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Manfred comments on Bayes Slays Goodman's Grue - Less Wrong
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Comments (120)
The problem seems trivially easy.
Each observed emerald is evidence for both "the emerald is green" and "the emerald is grue." The first is preferred because it is vastly simpler (and picking any particular T, of course, is hugely privileging the hypothesis!) Evidence that is equally strong for two propositions doesn't change their relative likelihoods - so it starts out more likely that the emeralds are green than grue, and it ends more likely that the emeralds are green than grue, but both are quickly more likely than the proposition that emeralds are uniformly red.
What's weird about this?
To clarify what potato said:
If someone was brought up from birth with the words "grue" and "bleen," how would they say something was "green," in their language? Well, they'd have to say that something was grue before, say, 2050, but bleen after. Something that changes from grue to bleen is clearly more complicated to write down than something that just stays grue all the time.
And this is just hiding the complexity, not making it simpler. Complexity isn't a function of how many words you use, cf. "The lady down the street is a witch; she did it." If we are writing a program that emits actual features of reality, rather than socially defined labels, the simplest program for green is simpler than the simplest program for grue or bleen. That you can also produce more complex programs that give the same results (defining green in terms of bleen and grue is only one such example) is both trivially true and irrelevant.
Agreed.
Wait, actually, I'd like to come back to this. What programming language are we using? If it's one where either grue is primitive, or one where there are primitives that make grue easier to write than green, then true seems simpler than green. How do we pick which language we use?
This is a trick of definition only, however. Changing the definition does not cause those things affected by the old definition to conform to the new one.
Obviously they'd have to invent a new word, for an object that emits light that causes certain kind of qualia.