In the original comment thread there was a reference to the raven paradox: Why should the observation of a non-black non-raven count as evidence in support of the proposition “All ravens are black”?
After reading the description of the paradox in the first section of the Wikipedia article, it seemed immediately obvious to me what’s going on here: mathematically, it’s evidence; but it’s just very weak evidence. Sure enough, this turned out to be the Bayesian solution described further down.
But it seems there’s another step to be taken. It’s not just weak evidence; in the real world it’s evidence below the noise floor of everyday (non-mathematical) cognition. Seeing my green watering-can is evidence for the blackness of ravens … but it’s evidence weaker than the possibility that I’m hallucinating a watering-can where there’s actually a green raven, or have misremembered what color ravens are or what the paradox was about.
If R is “all ravens are black”, G is “I see a green watering-can”, X is my background knowledge, and C is “I am hallucinating, misremembering, mistaken, or otherwise full of crap”:
P(R|GX) – P(R|X) < P(C|X)
Which is to say, it’s not worth the effort to update on such weak evidence, because it’s just as likely that I’m full of crap. That’s why the “paradox” seems paradoxical: because it’s a discrepancy caused by implementing good math on flaky human hardware.
I had an almost identical reaction when I was first introduced to this problem; when I said so to my philosophy professor, she told me you had to “bite a bullet” to think that a non-black non-raven object is evidence for black ravens. After going home and re-reading Eliezer’s Intro to Bayes’ Theorem the answer seemed even more obvious, and I couldn’t figure out why anyone would think otherwise. I wrote down a few notes and went into the next class ready to argue the point, but before the discussion began my professor went on a digression about how she is (gasp!) a non-reductionist. I made a mental note to reread “Against Modal Logics” and didn’t give the raven matter any more thought.
In the original comment thread there was a reference to the raven paradox: Why should the observation of a non-black non-raven count as evidence in support of the proposition “All ravens are black”?
After reading the description of the paradox in the first section of the Wikipedia article, it seemed immediately obvious to me what’s going on here: mathematically, it’s evidence; but it’s just very weak evidence. Sure enough, this turned out to be the Bayesian solution described further down.
But it seems there’s another step to be taken. It’s not just weak evidence; in the real world it’s evidence below the noise floor of everyday (non-mathematical) cognition. Seeing my green watering-can is evidence for the blackness of ravens … but it’s evidence weaker than the possibility that I’m hallucinating a watering-can where there’s actually a green raven, or have misremembered what color ravens are or what the paradox was about.
If R is “all ravens are black”, G is “I see a green watering-can”, X is my background knowledge, and C is “I am hallucinating, misremembering, mistaken, or otherwise full of crap”:
P(R|GX) – P(R|X) < P(C|X)
Which is to say, it’s not worth the effort to update on such weak evidence, because it’s just as likely that I’m full of crap. That’s why the “paradox” seems paradoxical: because it’s a discrepancy caused by implementing good math on flaky human hardware.
I had an almost identical reaction when I was first introduced to this problem; when I said so to my philosophy professor, she told me you had to “bite a bullet” to think that a non-black non-raven object is evidence for black ravens. After going home and re-reading Eliezer’s Intro to Bayes’ Theorem the answer seemed even more obvious, and I couldn’t figure out why anyone would think otherwise. I wrote down a few notes and went into the next class ready to argue the point, but before the discussion began my professor went on a digression about how she is (gasp!) a non-reductionist. I made a mental note to reread “Against Modal Logics” and didn’t give the raven matter any more thought.