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Stuart_Armstrong comments on Green Emeralds, Grue Diamonds - Less Wrong Discussion
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I'm going to raise an issue, and it could be fair to consider it a nitpick, but considering that you're trying to be rigorous, perhaps it is okay to be unusually technical.
Blue and green are not natural categories, or at least they are as natural as "sour tasting" or "stinky". To quote Bruce MacEvoy, "color is a complex judgment experienced as a sensation"; color is not an objective property of things in the world. When a human gazes at something, the color sensation they experience is highly dependent on all sorts of visual factors in the scene, and even depends on the memory and expectation of the human.
When I say, "that object is red", I mean it as shorthand for "that object has a reflectance, transmittance, and emittance profile that usually leads humans to experience a red color sensation when viewing the object in neutral-ish conditions". And let it be known that "red color sensation" and "neutral-ish conditions" are still massive shorthand. So really, "that object is red" is a statement concerning 1) the object 2) the human visual system 3) qualia 4) common viewing environments for humans.
I point this out because it seems wrong to try to do a bunch of rigorous thinking founded upon an extremely flawed example (flawed in the example is supposed to be about objective things, but is actually about subjective things). We even have Eliezer Yudkowsky talking about the nature of truth and using statements like "snow is white if and only if snow is white". It might sound like he's talking about facts, but imagine the analogous sentence "skunks are stinky if and only if skunks are stinky" or "chess is interesting if and only if chess is interesting". Now it is more clear the statement is about subjective experiences and actually fails to have a definite truth value.
Would you be comfortable if your natural category example was whether some music was soothing, or whether some object was bitter? If you would not be comfortable with using those subjective examples, you should not be comfortable using color as an example. If you are comfortable with those examples, you can disregard the issue I raise.
I think a lot of your points still stand, but you're taking unnecessary risks by using a flawed example.
Cheers! I used blue and green because the grue and bleen example is a standard philosophical one, and it's not hard to make pretty rigorous (as Lumifer suggested, with the radiation frequency, and some outside conditions added to it). The pretty rigorous definition is only a partial match for the subjective blue and green, as you pointed out, and I'll try and make that clearer in any subsequent write-up.
Taking "outside conditions" into account to produce an objective definition of color that does a good job of corresponding to human color sensations is actually extremely complex and a very difficult task. Human color sensations are the result of extremely complex and highly contextual processing. I have studied color vision a great deal, and it is very, very common for people to underestimate the complexity and contextual nature of color perception.
Also, you're already conceding that color is not a property of a single object, which would make color a poor example of a property of an object.
Anyway, I'll take your response as a sign that you are comfortable with the problematic nature of your example, and the more pressing concern is playing nice with philosophical tradition/convention. So, I consider the issue closed.