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PhilGoetz comments on You can't believe in Bayes - Less Wrong
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Comments (58)
I don't know how I can re-explain it other than just repeating the examples in my post. People see that proposition X implies action A. They then try to decide whether they believe X. If they don't, they don't take action A. This is wrong.
Also, "I believe it's possible that I'll die in a car accident" is a statement of certainty. Parse it.
The solution to this isn't to reject the very useful concept of belief (which is already generally used to mean "probability 1 minus epsilon" by many people), but to
Yes. Belief is still useful. It's mainly in situations where a low-probability outcome has a high cost or benefit that it causes problems.
It looks like I agree with you but disagree with your original post. What's the problem with saying we believe Bayes' Theorem, and clarifying if asked that we ascribe probability 1 minus epsilon to it?
The rest of your post is of value, but the "You can't believe in Bayes' Theorem" hook goes awry.
Fair enough.
Fantastically concise summary to a great post. I've tried to explain this to others a few times, and came nowhere near such a direct statement of the problem.
Phil, nothing is a statement of absolute certainty, natural language doesn't express anything precisely. It's wrong to read even "I'm absolutely certain that 2+2=4" as a statement of absolute certainty.
Um, how is that relevant? You're the one who introduced the word 'certainty'.
"I believe it's possible that I'll die in a car accident" is a statement of uncertainty in the event "I'll die in a car accident", so how is it relevant that the statement as a whole is a statement of certainty? I misjudged, trying to find the cause of you mentioning that, which now opens that question explicitly.
Nitpick: No, it's not. Things that are necessary are all also possible. For instance, it is possible that 2+2=4, because it is not impossible that 2+2=4. It's not as strong a statement as someone who believed that death by car accident was inevitable could make, but it's not an expression of uncertainty all by itself unless the speaker is doing something with tone of voice ("Sure, I guess I think it's possible that I could die in a car accident...")
That's not what I was talking about, interpreting "It's possible that X will happen" as "the event X is non-empty" is as wrong as interpreting "I believe X will happen" as "negation of even X is empty". Uncertainty is just lack of certainty, "it's possible" expresses probability lower than that of "it's probable", way below "it's certain". See also the references from the Possibility article on the wiki.
No it's not. It's an assertion about someone's understanding and expectations. You're confusing the subject of the sentence with the subject of the subordinate clause.
No; it's a statement of certainty; but it is expressing certainty that the proposition "it is possible that I will die in a car accident" is true, not that "I will die in a car accident" is true.
Of course it can and does. People just don't care much about precision.
The problem lies in making the precision explicit. That's why various non-natural languages like the conventions of mathematics were generated.