There's a difference between buying an argument in an abstract sense and finding it personally motivating. For instance, even when I think that Longtermist groups are the highest expected value places to donate, I still find it really hard to motivate myself to give all my money to them.
(1) acting rightly will be part of taking the Wager for whatever religion has the best chance of being true
(2) even if one thinks religion X has the highest odds, it may still be immoral—by the lights of X—to evangelise on its behalf if your credence in it is only 1% or something (more plausibly, even if it’s not inherently wrong, it might be morally risky: if your credence in the religion is too low, you risk being the religion into disrepute [unless you lie about your credences, which will be wrong according to most religions, including those that deserve the most credence]
The confidence to quality of arguments ratio in these Dylan articles is just infuriating. The 'wrestling with pigs' one especially. I don't understand why he's writing these if he doesn't think it's incumbent on him to, like, engage with any of the arguments whatsoever. You know you're phoning it in when you have to write a follow up article the thesis of which is "actually, I don't have to make arguments."
I think sometimes when people are new to philosophy they just take certain things as given or obvious, so when they observe others that disagree with them, the newbies assume that the dissenters are just misinformed about some basic issue. I suspect that’s what is happening here (also Matthew and Dylan got very heated, which probably didn’t help facilitate dialogue).
The 300,000 sided die is an extremely weak argument. Obviously the chance of *gaining utility* is 100%, even if each individual variation is vanishingly unlikely. This doesn’t apply to Pascal’s Wager because it’s a binary true-or-false.
Also, there is no possible way for the following things to all be true:
A) Hell is real
B) Hell is as bad as it has been described (eternal torture, not in the metaphorical CS Lewis way, actual literal eternal torture)
C) God will send you to Hell for not worshipping him
D) God is good
Someone who threatens you with eternal torture for not worshipping them is a bad person. It is morally indefensible.
But then you'll need some objective and precise way of divvying up outcomes. And while the odds of gaining utility are 100%, the probability of gaining any amount of utility is 1/300,000.
As I said, I don't believe in eternal hell. But there are plausible non-infernalist views on which believing in God has infinite value still.
What percentage of the time do I gain utility on net?
What percentage of the time do I lose utility on net?
What percentage of the time do I neither gain nor lose net utility?
My tail-discounting applies to my consideration of *those categories*, not my consideration of the *factors that make up those categories*.
So the die rolls add up to a 100% chance of gaining utility, which is far above the tail-discount threshold.
But PW (assuming we take 1/300000 as credence in Christianity) has nothing else to be added with, because Christianity being true is the only outcome that results in positive utility. So when I consider the odds that I gain utility, the total is rounded down (because of tail discounting) to 0%, meaning the EV is 0 (this is without factoring in the costs of christianity, which would actually make the EV negative).
But the odds you follow Christianity and that gets you utility aren't zero obviously or anywhere near zero! "Christianity being true is the only outcome that results in positive utility" is false--it might be good for you to believe it but be false. Also, for reasons I explain in the post, tail discounting is wrong. It violates Background Independence, for example, the notion that Some prospect A is better than another prospect B if and only if the combined prospect A plus some far away outcome O is also better than the combined prospect B plus the same far away outcome O.
Given that believing in Christianity would require that I adhere to a value framework that I find to be utterly repulsive and evil, Christianity being true is indeed the only possible way believing would benefit me.
How does my position violate background independence exactly?
It’s explained in the fanaticism post though a bit complicated.
It doesn’t follow from “I find X value system evil,” that “adopting it would be bad for me unless it’s true.” Like there’s a non trivial chance you’d be happier as a church going Christian—your life would be very different and so you shouldn’t be super confident whether you’d be happier.
I just reread the post, and I’m pretty sure you never say that tail discounting violates Background Independence. You do say it violates Negative Reflection. Am I misunderstanding you or did you mean to say Negative Reflection?
Second of all, while it is possible that I could in theory be happier as a Christian, in the same way that you could in theory be happier if you dedicated your entire life towards financing Dylan’s Substack, I find that the odds of that being the case are so low that they can be safely ignored.
Listen, Matt, I believe people don't care about non-eternal hell wager, or pascal's wager with universal salvation because - after a certain satisficing level of wellbeing (which they know shall last forever), people seem to naturally stop caring about more. Like... i remember me and Amos talked about how someone will be infinitely ahead (in terms of wellbeing) of you if they took pascal's wager earlier and believed more strongly or something, and i thought at that time... i am cool with that, i guess. Like... yeah, I shall be infinitely behind some individuals, but I don't feel that I need to race anymore. In fact, this rat race would make me more sad. So, to me, the whole premise of pascal's wager with universal salvation is like... "well, i am just glad that God is a wonderful being! And he shall not torture people forever or kill(annihilate) some people! And also, God shall give all beings at least a satisficing level of wellbeing forever! So, even if some beings get like infinitely more than satisficing level of wellbeing, I guess, I am cool with that. Good for them! I just... just don't wanna be in a race." I should mention that I am cool with bonus pleasure (more than satisficing level of pleasure or wellbeing) but i am not like.... i really really really need that. I am not like addicted after a certain level of wellbeing that i worry a lot about pascal's wager.
And additionally, I also don't believe in free will of any kind, so I don't believe in either libertarian or compatibilist free will. So, to me, the beings who are ahead of me aren't because some extra merit or that I missed some great opportunity. If my nature or personality simply is such that I shall not be persuaded by the wager, then that's it, I guess. What else can i do?
Also, have you ever thought of animals in this wagering stuff you talk about? Have you ever thought that... a tortoise or an elephant shouldn't be getting significantly less pleasure (or wellbeing) purely and purely because he cannot take the wager? Whenever, I think about human beings and our connection with animals, I always feel that all this pascal's wager and rational bro free will arguments are just totally refuted given so so so many animals are in the same boat as non-pascalians (or those who don't take the wager or care about it).
And also, many different Gods or religions objections still seems pretty powerful to me because which one should I choose? And what is even the ethics of this universalist pascal's wager God? Why are some beings behind while some beings ahead in terms of wellbeing? Because punishment? For non-belief? Why not for egoistic belief? Why not for epistemic vice? Why not for harming queer people? There is something also quite strange about an egoist who committed mass murder but strongly believed because of pascal's wager and that egoist got infinitely ahead of a compassionate chill person who did a lot of good in this world (and yes, compassionate, chill person does get heaven because we are indeed talking about universalist pascal's wager and not the infernalist one)! Would a utilitarian or even (mostly) welfarist consequentialist God behave in the way even the universalist pascal's wager imply? Like... some beings are infinitely ahead while others are infinitely behind? Why? Because they didn't believe? And so they believe because they egoistically choose the wager? But egoism is NOT compassion. The being who does what God likes purely because of pascal's wager or primarily because of the wager doesn't sound like an empathetic or compassionate being but simply a self-interested or mostly egoist actor.
The fact that people have still found ways to believe and reconcile all of those things just goes to show that everything is morally defensible if you’re clever enough to make it sound somewhat rational
I've never been particularly convinced by Pascal's Wager. From what I understand of Christianity at the very least, God is not someone who would consider you hedging your bets as genuine faith. You have to genuinely, wholeheartedly believe. I don't think He would appreciate "this religion has a 2% chance of being real, so I'm going to follow along"
This. I know that people have put forth arguments for why he actually would, but I don’t find them very convincing. Christianity, especially Catholicism and Orthodoxy (the only two denominations I’d personally consider legitimate), do not just require you to simply try to believe and go through the motions, but to dedicate your entire life, heart, body, and mind to a belief system that may or may not be true. And this can cost people a lot.
Think of people who are scrupulous and develop some form of religious OCD, people who are very troubled by the doctrine of hell to the point where it hurts them to believe anyone could go there, wives having to submit to abusive or difficult husbands, women who aren’t physically or emotionally capable of safely having more children not being allowed to use contraception, etc. It requires major sacrifices.
