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 :-).
“If this expectation of mine is ever violated, I’ll have to rebuild my world view from scratch anyway, discarding all major priors”?
I’ve had to rebuild huge chunks of my priors due to major system collapses a couple times now, so the idea doesn’t really bother me. I’ve also done maths where 2+2=3, thanks to a hobbyist interest in abstract algebra.
I’d rather seek Truth than Convenience, even if it does mean rebuilding everything again. Besides, a compelling proof that 2+2=3 probably means something fundamental has changed in the world, and that believing 2+2=4 will cause me some serious issues.
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...)
I find it amusing that you responded to a comment from August 2007 by linking to a post from September 2007.
If only Doug_S. had bothered to read that post before making that comment, there wouldn’t have been any confusion!
laughs Cute, I hadn’t paid attention to either of the timestamps :)
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
I’ve had to rebuild huge chunks of my priors due to major system collapses a couple times now, so the idea doesn’t really bother me. I’ve also done maths where 2+2=3, thanks to a hobbyist interest in abstract algebra.
I’d rather seek Truth than Convenience, even if it does mean rebuilding everything again. Besides, a compelling proof that 2+2=3 probably means something fundamental has changed in the world, and that believing 2+2=4 will cause me some serious issues.