I pointed out that with these sorts of questions you can lodge objections and counter-objections ad nauseum. If you waited for a philosophical conclusion to be conclusively decided before you acted, you'd probably starve to death.
Especially when you start getting into objections that don't pass the smell test - let's have a look at one.
If you employ finite utilities, you also must explain why the "atheist's wager", which allows for other theologies (e.g. a God which condemns all believers to Hell and sends atheists to heaven) and ascribes them lower probability. Even now, we're not being comprehensive enough, as we still have the possible case that strategy effects outcomes.
First, that's not an "atheist's wager" even as stated - it's yet another theistic wager.
Second, this is a good example of an objection that doesn't pass the smell test - it's amusing, but that's about it. Especially since my (lazy) approach to the argument is that it encourages one to start evaluating the evidence and claims of religion with a more open, theistic-friendly mind.
By all means, you're welcome to mount arguments and supply evidence for the God who condemns all believers and rewards all atheists. Let's see it!
I don't say that's the intended conclusion of the Wager as well, as you'd know if you'd read my post.
Considering, in both your comments here and in your thread, you've strongly implied that the purpose of the Wager is to get someone to arrive specifically at the embrace of Christianity, I'm going to suggest you're a pretty bad communicator.
C'mon, I think you're getting a bit testy about this without warrant. Why, I'm actually being nice here.
I'm not sure how the religious perspective will afford a `better attitude'. But this is obviously completely different from the conclusions of the Wager. On such grounds, one could defend the OTF as `simply inviting believers to inspect their faith', as many defenders of the same have.
The OTF rendered as 'Inspect your faith and try to be fair with the evidence' is an OTF pretty much everyone thinks is reasonable (and wildly unoriginal - see Chesterton on this).
As I said earlier, consider this a reasonable reformulation of the wager, or a close variant of it. I'm not too concerned about whether it's strictly "Pascal's Wager" 100%, but it certainly has a very similar spirit.
But again, such a Wager depends completely on getting the target atheist to ascribe high probabilities to a wide range of theological commitments while having a suitably high confidence in Christianity.
And here we go again, this suggestion that the wager has the aim of getting an atheist to arrive at Christianity specifically. I don't think that's the only aim of the wager, or the make/break point.
Again, if the wager or wager-variant can succeed in getting atheists to reconsider their atheism and/or approach theism and religion broadly with a more open attitude, it's done one hell of a job. In fact, I'd go so far as to say that the most exclusivist apologist would gladly use an argument which merely pushed an atheist to give up or weaken their commitment to their atheism, even if it didn't in and of itself result in said (ex-)atheist committing to their religion.
Yes yes, you're adorable. I didn't say that, and you know I didn't.
No, that was merely the logical implication of what you were saying.
I pointed out that with these sorts of questions you can lodge objections and counter-objections ad nauseum. If you waited for a philosophical conclusion to be conclusively decided before you acted, you'd probably starve to death.
In this case, I don't think we have to sit around that long. Unless you really really really want there to be such a Wager, of course. Then you have a lot of time ahead of you.
First, that's not an "atheist's wager" even as stated - it's yet another theistic wager.
Note the quotes. That's what this alternative has been called by Richard Dawkins. And it's not a theistic wager, since it only works on the possibility of such a God. (If atheism requires certainty about the non-existence of any God, Dawkins is not an atheist.) One could get rid of theism entirely and posit some other mechanism by which atheists exclusively reach a paradise.
Second, this is a good example of an objection that doesn't pass the smell test - it's amusing, but that's about it. Especially since my (lazy) approach to the argument is that it encourages one to start evaluating the evidence and claims of religion with a more open, theistic-friendly mind.
By all means, you're welcome to mount arguments and supply evidence for the God who condemns all believers and rewards all atheists. Let's see it!
Oh goodness, where to begin... You realize we're talking about arguments for strategy, not for increased probability, correct? And no, my objection is not invalid since it prevents someone from using threats of Heaven and Hell to come to a more `theistic-friendly' state of mind. If that's the case, all objections are invalid.
Considering, in both your comments here and in your thread, you've strongly implied that the purpose of the Wager is to get someone to arrive specifically at the embrace of Christianity, I'm going to suggest you're a pretty bad communicator.
Reread my comment. (Re)read my post. I've said it was about adoption of a strategy intended to produce Christian belief, not just `one should immediately embrace Christianity'.
The OTF rendered as 'Inspect your faith and try to be fair with the evidence' is an OTF pretty much everyone thinks is reasonable (and wildly unoriginal - see Chesterton on this).
I agree, but then why call that suggestion a `reformulation' of the OTF? And why call the repeating of threats of Hell and promises of Heaven a `reformulation' of the Wager?
And here we go again, this suggestion that the wager has the aim of getting an atheist to arrive at Christianity specifically. I don't think that's the only aim of the wager, or the make/break point.
Then you're talking about somebody other than Pascal and some decision matrix entirely different from any that have been introduced thus far. Care to give it a go?
Again, if the wager or wager-variant can succeed in getting atheists to reconsider their atheism and/or approach theism and religion broadly with a more open attitude, it's done one hell of a job. In fact, I'd go so far as to say that the most exclusivist apologist would gladly use an argument which merely pushed an atheist to give up or weaken their commitment to their atheism, even if it didn't in and of itself result in said (ex-)atheist committing to their religion.
I've said it before; I'll say it again. I'm interested in any valid argument, and the sort of person it should convince.
I'm all ears: present your new Wager. I would recommend reading a few related articles by Hájek first, though. And I assume you have the background in decision theory required.
Jesse,
No, that was merely the logical implication of what you were saying.
Except it wasn't a 'logical implication' of what I was saying. I was pointing out the practical reality of these things.
In this case, I don't think we have to sit around that long. Unless you really really really want there to be such a Wager, of course. Then you have a lot of time ahead of you.
Not really - it's pretty easy to reasonably arrive at the position I'm maintaining. You're the one who's bending over backwards to resist it.
And it's not a theistic wager, since it only works on the possibility of such a God. (If atheism requires certainty about the non-existence of any God, Dawkins is not an atheist.) One could get rid of theism entirely and posit some other mechanism by which atheists exclusively reach a paradise.
It's still a theistic wager in that it, as presented, still relies on a God. A reality where a God exists who only saves the atheists is still a theistic reality.
As for your other option, by all means, develop that line of thought. Even before asking you to present it and put it up against the other religious and theistic option, it's still placing you far, far afield from contemporary atheism.
Oh goodness, where to begin... You realize we're talking about arguments for strategy, not for increased probability, correct? And no, my objection is not invalid since it prevents someone from using threats of Heaven and Hell to come to a more `theistic-friendly' state of mind. If that's the case, all objections are invalid.
Mercy me, how to reply to this. (Hey, I can use language like that too. It's fun!)
You do realize that one can form a strategy that is informed by evidence, right? In the wager I'm outlining, the commitment does not require swearing off evaluation of evidence and claims regarding God and religion. Or are you denying that evidence evaluation can be part of a strategy?
Reread my comment. (Re)read my post. I've said it was about adoption of a strategy intended to produce Christian belief, not just `one should immediately embrace Christianity'.
Wonderful - reread MY comments. I've pointed out that 'producing Christian belief' is not the only possible desirable result of these wagers, and that the argument on its own could utterly fail to produce specifically Christian belief yet still have considerable value to the apologist.
I agree, but then why call that suggestion a `reformulation' of the OTF? And why call the repeating of threats of Hell and promises of Heaven a `reformulation' of the Wager?
I didn't say it was necessarily a strict reformulation - in fact I copped to it possibly being a variant argument that had the same spirit of the 'original wager'.
Then you're talking about somebody other than Pascal and some decision matrix entirely different from any that have been introduced thus far. Care to give it a go?
No, it's not 'entirely different'. It's damn similar in that it's been using very similar basic assumptions and framing to arrive at a broadly similar destination. I'd call it a different take on the wager. Maybe you'd call it merely inspired by the wager.
And give it a go? I've been laying it out here. Feel free to respond to it. So far your best reply has been 'Well maybe there's a God who punishes all the theists and rewards all the atheists' and 'Well maybe there's eternal life and theism is not true'. The former has failings I pointed out with the additional wrench of still being a world where theism is true. The latter wreaks havoc on popular atheism in and of itself, and is subject to replies similar to those I pointed out for the atheist-rewarding God.
Got any more shots to take?
Crude,
Except it wasn't a 'logical implication' of what I was saying. I was pointing out the practical reality of these things.
You said: "But I think the more down to earth and basic reasoning has some persuasive power that places one in a situation where theism or general religious belief is arguably preferable to atheism", after saying, "Who wants to be rigorous about it? As I said, you can spin off into objections and counter-replies ad nauseum in either direction." I took that latter as assenting to the (rigorous) invalidity of the Wager, and the former as rationalizing distributing it anyways, all with the goal of "dislodging a person from a content or committed atheism to a more favorable approach and consideration of theism broadly, and on approaching religion generally with a (say, from the religious perspective) better attitude."
My paraphrase: "Pascal's Wager is not valid, but we should use it anyways to try to persuade atheists."
Your `practical' statements struck me as equivalent to `lying in the service of the truth.' If I've misunderstood, correct me.
Not really - it's pretty easy to reasonably arrive at the position I'm maintaining. You're the one who's bending over backwards to resist it.
I've cheated by reading ahead. You've yet to `show' anything. Apparently, the project is harder than it looks. I've told you some of what it will take, even for your weaker intended conclusions.
It's still a theistic wager [...] is still a theistic reality.
Ok, I could repeat the thing about the quotes and add verbiage about how normal people use language. I could repeat that atheists using this alternative table would still be atheists. I'm just not sure that my repeating anything will help you at this point.
You do realize that one can form a strategy that is informed by evidence, right? In the wager I'm outlining, the commitment does not require swearing off evaluation of evidence and claims regarding God and religion. Or are you denying that evidence evaluation can be part of a strategy?
No. The point is that if the Wager fails, the important arguments concern the evidence, not the risks. The point is that if one cannot be successful with a `superdominating' decision matrix in favor of Christianity, one must talk in terms of finite utilities and probability thresholds. The point is that it must be about evidence.
Wonderful [...] to the apologist.
No need; I've already gotten your (intended) point. I was merely demonstrating that I didn't need your correction.
I didn't say it was necessarily a strict reformulation - in fact I copped to it possibly being a variant argument that had the same spirit of the 'original wager'.
Excellent. Formulate it already.
[Cont]
And give it a go? I've been laying it out here. Feel free to respond to it.
Then where the Hell is your decision matrix? What are your possibilities? Are you employing infinite utilities? If not, why should Heaven and Hell only be considered finite rewards? What are the probabilities which we should ascribe to any particular outcomes? What strategies maximize utility? Could these strategies affect the probabilities of the outcomes, and if so, in what way and by how much?
I wouldn't even call my previous comments `objections' to `your argument', since I don't think `your argument' exists. Rather, they are potential objections which your reformulation must be capable of handling.
You've made vague noises. You haven't made an argument. If you have a decision theoretic argument, show it to me. If you know LaTeX, you can use this site to produce nice-looking mathematical symbols. Put them in a blog post.
Stun me and with a valid `reworking' of the Wager, as applied to Christianity or theism. Until you do so, I'll work on the well-evidenced assumption that you don't know what you're talking about.