Following a religion that is so demanding is not free of cost. And it is difficult for many people to choose an afterlife that may or may not be real, over the life that they know they have. Especially when Christianity expects you to do so wholeheartedly, not out of fear or obligation. You’re supposed to do it and love it. You’re not really allowed to think, “I wish this wasn’t true.” But for some of us, that’s inevitable.
Just as the father welcomed the prodigal son back home with open arms, so too will God welcome all those who come to Him, even the reluctant ones. C. S. Lewis put it well when he described his own conversion:
"You must picture me alone in that room in Magdalen, night after night, feeling, whenever my mind lifted even for a second from my work, the steady, unrelenting approach of Him whom I so earnestly desired not to meet. That which I greatly feared had at last come upon me. In the Trinity Term of 1929 I gave in, and admitted that God was God, and knelt and prayed: perhaps, that night, the most dejected and reluctant convert in all England. I did not then see what is now the most shining and obvious thing; the Divine humility which will accept a convert even on such terms. The Prodigal Son at least walked home on his own feet. But who can duly adore that Love which will open the high gates to a prodigal who is brought in kicking, struggling, resentful, and darting his eyes in every direction for a chance of escape?"
I don't think I have the ability to decide to believe something if I think it is more likely false than true. I also don't think I have the ability to decide to trust someone whom I believe more likely than not does not exist. These are two reasons why I don't find the wager convincing; they require that I do something which I don't have the ability to do. One might respond that I could still try to increase credence that Christianity is true by going to Church, participating in Christian rituals or looking exclusively at theistic arguments or ideas and not at their critics. This sounds to me like trying to psyche myself into believing something. This seems to me to be epistemically vicious. I think there is a duty to know the truth and having the goal of believing some specific proposition is antithetical to this duty. Moreover, I'm not sure that such things are relevant to the truth of Christian propositions. It seems that whether one prays or goes to church is not relevant to whether say Jesus rose from the dead. If these things are irrelevant to whether Christianity is true, it seems that it is epistemically vicious to allow them to influence's one's belief in Christianity. However, perhaps one might argue that the existence of such practices increases the chance that Christianity is true or gives one special insight into the truths of Christianity as they allow grace to operate upon one's intellect giving them the power to assent to such truths.
Here's an objection to Pascal's Wager that I haven't seen made, and which seems to take into account the strangeness of infinite utilities. Ok, so maybe there's a 1% chance that Christianity is true, belief in Christianity is required to get into Christian heaven, and therefore it's a 1% chance of infinite positive utility. But what about the case of an exceedingly petty God who puts everyone who believes in Christianity in hell, and rewards everyone else with heaven? You might say this is much more unlikely than Christianity being true, maybe you give it a credence of 0.000001%. But this number times infinity is still infinity! Believing in Christianity gets you infinite expected positive value if Christianity is true, but infinite expected negative value if the petty God religion is true, and lack of belief in Christianity gets you infinite expected positive value under the petty God. It seems like you can do this with any religion, or any belief, or any arbitrary condition in general: no matter how unlikely, there is a chance that there is a petty God who will infinitely punish or reward that exact arbitrary action, therefore all actions and beliefs have simultaneously both infinite positive and infinite negative value. This being the case, it seems as if we can discount all claims of infinite expected value, because no matter how big or small the probabilities of them, infinity times a finite number is the same infinity, so they all cancel out. Therefore, you should ignore Pascal's Wager, Pascal's mugging, and any other claim that there is a finite chance of you achieving infinite value, because that is true (both for positive and negative infinite value) for literally any choice you could make.
God appears to you and says he will roll a 100-sided fair die to determine if you go to infinite heaven or infinite hell. You can either bet on the number being 69 or the number not being 69. Each bet has undefined expected value. What do you do?
I would bet on it not being 69 because I am an imperfect, irrational human consciousness running on evolved wetware. But let's look at what would happen if this bet were iterated over multiple people. Suppose that of those who bet on it not being 69, 1/100 go to hell. And out of those who bet on it being 69, 99/100 go to hell. But 0.01 times infinity is the exact same infinity as 0.99 times infinity. So assuming at least one person goes to heaven and one person goes to hell, the total net utility c̶a̶n̶c̶e̶l̶s̶ ̶o̶u̶t̶ EDIT: sums to undefined, it's the exact same infinities being compared against each other, no matter how many more people are in hell or heaven. Infinities make common sense reasoning about choices break down, and that is why I claim that you shouldn't make choices based on finite chances of infinitely good or bad outcomes.
This is a bit of a strange question since you have explicitly said the bets have undefined expected value. I don't really understand what this means. If I interpret it as being "unknown", then I guess since god has not given me any symmetry breaker, I should just assume that there is a symmetry between the heaven and hell on offer, and so I would go with not being 69.
I think the issue is with the symmetry. A better question might be: god gives you an infinite sequence of bets with probability 2^-n and payouts an increasing sequence of cardinalities. Which do you take? (I don't actually know if invoking cardinalities like this makes sense, but perhaps one should imagine that the payoffs are rewards of infinite duration and progressively increasing intensity.)
This has nothing to do with either of the critical responses; let me post it here nevertheless. Let Hell+ be a state which has a strictly higher intensity of suffering per unit of time than the Christian hell, and let A be the action of actively trying to disbelieve Christianity. Consider the following proposition:
P: "If you avoid A, then everybody will wind up in Hell+, including people who would not go to (normal) hell under Christianity."
Now, following the usual way of framing these arguments: surely the probability of P is not exactly 0. It may be extremely unlikely, but it is not less likely than winning the lottery a googolplex times in a row. And naively, A seems infinitely worse than going to hell. So shouldn't one actively try to disbelieve Christianity?
Of course, this argument can be bootstrapped by replacing A with A' = actively trying to believe Christianity, and replacing Hell+ with a worse Hell++ in some way. Continuing like this, we never reach a conclusion. So now I don't know what to think...
EDIT: Jackson & Rogers discuss something like this in section 5.1 of Salvaging Pascal’s Wager. In my understanding it amounts to discarding certain worldviews because in decision theory, one always has to truncate the space of options under consideration. This is fair enough, but personally I don't find it convincing: if we're considering infinite potential payoffs in the afterlife, surely it is not entirely unreasonable to include some more nonstandard views? If in a normal decision problem, including some previously ignored and not too exotic options completely changes the landscape of the problem, it seems to be ill-posed in some way.
Good post but I think your response to Hanania is unsatisfactory for a couple of points
-While it’s true that the wager still works with only heaven in the equation, I feel like it looses a considerable amount of force because it goes from: “join x religion or you’ll be in hell forever” to “join x religion or *maybe* you’ll lose some good in heaven”.
-Following the wager, we shouldn’t even bet on the religion which we find more plausible, but on the one with the worst hell. Say you find Buddhism or Hinduism to be probably true, shouldn’t you actually follow some other religions that teach hell based on unbelief (even if you think they are reallyyy unlikely to be true)?
-Of course sometimes is rational to follow extortions, and of course if god exists and he’s really all-good then everything it does is justified (and this includes literally the worst atrocities one can think of). But the pount is that I find really hard to believe that to be consistent with a being who is all good and worth of worship. I find much more likely that an all good god would be angry at you for even contemplating this idea.
Pascal's Wager isn't a good argument. It is a work of Christian apologetics. Pascal isn't speaking generally about theism, or the probability of God's existence. He is telling the non-believer what it rational to believe, based on what his particular religion teaches. But Christianity, as defined by the Nicene Creed, has absolutely zero probability of being true. (That is different than saying that God doesn't exist; it's saying that the historical revelation of God through Jesus Christ's death and resurrection is categorically false.) A probability of zero times an infinte reward is still zero. Therefore, Pascal's Wager isn't sound.
However, if you are going to assign a positive probability to the truth of Christianity, and if you are going to accept the Wager as logically valid, you should probably swallow your pride and convert to Catholicism.
