Don’t make this mistake about Pascal's Wager

0:00 - The Problem
5:28 - Cardinalities
9:41 - Ordinals
12:54 - Calculus
14:58 - Surreals

[gavinhatcher]

You're amazing Squared! Also the: "couldn't think of a more natural sounding way to script this conversation ending so: Goodbye" was hilarious 🤣🤣🤣

[baxterwilliams]

Well done video! Gives me something new to think about with Pascal's wager arguments.

[musicappreciate]

Great stuff, man! If you have faith as a grain of mustard seed, nothing shall be impossible to you.

[ChaoticFoxxx]

Hello! Atheist in a hat here. (Unfortunately I am not actually wearing a hat.) Very interesting video, didn't expect to learn math from an apologist! Very well spoken, and great visuals too! There are a few weaknesses in the argument I'd like to address.

1) The utility is pre-supposed. The infinite reward boils down to "Source: Dude trust me." For someone like me, the promise of heaven is similar to the promise of a pot of gold at the end of a rainbow. I have absolutely no reason to believe it's there. (If someone does believe in an afterlife, this does not apply.)

2) The cost of pressing the button. Decision theory doesn't just multiply reward by probability, it also multiplies cost by the inverse. (For someone whose religion is a very positive force in their life, and does not have a cost for them, this does not apply.) For someone like me, who is a part of the LGBTQ+ community and thoroughly enjoys a number of sins (don't worry I promise I don't hurt anyone else), giving that up is a *significant* cost (assuming that the branch of Christianity follows that doctrine). While it is true that the infinite reward would outweigh that, I refer back to problem 1. And I refer forward to...

3) There are so many buttons. So many. Christianity alone has 200 different denominations in the US alone, and over 45, 000 worldwide. You're telling me that beyond a shadow of a doubt in your mind, you picked the right one (or more likely, you were born into the right one (note more likely, not guaranteed. Converts do exist.)). Even though someone from every other denomination would say the same thing, I should trust you. And if I pick the wrong one, whoops eternal torment. In the space of an estimated 5, 000 religions, with countless denominations therein, even if your branch of Christianity is 1, 000x more likely than any other, as mentioned in the video, there's still a *huge* chance of being wrong.

4) The use of probabilities in the first place. Probability describes the likelihood of an event occurring. In this case, the event is "X religion is true." However, probability requires observation to be rigorous. We can never, and will never, observe that any religion is true because of their supernatural nature. The supernatural cannot be observed from within the natural, and as beings constrained to the natural world, we are incapable of observing the supernatural. The probability of a religion being true is pure guesswork. It is no more correct to say a religion has a 1/5 chance of being true, than it having a 1/1, 000, 000 chance. Both have the same weight behind the estimate: None.

Overall, the situation from my perspective boils down to this: I'm in a room with 100, 000 buttons, 20 denominations for each religion. Every button has the same reward: a unicorn that grants me as many wishes as I want. Every button has a different cost, from never drinking alcohol again, to never allowing me to love who I want to love (only consenting adults, don't hit me with that groomer bull), to abandoning all modern comforts and living as a farmer. Every button has someone standing next to it, saying the same thing: "I'm right, everyone else here is wrong, press my button. Trust me." Even if your button is 1, 000x more likely than everyone else's there (ignoring objection 4 for the sake of argument), that's still over 99% chance of being wrong (assuming the probability of every button adds up to 1, meaning that at least one of them is true, which is not guaranteed). Both paying the finite cost of pushing your button, and the infinite cost of being wrong.

Frankly? I'm walking out of that room. I'm practically guaranteed to lose anyway, and I don't even believe that the utility exists. Why would I pay the price of admission?

[danielboone]

Hey squared. Do you think think you’ll be doing a response to Natiralism Next’s cumulative case for atheism, particularly his argument that evolution is more probable on naturalism than theism?

Personally, his video made me wonder if there’s much value in atheistic arguments as it seems rather difficult to try to a priori predict the actions of an omniscient and omnipotent Being.

[ValkyRiver]

12:33 There is actually a type of infinity in projective geometry which has the property that +∞ = −∞. This way, 1/0 is now defined (to be ∞). This occurs when you curl the number line into a circle and joins the two ends with ∞.
If you extend it to the complex plane, you get the Riemann sphere, which is a stereographic projection of the complex plane onto the unit sphere with ∞ at the north pole. The point at infinity of the Riemann sphere is "complex infinity", and it is also equal to 1/0.

[ShaunCKennedyAuthor]

Thank you. I'm not a mathematician, but I enjoy reading about various ways that knowledge has been expanded in various fields. I had heard of surreal numbers before and even seen a few explanations, but it never really clicked until now. I never expected to get a handle on math I was struggling with from an apologetics channel.

