Comments on: Pascal’s Wager and the Ad Baculum Fallacy https://www.richardcarrier.info/archives/13810 Announcing appearances, publications, and analysis of questions historical, philosophical, and political by author, philosopher, and historian Richard Carrier. Mon, 13 Jul 2026 19:12:44 +0000 hourly 1 https://wordpress.org/?v=7.1.2 By: Richard Carrier https://www.richardcarrier.info/archives/13810#comment-44630 Mon, 13 Jul 2026 19:12:44 +0000 https://www.richardcarrier.info/?p=13810#comment-44630 In reply to Ulka.

That doesn’t matter.

That’s what my article explains.

It literally cannot matter whether I “just make something up,” because anything logically possible has a nonzero probability of being true, and any nonzero probability multiplied by infinity is infinity—and not just infinity, but exactly the same infinity.

Do you understand the problem now?

If we rely on the wager, its own faulty logic entails even the most improbable religion logically conceivable is just as good as any sect of Christianity you want to settle on. Because the wager converts all probabilities into infinite net goods. All. Not “the higher probabilities.” All of them. They all flatten out as the same.

This is what I am pointing out is broken mathematically with the wager. It can’t do the thing you want to do. Its own mathematics rules your point out of court. Which should make us suspicious of its mathematics.

Which is what the rest of my article exposed and debunks: the wager’s math is wrong. You can’t make a religion attractive by increasing the absurdity of its promises. That’s as true of Christianity as Islam or Buddhism or Taoism or Cthulhuism or Pastafarianism or [insert made-up religion here].

So all we have left is the evidential status of the religion compared to alternatives. And on that, Christianity always loses. But that’s not because of the wager. It’s because of precedent, parsimony, and evidence. And turning Christianity into a cosmic conspiracy theory doesn’t save it.

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By: Ulka https://www.richardcarrier.info/archives/13810#comment-44626 Mon, 13 Jul 2026 18:09:14 +0000 https://www.richardcarrier.info/?p=13810#comment-44626 In reply to Richard Carrier.

Your wager’s God doesn’t come from any religion or holy book, it’s just made up to make the argument work. But Christianity or Islam have thousands of years of philosophy, scholars, and followers behind their God. Doesn’t that make the Christian or Islamic God more likely to be real than your wager’s God, which feels kind of made-up?

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By: Richard Carrier https://www.richardcarrier.info/archives/13810#comment-44617 Mon, 13 Jul 2026 14:56:27 +0000 https://www.richardcarrier.info/?p=13810#comment-44617 In reply to Ulka.

That’s not two hypotheses it’s “infinitely many.” And it includes organically constructed religions not reverse engineered from Christianity at all but often even predating it. But even the engineered examples have the same epistemic status because Christianity (and all its tens of thousands of mutually refuting sects) is a made-up false religion, so “making up” more false religions has no effect on the relative likelihoods.

Which may signal that you don’t understand Pascal’s Wager. The point of the wager is to address the implausibility of Christianity: whereby yes, even if the evidence signals it is false, the wager is the last resort to ensuring you believe it anyway. The flaw in that is that it assumes it is the only available hypothesis of long-term outcomes. Once you reintroduce all infinitely many alternative theories, the wager washes out as warranting no belief at all. So you have to go back to the original basis for believing things: the thing with the most real evidence. A contest Christianity always loses.

Now, back to the point of this article: even granting the wager’s invalid logic, we get the result…

These two Wagers have the exact same utility value (even if it’s infinite)—and therefore negate each other. Therefore all such Wagers are invalid. That wouldn’t necessarily be the case, but it is the case for Pascal’s Wager because of that invalid premise of an irrational utility function we just examined. If we grant that the utility function for a God is infinite, then it is infinite for every contrary God; and the mathematical result is zero net utility

Notice that the wager’s own logic entails that differences in likelihood for alternative hypotheses can never matter because they multiply that by infinite utility functions, and any finite number multiplied by infinity equals the same value: infinity (in particular aleph-1, the set of all real numbers). So even if I pair Christianity against a made-up religion that is ten billion times less likely to be true than Christianity, they both end up infinitely preferable, and so it is impossible to choose based on the wager’s logic. In short, the wager’s own logic eliminates any function that differences in epistemic probability would have had, because it makes all theories infinitely rewarding no matter how unlikely they are.