If something has a probability of zero then no amount of evidence for it could convince you. So if the second coming occurred, Jesus came riding on the clouds, and then you spent a trillion years in heaven, you would still think that the odds that Christianity is false are less than the odds that you'd throw a dart across the known universe and hit a particular atom. Nuts!
The second coming of Jesus was supposed to happen within the lifetimes of the apostles. Jaroslav Pelikan details how the church doctrine had to reinterpret the idea that Christ was coming soon (1 Thessalonians 4:17) to accommodate the fact that he didn't return as expected. So yes, I believe wholeheartedly that there is zero probability.
But you just didn't address my argument against! To think the prior is zero is to think it's infinitely unlikely and be unshakeable by evidence.
Now, while I grant that Jesus apparently incorrectly predicting his return is *evidence* against his divinity, it's obviously not infinitely strong evidence. First of all, Christians can just think he got it wrong! Jesus was limited as a human! He didn't know everything in his human state.
Now, Christianity takes a probabilistic hit from doing that, but obviously not an infinitely strong one!
Modest principle: you should not be *infinitely certain* that lots of very smart people who could crush you in a debate on a subject are wrong. You should not think the odds they're right are lower than the odds that you'd throw a dart randomly across the known universe and hit the same atom 50,000 times in a row, purely by chance.
Why can’t one say one’s probability is zero *given available evidence*? If we’re considering hypothetical evidence, then it seems impossible to make a decision, because the strongest hypothetical evidence for Islam is just as strong as the strongest hypothetical evidence for Christianity.
Thanks, I hadn’t known that! I guess it makes sense given how multiplication works. I’d expect, though, that when people say zero they mean it in the sense I said.
Christ's immediate return was supposed to vindicate the truth of Christianity. Christ promised to come soon (Revelation 22:12), and not in an allegorical sense, as you are suggesting. Allegorical reading is more appropriate to the middle- and neo-platonists of the time, and not to the early Christians. That he didn't return goes again against scripture that God cannot lie (Hebrews 6:17-19). If God meant it allegorically he was being deceitful. If he meant it literally, he didn't abide by his promise. Thus again, the probability that Christianity is true is absolutely zero, because either God deceived his followers, or he abandoned them to this world.
If you allow infinitesimal probabilities, then you can have a hypothesis that is infinitesimally unlikely that can only be moved to a non-infinitesimal probability by observing evidence that is infinitesimal of the same order or smaller than the prior on your hypothesis.
I think that's a reasonable way to treat some of these religious claims: if I assign infinitesimal probability to Jesus riding in on a dinosaur from the clouds, then that is sufficient evidence to budge me away from my infinitesimal prior that Christian is false, but in most "normal" respects the Christianity hypothesis will function like it has probably 0.
You might object that I nevertheless *shouldn't* assign my probabilities in that way, but that's a question of calibration, which a) is outside of the bounds of Bayesian updating anyway and b) I think will actually go worse for the believer in infinite reward: how do you calibrate a finite probability of an infinite event?
But again, you are ignoring my arguments. Do you really think it’s less likely you’re interpreting wrong than that you’d win the lottery 150 consecutive times by chance alone?
I think it is far more likely that my interpretation is correct. That isn't blind confidence. That's because I studied theology, specifically exegesis, and I very knowledgeable about the history of the early church and its detractors.
But even if it is far more likely your interpretation is correct, that doesn't mean the alternative has a probability of zero. I have now several times given an argument against that, and each time you have ignored it and simply reiterated that you think it is improbable. Let me repeat it once again.
"If something has a probability of zero then no amount of evidence for it could convince you. So if the second coming occurred, Jesus came riding on the clouds, and then you spent a trillion years in heaven, you would still think that the odds that Christianity is false are less than the odds that you'd throw a dart across the known universe and hit a particular atom. Nuts!"
If Christ came back on the clouds, my confidence would be absolutely false, and I would justly earn my eternal damnation. That would vindicate the truth of Christianity against my argument that God is a liar.
You face an equivalent problem. Given the infinite EV of Pascal's Wager, what amount of evidence could convince you of naturalism + atheism? If technology allowed you to live a thousand years, time travel to see every supposed miracle was actually fake, all religious prophets were lying (due to sci-fi tech brain scans, etc), the infinite EV of Pascal's Wager would remain. Nuts!
There are an infinite number of “functionally equivalent” Christianities. Take Christianity. Now take Christianity + X, where X is some other small detail.
By your logic, each Christianity + X needs some finite probability, but because there are an infinite number of X’s, this would lead to a contradiction.
That doesn't lead to a contradiction--you could give random extra additions to Christianity a prior of infinitesimal, or you could give them probabilities that drop off and approach zero (E.g. 1/100, 1/200, 1/400, etc).
> First of all, sometimes you should give into extortion. If someone was going to torture me unless I firmly committed to adopt some religion, I’d adopt that religion.
Epictetus wouldn’t, or at least he’d say he wouldn’t! (Hilariously, autocorrect took my garbled attempt to type “Epictetus” and turned it into “Epicurus.” Couldn’t be more wrong, autocorrect!)
"A man who is good for anything ought not to calculate the chance of living or dying; he ought only to consider whether in doing anything he is doing right or wrong - acting the part of a good man or of a bad." -Plato
Pascal’s wager always struck me as a very cowardly way to come to religious conviction. If you are going to believe make it the belief of Kierkegaard, not the limp fish facsimile of belief of the wager.
Yep, you should give into extortion sometimes. I could be coerced to publicly convert to any religion, but that doesn't mean I believe it. I feel like this is the problem with Pascals wager the way you defend it. Even if it is rational to believe, belief isn't rational.
Among the self-described religious, I think very few really believe, the rest are just giving in to extortion. If someone really believes in infinite heaven and hell any suffering on earth to achieve heaven is justified and fully rational. Yet, almost nobody actually behaves this way. Religious suicide bombers and Mother Theresa are the exceptions that prove the rule. The rest of us can barely be bothered to go to church a couple times a month.
I disagree with your claim about the religious. I think a better explanation is most people just generally default to social norms and so don't do crazy things their religion says.
Yes, people do follow social norms. Religious behavior has a normal distribution. This is evidence of disbelief. In religion, or fitness, or shrimp welfare the people on the tails of the distribution are the ones who actually give a shit. Everyone else is a nonbeliever even if they pay lip service otherwise.
That makes no sense. The burden of proof is not commensurate with the rewards. It's not like you need extra evidence to think someone will torture you rather than that someone will slap you. That's not how Bayesian reasoning works!
The whole point of Pascal's wager is that you should wager even if the probability is low, so the burden of proof doesn't have to be infinite.
I don't think it's linear, and I agree that there may be ways to agree with Josh and still have non-infinitesimal probabilities of infinite rewards, but I think the generic situation is that there will be a pretty straightforward inverse relationship between reward and probability, such that you should generically expect that a reward of infinite size w should have probability on the order of infinitesimal 1 / w.
A few reasons to think this:
First, Kolmogorov complexity, the probability of a hypothesis should be proportional to its complexity. I think it is pretty plausible that all else equal, hypotheses with more utility in them are more complex--to have more utility you need either a higher density of utility per person, in which case you may need to specify more details to explain how this extra utility comes about; or constant density but more people, in which case you need to specify the extra people at a complexity penalty; or constant density and constant people but longer time, in which case you incur complexity cost for the additional time.
Now, how exactly that complexity penalty grows isn't obvious, but I think it's clear that you want the complexity penalty to grow at least as fast as the utility in general, otherwise you just lose the ability to do decision theory at all: the cost of specifying a new theory with infinite reward if and only if you do the *opposite* of what some other hypothesis suggests needs to be large enough that we avoid having that every action has infinite expected value. Only the "most principled" infinities can be exempted from this, so the generic case is that indeed infinite reward hypotheses have infinitesimal probability.
Obviously, that leaves the exemptions, but it does establish that you should have to make a positive case for why your hypothesis is one of those principled exceptions.
