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Comment by joe_the_user | Hacker News Reader

Good stuff,

It is worth saying that there are still situations where any use of quantitative probabilities becomes something of an abuse. The most extreme example is Pascal's Wager[1]; if you can assign a "small but meaingful" probability to any X you happen to mention in the discussion, you can assign a probability to the existence of the Great Old Ones or the Flying Spaghetti Monster or whatever implausible entity is going to create a hypothetical action of negative utility sufficient to counter it's unlikeliness.

And, of course, acknowledging some stuff outside of the domain of probability means you need a fuzzy border between two realms, which also can't be determined by probability.

[1]https://en.wikipedia.org/wiki/Pascal%27s_Wager

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The problem with Pascal's Wager is the infinities in the loss function, not the use of probability to represent uncertainty.

I'd claim assigning a probability to the existence of God is problematic in itself. Could you assign a probability to the inconsistency of mathematics?

Under the Bayesian school of thought, probability represents our degree of belief and is ultimately subjective. There is no a priori reason I can't assign a probability to the existence of God, since the probability reflects my belief about God's existence. Evidence lets us update our beliefs, and therefore our probabilities.

While I have no issue at all with assigning a probability to the inconsistency mathematics, the value I'd assign varies with the branch and mathematics. For Zermelo–Fraenkel set theory, for example, I'd assign a probability very very very close to 0, but not equal to zero (because to be equal to zero, I'd need a proof).

The inconsistency of math was a trick question. It doesn't matter what probability you assign to it since if math is inconsistent, all numbers are equal!

>since if math is inconsistent, all numbers are equal!

That doesn't follow.

It does, insofar as you can express anything meaningful in an inconsistent system. A formal system being inconsistent implies being able to prove some statement A, and also its converse ~A. If both A and ~A are true, then we can prove that every other statement in this system is also true. A quick proof:

1. A 2. A v B 3. ~A & A v B 4. B

We start with A. The union (logical-or) of true statement (here A) and any other statement (say B) is a true statement, thus A v B. Then we introduce another true statement, ~A, via logical-and to get ~A & (A v B), which simplifies (disjunctive syllogism) to just B.

So we have proved B, but B was arbitrary. It could be anything, including the statement that x = y for x and y two ostensible non-equal numbers.

See here for examples why such inconsistency doesn't disqualify math in toto:

https://plato.stanford.edu/entries/mathematics-inconsistent/

Exactly! If your prior is such that things with |utility| = X occur with probability less than 1/X, then Pascal's wager doesn't work.

They also mean futures with a large number of humans, for someone who cares about that as part of their utility, are incredibly unlikely. This is implausible.

This is not the only problem - there is also the small problem of worshiping the wrong god if the real god is jealous and vengeful. Will this god be more angry if you worship the wrong god or no god?

That's not much of a problem for Pascal, because he made his wager in an environment where the cultural bias regarding god was that there was either the Christian god or no god.

I would be pretty certain that Pascal knew there were other gods worshiped in the world. He might have thought all the other gods were false gods, but he would have been aware of the concept of different gods.

Still doesn't change the problem of worshiping the wrong god. Is it better to worship no god than worship the wrong god?

>The most extreme example is Pascal's Wager[1]; if you can assign a "small but meaingful" probability to any X you happen to mention in the discussion, you can assign a probability to the existence of the Great Old Ones or the Flying Spaghetti Monster or whatever implausible entity is going to create a hypothetical action of negative utility sufficient to counter it's unlikeliness.

Yes, but Pascal used a big prior of his cultural upbringing and 2.5+ millennia of Jewish+Christian religion to consider just one God as plausible, not every random possible entity.

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