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:
An object is grue iff it is first observed before time T, and it is green, or it is first observed after time T, and it is blue.
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).
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.