Second, think about how you would assign probabilities to infinite reward scenarios as distinct from any of their finite-reward subscenarios. What I mean is, suppose I have a probability p(w) of an infinite number of people all enjoying constant positive utility C. What probability p(n) should I assign to the hypothesis that there are at least n people enjoying utility C, for any finite n? Clearly, n people enjoying C utility is a superset of infinite people in that same situation; so p(w) must be less than p(n) for all finite n.
Now let q(n) be the probability that there are *exactly* n people in that situation, i.e. that there are at least n people, and that there are *not* at least n+1 people. This is q(n)=p(n) - p(n+1). Since these are probabilities and they're exhaustive and exclusive, we have that their sum must be 1:
This is a telescoping sum with value 1 = p(0) - lim p(n) -- but we need that p(0) to be 1, as this is the probability that at least 0 people are in the situation described, which is obviously tautologically true, so the limit of p(n) as n goes to infinity is 0, so p(w) which is less than every p(n) must be 0, or infinitesimal, and it must be a smaller infinitesimal than whatever the limit of p(n) is.
This is obviously a particular modeling choice, but I think unless you can offer a superior model, I think it should be broadly applicable: if you have some probability of a (in)finite population of people enjoying a (in)finite of utility each for a (in)finite amount of time, at least one of those (in)s must be included to achieve infinite utility. So, whether it's time, or people, or average utility per person, you're going to be saying there is a probability p(w) of infinite (people/time/average utility), in which case you can play the same game with p(n) for at least n (people/units of time/average utils), and the only consistent way to assign probabilities is to make p(w) infinitesimal or 0.
I withdraw my infinite sum argument, because there's a mistake: the sum q(0) + q(1) +... does not have to equal 1, precisely since there's non-zero probability on the hypothesis that the correct number is *not* any finite n.
As an extreme example, you could have q(n)=0 for all finite n, and so p(n)=1 for all finite n, and p(w)=1, corresponding to absolute certainty that the true number will be infinite.
I think all you can say for certain is that, in order to have a non-zero probability for p(w), you need that the series \sum_n 1 - p(n+1|n) converges--that your credence that, having observed n steps of your series, the series will stop now, must shrink fast enough for those credences to form a convergent series.
So, for example if you think that, a series that has continued for n steps so far has a probability 1/n of failing to continue, then that's not enough; the sum \sum_n 1/n is the famously diverging harmonic series.
You would be okay if you believe that a series that you've seen n steps of will fail with a probability 1/n^2 though.
I think one can still dispute if such a form for a conditional probability is reasonable (at any finite stage you still have infinitely many steps left to go, so in some sense, the fraction of probability space you've excluded after Tree(3) steps is the same as after 2 steps, so your conditional probabilities at those two stages shouldn't be too different, would be one possible argument) for anything other than a proof by induction or something like that, but mathematically as far as I can tell it is possible to have such credences.
Why not? If you have a religious belief in a just universe, the obvious expectation for years in heaven woudl be proportional to your good deeds in life.
I agree with you, but I think it’s also worth noting that every additional moment in Heaven also confirms an infinite set of hypotheses whereby you will be in Heaven for a finite amount of time (e.g., pretending that time is discrete for a moment, experiencing the Nth moment in Heaven, confirms that you will be in Heaven forever and also that you will be in Heaven for exactly K moments for all K>N).
See my comment above: it matters how you quantify "very unlikely"--if you think the probability is 1/googol (because the probability of stopping after n steps is 1/n), that is not enough to give you a non-zero credence in it lasting infinitely long; even though 1/googol is very, very unlikely!
Maybe, but I suspect this is just a matter of priors and a lot of priors would be rationally permissible here. For example, what would be unreasonable about, every time you pass some significant threshold, just thinking that the true end of your time in Heaven is even further away? Maybe you experience googol moments in Heaven and then you think “well, now I think, I will experience at most googol ↑↑↑ googol moments in Heaven” (iterating once you pass each threshold, supposing your time in Heaven will in fact be infinite).
Were this how you reasoned, it seems like you would be sensitive to the fact that, the more time you experience in Heaven, the less likely the next moment will be your last. But you may never think that the finitude of your time in Heaven is particularly improbable.
> The burden of proof is not commensurate with the rewards.
That might work for torture because some people are just sadistic and enjoy torture, even though no-one benefits.
But for me it does work with unearned rewards. I have a baseline of what kind of rewards one can get in the world, from working for money, to enjoying good friendship, to picking herbs and mushrooms for free.
If someone comes offering rewards that are way above the usual effort/reward proportion, I should very much be skeptical. In the real world, it's more likely to be a scammer than anything else. That means that the accrued burden of proof is actually *higher* than commensurate with the promised rewards.
The downside risk angle of Pascal's Wager is self-undermining. The reason why Pascal's Wager is convincing at all is because Christianity has a decently high probability of being true (compared to any other supernatural belief system someone could make up), and a decent part of that high likelihood rests on the fact that God is fairly simplistic, i.e. the most good agent. And this conception of God as the most good agent directly conflicts with eternal hell! Conditional on eternal hell being real, the likelihood of Christianity plummets, and in order to follow Pascal's Wager to mitigate downside risk we should convert to a religion (e.g. call it torturism) which is much more likely to exist given eternal hell is real.
Yeah, I agree generally, I think Christianity dominates the upside of Pascal's Wager, and when it comes to the downside, Christianity is on equal footing with many other belief systems, even more arbitrary ones.
I think Christianity is on worse footing. If Christianity is true, there's some nontrivial chance that universal salvation is true. So you should wager on Torturism, because you may end up in Christian heaven regardless, and Torturism offers no such leniency.
An anthropic argument against the existence of heaven:
Supposing that there was a non-zero probability that heaven existed. What is the probability that a randomly chosen observer at a randomly chosen moment in time would observe itself to not be in heaven? Zero.
I observe myself to not be in heaven. Therefore heaven does not exist.
"Two people have written replies to me on Pascal’s wager"
Not only two!
There are too many other possible Gods for whom Pascal's Wager would be a bad bet, nullifying any benefit that would be had from accepting the Wager for the Christian God, even assuming that's how the Christian God really works.
I don’t think you fully buy your own argument. If you did, you would abandon the shrimp and dedicate the rest of your life to Effective Evangelism
There's a difference between buying an argument in an abstract sense and finding it personally motivating. For instance, even when I think that Longtermist groups are the highest expected value places to donate, I still find it really hard to motivate myself to give all my money to them.
It does sort of strike me as a devil's (god's) advocate type of thing...
(1) acting rightly will be part of taking the Wager for whatever religion has the best chance of being true
(2) even if one thinks religion X has the highest odds, it may still be immoral—by the lights of X—to evangelise on its behalf if your credence in it is only 1% or something (more plausibly, even if it’s not inherently wrong, it might be morally risky: if your credence in the religion is too low, you risk being the religion into disrepute [unless you lie about your credences, which will be wrong according to most religions, including those that deserve the most credence]
The confidence to quality of arguments ratio in these Dylan articles is just infuriating. The 'wrestling with pigs' one especially. I don't understand why he's writing these if he doesn't think it's incumbent on him to, like, engage with any of the arguments whatsoever. You know you're phoning it in when you have to write a follow up article the thesis of which is "actually, I don't have to make arguments."
I know dude, it pissed me off so much.
I don't mind describing a view as crazy. What is irritating is the combination of:
1) acting like every reasonable person would inevitably agree with you.
2) failing to address counterarguments even in the post you're responding to.
3) doubling down repeatedly.
I don't think I've done that!
That was painful.
I think sometimes when people are new to philosophy they just take certain things as given or obvious, so when they observe others that disagree with them, the newbies assume that the dissenters are just misinformed about some basic issue. I suspect that’s what is happening here (also Matthew and Dylan got very heated, which probably didn’t help facilitate dialogue).
The 300,000 sided die is an extremely weak argument. Obviously the chance of *gaining utility* is 100%, even if each individual variation is vanishingly unlikely. This doesn’t apply to Pascal’s Wager because it’s a binary true-or-false.
