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amcknight comments on Bayes Slays Goodman's Grue - Less Wrong Discussion
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Solomonoff Induction is a formalized answer to problems of inference which also applies to the grue problem. It basically just says to weigh all possible explanations that fit your data by their complexity, but it is specified mathematically. Since grue is more complex than green, it weighs green much higher until reason to believe in grue shows up.
This is slightly off topic though, because the key is reducing the items you're talking about to what they are made up of so that you can properly encode them in order to compare the complexity. As said here, it just takes reductionism.
Solomonoff induction involves defining complexity. Green and blue aren't the most basic possible things, so you can't straight up stick in grue and bleen, but you still can come up with some language where grue and bleen are just as easy to define as blue and green are in whatever we'd be likely to use. All Solomonoff induction can really do is specify that the probabilities must add up to 100%.