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Gillitrut  Reading from the golden book under bright red stars  1yr ago (link.springer.com)   Edited 1yr ago   1592 thread views

Pay no attention to the Model Behind the Curtain!

link.springer.com

Many widely used models amount to an elaborate means of making up numbers—but once a number has been produced, it tends to be taken seriously and its source (the model) is rarely examined carefully. Many widely used models have little connection to the real-world phenomena they purport to explain. Common steps in modeling to support policy decisions, such as putting disparate things on the same scale, may conflict with reality. Not all costs and benefits can be put on the same scale, not all uncertainties can be expressed as probabilities, and not all model parameters measure what they purport to measure. These ideas are illustrated with examples from seismology, wind-turbine bird deaths, soccer penalty cards, gender bias in academia, and climate policy.

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Perhaps our disagreement about comparability is merely verbal, but for future reference your usage of the term is widely divergent from most philosophical treatments of "comparability" in value theory (e.g. see here), so you may want to change it to avoid confusion in the future.

The author is a statistician, not a philosopher, and based on what I was responding to I think what I said makes sense. Maybe you should assume more common definitions instead of esoteric ones, and explain in advance that you are using such an obscure meaning, unless the context is highly specific. I'm certainly not going to warp how I use words around some academics' redefinition.

Your link is paywalled, so I can't really comment on it.

Well, I don't think that anyone says "the completely precise probability of X is Y" about much of anything, because people usually don't work with completely exact probabilities at all. Which I take to be among the claims of the paper.

That's not how I read it. The author said that the entire notion of probability is inapplicable in situations where you lack the information to calculate an exact probability, as you would with a fair coin or fair die.

That is completely different from saying that it makes no sense to draw conclusions about what would follow if it were true, like values of conditional probabilities, which mathematicians and logicians do all the time.

You can certainly discuss what consequences the axiom of choice implies. My point was that if your position about real-world empirical work (or even pure mathematics) depends on whether the AoC "is true" then you have most likely lost the plot. A statement like "if the axiom of choice, then probability is inapplicable in many real world scenarios, but if not AoC, then it is applicable" is almost certainly wrong.

I don’t think that my definition is any more obscure than your personal usage of the term. I’ve never heard anyone else use the term like you do, whereas my usage at least conforms to an extant literature. Here’s a sci-hub link to that paper, sorry, it wasn’t paywalled for me: https://sci-hub.st/https://www.journals.uchicago.edu/doi/full/10.1086/339673?

Lots of empirical work depends upon a background mathematical framework. Statistics is no different. And I never said that probability wasn’t applicable if the AoC is true, all I said was that the AoC would have to be absolutely, determinately false if every uncertainty is to be reducible to precise probabilities.

I don’t think that my definition is any more obscure than your personal usage of the term. I’ve never heard anyone else use the term like you do, whereas my usage at least conforms to an extant literature. Here’s a sci-hub link to that paper, sorry, it wasn’t paywalled for me: https://sci-hub.st/https://www.journals.uchicago.edu/doi/full/10.1086/339673?

This is not "my personal usage", this is just what the word means in English, and how it's used all the time.

https://www.dictionary.com/browse/compare

"to examine (two or more objects, ideas, people, etc.) in order to note similarities and differences"

Lots of empirical work depends upon a background mathematical framework. Statistics is no different. And I never said that probability wasn’t applicable if the AoC is true,

Lots of empirical work depends on the mathematical framework, but the axiom of choice is not one that should be very relevant.

all I said was that the AoC would have to be absolutely, determinately false if every uncertainty is to be reducible to precise probabilities.

Again, I think you're making an entirely different claim to the one that was in the paper, but using similar terminology in a way that's confusing.

Then I don’t understand what you meant in saying that the environment and culture will turn out to be non-comparable given what the paper says. What would it even mean to not be able to examine them for similarities and differences? On your definition, it is just trivially true that everything is comparable.

The axiom of choice is a central part of set theory, which is used to axiomatize all the rest of mathematics. I see no basis for thinking it should be irrelevant to any particular part of mathematics, unless that part is entirely constructive, which statistics in general is not.

I was reacting to the claims that you made in response to the paper, not the paper alone.

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