Also, there is no possible way for the following things to all be true:
A) Hell is real
B) Hell is as bad as it has been described (eternal torture, not in the metaphorical CS Lewis way, actual literal eternal torture)
C) God will send you to Hell for not worshipping him
D) God is good
Someone who threatens you with eternal torture for not worshipping them is a bad person. It is morally indefensible.
But then you'll need some objective and precise way of divvying up outcomes. And while the odds of gaining utility are 100%, the probability of gaining any amount of utility is 1/300,000.
As I said, I don't believe in eternal hell. But there are plausible non-infernalist views on which believing in God has infinite value still.
Here’s how I’d divvy up outcomes:
What percentage of the time do I gain utility on net?
What percentage of the time do I lose utility on net?
What percentage of the time do I neither gain nor lose net utility?
My tail-discounting applies to my consideration of *those categories*, not my consideration of the *factors that make up those categories*.
So the die rolls add up to a 100% chance of gaining utility, which is far above the tail-discount threshold.
But PW (assuming we take 1/300000 as credence in Christianity) has nothing else to be added with, because Christianity being true is the only outcome that results in positive utility. So when I consider the odds that I gain utility, the total is rounded down (because of tail discounting) to 0%, meaning the EV is 0 (this is without factoring in the costs of christianity, which would actually make the EV negative).
But the odds you follow Christianity and that gets you utility aren't zero obviously or anywhere near zero! "Christianity being true is the only outcome that results in positive utility" is false--it might be good for you to believe it but be false. Also, for reasons I explain in the post, tail discounting is wrong. It violates Background Independence, for example, the notion that Some prospect A is better than another prospect B if and only if the combined prospect A plus some far away outcome O is also better than the combined prospect B plus the same far away outcome O.
Given that believing in Christianity would require that I adhere to a value framework that I find to be utterly repulsive and evil, Christianity being true is indeed the only possible way believing would benefit me.
How does my position violate background independence exactly?
It’s explained in the fanaticism post though a bit complicated.
It doesn’t follow from “I find X value system evil,” that “adopting it would be bad for me unless it’s true.” Like there’s a non trivial chance you’d be happier as a church going Christian—your life would be very different and so you shouldn’t be super confident whether you’d be happier.
I just reread the post, and I’m pretty sure you never say that tail discounting violates Background Independence. You do say it violates Negative Reflection. Am I misunderstanding you or did you mean to say Negative Reflection?
Second of all, while it is possible that I could in theory be happier as a Christian, in the same way that you could in theory be happier if you dedicated your entire life towards financing Dylan’s Substack, I find that the odds of that being the case are so low that they can be safely ignored.
Listen, Matt, I believe people don't care about non-eternal hell wager, or pascal's wager with universal salvation because - after a certain satisficing level of wellbeing (which they know shall last forever), people seem to naturally stop caring about more. Like... i remember me and Amos talked about how someone will be infinitely ahead (in terms of wellbeing) of you if they took pascal's wager earlier and believed more strongly or something, and i thought at that time... i am cool with that, i guess. Like... yeah, I shall be infinitely behind some individuals, but I don't feel that I need to race anymore. In fact, this rat race would make me more sad. So, to me, the whole premise of pascal's wager with universal salvation is like... "well, i am just glad that God is a wonderful being! And he shall not torture people forever or kill(annihilate) some people! And also, God shall give all beings at least a satisficing level of wellbeing forever! So, even if some beings get like infinitely more than satisficing level of wellbeing, I guess, I am cool with that. Good for them! I just... just don't wanna be in a race." I should mention that I am cool with bonus pleasure (more than satisficing level of pleasure or wellbeing) but i am not like.... i really really really need that. I am not like addicted after a certain level of wellbeing that i worry a lot about pascal's wager.
And additionally, I also don't believe in free will of any kind, so I don't believe in either libertarian or compatibilist free will. So, to me, the beings who are ahead of me aren't because some extra merit or that I missed some great opportunity. If my nature or personality simply is such that I shall not be persuaded by the wager, then that's it, I guess. What else can i do?
Also, have you ever thought of animals in this wagering stuff you talk about? Have you ever thought that... a tortoise or an elephant shouldn't be getting significantly less pleasure (or wellbeing) purely and purely because he cannot take the wager? Whenever, I think about human beings and our connection with animals, I always feel that all this pascal's wager and rational bro free will arguments are just totally refuted given so so so many animals are in the same boat as non-pascalians (or those who don't take the wager or care about it).
And also, many different Gods or religions objections still seems pretty powerful to me because which one should I choose? And what is even the ethics of this universalist pascal's wager God? Why are some beings behind while some beings ahead in terms of wellbeing? Because punishment? For non-belief? Why not for egoistic belief? Why not for epistemic vice? Why not for harming queer people? There is something also quite strange about an egoist who committed mass murder but strongly believed because of pascal's wager and that egoist got infinitely ahead of a compassionate chill person who did a lot of good in this world (and yes, compassionate, chill person does get heaven because we are indeed talking about universalist pascal's wager and not the infernalist one)! Would a utilitarian or even (mostly) welfarist consequentialist God behave in the way even the universalist pascal's wager imply? Like... some beings are infinitely ahead while others are infinitely behind? Why? Because they didn't believe? And so they believe because they egoistically choose the wager? But egoism is NOT compassion. The being who does what God likes purely because of pascal's wager or primarily because of the wager doesn't sound like an empathetic or compassionate being but simply a self-interested or mostly egoist actor.
The fact that people have still found ways to believe and reconcile all of those things just goes to show that everything is morally defensible if you’re clever enough to make it sound somewhat rational
The problem is god gets to decide the definition of good, it's really messed up.
I've never been particularly convinced by Pascal's Wager. From what I understand of Christianity at the very least, God is not someone who would consider you hedging your bets as genuine faith. You have to genuinely, wholeheartedly believe. I don't think He would appreciate "this religion has a 2% chance of being real, so I'm going to follow along"
This. I know that people have put forth arguments for why he actually would, but I don’t find them very convincing. Christianity, especially Catholicism and Orthodoxy (the only two denominations I’d personally consider legitimate), do not just require you to simply try to believe and go through the motions, but to dedicate your entire life, heart, body, and mind to a belief system that may or may not be true. And this can cost people a lot.
Think of people who are scrupulous and develop some form of religious OCD, people who are very troubled by the doctrine of hell to the point where it hurts them to believe anyone could go there, wives having to submit to abusive or difficult husbands, women who aren’t physically or emotionally capable of safely having more children not being allowed to use contraception, etc. It requires major sacrifices.
Following a religion that is so demanding is not free of cost. And it is difficult for many people to choose an afterlife that may or may not be real, over the life that they know they have. Especially when Christianity expects you to do so wholeheartedly, not out of fear or obligation. You’re supposed to do it and love it. You’re not really allowed to think, “I wish this wasn’t true.” But for some of us, that’s inevitable.
Just as the father welcomed the prodigal son back home with open arms, so too will God welcome all those who come to Him, even the reluctant ones. C. S. Lewis put it well when he described his own conversion:
"You must picture me alone in that room in Magdalen, night after night, feeling, whenever my mind lifted even for a second from my work, the steady, unrelenting approach of Him whom I so earnestly desired not to meet. That which I greatly feared had at last come upon me. In the Trinity Term of 1929 I gave in, and admitted that God was God, and knelt and prayed: perhaps, that night, the most dejected and reluctant convert in all England. I did not then see what is now the most shining and obvious thing; the Divine humility which will accept a convert even on such terms. The Prodigal Son at least walked home on his own feet. But who can duly adore that Love which will open the high gates to a prodigal who is brought in kicking, struggling, resentful, and darting his eyes in every direction for a chance of escape?"
