
How to do with probabilities what people say you can’t (1985) [pdf] - sytelus
https://ftp.cs.ucla.edu/pub/stat_ser/r49.pdf
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sytelus
For the context, this was written at the time when there was still a lot of
confusion on how to represent uncertainty. There were at least 3 different
ideas besides using probabilities and in fact the probabilities were
considered not good enough.

Judea Pearl pioneered erasing this view by inventing Bayesian Networks. More
here:
[https://ftp.cs.ucla.edu/pub/stat_ser/r476.pdf](https://ftp.cs.ucla.edu/pub/stat_ser/r476.pdf)

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joe_the_user
Ah, references "fuzzy logic". That was one system that really needed to go
away. I actually took a course in multivalued logic at UCB in the 80s. Fuzzy
logic was "kinda like probability but with no logical basis, just a cute
name".

That said, I think "quantitative measures of likelihood that we can't easily
reduce to probabilities" deserve study.

I mean, it seems like, in rough, "fuzzy" sort of way, neural network
activations are such measures of likelihood and certain they are used.

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gowld
What do you mean by no logical basis?

[https://en.wikipedia.org/wiki/Fuzzy_logic](https://en.wikipedia.org/wiki/Fuzzy_logic)
discusses axiomitizations.

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joe_the_user
I don't mean to be negative here but you can axiomatize anything if
"axiomatize" one just means "describe what you do".

It took quite a while but Kolmogorov and company actually formalized what is
really meant by a "random sequence". But now you have a strong description of
the real world behaviors are expected asymptotically if a probability is
assigned to a behavior. As far as I can tell, all that's being axiomatized
here is how the arbitrary quantities people make up for the fuzzy logic of
things get manipulated. IE, there's not description of the relation of fuzzy
logic and "reality" (because if there were, it would map to either regular
logic or probability).

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sriram_malhar
Judea Pearl has added considerably to this line of thinking (Bayesian
Networks), by annotating them with causality. This allows us to explicitly
model the traditional notion of "hidden variables", or "confounders", and make
sound inferences in many (most?) practical cases even when one can't directly
observe -- but merely suspect the existence of -- some hidden cause.

I _thoroughly_ enjoyed his "The Book of Why", a lay introduction to this
subject.

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joe_the_user
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](https://en.wikipedia.org/wiki/Pascal%27s_Wager)

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

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danieltillett
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?

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coldtea
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.

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danieltillett
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?

