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timtyler comments on Taking Ideas Seriously - Less Wrong
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Further comments on Yudhowski's explanation of Bayes:
Science revolves around explanation and criticism. Most scientific ideas never get to the point of testing (which is a form of criticism), they are rejected via criticism alone. And they are rejected because they are bad explanations. Why is the emphasis in the quote solely on evidence? If science is a special case of Bayes, shouldn't Bayes have something to say about explanation and criticism? Do you assign probabilities to criticism? That seems silly. Explanations and criticism enable us to understand things and to see why they might be true or false. Trying to reduce things to probabilities is to completely ignore the substance of explanations and criticisms. Instead of trying to get a probability that something is true, you should look for criticisms. You accept as tentatively true anything that is currently unproblematic and reject as tentatively false anything that is currently problematic. It's a boolean decision: problematic or unproblematic.
The chance of a criticism being correct can unproblematically be assigned a probability.
A criticism can have many components, some of which are correct and some of which are incorrect. Breaking a criticism down into its components can be difficult/problematic.
Edit: The way I put that sounds stupid. Let me try again: occasionally, a pair of math papers are released, one purports to prove a conjecture, and one purports to disprove it. The authors then criticize each others papers (let's say). Would you really characterize the task of assigning probabilities in this situation as "unproblematic"?
The point is that - if you were asked to bet on the criticism being correct - you would come up with some odds ratio.
Maybe you would do that. I would instead bog down in a discussion of whether the criticism was a nitpick or a "real" criticism. But I would be interested to see what odds ratio you come up with for this criticism being correct.
Heh - is that your criticism? - or did you get it from Douglas Hofstadter? ;-)
And in the math papers example, how exactly are you going to do that? Presumably you are going to go through the papers and the criticisms in detail and evaluate the content. And when you do that you are going to think of reasons why one is right and the other wrong. And then probabilities become irrelevent. It's your understanding of the content that will enable you to choose.
Right - but you don't "choose" - you assign probabilities. Rejecting something completely would be bad - because of:
http://lesswrong.com/lw/mp/0_and_1_are_not_probabilities/
I don't think anyone is falling into this trap. It sounds like the Popperian version is replacing "true" and "false" by "tentatively true" and "tentatively false."
"Tentatively true" and "tentatively false" sound a lot like probabilities which are not expressed in a format which is compatible with Bayes rule.
It is hard to see how that adds anything - but rather easy to see how it subtracts the ability to quantitatively analyse problems.
That's what I said.
Edit: That refers to the first sentence only.
Theories are either true or false. The word "tentative" is there as an expression of fallibility. We cannot know if a theory is in fact true: it may contain problems that we do not yet know about. All knowledge is tentative. The word is not intended as a synonym for probability or to convey anything about probabilities.
Observers can put probabilities on the truth of theories. They can do it - and will do it - if you ask them to set odds and prepare to receive bets. Quantifying uncertainty allows it to be measured and processed.
It is true that knowledge is fallible - but some knowledge is more fallible than others - and if you can't measure degrees of uncertainty, you will never develop a quantitative treatment of the subject. Philosophers of science realised this long ago - and developed a useful framework for quantifying uncertainty.