Side question: what would you charge as a beta-reader/proof reader?

[Oskar]

There is a fun problem with surreal numbers

Assume you are already in heaven experiencing infinity utility
Then some betting-man approaches you and says, let's roll a 10 sided dice.
If you roll a 10 you will get 100 * infinite utility
Roll anything but a 10, you will be annihilated at once.

If we use surreal numbers we can actually make the comparison

Option 1: Do not accept the bet, 100% chance of w, expected utility 1*w = w
Option 2: Accept bet, 10% chance of 100 w + 90% of 0 = 0.1 * 100 w + 0.9 * 0 = 10w

So option 2 is better, this result strikes me as absolutely bonkers, you already have infinite utility, why bet?

I agree that .0001% * infinity is a worse bet than 99.9999% * infinity. But I don't like the surreal number solution.

[MatthewFearnley]

Great explanation!

Dare I ask... Can we define the surreal 'ω' as less than [an empty list of numbers], if it's actually smaller than 2ω?
Or is it just the case that when we define 'ω', 2ω doesn't exist yet?

(Or perhaps is it just that this is a simplified explanation, and there are ways of defining surreal numbers that don't run into this problem?)

[WAIT_TG]

My response to pascal's wager is that to me, the probability that <an all loving God who sends people to a place of infinite negative utility against their will> exists is low enough that it has about the same probability as, say, the chance that God will send you to hell if you believe that he exists. Since they both have roughly equal probabilities, the expected utility of believing in one of them, both of them, or none of them is the same: 0

I think that a God who allows people to reject him if they choose to do so is far more probable, but I am fairly confident that I will not reject God if I knew he existed, thus for the more probable version of God, the expected utility is infinite either way, as long as I remain a non-resistant unbeliever.

[ishtaraletheia]

Silly but potentially troublesome question: What infinite positive surreal number is the utility of Heaven? Why not that plus one? Or times two? Or times omega?

[multienergy]

Hey squared, a question, do you know Clarke's third law? Shermer's law? Imagine that God appears to you in a vision, how would we konw that he is God and not the the result of a Technology which misleads our brains created by a super advanced civilization ? Also, couldn't any proof for the existance of God be used not only for the existence a super advanced civilization but maybe for some type of demigod, like cthulhu? Is there a way to free theism from this possibility?

[roberthaskins]

Given the ability to quantify variances in expected utility given probabilities and infinite utility, is it also possible to quantify differences in infinite utilities such that one would be superior to another despite both being labeled as infinite?

[gnomesurf]

It's funny, even in Calc 3 the professor still had to explain that infinity and 1 and 0 aren't numbers. It trips up us math people too!

[jgone]

Why would you wager on something you already know? I'm sorry, I'm an atheist myself but that didn't make much sense to me. You wager based on probability, meaning you don't know one way or the other

[Finfie]

I am pretty sure you need the absorption property. Your claim isn't just that the utillity is great, you want to say that the utillity is greatest. With w of the surreals you can not express that, since one could come along and say: The expected utillity of my religion is w^w!
Now you can argue about the utillity of your respective religions, but both of you have absolutly no viable argument whether or not the respective utillities are *actually* w, w^w, w/2, etc...

[domahidipeter]

but what about other religions? or possible god who doesnt want to people belive them.. and punish (eternally) people who belive in god .

[johnfeusi]

However, I do think even with this consideration, the core problem still remains. The atheist can simply posit that there is a god who rewards only atheists with ω^2 utility. Without any way to come up with reasonable estimates of a priori probabilities and associated utility it turns into a non-sensical arms race of who can posit bigger numbers.

[doomedcells]

I think it's funny how despite getting an infinite reward, God would always be infinitely more powerful as if you had a finite number of resources at your disposal when compared against the infinite resources of the guy upstairs. Once you scale it back down with the idea of just living eternally your suffering might as well be a pin prick in what could arguably still be better than being alive.

Despite any of that, I still won't believe in any religion because every time I've talked to a muslim in the past year they have whittled down their argument to saying that Christianity's prophet Jesus is synonymous with their own Jesus, advocating for both religions with equal temperament. This occurs just before Christians start helicoptering their cocks on Niagara Falls and taking a page out of the book of Satan. And then other christians with more self-respect double down and beat their kids to make sure they don't fuck up.

[ShouVertica]

Do we know heaven exist? No.
Do we know hell exist? No.
Wellp, seems kind of silly to make a wager on something we cant even prove exist at all.
Why even bother with the wager since there is a conceptual infinite other possibilities and paths towards those possibilities?

Theist don't seem to understand where the actual problems are and where the evidence stands.

If you're actually trying to justify Pascal's Wager then you've already committed to there being no sufficient evidence otherwise and that religious claims are unfounded.