I repeat that any successful reformulation of the Wager would be of interest. If one had a limited version that was valid for atheists who ascribe (say) prob(theism)=0.49 or prob(Christianity)=0.4, then for other arguments directly concerning the probability of these cases I would use a different target threshold probability than current standards like 1/2, 0.9, 0.95, and 0.995. In other words, it would make the project of convincing atheists easier - even if it did not apply to strongly convinced atheists - as the requisite strength of the cumulative evidential case would be lessened.
Hence my interest, even though I ascribe prob(Christianity)<<0.4.
Jesse,
Your `practical' statements struck me as equivalent to `lying in the service of the truth.' If I've misunderstood, correct me.
Bwahaha. Considered yourself corrected, then.
No, I was regarding the desire to 'rigorously formulate' and argue ad nauseum about these things as a ridiculous prerequisite for having a reasonable belief. How you managed to get "Sure, I think it's invalid, but use it anyway!" out of that is bizarre to me, but whatever. It's handled.
I've cheated by reading ahead. You've yet to `show' anything. Apparently, the project is harder than it looks. I've told you some of what it will take, even for your weaker intended conclusions.
I've shown plenty. You've actually helped by offering up the objections you have. If that's what you have to reach for, it speaks for itself.
Ok, I could repeat the thing about the quotes and add verbiage about how normal people use language. I could repeat that atheists using this alternative table would still be atheists. I'm just not sure that my repeating anything will help you at this point.
Do I have to repeat that an objection to Pascal's wager that basically points out an alternative theistic or near-theistic possibility isn't much of an objection? This is a little like those moves where someone gives a general argument for God (say, Kalam) and an atheist replies "Well, even if I grant that this argument works, it doesn't show that YOUR God is this God!" Then comes the task of reminding them that if any God exists, atheism is false.
The point is that if the Wager fails, the important arguments concern the evidence, not the risks. The point is that if one cannot be successful with a `superdominating' decision matrix in favor of Christianity, one must talk in terms of finite utilities and probability thresholds. The point is that it must be about evidence.
And I'm saying that you don't need the result to 'favor Christianity' for the wager - yes, or something very similar to the wager - to have considerable force. The risks could still be playing a major role even if they weren't exclusively relied on.
Excellent. Formulate it already.
...
If you know LaTeX, you can use this site to produce nice-looking mathematical symbols. Put them in a blog post.
Nah, I'm not drawing decision matrixes for you or using LaTeX. I'm going to speak in casual, down to earth language. Grating, I know.
Let's start with some simple basics. On popular, contemporary atheism, no God/gods exists, no God/gods ever existed, no God/gods will exist in the future. All men have finite life, and death is permanent.
It's in the space of live possibilities - let's put aside the question of odds entirely for now, other than saying > 0 - that there is some desirable life after death attainable by us, which depends on our actions.
It's a reasonable working assumption to believe that if any one of those live possibilities is actual, reason can assist us in comparing and contrasting all of those live possibilities.
If none of those live possibilities is actual and atheism as stated is true, then choosing wrongly ultimately does not matter.
Disagree with me yet? I'm guessing 'yes, on every single point', but either way - go for it.
Crude,
No, I was regarding the desire to 'rigorously formulate' and argue ad nauseum about these things as a ridiculous prerequisite for having a reasonable belief.
I don't argue that at all. But if you claim a valid decision theoretic argument for theism, I will expect you to use... decision theory. I know that sounds absurd.
Disagree with me yet? I'm guessing 'yes, on every single point', but either way - go for it.
Yes, but I shouldn't need to repeat myself. Sorry, `down to earth' language is not usually a substitute for rigorous argument, especially not in matters near probability theory. I note that you've yet to defend your decision table, and you've assumed that if theism is true, then exclusive salvation/immortality as based on belief is true.
Interestingly, your (finite) utilities and probabilities are strangely absent.
Again, you'd see the gaps in the argument if you actually tried to argue. I'm not merely demanding your time here.
*as based on belief/action is true.
Jesse,
I don't argue that at all. But if you claim a valid decision theoretic argument for theism, I will expect you to use... decision theory. I know that sounds absurd.
I have this funny standard, one I've seen philosophers and scientists alike use as a rule of thumb: If it can't be communicated in plain language, chances are most people don't need to know it.
I have no problem making reference to solid reasoning based on decision theory. No, I'm not going to learn or rely on notation that I feel would obscure my point.
Speak plainly.
Yes, but I shouldn't need to repeat myself. Sorry, `down to earth' language is not usually a substitute for rigorous argument, especially not in matters near probability theory. I note that you've yet to defend your decision table, and you've assumed that if theism is true, then exclusive salvation/immortality as based on belief is true.
Like I said, I'm going to stick with plain language. Try it, you may like it. I've laid out some starting assumptions here - this isn't even a complete argument, it's the beginnings of it, letting you know what I'm reasonably taking for granted.
Further, here's a problem. You say I've 'assumed that if theism is true, then' - but read what I wrote again. The space of possibilities I gave is not exclusively theistic.
Now, you can object that my possibility space leaves out, say... universalism. Alright, include universalism in the possibility space.
So what are your objections so far? Are you claiming it's unreasonable to assume that reason can be useful in comparing/contrasting the possibilities?
Crude,
I have this funny standard, one I've seen philosophers and scientists alike use as a rule of thumb: If it can't be communicated in plain language, chances are most people don't need to know it.
`Most people' might not, but for people (like me) who want to know what threshold of probability is important in arguments about theism, it is. And I wonder whether a philosopher familiar with Pascal's Wager and the objection feels safe ignoring decision matrices into which `plain speak' could easily be interpreted. In probability and decision theory, it is a truism that errors are usually subtle. Standard exercises in relevant texts all insist on this point. Show me a philosopher who feels comfortable about fudging math in these contexts, and I will show you a poor philosopher. (It might be possible that trivial math has been omitted in a paper, but the math should have been done.)
So what are your objections so far? Are you claiming it's unreasonable to assume that reason can be useful in comparing/contrasting the possibilities?
No, as I've said again and again, which is why you need to make the various utilities and probabilities explicit. If you had read my post, you would know that even with finite utilities, the simplest decision table, and the assumption of dominance, errors still happen.
Another key omission: for a decision theoretic argument, it is odd that you have yet to propose a strategy as a conclusion.
I note that your proposals could easily be simplified, as you have presented them. Here is how you could do it instead:
1. Outcomes: Either immortality occurs, or it does not.
2. A mortality condition: If atheism is true, immortality is not realizable.
3. Possibility condition: If theism is true, it is possible to realize immortality through action.
4. Disparity condition: Actions of type X most probably realize immortality.
5. Ergo, one should perform a strategy of type X.
Now, for this to be valid, one has to ascribe utilities for the outcomes in (1), carefully deciding the various possible afterlifes that might result and correspondingly ascribing realistic utilities and probabilities. I won't take (2) as controversial; if all else fails, I'm happy to let you stipulate it. (3) is a little more difficult, as it is by conjunction rule going to be less probable than immortality, and this is more strongly the case for (4). Even now, we haven't yet gotten to a valid argument, since we still have to spell out the details of X and ascribe differing probabilities of `success' to differing strategies.
But to know exactly what magnitudes are important, you'll have to do the maths.
Jesse,
Show me a philosopher who feels comfortable about fudging math in these contexts, and I will show you a poor philosopher. (It might be possible that trivial math has been omitted in a paper, but the math should have been done.)
Show me a philosopher who demands that everyone get rigorous when discussing these subjects, and I'll show you a philosopher who no one talks to and few people listen to.
Really, what's wrong with just relaxing and conversing on this point? I could understand if I was booming about what a brilliant philosopher I am and how I was presenting a knock-down unassailable argument - but really, I'm just defending what I see as a reasonable argument in a combox. And hey, I'm interested in your feedback.
No, as I've said again and again, which is why you need to make the various utilities and probabilities explicit. If you had read my post, you would know that even with finite utilities, the simplest decision table, and the assumption of dominance, errors still happen.
You haven't said it 'again and again', and I haven't even suggested I've laid out an entire argument here. I was starting out with the assumptions an argument I'd make would be based on, and seeing if we're on the same page with them.
I'll comment on a couple things.
3. Possibility condition: If theism is true, it is possible to realize immortality through action.
Have you missed the part where I explicitly said that the space of possibilities I outlined were not exclusively theistic? And that I followed up with admitting universalism into the mix?
2. A mortality condition: If atheism is true, immortality is not realizable.
I said 'on popular, contemporary atheism'. I think that's a reasonable qualifier - do you deny that popular, contemporary atheism rules that immortality is not realizable?
C'mon, you can see some humor in here from my perspective, can't you? Where you're really mixing up what I'm saying in a frank manner?
How about this: Freaking relax. We're not in a knock-down drag-out debate-fight here. We're two guys in a combox having a conversation. If you don't have time for this because you've got Serious Business to attend to with Serious Philosophers (like Loftus!), alright. Maybe you can't stand just talking in plain language about these things, but what can I say. I find that weird.
Crude,
Some things out of order:
Have you missed the part where I explicitly said that the space of possibilities I outlined were not exclusively theistic? And that I followed up with admitting universalism into the mix?
I didn't miss it. I was granting you a stronger assumption for the purposes of simplification. I hope you don't mind. I also caught the part about universalism, which you'll notice is accounted for in the premises.
You haven't said it 'again and again', and I haven't even suggested I've laid out an entire argument here. I was starting out with the assumptions an argument I'd make would be based on, and seeing if we're on the same page with them.
Oh, so earlier when I asked for an argument and you said you already had one, you were having a bit of fun?
On to that subject: I'm noticing a trend here. Whenever you're backed into a corner, you suddenly become intensely humorous and ask for me to relax. On this occasion, I'm really not worked up at all, but I'm happy to insist that you `put up or shut up' so long as you're happy to continue fudging. I'm wholly aware that you're just some guy on the internet, and this is a comment box conversation.
I note that I do think it still has some interest, as I am curious as to what Dr. Reppert thinks of Pascal's Wager and the objections. I think that his opinion is important and more influential than my own, and that it will matter to those who `audience-free' philosophers who actually care about rigor.
And an obvious note: I'm happy to talk in plain language, until plain language no longer works. Physics can be talked about in normal prose, but only to a limited extent. The same is true of math and much of philosophy.
So you'll notice that when I reworked your argument - here I am again, as always, doing your work for you - I used plain English. But then I stated that to complete the argument, one would have to start assigning numbers.
Without mathematical notation, it's hard to express real numbers (and their ordering) in `plain English'. I imagine that if that were possible, it would actually over-complicate things. Yet what we've been discussing reduces entirely to a question of an order relation on the reals.
I took you as far as I think plain language can take you. If you like, you can go further.
My reaction to this post was somewhat more simplistic, but it seems to me that:
1. Pascal's Wager is for those who are actively looking for an answer to the question of religious belief, not for those who have a settled view.
2. Whatever its merits logically, it doesn't seem to compel belief in many people - either because we can think of extra possibilities that a simple statement of the wager omits, or because it doesn't add any new evidence and so (if successful) leaves a person wanting to believe but still not having sufficient evidence.
3. Nevertheless it is not devoid of truth and effectiveness because we all understand risk management and its benefits, and the wager is a form of risk management.