I don't think I have the ability to decide to believe something if I think it is more likely false than true. I also don't think I have the ability to decide to trust someone whom I believe more likely than not does not exist. These are two reasons why I don't find the wager convincing; they require that I do something which I don't have the ability to do. One might respond that I could still try to increase credence that Christianity is true by going to Church, participating in Christian rituals or looking exclusively at theistic arguments or ideas and not at their critics. This sounds to me like trying to psyche myself into believing something. This seems to me to be epistemically vicious. I think there is a duty to know the truth and having the goal of believing some specific proposition is antithetical to this duty. Moreover, I'm not sure that such things are relevant to the truth of Christian propositions. It seems that whether one prays or goes to church is not relevant to whether say Jesus rose from the dead. If these things are irrelevant to whether Christianity is true, it seems that it is epistemically vicious to allow them to influence's one's belief in Christianity. However, perhaps one might argue that the existence of such practices increases the chance that Christianity is true or gives one special insight into the truths of Christianity as they allow grace to operate upon one's intellect giving them the power to assent to such truths.
Here's an objection to Pascal's Wager that I haven't seen made, and which seems to take into account the strangeness of infinite utilities. Ok, so maybe there's a 1% chance that Christianity is true, belief in Christianity is required to get into Christian heaven, and therefore it's a 1% chance of infinite positive utility. But what about the case of an exceedingly petty God who puts everyone who believes in Christianity in hell, and rewards everyone else with heaven? You might say this is much more unlikely than Christianity being true, maybe you give it a credence of 0.000001%. But this number times infinity is still infinity! Believing in Christianity gets you infinite expected positive value if Christianity is true, but infinite expected negative value if the petty God religion is true, and lack of belief in Christianity gets you infinite expected positive value under the petty God. It seems like you can do this with any religion, or any belief, or any arbitrary condition in general: no matter how unlikely, there is a chance that there is a petty God who will infinitely punish or reward that exact arbitrary action, therefore all actions and beliefs have simultaneously both infinite positive and infinite negative value. This being the case, it seems as if we can discount all claims of infinite expected value, because no matter how big or small the probabilities of them, infinity times a finite number is the same infinity, so they all cancel out. Therefore, you should ignore Pascal's Wager, Pascal's mugging, and any other claim that there is a finite chance of you achieving infinite value, because that is true (both for positive and negative infinite value) for literally any choice you could make.
God appears to you and says he will roll a 100-sided fair die to determine if you go to infinite heaven or infinite hell. You can either bet on the number being 69 or the number not being 69. Each bet has undefined expected value. What do you do?
I would bet on it not being 69 because I am an imperfect, irrational human consciousness running on evolved wetware. But let's look at what would happen if this bet were iterated over multiple people. Suppose that of those who bet on it not being 69, 1/100 go to hell. And out of those who bet on it being 69, 99/100 go to hell. But 0.01 times infinity is the exact same infinity as 0.99 times infinity. So assuming at least one person goes to heaven and one person goes to hell, the total net utility c̶a̶n̶c̶e̶l̶s̶ ̶o̶u̶t̶ EDIT: sums to undefined, it's the exact same infinities being compared against each other, no matter how many more people are in hell or heaven. Infinities make common sense reasoning about choices break down, and that is why I claim that you shouldn't make choices based on finite chances of infinitely good or bad outcomes.
Disagree with this way of treating infinities https://arxiv.org/abs/2509.19389
This is a bit of a strange question since you have explicitly said the bets have undefined expected value. I don't really understand what this means. If I interpret it as being "unknown", then I guess since god has not given me any symmetry breaker, I should just assume that there is a symmetry between the heaven and hell on offer, and so I would go with not being 69.
I think the issue is with the symmetry. A better question might be: god gives you an infinite sequence of bets with probability 2^-n and payouts an increasing sequence of cardinalities. Which do you take? (I don't actually know if invoking cardinalities like this makes sense, but perhaps one should imagine that the payoffs are rewards of infinite duration and progressively increasing intensity.)
Migrated this here since I it's related:
This has nothing to do with either of the critical responses; let me post it here nevertheless. Let Hell+ be a state which has a strictly higher intensity of suffering per unit of time than the Christian hell, and let A be the action of actively trying to disbelieve Christianity. Consider the following proposition:
P: "If you avoid A, then everybody will wind up in Hell+, including people who would not go to (normal) hell under Christianity."
Now, following the usual way of framing these arguments: surely the probability of P is not exactly 0. It may be extremely unlikely, but it is not less likely than winning the lottery a googolplex times in a row. And naively, A seems infinitely worse than going to hell. So shouldn't one actively try to disbelieve Christianity?
Of course, this argument can be bootstrapped by replacing A with A' = actively trying to believe Christianity, and replacing Hell+ with a worse Hell++ in some way. Continuing like this, we never reach a conclusion. So now I don't know what to think...
EDIT: Jackson & Rogers discuss something like this in section 5.1 of Salvaging Pascal’s Wager. In my understanding it amounts to discarding certain worldviews because in decision theory, one always has to truncate the space of options under consideration. This is fair enough, but personally I don't find it convincing: if we're considering infinite potential payoffs in the afterlife, surely it is not entirely unreasonable to include some more nonstandard views? If in a normal decision problem, including some previously ignored and not too exotic options completely changes the landscape of the problem, it seems to be ill-posed in some way.
This seems very similar to my comment. Should I migrate it as a reply to yours, so that we have a unified comment thread?
Idk man, you do you
Well done but you should try to cultivate a little more Britishness in your mockery. Read "Heretics."
Good post but I think your response to Hanania is unsatisfactory for a couple of points
-While it’s true that the wager still works with only heaven in the equation, I feel like it looses a considerable amount of force because it goes from: “join x religion or you’ll be in hell forever” to “join x religion or *maybe* you’ll lose some good in heaven”.
-Following the wager, we shouldn’t even bet on the religion which we find more plausible, but on the one with the worst hell. Say you find Buddhism or Hinduism to be probably true, shouldn’t you actually follow some other religions that teach hell based on unbelief (even if you think they are reallyyy unlikely to be true)?
-Of course sometimes is rational to follow extortions, and of course if god exists and he’s really all-good then everything it does is justified (and this includes literally the worst atrocities one can think of). But the pount is that I find really hard to believe that to be consistent with a being who is all good and worth of worship. I find much more likely that an all good god would be angry at you for even contemplating this idea.
1) It's not some good in heaven, it's infinite good! It's such a great good that you'd be rational to be tortured for a thousand years for that good.
2) I think believing in some ghastly and wicked religion doesn't actually maximize your odds of avoiding hell, and getting into a nice heaven.
3) I agree it's unlikely but still works out for infinite EV.
1) I agree that it works, I just said it’s much less emotionally moving
2) why so? I think some would consider every religion that teaches eternal hell to be “wicked”
3) what if you thought that it was more probable that god would punish you for reasoning that way?
This is a good post on pascal's wager style arguments - https://substack.com/home/post/p-173021362
and this recent paper by Toby Ord is good too - https://forum.effectivealtruism.org/posts/4FxCr3iqZPYa62pdM/evaluating-the-infinite?utm_user_id=KEtTrgk8xYLvTvr73
Pascal's Wager isn't a good argument. It is a work of Christian apologetics. Pascal isn't speaking generally about theism, or the probability of God's existence. He is telling the non-believer what it rational to believe, based on what his particular religion teaches. But Christianity, as defined by the Nicene Creed, has absolutely zero probability of being true. (That is different than saying that God doesn't exist; it's saying that the historical revelation of God through Jesus Christ's death and resurrection is categorically false.) A probability of zero times an infinte reward is still zero. Therefore, Pascal's Wager isn't sound.
However, if you are going to assign a positive probability to the truth of Christianity, and if you are going to accept the Wager as logically valid, you should probably swallow your pride and convert to Catholicism.
If something has a probability of zero then no amount of evidence for it could convince you. So if the second coming occurred, Jesus came riding on the clouds, and then you spent a trillion years in heaven, you would still think that the odds that Christianity is false are less than the odds that you'd throw a dart across the known universe and hit a particular atom. Nuts!