Hence the rest of my article addresses what is going wrong here: you can’t just multiply a probability by infinity. The more outrageous the promise, the lower the probability. So the epistemic value of eternal reward is not infinity, but infinitesimal. For reasons the article explains. But when we use the correct math, the wager gets no usable result. Hence it is fallacious.

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By: Ulka https://www.richardcarrier.info/archives/13810#comment-44605 Sat, 11 Jul 2026 20:15:51 +0000 https://www.richardcarrier.info/?p=13810#comment-44605 In reply to Richard Carrier.

Since there are infinitely many possible diverse outcomes (infinitely many possible gods, systems of gods, and systems lacking gods), they all negate each other. For example, for any “believe in God(x) or else” Wager, there is a contrary Wager that is equally valid, such as “God(y) will punish you for believing in God(x), therefore you should believe in God(y).” These two Wagers have the exact same utility value (even if it’s infinite)—and therefore negate each other. Therefore all such Wagers are invalid.

My point is: If you construct an ‘anti-Pascal God’ specifically to counter the Christian God, that anti-Pascal God is reverse engineered.

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By: Richard Carrier https://www.richardcarrier.info/archives/13810#comment-44593 Fri, 10 Jul 2026 22:37:41 +0000 https://www.richardcarrier.info/?p=13810#comment-44593 In reply to Ulka.

I am not sure what you mean by “both hypotheses.” Can you quote the exact text of the article you are asking about?

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By: Ulka https://www.richardcarrier.info/archives/13810#comment-44568 Sun, 05 Jul 2026 14:40:31 +0000 https://www.richardcarrier.info/?p=13810#comment-44568 I understand your point, but I want to ask something. You keep saying both hypotheses have the exact same probability — but I’m not sure that’s fully correct. By Occam’s razor, shouldn’t a purpose-built counter-hypothesis (like the Anti-Pascal God) get some penalty for complexity, since it wasn’t built from evidence but reverse-engineered specifically to counter the other claim? A hypothesis built backward from a wanted conclusion feels different from one that comes from actual observation, like in science.
Also, in Bayesian reasoning, likelihood can be different from person to person, depending on their background knowledge and assumptions. So how can you say both hypotheses have exactly the same probability for everyone, when Bayesian reasoning itself allows for different priors and likelihoods between people?

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By: albattani https://www.richardcarrier.info/archives/13810#comment-40274 Tue, 25 Mar 2025 08:44:38 +0000 https://www.richardcarrier.info/?p=13810#comment-40274 Excellent Blog, as usual! But still, the best answer to Pascal’s wager is the poem by Jacques Prévert…

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By: Richard Carrier https://www.richardcarrier.info/archives/13810#comment-39973 Sat, 18 Jan 2025 19:48:10 +0000 https://www.richardcarrier.info/?p=13810#comment-39973 In reply to secretlytastemaker867ef0866b.

Refuted in the article you are commenting on.

Please stop commenting without addressing the article. That will get you permanently banned if you do it again.

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By: Richard Carrier https://www.richardcarrier.info/archives/13810#comment-39972 Sat, 18 Jan 2025 19:46:36 +0000 https://www.richardcarrier.info/?p=13810#comment-39972 In reply to secretlytastemaker867ef0866b.

That isn’t true.

Almost no religions by count have any heaven-hell adjudicated by belief (rather than worth). Few even have heaven-hell.

And even counting the rare few religions that are the most popular now solely due to relatively recent imperialism in human history (occupation, compulsion, lock-in, and warfare), i.e. Christianity and Islam, roughly a third of their adherents don’t believe in these ideas, and those are just antiquated sects of Judaism, most of whose adherents have actually abandoned these ideas.

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By: secretlytastemaker867ef0866b https://www.richardcarrier.info/archives/13810#comment-39962 Sat, 18 Jan 2025 17:38:43 +0000 https://www.richardcarrier.info/?p=13810#comment-39962 In reply to ou812invu.

Russel invented the Celestial Teapot by his own admission so it seems less probable than God.

The key to Pascal’s Wager is to wager by probability.

The probability that theists go to Heaven and atheists do not seems higher than the reverse, IMO.

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