4. Therefore I think the wager's main value is in providing a motive to look hard for more evidence either way. A person who understands the wager and hasn't considered the evidence seriously may reveal something about their openness to evidence. I doubt that includes present company.
unkleE,
What you've said sounds fair enough, since you appear to think the Wager useful for inviting investigation of evidence - a worthwhile invitation to make, I think. However, since it is not sound or valid, I would recommend finding a different way to invite investigation.
For example - and this is always important - you could find common slogans, e.g. "there is no evidence for God", and refute them. Or, you can take a widely misunderstood argument - any serious cosmological argument would do - and show how they are misunderstood, and what the atheist must reject in order to maintain incredulity.
Due to my own small experience, I feel that philosophy of religion is best introduced as a competitive, polemical field of practice for virtually any item of philosophical interest, whether it be free will, epistemology, metaethics, idealism v. materialism, etc., etc.
There are many good ways to invite a look at the evidence and serious argumentation. I don't see Pascal's Wager as particularly useful for this. Indeed - and I think wrongly - I think it prevents atheists from investigating such things. (So that's the best they have to offer? A threat of Hell? This is hucksterism, oh yawn, and so on.)
Jesse,
I was granting you a stronger assumption for the purposes of simplification. I hope you don't mind. I also caught the part about universalism, which you'll notice is accounted for in the premises.
I do mind, because it's a stronger assumption than I need it to be. No, I don't see where in 1-5 you account for universalism.
Oh, so earlier when I asked for an argument and you said you already had one, you were having a bit of fun?
You mean earlier when I said that I've been laying it out in my comments, then when you insisted I lay out the whole argument I started anew - complete with offering up the assumptions I was working with for your evaluation, seeing what agreement we had before working forward?
Do you know the difference between 'I have an argument', 'I've fully laid out the argument here', and 'I've laid out some of the argument, but it's incomplete at this point'?
On to that subject: I'm noticing a trend here. Whenever you're backed into a corner, you suddenly become intensely humorous and ask for me to relax. On this occasion, I'm really not worked up at all, but I'm happy to insist that you `put up or shut up' so long as you're happy to continue fudging.
"Intensely humorous"? Where? As much as I love humor, I've been pretty goddamn plain throughout this conversation. As for being backed in a corner - what "corner" am I backed into? So far we're discussing preliminary considerations and mostly bitching about method. Not exactly corner-backing.
Yes, I've suggested you're being a little uptight here, since you're spending a lot more time complaining about my lack of rigorous notation than anything else.
So you'll notice that when I reworked your argument - here I am again, as always, doing your work for you - I used plain English.
"As always". Adorable, as if we've talked more than what, once in the past?
And "doing my work for me"? I think it's clear you're largely understanding what I'm saying without my 'reworking the argument', so what's the point? But hey, glad to hear you admit that at least so far plain language has been serviceable in this conversation.
I took you as far as I think plain language can take you. If you like, you can go further.
Then I'll assume you accept what I've laid out so far as reasonable and move on in a followup.
Crude,
I do mind, because it's a stronger assumption than I need it to be. No, I don't see where in 1-5 you account for universalism.
For the latter: Look at your objection to (3) and reread (3). Where is the contradiction between (3) and universalism? For the former: suppose your argument works against all atheists except for those who ascribe a significant probability to an atheistic afterlife. Would that not itself be of interest? If that's what saves an atheist from accepting your intended conclusion, that would represent serious progress.
Do you know the difference between 'I have an argument', 'I've fully laid out the argument here', and 'I've laid out some of the argument, but it's incomplete at this point'?
And do you understand "your purported argument is fatally incomplete, and I do not have to let you `Fermat' your way out of this."
So far we're discussing preliminary considerations and mostly bitching about method. Not exactly corner-backing.
No, we're really at an impasse here: you cannot go further without the math. I don't think you can do the math. I call that a corner, and it's not the only one you have a foot stuck in. For the note on the trend, I could dig up thread history, but I'm not that bored yet.
"As always". Adorable, as if we've talked more than what, once in the past?
Four or five times at this point, I think, and on several occasions I've had to spell out to you what you need to do and how you'd need to do. I won't count the number of times I have had to give reading lessons.
Then I'll assume you accept what I've laid out so far as reasonable and move on in a followup.
I wouldn't go that far, since much of what you've said is confused. If you're ready to move on to the math corresponding to (1)-(5), I'm ready to look.
Jesse,
For the latter: Look at your objection to (3) and reread (3). Where is the contradiction between (3) and universalism?
There's an implied contradiction, since it makes reference to 'possible through action', but at least on the forms of universalism I'm most familiar with, 'action' isn't required for salvation.
For the former: suppose your argument works against all atheists except for those who ascribe a significant probability to an atheistic afterlife. Would that not itself be of interest?
Depends what you mean by 'of interest'. I've already made it clear what sort of atheists I principally have in mind here - I'd consider the move from atheists who reject and act as if they reject any afterlife, to atheists who accept and act as if they accept even an atheistic afterlife, to be progress.
And do you understand "your purported argument is fatally incomplete, and I do not have to let you `Fermat' your way out of this."
Yes, I understand "fatally incomplete". It's pretty pointless to lodge that one while the argument is in the process of being laid out.
No, we're really at an impasse here: you cannot go further without the math. I don't think you can do the math. I call that a corner, and it's not the only one you have a foot stuck in. For the note on the trend, I could dig up thread history, but I'm not that bored yet.
Hey, we'll see how far I can get without the math then. Worst case, I really do have to figure out how to get the math involved - that'd be fine by me.
As for the 'trend', baloney. More below.
Four or five times at this point, I think, and on several occasions I've had to spell out to you what you need to do and how you'd need to do. I won't count the number of times I have had to give reading lessons.
Geez, still worked up over the whole feminist thing? We've talked there, here, and at one other incidental point in the past. Will you feel better if I admit you're just a shining knight of Girl Power? ;)
I wouldn't go that far, since much of what you've said is confused. If you're ready to move on to the math corresponding to (1)-(5), I'm ready to look.
Nah, let's see what I can do without math. It'll be fun!
Crude,
There's an implied contradiction, since it makes reference to 'possible through action', but at least on the forms of universalism I'm most familiar with, 'action' isn't required for salvation.
Then looking at (4), you'll notice I've left `type X' open. In this case, `X' would be `anything'. (Up to strategy, then, there should be no difference between the implications of (normal forms of) atheism and universalism.)
Depends what you mean by 'of interest'. I've already made it clear what sort of atheists I principally have in mind here - I'd consider the move from atheists who reject and act as if they reject any afterlife, to atheists who accept and act as if they accept even an atheistic afterlife, to be progress.
If you think it really important to remove the premise, I won't stop you. But it will unnecessarily complicate things in the future.
A note: in this and other comments, you appear to think that conclusions from decision theory involve `acting on the truth' of conflicting hypotheses. That's obviously not what they show, as that would be asking agents to be contradictory. Rather, one is acting on probabilities of possibilities, and preferences regarding the same.
For example, if I am told that I can enter a game - a roll of a fair die - in which I win $100 if it lands on 2, 3, 4, 5, or 6, and in which I am shot in the head if it lands a `1', I would not play. By doing so, I am not assuming that by playing, I would be shot. Rather, by playing there is a significant chance I might be shot, which is not worth the more significant chance of a relatively less important reward.
It's pretty pointless to lodge that one while the argument is in the process of being laid out.
And it's pointless to say that you are dealing with my objections to an argument that does not exist, and act as though the argument has been made. You simply were not clear about this. If anything, you were clearly doing something else.
Geez, still worked up over the whole feminist thing? We've talked there, here, and at one other incidental point in the past. Will you feel better if I admit you're just a shining knight of Girl Power? ;)
And I've even devoted several comments already to what you think I think is important, this `badge' or `shining knight' noise. I could do you work for you again, and repost those comments here, but instead I'll take my point as made.
Nah, let's see what I can do without math. It'll be fun!
I know what you can do without math beyond what we've covered: nothing worthwhile. I know what you can also do: make a lot of mistakes.
If you want to make a decision-theoretic argument - especially one involving controversial premises on which there is no consensus - use decision theory. Everything else is noise.
Note on humor: I like humor (even sarcasm), and I think it has great potential for aiding rationality. It can help one to avoid improper focus and reveal subtle fallacies. However and especially when selectively applied, it can be used to mask errors, becoming a detriment to one's rationality. So when I notice a correlation between a certain state of argument and your invocations of `humor/relax/this is the internet', I have to wonder...
Moving on, a repeat of the assumptions I'm bringing into this.
On contemporary, popular atheism (cpa), no God/gods exist, no God/gods ever existed, no God/gods will exist in the future, all men have finite life, and death is permanent.
A wide range of possibilities that entail a desirable eternal life are live options, both theistic and not. (Naturally, even the 'atheistic' options would differ from contemporary, popular atheism as stated.)
It's a reasonable working assumption to believe that reason can assist us in comparing and contrasting the live possibilities.
If none of those live possibilities are actual and contemporary, popular atheism as stated is true, then believing wrongly ultimately doesn't matter.
Moving on...
If believing wrongly ultimately doesn't matter in the case that cpa is true, but believing wrongly possibly matters in the case that cpa is false, the believer in cpa already has some reason to abandon cpa. It doesn't need to certainly matter ("Believe wrongly or face hell / miss heaven") - it could be the case that universalism is true, for example. But a similar situation applies to such believers (Believing wrongly won't matter if universalism is true either.)
If it's a reasonable working assumption to believe that reason can help us compare and contrast the live possibilities, then we can discount possibilities that are at the level of mere logical possibilities (Say, the God who damns all theists and grants heaven to all atheists, or the God who only grants heaven to people who own the complete ALF on laserdisc, and who never tells anyone of this and who leaves no evidence of this) if reason and evidence suggest other possibilities are more likely.
That still leaves a variety of live possibilities, maybe not all of them necessarily theistic. And we're still left with the task of evaluating the evidence, and reasoning which among these possibilities to invest ourselves in. But whatever we end up deciding is the best choice to invest in, we're still extremely far away from cpa (unless the cpa believer can argue that belief in and acting according to cpa was also the best choice for securing a possible eternal life.), and - granting what I've laid out at the beginning,a nd unless that 'unless' can be justified - we're still making the more reasonable decision compared to content belief in cpa.
Jesse,
Then looking at (4), you'll notice I've left `type X' open. In this case, `X' would be `anything'. (Up to strategy, then, there should be no difference between the implications of (normal forms of) atheism and universalism.)
I don't think it's very clear when the 'actions' in question are 'nothing'. But there you go.
And I've even devoted several comments already to what you think I think is important, this `badge' or `shining knight' noise. I could do you work for you again, and repost those comments here, but instead I'll take my point as made.
So long as the point is 'I'm really worked up over that conversation and am just itching to lay into you for any imaginary or piddly reason', yeah, point made. Hold whatever grudge you want, I suppose.
I know what you can do without math beyond what we've covered: nothing worthwhile. I know what you can also do: make a lot of mistakes.
No doubt - you're the mathematician here, not me. But I never presented myself as being extremely adept with math anyway - I don't think it's necessary here to make the point I intend to.
Note on humor: I like humor (even sarcasm), and I think it has great potential for aiding rationality.
