[YeGoblynQueenne]

Thanks, that's an interesting read. But I don't think it addresses my question: why shouldn't Pascal place the probability that the Mugger is an Operator from the Seventh dimension to _zero_ (rather than an infinitissemally small number)?

The point is that, at the time when the Mugger declares himself to be an Operator from the Seventh Dimension who can offer large rewards etc, there is no evidence to suggest he's saying the truth. No evidence at all. Accordingly, the probability that he's telling the truth must be zero. Where does a non-zero probability value come from?

Are you then saying that the probability of any reward should never be placed to zero because that would not maximise rewards?

[Dylan16807]

Probability zero is the same as saying that it would take infinite evidence to convince you. Even if someone provides amazingly convincing evidence, better than you've ever seen, a flat 0 or 1 eats it.

> there is no evidence to suggest he's saying the truth. No evidence at all. Accordingly, the probability that he's telling the truth must be zero.

I don't think that logic works. What if the claim was "I have a five dollar bill in my pocket"?

[YeGoblynQueenne]

>> Probability zero is the same as saying that it would take infinite evidence to convince you.

That assumes I can't go back and change my earlier beliefs. But I don't see why that's necessary. If I have no evidence that X is true at time t, I assing a probability of 0 to it. If I acquire evidence that X is true at time t+1, I throw out the 0 and assign a higher probability to X.

The world changes all the time. Why am I condemned to hold on to obviously unsound beliefs for all eternity?

>> I don't think that logic works. What if the claim was "I have a five dollar bill in my pocket"?

That depends. I've seen five dollar bills coming out of peoples' pockets before (actually, I haven't because dollars are not common where I live but Ok). I don't have to assing a zero probability to that. I have some evidence that it's possible.

But I have no evidence that there even exists such a thing as a Seventh Dimension etc.

[Dylan16807]

> If I acquire evidence that X is true at time t+1, I throw out the 0 and assign a higher probability to X.

> The world changes all the time. Why am I condemned to hold on to obviously unsound beliefs for all eternity?

Normally when you update a probability, how much you change it is based on the strength of the evidence. If your probability of something is ultra-low, and you see an event that's a million times more likely if that thing is true, your new probability is roughly a million times higher. And for a probability that's sufficiently close to 0 or 1, that pit is basically impossible to climb out of.

Do you have an alternate method to suggest? What's the calculation you would use? Note that "I'm seeing this with my own eyes" should only give you so much change, because you might have accidentally taken a whole bunch of hallucinogens.

> But I have no evidence that there even exists such a thing as a Seventh Dimension etc.

If you're setting a hard cutoff based on the silly Seventh Dimension stuff, then you still fall for the version where I come to your house and sign a document giving you a giant pile of money. That's how mortgages and business deals work every day after all.

> How about the statement "Hillary Clinton is the President of the United States"? What probability should I assign to that? I know that the PotUS is Donald Trump. Does Cromwell's Rule mean that I have to believe that Hillary Clinton is the PotUS at least a little, because otherwise I will never be able to believe it if she ever gets elected president?

Not for that reason. But you have to factor in the chance that you got confused, or your brain is failing to make new memories and it's actually 2022, or you just woke up from a really detailed dream about the wrong president.

[YeGoblynQueenne]

>> Do you have an alternate method to suggest? What's the calculation you would use? Note that "I'm seeing this with my own eyes" should only give you so much change, because you might have accidentally taken a whole bunch of hallucinogens.

I don't understand. How would it happen that I've accidentally taken a whole bunch of hallucinogens? I never go near that kind of stuff.

>> Not for that reason. But you have to factor in the chance that you got confused, or your brain is failing to make new memories and it's actually 2022, or you just woke up from a really detailed dream about the wrong president.

I don't see how that would happen either. Why would my brain fail to make new memories? Why are you saying that this might be the case?

I think this is just enhancing the deep unreality of what you are proposing. If we need to assume that I'm in some kind of weird mental state that I have no reason to be in for your whole proposition to make sense then I really don't see the point of it, other than perhaps an interesting theoretical game.

[Dylan16807]

You can't come up with a one in a billion scenario that you would accidentally take a hallucinogen?

You never ever have a dream that seems real for a few moments?

And failing to make new memories would be a specific but possible injury.

We're supposed to be working with very low probabilities here. That's the whole point of the thought experiment. If you're going to round anything below one-in-a-million to exactly zero then that's your prerogative, and it works in everyday life, but it's objectively wrong; it would falsely reject the idea of lightning strikes and winning the lottery.

> I think this is just enhancing the deep unreality of what you are proposing.

You didn't even reply to the part about removing all the silly stuff and cutting it down to just "guy offers to sign a document for lots of money"...

[YeGoblynQueenne]

But I'm not hallucinating and I'm not dreaming either.

Also, I don't know why you're saying I'd round anything below one-in-a-million to zero. I wouldn't. But would assign zero probability to a mugger being an Operator from the Sevent Dimension because that's a patently absurd idea that I see no good reason to grace even with the slightest degree of belief.

I mean, if you take what you are saying here at face value I actually have to assume that there is a probability that there exists a Seventh Dimension with magikcally powerful Operators inhabiting it. In real life, not just in the context of Pascal's Wager. Because I can't assign zero probability to anything.

That just doesn't make any sense at all.

>> You didn't even reply to the part about removing all the silly stuff and cutting it down to just "guy offers to sign a document for lots of money"...

Apologies. I didn't understand what you meant with that and I didn't want to clutter the comment space with more clarifying questions.

[TeMPOraL]

As the saying goes, "zero and one are not probabilities". Like 'Dylan16807 says, they eat evidence. When doing maths, when transforming to log probabilities, 0 becomes -Infinity; when transforming to odds ratios, 1 goes to infinity.

A longer explanation: https://www.lesswrong.com/posts/QGkYCwyC7wTDyt3yT/0-and-1-ar....

See also https://en.wikipedia.org/wiki/Cromwell%27s_rule, mentioned by 'edflsafoiewq.

[YeGoblynQueenne]

Yes, I get the arithmetic, thank you. What I don't get is why I'm forced to perform it in the way that you say. Why do I have to hold on to that 0 probabilty no matter what happens? Clearly it's much more reasonable to change my mind given that the world has changed and assign a non-zero probability to an event for which I now have evidence. Why would I not?

>> See also https://en.wikipedia.org/wiki/Cromwell%27s_rule, mentioned by 'edflsafoiewq.

How about the statement "Hillary Clinton is the President of the United States"? What probability should I assign to that? I know that the PotUS is Donald Trump. Does Cromwell's Rule mean that I have to believe that Hillary Clinton is the PotUS at least a little, because otherwise I will never be able to believe it if she ever gets elected president?