The second coming of Jesus was supposed to happen within the lifetimes of the apostles. Jaroslav Pelikan details how the church doctrine had to reinterpret the idea that Christ was coming soon (1 Thessalonians 4:17) to accommodate the fact that he didn't return as expected. So yes, I believe wholeheartedly that there is zero probability.
But you just didn't address my argument against! To think the prior is zero is to think it's infinitely unlikely and be unshakeable by evidence.
Now, while I grant that Jesus apparently incorrectly predicting his return is *evidence* against his divinity, it's obviously not infinitely strong evidence. First of all, Christians can just think he got it wrong! Jesus was limited as a human! He didn't know everything in his human state.
Second, there are various ways of interpreting the passages that don't have them be incorrect predictions http://www.wall.org/~aron/blog/comparing-religions-ix-delayed-return/
Now, Christianity takes a probabilistic hit from doing that, but obviously not an infinitely strong one!
Modest principle: you should not be *infinitely certain* that lots of very smart people who could crush you in a debate on a subject are wrong. You should not think the odds they're right are lower than the odds that you'd throw a dart randomly across the known universe and hit the same atom 50,000 times in a row, purely by chance.
Why can’t one say one’s probability is zero *given available evidence*? If we’re considering hypothetical evidence, then it seems impossible to make a decision, because the strongest hypothetical evidence for Islam is just as strong as the strongest hypothetical evidence for Christianity.
This just follows from Bayes theorem that if you have a probability of zero it will always stay zero in response to evidence
Thanks, I hadn’t known that! I guess it makes sense given how multiplication works. I’d expect, though, that when people say zero they mean it in the sense I said.
Christ's immediate return was supposed to vindicate the truth of Christianity. Christ promised to come soon (Revelation 22:12), and not in an allegorical sense, as you are suggesting. Allegorical reading is more appropriate to the middle- and neo-platonists of the time, and not to the early Christians. That he didn't return goes again against scripture that God cannot lie (Hebrews 6:17-19). If God meant it allegorically he was being deceitful. If he meant it literally, he didn't abide by his promise. Thus again, the probability that Christianity is true is absolutely zero, because either God deceived his followers, or he abandoned them to this world.
If you allow infinitesimal probabilities, then you can have a hypothesis that is infinitesimally unlikely that can only be moved to a non-infinitesimal probability by observing evidence that is infinitesimal of the same order or smaller than the prior on your hypothesis.
I think that's a reasonable way to treat some of these religious claims: if I assign infinitesimal probability to Jesus riding in on a dinosaur from the clouds, then that is sufficient evidence to budge me away from my infinitesimal prior that Christian is false, but in most "normal" respects the Christianity hypothesis will function like it has probably 0.
You might object that I nevertheless *shouldn't* assign my probabilities in that way, but that's a question of calibration, which a) is outside of the bounds of Bayesian updating anyway and b) I think will actually go worse for the believer in infinite reward: how do you calibrate a finite probability of an infinite event?
But again, you are ignoring my arguments. Do you really think it’s less likely you’re interpreting wrong than that you’d win the lottery 150 consecutive times by chance alone?
I think it is far more likely that my interpretation is correct. That isn't blind confidence. That's because I studied theology, specifically exegesis, and I very knowledgeable about the history of the early church and its detractors.
But even if it is far more likely your interpretation is correct, that doesn't mean the alternative has a probability of zero. I have now several times given an argument against that, and each time you have ignored it and simply reiterated that you think it is improbable. Let me repeat it once again.
"If something has a probability of zero then no amount of evidence for it could convince you. So if the second coming occurred, Jesus came riding on the clouds, and then you spent a trillion years in heaven, you would still think that the odds that Christianity is false are less than the odds that you'd throw a dart across the known universe and hit a particular atom. Nuts!"
If Christ came back on the clouds, my confidence would be absolutely false, and I would justly earn my eternal damnation. That would vindicate the truth of Christianity against my argument that God is a liar.
Ladies and gentlemen: we got him.
Maybe you should chime in and try to get your pal to follow through on his conversion?
You face an equivalent problem. Given the infinite EV of Pascal's Wager, what amount of evidence could convince you of naturalism + atheism? If technology allowed you to live a thousand years, time travel to see every supposed miracle was actually fake, all religious prophets were lying (due to sci-fi tech brain scans, etc), the infinite EV of Pascal's Wager would remain. Nuts!
There are an infinite number of “functionally equivalent” Christianities. Take Christianity. Now take Christianity + X, where X is some other small detail.
By your logic, each Christianity + X needs some finite probability, but because there are an infinite number of X’s, this would lead to a contradiction.
That doesn't lead to a contradiction--you could give random extra additions to Christianity a prior of infinitesimal, or you could give them probabilities that drop off and approach zero (E.g. 1/100, 1/200, 1/400, etc).
I address this in my post.
That's a really cool proof that the probability of every proposition is 0!
Not if your proposition is some Borel subset with a finite measure!
https://sorenj.substack.com/p/pascals-wager-and-prior-probabilities
> First of all, sometimes you should give into extortion. If someone was going to torture me unless I firmly committed to adopt some religion, I’d adopt that religion.
Honestly, this is just disappointing.
???
If someone threatened to torture you unless you firmly committed to believing in the Aztec god Tlaloc, would you believe in the Aztec God Tlaloc?
I mean, if a bunch of people were credibly going to torture me unless I joined the Tlaloc religion, I probably would. Wouldn't you?
Epictetus wouldn’t, or at least he’d say he wouldn’t! (Hilariously, autocorrect took my garbled attempt to type “Epictetus” and turned it into “Epicurus.” Couldn’t be more wrong, autocorrect!)
"A man who is good for anything ought not to calculate the chance of living or dying; he ought only to consider whether in doing anything he is doing right or wrong - acting the part of a good man or of a bad." -Plato
Pascal’s wager always struck me as a very cowardly way to come to religious conviction. If you are going to believe make it the belief of Kierkegaard, not the limp fish facsimile of belief of the wager.
Yep, you should give into extortion sometimes. I could be coerced to publicly convert to any religion, but that doesn't mean I believe it. I feel like this is the problem with Pascals wager the way you defend it. Even if it is rational to believe, belief isn't rational.
Among the self-described religious, I think very few really believe, the rest are just giving in to extortion. If someone really believes in infinite heaven and hell any suffering on earth to achieve heaven is justified and fully rational. Yet, almost nobody actually behaves this way. Religious suicide bombers and Mother Theresa are the exceptions that prove the rule. The rest of us can barely be bothered to go to church a couple times a month.
It's an argument for commitment.
I disagree with your claim about the religious. I think a better explanation is most people just generally default to social norms and so don't do crazy things their religion says.
Yes, people do follow social norms. Religious behavior has a normal distribution. This is evidence of disbelief. In religion, or fitness, or shrimp welfare the people on the tails of the distribution are the ones who actually give a shit. Everyone else is a nonbeliever even if they pay lip service otherwise.
When infinity is invoked as a reward or punishment to factor into EV calculations, how would that not set the burden of proof to infinity as well?
That makes no sense. The burden of proof is not commensurate with the rewards. It's not like you need extra evidence to think someone will torture you rather than that someone will slap you. That's not how Bayesian reasoning works!
The whole point of Pascal's wager is that you should wager even if the probability is low, so the burden of proof doesn't have to be infinite.
The probability of me believing a reward claim is not tied to the extent of the reward? Am I understanding this correctly?
Yes! There might be some cases where there is a connection, but it’s not anything like linear.
I don't think it's linear, and I agree that there may be ways to agree with Josh and still have non-infinitesimal probabilities of infinite rewards, but I think the generic situation is that there will be a pretty straightforward inverse relationship between reward and probability, such that you should generically expect that a reward of infinite size w should have probability on the order of infinitesimal 1 / w.
A few reasons to think this:
First, Kolmogorov complexity, the probability of a hypothesis should be proportional to its complexity. I think it is pretty plausible that all else equal, hypotheses with more utility in them are more complex--to have more utility you need either a higher density of utility per person, in which case you may need to specify more details to explain how this extra utility comes about; or constant density but more people, in which case you need to specify the extra people at a complexity penalty; or constant density and constant people but longer time, in which case you incur complexity cost for the additional time.