Sir, I question your estimation of the utility of humor. You must be an interesting person to go to the movies with.
So when I notice a correlation between a certain state of argument and your invocations of `humor/relax/this is the internet', I have to wonder...
Yes, I'm sure the pull to dream up imaginary correlations when you're really angry at someone and want to show them what-for is strong. Try to resist it, though. Rather impedes the ol' rationality. ;)
If believing wrongly [...] (Believing wrongly won't matter if universalism is true either.)
Assuming that `belief' is the type X category of actions making the `desirable outcome' more probable than others, and to a very large degree, there might be room to make this valid.
If it's a [...] possibilities are more likely.
Or we can keep the decision matrix comprehensive. In order to know which options are `safe' to discount, you would have to find an upper bound for the probabilities. You would also have to know their relative utilities. After all, I might prefer a Heaven that involves coffee shops and conversations with (even heretical) historical figures instead of one of eternal praising of the Creator. And here again, defending your `X' is vital.
And [...] we're still making the more reasonable decision compared to content belief in cpa.
Where did this come from? Where is the strategy? Where is the description of actions? What are the threshold probabilities? Who are you talking to?
Some possibilities are more probable than others. Color me wow-ed. We're back to where we started, as was predictable.
Crude,
I don't think it's very clear when the 'actions' in question are 'nothing'. But there you go.
No, the actions in question are `anything'. `Some set of actions' includes this as a special case, as is wholly unmysterious to those who are familiar with math.
No doubt - you're the mathematician here, not me. But I never presented myself as being extremely adept with math anyway - I don't think it's necessary here to make the point I intend to.
I think it is. As again, you'd know if you knew the math.
Yes, I'm sure the pull to dream up imaginary correlations when you're really angry at someone and want to show them what-for is strong. Try to resist it, though. Rather impedes the ol' rationality. ;)
So far, I've used my `imaginary correlations' to predict your behavior rather well. I'll stick with them.
(Oh, and until I'm published, I prefer `math major' or `nerd' to `mathematician'. I don't think I need the career title yet.)
And a note: So far, nearly everything you've said has been entirely consistent with the traditional, fallacious Wager, just with different words. If you are using finite utilities, it's a simple mathematical fact - using the expected utility equation of a strategy - that you are going to have boundaries on the involved probabilities of the outcomes given the adoption strategy, as compared with the probabilities of the outcomes (with the same utilities) on adoption of differing strategies. Formally, you want to show: for S in X and T in `not X', utility(S)>utility(T). (For the case of universalism, `not X' is empty, so this criterion remains valid (vacuous truth).)
Now, in order to do this, you have to show that for every such S, you get that inequality across all possible outcomes, including varieties of afterlife and varieties of theology generally. Again, this task is simplified if one has specified utilities which render certain outcomes of very low probability insignificant. And of course, for certain theologies, you have to check for the effect of strategies on the probability of the outcomes.
But you need the math for all of this! Hard work! How frustrating!
Or we can keep the decision matrix comprehensive. In order to know which options are `safe' to discount, you would have to find an upper bound for the probabilities.
What's the probability that one can secure a pleasant afterlife by watching and owning the complete 'ALF' series?
You would also have to know their relative utilities. After all, I might prefer a Heaven that involves coffee shops and conversations with (even heretical) historical figures instead of one of eternal praising of the Creator.
I think that sort of consideration opens the door to a lot of problems - what if the afterlife I think is the most likely also entails things I'm not a fan of, like spending a lot of time talking to Roseanne Barr? Well, wait, what if I can learn to enjoy taking to Roseanne Barr a lot?
Where did this come from? Where is the strategy? Where is the description of actions? What are the threshold probabilities? Who are you talking to?
The strategy is "abandon cpa and investigate the live possibilities to choose one from among them, unless your investigations lead you to think that believing the cpa provides the best option for an afterlife". All the rest rather depends on those investigations, eh?
Some possibilities are more probable than others. Color me wow-ed. We're back to where we started, as was predictable.
I think I've given, especially if you grant what I laid out at the start, reason to abandon cpa (at least initially, depending on how that investigation goes.)
So far, nearly everything you've said has been entirely consistent with the traditional, fallacious Wager, just with different words.
How? What I've argued leaves atheism open as a live possibility to be investigated, though it's obviously different from atheism on the cpa. My conclusion wasn't that one should take acts that are likely to lead them to believe in Christianity specifically, or any particular belief other than the rejection of the cpa (and even then it's conditional.) That doesn't seem very consistent with the traditional wager, certainly not as you've presented it earlier.
But you need the math for all of this! Hard work! How frustrating!
Hey, I didn't say you couldn't use math in your investigation of the various possibilities. Why, maybe you can even argue that you're absolutely going to need math at that point. In which case, math it up.
What's the probability that one can secure a pleasant afterlife by watching and owning the complete 'ALF' series?
Probably lower than missionary work. But this strategy is just as good as doing missionary work on Pascal's assumptions. And had Pascal checked his assumptions against a mixed strategy, we might not have needed to have this conversation.
It also might be just as good depending on the ratio of the probabilities of exclusive salvation to the differing utilities of atheism/theism, where theism has a variety of possible, conflicting results.
To know, you'll have to do the work. I know it's hard.
I think that sort of consideration opens the door to a lot of problems - what if the afterlife I think is the most likely also entails things I'm not a fan of, like spending a lot of time talking to Roseanne Barr? Well, wait, what if I can learn to enjoy taking to Roseanne Barr a lot?
Hence the difficulties of arguing based on (possibly quite small) probabilities of the realization of threats/promises. If I promised you thirty trillion dollars so long as you kicked a kitten, you probably wouldn't kick that kitten, even if the utility of `not kicking a kitten' is far lower than thirty trillion dollars. Because, alas, the worthwhileness of my promised reward depends on the probability of your realizing it, which is very, very tiny indeed. In fact, you probably wouldn't do it no matter what reward I promised you, even if you admitted that there is a possibility of my granting it to you, however slim.
The strategy is "abandon cpa and investigate the live possibilities to choose one from among them, unless your investigations lead you to think that believing the cpa provides the best option for an afterlife". All the rest rather depends on those investigations, eh?
And a great deal more besides.
Why does that strategy - which isn't a strategy, but a command - follow? How does abandoning `cpa' increase my expected utility? Why not simply investigate the `live possibilities' while remaining an adherent of `cpa'? (Hint: You'll need to introduce actual symbols for utilities and probabilities.)
I think I've given, especially if you grant what I laid out at the start, reason to abandon cpa (at least initially, depending on how that investigation goes.)
Except for the whole validity thing. I know, I'm a pedant: I expect arguments to be valid and sound, which is admittedly old-fashioned.
How? What I've argued leaves atheism open as a live possibility to be investigated, though it's obviously different from atheism on the cpa.
As does Pascal's wager. The intended conclusion of the argument has nothing to do with the probability of atheism.
My conclusion wasn't that one should take acts that are likely to lead them to believe in Christianity specifically, or any particular belief other than the rejection of the cpa (and even then it's conditional.) That doesn't seem very consistent with the traditional wager, certainly not as you've presented it earlier.
Substitute the words. The structure - and the failures of validity - remain, unless you specify finite utilities and finite probabilities for which it holds, and check your intended strategy for dependencies.
Hey, I didn't say you couldn't use math in your investigation of the various possibilities. Why, maybe you can even argue that you're absolutely going to need math at that point. In which case, math it up.
Hint: The math isn't going to help you. I've done sketches, but if you want to do the math for your argument, you'll need to spell out the assumptions you need explicitly and formalize them.
You could take my word for it (or the words of Hájek, last I checked) that such an approach isn't going to get you anywhere. But to see the beauty of that time-saving insight in its full generality... Care to guess what you'll need?
Probably lower than missionary work. But this strategy is just as good as doing missionary work on Pascal's assumptions. And had Pascal checked his assumptions against a mixed strategy, we might not have needed to have this conversation.
...
To know, you'll have to do the work. I know it's hard.
So walk me through it. Math is a mystery to me, and I'd love to see you estimate the probability of attaining a pleasant afterlife if you own and watch the complete ALF collection.
Why, I may even learn something!
If I promised you thirty trillion dollars so long as you kicked a kitten, you probably wouldn't kick that kitten, even if the utility of `not kicking a kitten' is far lower than thirty trillion dollars. Because, alas, the worthwhileness of my promised reward depends on the probability of your realizing it, which is very, very tiny indeed.
What if I enjoyed kicking kittens and had nothing to lose by doing so besides? What if I had no idea of the probability of my realizing the reward?
How does abandoning `cpa' increase my expected utility? Why not simply investigate the `live possibilities' while remaining an adherent of `cpa'?
I think if you're investigating the possibilities and sincerely treating them as live, you've pretty much abandoned cpa anyway. At the very least you've moved from 'there is no afterlife and there is/was/never shall be any God' to a different position - these things aren't treated as live possibilities on cpa as I defined it.
As does Pascal's wager. The intended conclusion of the argument has nothing to do with the probability of atheism.
The intended conclusion does seem to be to ultimately lead one to reject atheism and to take actions which lead one to accept Christian theism and reject atheism. That's not an intended conclusion of my argument.
But to see the beauty of that time-saving insight in its full generality... Care to guess what you'll need?
An estimation of the probability of attaining a pleasant afterlife if one owns and watches the complete ALF series, for one thing. Maybe I'll learn how to manage that, with your input.
More things out of order:
What if I enjoyed kicking kittens and had nothing to lose by doing so besides? What if I had no idea of the probability of my realizing the reward?
For the first: my offer would be irrelevant. For the second: you could still calculate bounds on probabilities for which `kitten-kicking' strategies are wise. For an unstated third: do you like kicking kittens? If not, does my offer tempt you at all? If not, do you think that compromises your rationality? If not, do you understand that this implies - as a fact - something about your utilities and the probabilities you ascribe to the outcomes?
I think if you're investigating the possibilities and sincerely treating them as live, you've pretty much abandoned cpa anyway. At the very least you've moved from 'there is no afterlife and there is/was/never shall be any God' to a different position - these things aren't treated as live possibilities on cpa as I defined it.
Then you have defined it as ascribing probability 0 to all the various theologies, which is not the best description of popular atheism. Also, if your argument is addressed to `certain' atheists, then the expected utility of belief in a theology is... 0.
You'd notice this, had you the maths (or had you read the SEP article, which discusses this case.)
So walk me through it. Math is a mystery to me, and I'd love to see you estimate the probability of attaining a pleasant afterlife if you own and watch the complete ALF collection.
Why, I may even learn something!
Equivocating, you would ascribe the same probability to `success' on the `Alf strategy' as you would to other strategies for which you perceive no correlation with `success' to hold. You could treat this as a block of strategies in a partition of your possible strategies.
For the math, it will take you a while if you have no experience. I'm not going to pretend that it will be quick and easy. You will need (1) elementary probability theory, which requires (2) an introductory background in abstract mathematics/set theory, and you will also need (3) a Bayesian primer (I have one posted which presupposes math background, and there are many introductory texts which are better). After all of this, you'll need an introduction to decision theory. If you can understand Jeffrey's Subjective Probability: The Real Thing (google it), you're well on your way, but for much depth you may need his The Logic of Decision, which I cannot locate on the internet. However, many primers on decision theory are available.
