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RolfAndreassen comments on Bayes Slays Goodman's Grue - Less Wrong Discussion
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Comments (120)
What does 'first observed' mean? It seems like the sort of thing that someone with a passing knowledge of quantum mechanics would make up, giving a privileged status to conscious observers.
Apart from this objection, I see both in the post and in some of the comments a confusion about the meaning of 'grue'. Take again the definition:
Notice that no object ever changes colour. A green object, first observed before time T, is still grue provided it remains green until the end of time; the definition only refers to the colour at the time of first observation, not at the current moment. To say that an object is grue at time T-1 is not to predict that it will turn blue at time T; it is a prediction that it will remain green for all time.
Edit: Never mind the rest of the comment, I made a silly mistake.
I didn't mean to sound harsh at all btw; I wouldn't want to discourage anyone from making mistakes publicly on LW, which is a great place to have mistakes corrected.
A successful prediction does not weaken a hypothesis.
Also, your argument works just as well for G as for g; therefore, a green emerald is evidence against emeralds being green and against emeralds being grue.
You made an arithmetic mistake. I figured you might want to try and find it yourself, and reasoned: if you do want to be told, you can just ask, but if I had assumed you wanted to be told and was wrong, I couldn't untell you.
The assumption that P(O) is P(G) + P(g) is also incorrect; there is also the hypothesis that half the emeralds are green, for example. But either way you shouldn't end up with P(g|O) < P(g).
It can weaken it relative to a competing hypothesis.