I'd be adverse to assigning zero probability even to mathematical falsehoods :)
(Edit: Okay, finally checked the math. A zero probability means "I absolutely refuse to update this belief regardless of the evidence." I can see situations where I can't imagine ever running in to evidence against, but not anything where I'd refuse to update my belief even in light of evidence...)
Comment author:perry
03 August 2011 04:59:43PM
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How about, "If this expectation of mine is ever violated, I'll have to rebuild my world view from scratch anyway, discarding all major priors"? I'd say that's a valid reason to assign zero. Fudging it with an infinitesimal nonzero probability feels like cheating in that case. (All your eggs are in that basket.)
Anyway, mathematical falsehoods are internal contradictions in a mathematical system. So reliable evidence of mathematical falsehood means either confusion (probable), broken axioms in the system used (possible), or a break in your core logic (reload firmware and reboot brain :-).
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http://lesswrong.com/lw/jr/how_to_convince_me_that_2_2_3/
I'd be adverse to assigning zero probability even to mathematical falsehoods :)
(Edit: Okay, finally checked the math. A zero probability means "I absolutely refuse to update this belief regardless of the evidence." I can see situations where I can't imagine ever running in to evidence against, but not anything where I'd refuse to update my belief even in light of evidence...)
How about, "If this expectation of mine is ever violated, I'll have to rebuild my world view from scratch anyway, discarding all major priors"? I'd say that's a valid reason to assign zero. Fudging it with an infinitesimal nonzero probability feels like cheating in that case. (All your eggs are in that basket.)
Anyway, mathematical falsehoods are internal contradictions in a mathematical system. So reliable evidence of mathematical falsehood means either confusion (probable), broken axioms in the system used (possible), or a break in your core logic (reload firmware and reboot brain :-).
Cheers -- perry