Once you've done these things, you perform the following procedure:
1. Define a `Wager-like' procedure as an argument for a `strategy of theistic belief' as based on utilities concerning possible afterlifes.
2. Critique the original Wager and discover what would be required to make this argument sound, valid, and persuasive/interesting to an atheist.
3. Notice that what the argument requires is stronger/more controversial than what is required for extant, direct arguments for theism, and appropriately conclude that such an approach will be unsuccessful.
The intended conclusion does seem to be to ultimately lead one to reject atheism and to take actions which lead one to accept Christian theism and reject atheism. That's not an intended conclusion of my argument.
It is the structure that is the same, not the particular words. When validity is the article of dispute, that's what matters. I did not say, "your argument is identical to Pascal's Wager". It isn't. Rather, your argument - insofar as it is formulated - commits the same mistakes. It fails to account for the same cases - e.g. mixed strategies - which render the Wager invalid. It also fails to account for the same cases - e.g. incomplete outcome matrices - which affect the soundness of the Wager.
*Clarification: On the `0 probability' case, it's more accurate to say that the expected utility of any given strategy depends entirely on the utility of atheism, as the summands in the expected utility calculation are zero where the probability of the corresponding outcomes are zero.
For the first: my offer would be irrelevant.
Irrelevant? Possibly as far as kicking the cat is concerned, since I perhaps intend to kick the cat whether or not you make the offer. On the other hand, if I'm willing to kick the cat no matter what, then it seems like - if you made the offer - I should accept it.
Certainly I shouldn't reject it, right?
For the second: you could still calculate bounds on probabilities for which `kitten-kicking' strategies are wise.
Sure, but I'd be missing an important piece of information. I'm sure there'd be quite a lot I'd have to take in account (What are my feelings on cat kicking? Do I stand to lose anything by cat kicking? etc.)
For an unstated third: do you like kicking kittens? If not, does my offer tempt you at all? If not, do you think that compromises your rationality? If not, do you understand that this implies - as a fact - something about your utilities and the probabilities you ascribe to the outcomes?
1. Maybe I don't know. Hey, maybe this is a good way to find out. Maybe I don't, but could learn to like it. 2. That would depend heavily on who I was and what probabilities I was aware of, what I believed, etc. 3. That depends on a wide variety of factors that are currently up in the air for this example.
Then you have defined it as ascribing probability 0 to all the various theologies, which is not the best description of popular atheism.
Here I disagree on two counts. First, I'm not sure that one needs all the various religious claims to be raptly considered to have probability 0 for them not to be treated as live options and warranting investigation as you've described. Second, I think 'investigating these possibilities as live options' is actively discouraged in cpa.
Also, if your argument is addressed to `certain' atheists, then the expected utility of belief in a theology is... 0.
As I said above, I'm not convinced one needs to regard all religious possibilities as having probability 0 to not treat them as live options or deserving investigation.
Equivocating, you would ascribe the same probability to `success' on the `Alf strategy' as you would to other strategies for which you perceive no correlation with `success' to hold. You could treat this as a block of strategies in a partition of your possible strategies.
Alright, hold off on the Alf estimations. Let's try another tack.
You make reference to mixed strategies. I read your entry on this - you say the problem with Pascal's wager is that (putting it as I understand it) since Pascal puts the payoff for belief in God as infinite, then you have exactly equal reason to become a missionary (.99 probability of resulting Christian belief) as you do to drink a beer (.0001 probability of resulting Christian belief).
Am I getting that right?
Irrelevant? Possibly as far as kicking the cat is concerned, since I perhaps intend to kick the cat whether or not you make the offer. On the other hand, if I'm willing to kick the cat no matter what, then it seems like - if you made the offer - I should accept it.
Yes, I meant up to your desire to kick a kitten.
Sure, but I'd be missing an important piece of information. I'm sure there'd be quite a lot I'd have to take in account (What are my feelings on cat kicking? Do I stand to lose anything by cat kicking? etc.)
You can do that in-depth introspection, but it won't change the bounds on the probabilities/utilities required for you to wisely choose to not kick/kick a kitten. And if you're interested in finding a range of people who should be convinced to kick a kitten by that promise, those bounds are what interests you, however you might relate to them personally.
1. Maybe I don't know. Hey, maybe this is a good way to find out. Maybe I don't, but could learn to like it. 2. That would depend heavily on who I was and what probabilities I was aware of, what I believed, etc. 3. That depends on a wide variety of factors that are currently up in the air for this example.
For (3), actually, the boundaries remain no matter what you wind up doing. Decision theory doesn't have to be restricted to cases of `conscious choice'; it can be descriptive.
Here I disagree on two counts. First, I'm not sure that one needs all the various religious claims to be raptly considered to have probability 0 for them not to be treated as live options and warranting investigation as you've described. Second, I think 'investigating these possibilities as live options' is actively discouraged in cpa.
No, but your argument for abandoning cpa to enable `active consideration' - assuming it's valid elsewhere, and it isn't - assumes that cpa ascribes probability zero to the various theologies, unless you have bounds for the relevant probabilities and utilities. And that is precisely what you've been avoiding.
Am I getting that right?
Yes, that's one objection to Pascal's wager which I came across thanks to Hájek. Expected payoff remains infinite no matter what the mixed strategy employed.
(Interestingly, this means you have to convince atheists that the payoffs of true theistic belief are finite, not infinite, to allow for a successful reformulation. I'm not bothered by a finiteness requirement, but there are theological and intuitive difficulties to circumvent here.)
Yes, I meant up to your desire to kick a kitten.
Fair enough.
No, but your argument for abandoning cpa to enable `active consideration' - assuming it's valid elsewhere, and it isn't - assumes that cpa ascribes probability zero to the various theologies, unless you have bounds for the relevant probabilities and utilities. And that is precisely what you've been avoiding.
Again, I don't see why I need to assume the cpa ascribes probability zero to the various possible beliefs (it's broader than theologies, since I take those to entail a God's existence) in order for them to disregard doing any investigation and estimation.
Yes, that's one objection to Pascal's wager which I came across thanks to Hájek. Expected payoff remains infinite no matter what the mixed strategy employed.
Something seems off here. Let me try to understand this further.
Let's say I'm on my deathbed, and I only have time for one of two acts. On one act there's that .99 chance at infinite payoff. On the other, there's .0001.
You're saying that there's no reason to choose one act over the other?
Addendum: .99 chance at a chance at infinite payoff, I suppose, not a straight up .99 chance at infinite payoff.
Addendum: .99 chance at a chance at infinite payoff, I suppose, not a straight up .99 chance at infinite payoff.
The qualifier there is unnecessary when one is stipulating this to be the chances of success on the strategy.
You're saying that there's no reason to choose one act over the other?
Not when the payoffs are infinite, so long as probability of `success' on a mixed strategy is always non-zero. This is automatic for devotees of regularity, as Hájek notes. That's what it means for utilities to be infinite and for one outcome to superdominate another: the specific probabilities become irrelevant.
Jesse,
Not when the payoffs are infinite, so long as probability of `success' on a mixed strategy is always non-zero. This is automatic for devotees of regularity, as Hájek notes. That's what it means for utilities to be infinite and for one outcome to superdominate another: the specific probabilities become irrelevant.
It seems wrong. I'm guessing you could at least appreciate why it seems wrong given my example.
Let's say it were you in that situation. You're on your deathbed, you have the two choices - the .99 and the .0001, and you can only make one. Which would you personally make and why?
It seems wrong. I'm guessing you could at least appreciate why it seems wrong given my example.
Let's say it were you in that situation. You're on your deathbed, you have the two choices - the .99 and the .0001, and you can only make one. Which would you personally make and why?
But it isn't wrong, counter-intuitive though that is. Hence the widespread suspicion of infinite utilities.
Personally, I hope to enjoy a nice cool beer on the way out. If I'm not a believer at that point, I doubt I'll be interested in becoming one, and the time will be precious. That said, I don't think I'll be up for the sort of Wager Pascal had in mind, as it involves a lifelong commitment and cultivation of belief. I also don't think I'll be able to flip the `sincere belief' switch in my head. So I'm not worried about it even being relevant.
Jesse,
But it isn't wrong, counter-intuitive though that is. Hence the widespread suspicion of infinite utilities.
I don't see how you can maintain that. If the probability calculus says that the .99 and the .0001 are such that there's no difference between them in the situation I outlined and no reason to prefer one over the other, it seems like someone should take that to mean that something has gone wrong with the probability calculus.
You say you'd choose the beer, but I imagine you're being flippant. Isn't the proper response, giving your position and the example as it was laid out, 'I don't know, I'd just choose whichever.'?
Er, decision making theory. Whichever.
I don't see how you can maintain that. If the probability calculus says that the .99 and the .0001 are such that there's no difference between them in the situation I outlined and no reason to prefer one over the other, it seems like someone should take that to mean that something has gone wrong with the probability calculus.
You say you'd choose the beer, but I imagine you're being flippant. Isn't the proper response, giving your position and the example as it was laid out, 'I don't know, I'd just choose whichever.'?
First, I'm not being flippant. Quite apart from (or including) the results of decision theory, I do not predicate my ethics on expectations concerning the afterlife. I do not see any way that I should do so. And no, the point of my examples is that it doesn't matter what I do. I could flip a coin or be indifferent or worship Satan or start crying out Hosannas, and my expected utility would not be increased by that virtue.
For the counter-intuitiveness: read the SEP article. The math behind this isn't too complicated: for a,b positive reals (these correspond to probabilities) and c finite, a*(infinite value)+b*c = infinite value.
So it doesn't matter if a is very small or very close to one. An example I used in my post is prob(atheism)=1-1/[Graham's number]. Graham's number, to give you some idea of its size, is too large to be written in common mathematical notation; it is a nested series of towers of exponents. It makes googles of googles of googles look small.
Jesse,
For the counter-intuitiveness: read the SEP article. The math behind this isn't too complicated: for a,b positive reals (these correspond to probabilities) and c finite, a*(infinite value)+b*c = infinite value.
Pascal's Wager, part 5, "Is the argument valid?" I read it. Just reread it again. But I'm going to come back to the exact same hypothetical example in order to flesh out the reasoning, and I'm still going to end up with the conclusion that it indicates something has gone wrong with this kind of reasoning.
You only have one choice between two possible acts remaining in your life. One is the .99 (Heck, can you make it a '1' and would that change anything?), one is the .0001. I'm being told these choices are exactly equivalent. Assuring me that the math was done correctly will make me question the underlying assumptions and foundations the math rests on and is meant to represent.
I suppose I should ask that next. You tell me that, counter-intuitive as it is, that's the result - on your deathbed, you have a choice between two acts, one offering the .99 chance at the infinite and the .0001 chance, and rationally these choices are equivalent. Do you recognize any possibility that your judgment of this matter is wrong? And if you recognize the possibility that your judgment may be wrong, do you think it's more likely that the .99 or the .0001 result should be favored upon 'correction'?
One is the .99 (Heck, can you make it a '1' and would that change anything?)
If that is corresponding to the probability of a `believers' outcome, then yes. The objection from mixed strategies relies on non-zero probability of `success'; the counter-intuitive point is that any non-zero probability will do.
I'm being told these choices are exactly equivalent. Assuring me that the math was done correctly will make me question the underlying assumptions and foundations the math rests on and is meant to represent.