Now, how exactly that complexity penalty grows isn't obvious, but I think it's clear that you want the complexity penalty to grow at least as fast as the utility in general, otherwise you just lose the ability to do decision theory at all: the cost of specifying a new theory with infinite reward if and only if you do the *opposite* of what some other hypothesis suggests needs to be large enough that we avoid having that every action has infinite expected value. Only the "most principled" infinities can be exempted from this, so the generic case is that indeed infinite reward hypotheses have infinitesimal probability.
Obviously, that leaves the exemptions, but it does establish that you should have to make a positive case for why your hypothesis is one of those principled exceptions.
Second, think about how you would assign probabilities to infinite reward scenarios as distinct from any of their finite-reward subscenarios. What I mean is, suppose I have a probability p(w) of an infinite number of people all enjoying constant positive utility C. What probability p(n) should I assign to the hypothesis that there are at least n people enjoying utility C, for any finite n? Clearly, n people enjoying C utility is a superset of infinite people in that same situation; so p(w) must be less than p(n) for all finite n.
Now let q(n) be the probability that there are *exactly* n people in that situation, i.e. that there are at least n people, and that there are *not* at least n+1 people. This is q(n)=p(n) - p(n+1). Since these are probabilities and they're exhaustive and exclusive, we have that their sum must be 1:
1 = q(0) + q(1) + ... = p(0) - p(1) + p(1) - p(2) +...
This is a telescoping sum with value 1 = p(0) - lim p(n) -- but we need that p(0) to be 1, as this is the probability that at least 0 people are in the situation described, which is obviously tautologically true, so the limit of p(n) as n goes to infinity is 0, so p(w) which is less than every p(n) must be 0, or infinitesimal, and it must be a smaller infinitesimal than whatever the limit of p(n) is.
This is obviously a particular modeling choice, but I think unless you can offer a superior model, I think it should be broadly applicable: if you have some probability of a (in)finite population of people enjoying a (in)finite of utility each for a (in)finite amount of time, at least one of those (in)s must be included to achieve infinite utility. So, whether it's time, or people, or average utility per person, you're going to be saying there is a probability p(w) of infinite (people/time/average utility), in which case you can play the same game with p(n) for at least n (people/units of time/average utils), and the only consistent way to assign probabilities is to make p(w) infinitesimal or 0.
I withdraw my infinite sum argument, because there's a mistake: the sum q(0) + q(1) +... does not have to equal 1, precisely since there's non-zero probability on the hypothesis that the correct number is *not* any finite n.
As an extreme example, you could have q(n)=0 for all finite n, and so p(n)=1 for all finite n, and p(w)=1, corresponding to absolute certainty that the true number will be infinite.
I think all you can say for certain is that, in order to have a non-zero probability for p(w), you need that the series \sum_n 1 - p(n+1|n) converges--that your credence that, having observed n steps of your series, the series will stop now, must shrink fast enough for those credences to form a convergent series.
So, for example if you think that, a series that has continued for n steps so far has a probability 1/n of failing to continue, then that's not enough; the sum \sum_n 1/n is the famously diverging harmonic series.
You would be okay if you believe that a series that you've seen n steps of will fail with a probability 1/n^2 though.
I think one can still dispute if such a form for a conditional probability is reasonable (at any finite stage you still have infinitely many steps left to go, so in some sense, the fraction of probability space you've excluded after Tree(3) steps is the same as after 2 steps, so your conditional probabilities at those two stages shouldn't be too different, would be one possible argument) for anything other than a proof by induction or something like that, but mathematically as far as I can tell it is possible to have such credences.
Any finite observation of time spent in heaven can not be taken as evidence of an infinite reward for heaven.
Of course it can. Evidence is that which renders a conclusion more likely. Spending some time in heaven makes it likelier you’ll spend forever there.
I made a post
https://sorenj.substack.com/p/pascals-wager-and-prior-probabilities
Any finite amount of time in heaven is still ~0 probability for an infinite amount of time because time is a torsor.
See the section in my post for Number Land #1. The argument you just made is equivalent to:
"Observing more decimals of 0.50000 means its likelier that the actual number chosen was 1/2"
But you shouldn’t have an even credence over the years in heaven lol!
Why not? If you have a religious belief in a just universe, the obvious expectation for years in heaven woudl be proportional to your good deeds in life.
I am not sure what you mean by this
I agree with you, but I think it’s also worth noting that every additional moment in Heaven also confirms an infinite set of hypotheses whereby you will be in Heaven for a finite amount of time (e.g., pretending that time is discrete for a moment, experiencing the Nth moment in Heaven, confirms that you will be in Heaven forever and also that you will be in Heaven for exactly K moments for all K>N).
Yeah true, but surely if you spend like googol years in heaven with God, you should think it's very unlikely that will stop.
What is your probablity function for
P(Time spent in heaven is infinite | Finite time spent in heaven)?
See my comment above: it matters how you quantify "very unlikely"--if you think the probability is 1/googol (because the probability of stopping after n steps is 1/n), that is not enough to give you a non-zero credence in it lasting infinitely long; even though 1/googol is very, very unlikely!
Maybe, but I suspect this is just a matter of priors and a lot of priors would be rationally permissible here. For example, what would be unreasonable about, every time you pass some significant threshold, just thinking that the true end of your time in Heaven is even further away? Maybe you experience googol moments in Heaven and then you think “well, now I think, I will experience at most googol ↑↑↑ googol moments in Heaven” (iterating once you pass each threshold, supposing your time in Heaven will in fact be infinite).
Were this how you reasoned, it seems like you would be sensitive to the fact that, the more time you experience in Heaven, the less likely the next moment will be your last. But you may never think that the finitude of your time in Heaven is particularly improbable.
> The burden of proof is not commensurate with the rewards.
That might work for torture because some people are just sadistic and enjoy torture, even though no-one benefits.
But for me it does work with unearned rewards. I have a baseline of what kind of rewards one can get in the world, from working for money, to enjoying good friendship, to picking herbs and mushrooms for free.
If someone comes offering rewards that are way above the usual effort/reward proportion, I should very much be skeptical. In the real world, it's more likely to be a scammer than anything else. That means that the accrued burden of proof is actually *higher* than commensurate with the promised rewards.
The downside risk angle of Pascal's Wager is self-undermining. The reason why Pascal's Wager is convincing at all is because Christianity has a decently high probability of being true (compared to any other supernatural belief system someone could make up), and a decent part of that high likelihood rests on the fact that God is fairly simplistic, i.e. the most good agent. And this conception of God as the most good agent directly conflicts with eternal hell! Conditional on eternal hell being real, the likelihood of Christianity plummets, and in order to follow Pascal's Wager to mitigate downside risk we should convert to a religion (e.g. call it torturism) which is much more likely to exist given eternal hell is real.
As I explain in the post, even universalists can affirm the wager
Yeah, I agree generally, I think Christianity dominates the upside of Pascal's Wager, and when it comes to the downside, Christianity is on equal footing with many other belief systems, even more arbitrary ones.
I think Christianity is on worse footing. If Christianity is true, there's some nontrivial chance that universal salvation is true. So you should wager on Torturism, because you may end up in Christian heaven regardless, and Torturism offers no such leniency.
An anthropic argument against the existence of heaven:
Supposing that there was a non-zero probability that heaven existed. What is the probability that a randomly chosen observer at a randomly chosen moment in time would observe itself to not be in heaven? Zero.
I observe myself to not be in heaven. Therefore heaven does not exist.
"Two people have written replies to me on Pascal’s wager"
Not only two!
There are too many other possible Gods for whom Pascal's Wager would be a bad bet, nullifying any benefit that would be had from accepting the Wager for the Christian God, even assuming that's how the Christian God really works.
https://ramblingafter.substack.com/p/im-not-a-polytheist-but-i-believe