There you have it, and again, there are secular equivalents of this paradox. One way to avoid it is to stipulate that utilities should be finite. But you have to convince an atheist of this regarding paradise and avoid any theological paradoxes in doing so. (And that's only a necessary condition for a good argument, not a sufficient one.)
I suppose I should ask that next. You tell me that, counter-intuitive as it is, that's the result - on your deathbed, you have a choice between two acts, one offering the .99 chance at the infinite and the .0001 chance, and rationally these choices are equivalent. Do you recognize any possibility that your judgment of this matter is wrong? And if you recognize the possibility that your judgment may be wrong, do you think it's more likely that the .99 or the .0001 result should be favored upon 'correction'?
If I stick with standard decision theory, the probability of my incorrectly assessing the situation does nothing to change the outcome. For that too is a mixed strategy.
(It gets even worse from here for several reasons. I have a post in the works.)
And do keep the questions coming. I did emphasize that this stuff is tricky for a good reason. :D
Jesse,
There you have it, and again, there are secular equivalents of this paradox. One way to avoid it is to stipulate that utilities should be finite. But you have to convince an atheist of this regarding paradise and avoid any theological paradoxes in doing so. (And that's only a necessary condition for a good argument, not a sufficient one.)
It seems another way to do it is to give the example I did and ask, "Does this seem reasonable to you, or does it seem like something has gone off the rails?" I don't think saying "Well, it's counter-intuitive, but if you look at the math..." really solves this. As I said, I think the hypothetical I'm bringing up here, and the result the hypothetical gets on this decision theory, itself gives one reason to reject the conclusions you're aiming at.
On the flipside, I'm now wondering if the rough approach I gave actually avoided this particular debate altogether. Since my approach didn't depend on all possibilities among the live possibilities having infinite value. Maybe some do, maybe some just have very high finite value.
If I stick with standard decision theory, the probability of my incorrectly assessing the situation does nothing to change the outcome. For that too is a mixed strategy.
Isn't standard decision theory precisely what I'm calling into question here?
It seems another way to do it is to give the example I did and ask, "Does this seem reasonable to you, or does it seem like something has gone off the rails?" I don't think saying "Well, it's counter-intuitive, but if you look at the math..." really solves this. As I said, I think the hypothetical I'm bringing up here, and the result the hypothetical gets on this decision theory, itself gives one reason to reject the conclusions you're aiming at.
Oh no, I'm agreeing that the math appears to be getting the `wrong' results. So the question, in reformulating the Wager, is how to get atheists to accept a particular non-standard account of decision theory as applying selectively to Pascal's Wager while not forcing commitments on secular equivalents, e.g. the St. Petersburg Paradox.
I'm agreeing that a reasonable person might feel that the usual rules are inadequate. That's a widespread suspicion. But that also presents an intimidating obstacle to reformulations of the Wager.
Isn't standard decision theory precisely what I'm calling into question here?
At this point, you clearly are. And again, that's entirely understandable. Now, the question is whether or not atheists must share your intuition, and in building a replacement account - I know of none that helps the Wager (I'm surveying some of them in my post) - retain the intended conclusion of the Wager while avoiding similar paradoxes.
And then, of course, the problems of soundness and strategy-dependence (the most popular objections) are all still ahead of us.
(Are you beginning to see why I think that evidential approaches have much better prospects?)
Jesse,
Oh no, I'm agreeing that the math appears to be getting the `wrong' results.
Well, that's nice to hear. Not the impression I got up to this point, but perhaps I misunderstood.
So the question, in reformulating the Wager, is how to get atheists to accept a particular non-standard account of decision theory as applying selectively to Pascal's Wager while not forcing commitments on secular equivalents, e.g. the St. Petersburg Paradox.
Seems like this is the first you've mentioned of 'secular equivalents', but again, perhaps I missed something. That said, I'm skeptical of whether a full-blown 'account of decision theory' is needed for the wager or a related wager to be reasonable to offer and accept.
Let me put that another way. You say that you agree with me that the math is "appearing to get the wrong results". First, I question whether the problem lies with 'the math' or with the reasoning connected to it. But second, let's say someone agrees that in a case like this 'the math appears to get the wrong results'. Does that, to you, mean that they have to throw out this decision theory entirely, or at least come up with a solution before using it? Or is there room to say "alright, this decision theory is serviceable - in this particular situation, it's going off the rails. But we can see the right answer in this situation anyway."?
It seems like your objection here is that in the process of making a Wager argument you need a general decision theory. I'm wondering if that's at all necessary.
At this point, you clearly are. And again, that's entirely understandable. Now, the question is whether or not atheists must share your intuition, and in building a replacement account - I know of none that helps the Wager (I'm surveying some of them in my post) - retain the intended conclusion of the Wager while avoiding similar paradoxes.
Well, again I wonder if my loose and sloppy offering of the wager actually evaded some of these problems due to the spread of possibilities I was allowing.
(Are you beginning to see why I think that evidential approaches have much better prospects?)
Not really, because I'm not convinced the wager or something appropriately wager-like can't reasonably achieve some movement here. "Better" prospects in my view would be relative to the individual. And part of the value I saw in the wager as I attempted to state it was in it providing motivation to engage the evidential approaches seriously and prioritize a general inclination, even if not a specific conclusion.
Crude,
Well, that's nice to hear. Not the impression I got up to this point, but perhaps I misunderstood.
Either way, the fact that the result is intuitively `wrong' does not change the fact that the Wager compels us to recognize the `wrong' results, if we accept it. Here I note that my own intuitions, as you've noticed, nevertheless do not make deathbed scenarios any more compelling to me, but I admit that my feelings precede my understanding of decision theory. I've spelled out some of my reasoning, if only roughly.
Seems like this is the first you've mentioned of 'secular equivalents', but again, perhaps I missed something. That said, I'm skeptical of whether a full-blown 'account of decision theory' is needed for the wager or a related wager to be reasonable to offer and accept.
Insofar as you want to make a convincing decision theoretic argument, the failure of standard decision theory is important to recognize. Further, ad-hoc modifications - several are discussed by Hájek in a paper which requires access to JSTOR - are not convincing to atheists. One example is outright: an author proposes that "one should always maximize ones chances of achieving salvation", which rather begs the question. (And itself it admits the failure of the original wager, of course.) And even this only deals with the objection from mixed strategies; many others remain.
Does that, to you, mean that they have to throw out this decision theory entirely, or at least come up with a solution before using it? Or is there room to say "alright, this decision theory is serviceable - in this particular situation, it's going off the rails. But we can see the right answer in this situation anyway."?
To the first question: No, but at least it means that modification/care in application are required. One could restrict oneself, pragmatically, to more everyday and less controversial uses of decision theory. That's my impression of what most who employ it do, as such paradoxes remain intact to my knowledge. But without a modification of decision theory which makes a Wager-like argument successful, you're not going to be any more successful employing decision theory than you would be simply threatening hellfire to the infidel and ignoring the technicalities. And atheists, of course, will be happy to pursue the technicalities of this.
Well, again I wonder if my loose and sloppy offering of the wager actually evaded some of these problems due to the spread of possibilities I was allowing.
That actually compounds the problem and introduces many others. To see this in detail, you have to work with a comprehensive matrix, i.e. a sound premise.
Not really, because I'm not convinced the wager or something appropriately wager-like can't reasonably achieve some movement here. "Better" prospects in my view would be relative to the individual. And part of the value I saw in the wager as I attempted to state it was in it providing motivation to engage the evidential approaches seriously and prioritize a general inclination, even if not a specific conclusion.
Atheists have always been able to brush off promises of rewards and punishment with relative ease. As I noted earlier, I think it tends to discredit apologetics in their estimation more than anything. If your goal is to encourage careful examination of the evidence, I think that there are better strategies :D
(To note: that quotation is a paraphrase, albeit one that's a logical implication in this context.)
Jesse,
Here I note that my own intuitions, as you've noticed, nevertheless do not make deathbed scenarios any more compelling to me, but I admit that my feelings precede my understanding of decision theory. I've spelled out some of my reasoning, if only roughly.
Sure, and you're one individual. I'm not after a one size fits all argument here - I wonder if Pascal was, but perhaps.
Either way, the deathbed scenario was just to draw out what was boggling me about what you were saying, to be sure I was grasping it, and to point out my objections given that. I think this would factor into non-deathbed scenarios.
Insofar as you want to make a convincing decision theoretic argument, the failure of standard decision theory is important to recognize. Further, ad-hoc modifications - several are discussed by Hájek in a paper which requires access to JSTOR - are not convincing to atheists.
Ad hoc modifications, no. Modifications that appeal to strong and common intuitions? That's another question. Even you said, if I took you right, that the decision theory seemed to be giving the 'wrong' result here. Was that objection ad hoc in an appropriate sense of the term?
What I'm picking up here, perhaps wrongly, is that you think the standard I'm going for or should be going for is 'This will drag any atheist/irreligious to the conclusion I want, kicking and screaming'. I just don't think that's a good standard.
But without a modification of decision theory which makes a Wager-like argument successful, you're not going to be any more successful employing decision theory than you would be simply threatening hellfire to the infidel and ignoring the technicalities. And atheists, of course, will be happy to pursue the technicalities of this.
This is where I disagree, similar to what I just said above. This really sounds like you're presupposing that every atheist, every non-believer, is going to dive for every technicality, every possible out, rather than be moved even an inch by any amount of reasonable intuition or argument that has some force, even if imperfect.
Again, I'm not advocating the use of arguments that are flat out invalid or other dishonest tricks. But an imperfect argument, one that has certain technical caveats or an incompleteness to it, can still be persuasive to some degree. The same goes for one that has some reliance on intuitions or common sense.
That actually compounds the problem and introduces many others. To see this in detail, you have to work with a comprehensive matrix, i.e. a sound premise.
I have no doubt cracking the field open as wide as I did would introduce new problems. But I think it evades at least that quick objection, or at least makes it not quite as clear cut given the dt assumption.
Atheists have always been able to brush off promises of rewards and punishment with relative ease.
I wouldn't speak as broadly as that at all.
As I noted earlier, I think it tends to discredit apologetics in their estimation more than anything. If your goal is to encourage careful examination of the evidence, I think that there are better strategies.
And here I just disagree. Nor do I think atheists or the generally irreligious are quite that monolithic a group.
What I'm picking up here, perhaps wrongly, is that you think the standard I'm going for or should be going for is 'This will drag any atheist/irreligious to the conclusion I want, kicking and screaming'. I just don't think that's a good standard.
Not at all; but should what you're going for do anything to convince any atheist to adopt a strategy that results in belief?
If an atheist shares all of your intuitions and lacks other objections to the Wager - again, the objections to soundness are more common - then he will find it convincing, and may attempt to arrive at belief even if he feels other argumentation unconvincing. Of course, we would do as well by simply stipulating that arguments apply where sound and valid and convincing, so I do not think these provisos indicate any utility for the argument.
More primal-sounding threats should do just as well.
I have no doubt cracking the field open as wide as I did would introduce new problems. But I think it evades at least that quick objection, or at least makes it not quite as clear cut given the dt assumption.
Well, as you presented it earlier (when you said that the specific probabilities did not matter so long as they were non-zero) the same problems remain by implication. But if thresholds for probabilities do matter (as I recall, you've only admitted this for outlandish-feeling strategies and theologies) we by implication arrive at the finite case, and all of the complications that entails.
I wouldn't speak as broadly as that at all.
I did include a `relative' for ass-guarding purposes. But I think that virtually any atheist who ever studied any apologetics ran into some version of the Wager. Perhaps some have been convinced by it, but I have not heard of any particular cases.
And here I just disagree. Nor do I think atheists or the generally irreligious are quite that monolithic a group.
Not at all, but one must work on differing probabilities of success with differing strategies. And presumably, while you might note the possibility of Heaven/Hell, you would stipulate - out of purposes of honesty - that it does not to your knowledge translate into a decision-theoretic argument a la Pascal. So for those atheists who are unaware of the promises of Heaven and threats of Hell, maybe it's worth noting.
Jesse,
Not at all; but should what you're going for do anything to convince any atheist to adopt a strategy that results in belief?
Even in the sloppy 'version' of the wager I gave, the goal wasn't to get the atheist to adopt a strategy that results in belief (in Christianity, I take you to mean.) As I said earlier, I don't think the point of every argument is to 'result in belief' pure and simple.
Of course, we would do as well by simply stipulating that arguments apply where sound and valid and convincing, so I do not think these provisos indicate any utility for the argument.
If I've understood your replies right, it seems to me that there's a workaround for the argument re: it's validity, though it does rely on intuition. Soundness I haven't gotten into here too deeply, and I'm sure I'd have work ahead of me on that front. "Convincing" seems redundant.
As for the reference to 'primal sounding threats', no, I don't think they should work just as well. Here I've only tried to make the point that imperfect arguments still can have reasonable utility and justification.
Well, as you presented it earlier (when you said that the specific probabilities did not matter so long as they were non-zero) the same problems remain by implication. But if thresholds for probabilities do matter (as I recall, you've only admitted this for outlandish-feeling strategies and theologies) we by implication arrive at the finite case, and all of the complications that entails.
My sloppy presentation left the door open to both finite and infinite cases, or at least that was the intent.
I did include a `relative' for ass-guarding purposes. But I think that virtually any atheist who ever studied any apologetics ran into some version of the Wager. Perhaps some have been convinced by it, but I have not heard of any particular cases.
Supposedly Von Neumann converted on his deathbed due to the wager. And I also wonder how large the group of 'virtually any atheist (or irreligious, I'd add) who ever studied apologetics' to that degree really is.
Not at all, but one must work on differing probabilities of success with differing strategies. And presumably, while you might note the possibility of Heaven/Hell, you would stipulate - out of purposes of honesty - that it does not to your knowledge translate into a decision-theoretic argument a la Pascal. So for those atheists who are unaware of the promises of Heaven and threats of Hell, maybe it's worth noting.
Sure, presenting it honestly would be required. I don't think it would only apply to atheists 'unaware of the promises of Heaven and threats of Hell' - someone could be generally aware of those things, but still not have considered it in the appropriate light, or dwelled on the question from various directions.
"However, since it is not sound or valid, I would recommend finding a different way to invite investigation."
We all have lives to live and limited time and resources to investigate truth and make decisions. Thus we all make pragmatic decisions of what to think about and what to put aside. A sort of triage of things to think about.
So an agnostic might be inclined to think God's existence is not very likely, and put the question aside to focus on other things like earning a living or developing an ethical approach to life. But because the consequences of God's existence may be huge, she may decide to give it more attention. I don't see how that choice would be unsound.
"I would recommend finding a different way to invite investigation."
As a christian, I don't think I have ever used it, except in the form above, and not to argue someone else into thinking again, but to explain why I think the questions of God's existence are important.
"A threat of Hell? "
I have never thought of the wager in those terms, but rather as a matter of potentially lost opportunity, and I don't believe in the conventional hell anyway.
One main difference between global warming and Pascal's wager is that the first is derived from empirical evidence, the second from formal reasoning. Global warming can never be proven, but our models of warming have been tested and have been shown to be highly accurate. Pascal's wager is part of a model for thinking that will either be useful or not, and seems to not be very useful. Tyi8ng one to the other is a category error.
"Pascal's wager is part of a model for thinking that will either be useful or not, and seems to not be very useful."
I have a feeling the afterlife might provide you with cause for a reassessment of your estimate...
Crude,
As I said earlier, I don't think the point of every argument is to 'result in belief' pure and simple.
It works as well as applied `belief in theism' or even `accepting something other than popular version of atheism Y'. The assumptions which lead to the difficulties follow from wagering on possible outcomes in the afterlife. What you wager to is irrelevant to this, as the math remains the same (as seen from the mixed strategy objections or objections to soundness or the need for specified order relations between various combinations of utilities/probabilities, etc.)
"Convincing" seems redundant.
Not exactly; an argument can be sound and valid, but that soundness can be restricted. People have differing priors. And even if a theistic person sticks with finite utilities and finds that table `sound' and has reduced alternatives to e.g. Christianity to a very small probability, all of these premises may be disputed by an atheist. This is also true for premises based on intuitions, which might not be shared. (A particularly famous example involves Craig's KCA and actual infinities, though I am unsure that the intuition should even be relevant.)
Supposedly Von Neumann converted on his deathbed due to the wager.
Do you have a source for this? I read one brief biographical article, but the only mention of his deathbed was that he recognized (while disliking) his imminent demise and took the sacraments from a priest invited on a criterion of `intellectual compatibility'. It's entirely possible that he said, "oh yes, the Wager, that does it for me," but I have yet to see any account, or even a source for a rumor.
(You'll understand my general suspicion of deathbed conversion stories, I hope.)
unkleE,
But because the consequences of God's existence may be huge, she may decide to give it more attention. I don't see how that choice would be unsound.
I think that atheists tend to recognize the importance of religions in the here-and-now as we take them to be.
As a christian, I don't think I have ever used it, except in the form above, and not to argue someone else into thinking again, but to explain why I think the questions of God's existence are important.
All fair enough. Anyone even vaguely familiar with Christian doctrine should recognize things like this, whether it's the afterlife or exclusive salvation or The Great Commission or ethics generally or you name it.
I have never thought of the wager in those terms, but rather as a matter of potentially lost opportunity, and I don't believe in the conventional hell anyway.
This is how atheists often respond to the Wager - objecting even to promises of reward. I think it is often a mistaken response, since I don't think many realize that Pascal was not arguing for atheists to try to `trick' God or `flip the belief switch'. It's a little better than what Hitchens calls it, which is `hucksterism'. That, or they restrict themselves entirely to the `many gods objection' (more properly, the `many theologies objection'). But the paradoxes of decision theory are so much more interesting!
Jesse,
The assumptions which lead to the difficulties follow from wagering on possible outcomes in the afterlife. What you wager to is irrelevant to this, as the math remains the same
Let me ask you this, since I'm curious. Let's say someone is of the opinion that buying car X would be preferable to buying car Y. Would you maintain that the reasoning they supply couldn't be sound, valid and reasonable if they didn't make use of decision theory, complete with probabilities calculations and the matrixes?
It's not a flippant question, I'm really curious how you consider exchanges like that.
Not exactly; an argument can be sound and valid, but that soundness can be restricted. People have differing priors. And even if a theistic person sticks with finite utilities and finds that table `sound' and has reduced alternatives to e.g. Christianity to a very small probability, all of these premises may be disputed by an atheist.
Sure they can, but's back to my worry that this kind of thinking relies heavily on the assumption that any given irreligious will jump for any conceivable objection to resist any force of the argument. I'm skeptical of that. Maybe that sort of reasoning makes the argument less interesting to you (say, you want something with closer to universal force, or at least some threshold).
Do you have a source for this? I read one brief biographical article, but the only mention of his deathbed was that he recognized (while disliking) his imminent demise and took the sacraments from a priest invited on a criterion of `intellectual compatibility'.
Wikipedia's entry for Von Neumann gives a reference to a wager article which in turns gives another reference to Macrae's biography. It's thin on particular details - maybe the wager was what resulted indirectly in that intellectual compatibility - but there it is.
Let me ask you this, since I'm curious. Let's say someone is of the opinion that buying car X would be preferable to buying car Y. Would you maintain that the reasoning they supply couldn't be sound, valid and reasonable if they didn't make use of decision theory, complete with probabilities calculations and the matrixes?
That sort of reasoning would be sound, if put into actual decision-theoretic form. (Don't forget that we argue to strategies in decision theory, not directly to outcomes.) But I don't demand that everybody sit down and do the calculations. Rather, if they're rational (in the Bayesian sense), those calculations if performed would corroborate their decision.
Sure they can, but's back to my worry that this kind of thinking relies heavily on the assumption that any given irreligious will jump for any conceivable objection to resist any force of the argument. I'm skeptical of that. Maybe that sort of reasoning makes the argument less interesting to you (say, you want something with closer to universal force, or at least some threshold).
Well, I think there are plenty of objections which leave the argument without force. But there are a lot of conceivable objections to the Wager which I think misguided, as I've mentioned. Again, I think it's worth understanding.
Wikipedia's entry for Von Neumann gives a reference to a wager article which in turns gives another reference to Macrae's biography. It's thin on particular details - maybe the wager was what resulted indirectly in that intellectual compatibility - but there it is.
Thanks! I'll give it a look. I know very little about Von Neumann's life, except the usual legendary stuff about incredible head computations.
Jesse,
But I don't demand that everybody sit down and do the calculations. Rather, if they're rational (in the Bayesian sense), those calculations if performed would corroborate their decision.
Alright, then another question. Do you think a person can reject or be skeptical of decision theory and remain rational? The impression I'm getting is that you clearly believe a person can be rational while disputing a particular result of the math (back to the deathbed example.) I also get the impression you believe there are a number of rivals to decision theory (or rival decision theories?) a person could accept while still being rational.
Alright, then another question. Do you think a person can reject or be skeptical of decision theory and remain rational? The impression I'm getting is that you clearly believe a person can be rational while disputing a particular result of the math (back to the deathbed example.) I also get the impression you believe there are a number of rivals to decision theory (or rival decision theories?) a person could accept while still being rational.
There are various incompletenesses in the case for Bayesianism and in decision-theoretic accounts, in which there are differences. Some of these are surveyed by Hájek, but a few in particular are discussed in The Logic of Decision, mainly two. One important difference is whether or not utilities are subject to a fixed upper bound, as opposed to being allowed to take any finite value. Other differences include such criteria as `ratifiability' - proposed by Jeffrey - which states that `choiceworthy' (another issue) actions are those which may select one of multiple options in a way that the selected option remains optimal - as compared with the alternative possibilities - once one has decided to undertake it. As he puts it `romantically': choose in accordance with the person you expect to be when you have chosen. But even this is not comprehensive, and does not resolve `Newcomb-like' paradoxes.
And to note: the mixed-strategy objection does not make the preference of a death-bed conversion irrational; it makes it `equirational'. So a person who converts on their deathbed due to Pascal's Wager is not irrational by virtue of doing so. Instead, it is also rational to not do so.
What I find fascinating in the above discussions is in doing as the article says, and substituting global warming for Christianity in the comments above.
It actually does work to some degree. This says more about global warming than it does about any god :)
And to note: the mixed-strategy objection does not make the preference of a death-bed conversion irrational; it makes it `equirational'. So a person who converts on their deathbed due to Pascal's Wager is not irrational by virtue of doing so. Instead, it is also rational to not do so.
Right, that I understood - but I still think that's wrong for that situation, and arguably for situations preceding it. But we've been over that already, so I'll leave it at that for now.
As he puts it `romantically': choose in accordance with the person you expect to be when you have chosen. But even this is not comprehensive, and does not resolve `Newcomb-like' paradoxes.
Right, I get that there's no universally agreed upon 'perfect' decision theory out there as of now, possibly ever. But that seems to suggest that all of these theories come with a stipulation of, "This strategy is rational, IF (you take for granted these various points which can reasonably be questioned)". It goes in part back to the complaint that the reasoning would be ad hoc.
Pascal's Wager is nonsense, of course. Primarily because his perspective is based on the narrowest of religious views, the view that christianity is the one and only true religion. But is it? Who is to say that Ganesh, son of Shiva is not the right god?
In these days of wider recognition and acknowledgement that there are so many different forms and kinds of gods, are we to include every god extant in the world to hedge our bets against picking the wrong god?
Bloody nonsense.
And talking about the effects of Global Warming [used synonymously though incorrectly with Climate Change which is the correct climatological circumstance that characterize the wider ramifications of anthropogenic carbon release into the atmosphere], just talk to the Pacific Islanders, whose back yards are afloat with water each and every high tide.
http://www.youtube.com/watch?v=IovmF3MQrpc
http://www.oxfam.org.nz/what-we-do/issues/climate-change/videos
Please spend some time and watch these accounts. This has occurred not over centuries or millennia but over the past 50 years and increasingly so. To most of you the shift is imperceptible, inconsequential and either incremental or non-existence; to the Islanders, whose margins for existence on their lands is far more critical, they have experienced the change in their lifetime.
So take a moment to reflect.
So take a moment to reflect.
If there really is AGW, then by now most of the damage has been done or is inevitable and we should devote resources primarily to compensating for it rather than trying to halt it.
Loud and clear.
I like what Oxfam has done in Tuvalu.
I have some interest in Tuvalu, since I live in the tropical Pacific :)
At 2mm sea level rise a year, it will be centuries before well made seawalls are not enough there, _ignoring_ the typhoons.
The _real_ problem there is as it always has been: the surge from a big typhoon submerges everything.
That may only be worse in the future.
Wow! after reading this thread I think I agree with old Ambrose--"sed non in dialectica complacuit Deo salvum facere populum suum". Blessings!
I suppose I shouldn't be astounded at how often people repeat the same failed arguments, but, somehow, I still am. This proves I'm not yet cynical enough. There's so much wrong with the article linked to that I'm not sure where to begin.
a)The issue of anthropogenic global warming isn't a matter of faith. The hypothesis can be proven or disproven to as high a degree of certainty as anything can be, meaning, we are up to the "What if we're all brains in a jar?" level of "doubt" -- the sort of "doubt" that basically declares knowledge impossible in the first place. If someone is unconvinced by the evidence thus far, and if they're honest, they will be able to articulate precisely what evidence will convince them -- and, likewise, those who find the evidence convincing ought to be able to suggest an experiment which will make them change their mind.
b)Once again, though, we see the biggest fallacy of Pascal's Sucker Bet -- that the only choice is Atheism or Christianity (and, usually, only one narrow flavor of Christianity). To every "Well, surely hell is worth avoiding, right?" argument, I can reply, "What if we die and we find Odin has barred us from Valhalla because we died the straw death and did not slay many foes in battle?" Surely, an eternity barred from eternal drinking, wenching, and battle is horrid; I should go right out and attack someone with an axe! If you don't see this as exactly the same proposal... you are not thinking about the issue clearly. 'Nuff said.
c)The wager ignores opportunity cost. If this is the only life I have, then every hour spent in church, or every otherwise moral pleasure not indulged in because it is "sinful", or every choice I do not make solely because I fear God's wrath, is a loss I will never recover, and it's cold comfort to know I'll never KNOW how much I wasted my life because I won't exist.
Only if one could eliminate, absolutely, every single possible religion, faith, and belief system besides Christianity would the wager make any sense... and if you could do that, there'd be no wager, since there'd be no doubt remaining. Good luck with that. Until then, though, anyone bringing up Pascal's Wager can be pretty much dumped into one of two categories: Those so locked into their own belief systems they don't even realize the wager's flaw, and those who do realize it but hope their audience does not. (This is known among philosophers as Megatron's Question, from a time when he once asked Starscream "Are you lying or just stupid?")
Lizard,
Actually, (2) and (3) are not sound objections (unless you are ascribing infinite utility to your lost opportunities), and the Wager would not be valid even if you restricted yourself to the original table.
For details, see the thread.
Jesse,
Actually, (2) and (3) are not sound objections (unless you are ascribing infinite utility to your lost opportunities), and the Wager would not be valid even if you restricted yourself to the original table.
We've been over this, but I'd like to ask again. You say 'the wager would not be valid' - but that seems to depend on accepting the results of a decision theory that indicates, given the deathbed example, that even if you have one choice left between the .99 and the .0001 payoff, the math indicates that both choices are equivalently rational to make.
Now, you've said that's clearly counterintuitive. But if that's what the claim that the wager is invalid rests on, then it seems to me that you have good reason to reject the relevant DT calculation in the deathbed case, and arguably in previous cases - which seems to kick out the claim that the wager is invalid.
Now, if I understand you right then the reply here is 'But that would be ad hoc'. But putting that aside - big thing to put aside, I know - it really seems like the claim of the wager being invalid rests on accepting the dictates of a calculation which doesn't seem to work in this case anyway.
Now, you've said that's clearly counterintuitive.
The paradoxes of infinite utilities are counter-intuitive. But as I've said, I accept the intuition in this case, because - for reasons independent of my knowledge of decision theory - I do not feel that conversion/whatever strategy should have any effect on outcomes the afterlife.
As I've also noted, the Wager (2x2 table) is still invalid whatever your intuitions. To try to capture those intuitions, one must use finite utilities (and spell out boundaries for which the Wager holds, after doing lots of other work.)
I'm still working on a post, but since much of it is original research - to my knowledge - it's taking some time.
To test your intuitions on where the consequences of infinite utilities `work', try looking at an analogous case. (See e.g. my latest comment over at Christian Cadre's post.)
Jesse,
As I've also noted, the Wager (2x2 table) is still invalid whatever your intuitions. To try to capture those intuitions, one must use finite utilities (and spell out boundaries for which the Wager holds, after doing lots of other work.)
This is the part I'm trying to understand from you. Okay, you say the Wager is invalid 'whatever your intuitions'. But from what I've read you write, and from your SEP reference, that invalidity seems to be grounded on the results you get when taking into account mixed strategies with an infinite good. Am I right about this much?
If this is the only life I get (which is where all the evidence points), then, yes, there's infinite value, to me, in every hour of it, even those I spend playing World of Warcraft. Again, there is the constant repetition of assumptions of the non-atheist side as if they were proven facts -- that there is "infinite" pleasure in heaven or torment in hell. Why assume this? Perhaps you spend a year in heaven and then God recycles your soul and it's back to the grind. Perhaps Hell is far more pleasurable than Earth.. it's just "Hell" because it's not quite as good as heaven, sort of like being a millionaire but having to live next door to billionaires. Etc.
There's a problem here which some have called the "1%" problem, as in, many business plans say something like "If only 1% of iPod users buy our app, that's still a million dollars we'll make!" Sounds good. But the fact is, much of the time, you're not getting 1%. Or 0.01%. Or 0.00000000000001%. The logic that no matter how low you set the probability of success, it's still X% of infinity fails because that low probability has to balance against proven reality...and because no one has yet proposed any kind of filter which can provably distinguish between "an arbitrarily low chance of a given afterlife being valid" and "absolutely NO chance of a given afterlife being valid". Can you offer any argument that going to feast in Valhalla is LESS likely than going to the Pearly Gates? Any argument that I am more likely to burn in Hell than to wander by the River Lethe? If you can't, there is absolutely no basis to choose any religion over none, and many reasons to choose none -- opportunity costs, as noted above.
To use another example, I could argue that if there's a 1/20 million chance of winning 10 million dollars for the cost of a 1 dollar ticket, it's a bad gamble (You could say, statistically, I'll win 0.50 cents), but if it becomes a 1/20 million chance of winning 100 million dollars, it's a good gamble, since statistically, I "win" 5.00 with my 1.00 ticket. However... it's still a bad gamble, because there's many ways to get a much more certain return on that 1.00 investment (even going to a casino will give you a 94% return on the nickel slots!). And in the case of faith, you have no idea WHAT the odds are. One in a billion, one in a trillion, one in a googol... you can cling to that "infinity" caveat all you like, but there's no proof of THAT, either. To go back to the lottery example... you're asking us to buy a ticket where we a)don't know the odds of winning, and b)don't even know for sure if the prize exists. I am better off responding to that nice man from Nigeria who wants my help getting money out of the country.
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(Continuation)
Ultimately, there CANNOT be a rational reason to believe in God. (If he suddenly manifests himself in public, and submits to every conceivable test, it's not "belief" anymore.) Many very intelligent people believe in God... I count my wife among them... but no one comes to believe in God by pure reason. They create reasons to justify their emotional response, and that emotional response is part of how evolution has hard-wired most of our brains. (I do not anticipate humanity ever "growing out" of religion; it seems to be part of what defines humanity. I figure most atheists are, basically, the far end of the bell curve, with the truly insane religious fanatics at the other end, and most of humanity muddling along in the middle. That there is a personal, internal, experience "of the divine" is readily established by neurological studies, and it's very likely that some of us (like me) lack the requisite neurotransmitters or wiring. This experience is so intense, it seems, that it is impossible for even very intelligent people to accept that it is a purely INTERNAL phenomenon with no external cause, and devote their intelligence to complex philosophies to justify their faith. However, ultimately, all such philosophies are useless, because not one can do so much as prove if the Catholics or the Protestants are right... never mind Christians vs. Muslims, Monotheists vs. Polytheists, etc. Such "proofs" of the existence of "some kind of something which is sort of divineish" give us no moral guidance, no insights about the universe, no answers to any puzzles, nothing. Even if one accepts a "prime mover", who is to say it hasn't moved on? Who is to say that the creator(s) of this universe are not themselves the creations of an even greater entity? Etc, etc, etc. Rational "proofs" of God are just intelligent people's way of dealing with the cognitive dissonance caused by faith. The smart thing to do is just wall it off in your mind and accept your irrationality, just as I do when I decide that a particular D20 has "run out of good numbers". I know perfectly well this is irrational, and I *still* toss it back in the bag and get out another one. It is irrational to deny human irrationality.)
I'm not a fan of Youtube videos in place of written arguments, but this is one of those rare instances where I thought a nice job was done in short period of time:
http://www.youtube.com/watch?v=fZpJ7yUPwdU&feature=player_embedded
For me there's a sliding scale of interesting questions / arguments that make theism more or less worth considering. I'd place the cosmological argument at the head of that class, and Pascal's at the very, very back.
Tony,
That video, while sufficient for rejecting the Wager, actually makes several - albeit subtle - errors.
All,
I'm almost done with my post to end all posts about Pascal's Wager. I promise it will be epic.
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