Nelson Goodman is best known for his "new riddle of induction", which he set up by first defining what appears to be a new color adjective, grue: Something is "grue" if and only if it is examined before some particular time T and is green, or else is examined after time T and is blue. He also throws in, as a bonus, "bleen", which applies to anything examined before time T and is blue, or which is examined after time T and is green. Now, he says, how do we know that the grass is green and not grue before that time T arrives, and that the sky is blue and not bleen? This is for him, and for numerous other analytic philosophers who jumped into the fray, a very worrisome problem indeed!
But the first thing to ask is why Goodman and the others think that this silly little puzzle is so important in the first place! The answer is throughout the 20th century there was a strong (though often only half-conscious) bias among many Anglo-American bourgeois philosophers that only deduction is a valid form of reasoning. Thus induction and all other methods of reasoning were suspect. The strange thing is, however, that deduction is really not all that important in people's every-day rational thinking, and even induction is only a bit more common in our overt thinking. (It is implicit in most of our actions, however. We usually implicitly assume the floor will hold us up today just as it has every day for the past 25 years!) But the use of analogies is far more important in our actual conscious reasoning than either deduction or induction. Thus the implicit attempt to force all other forms of reasoning into the "induction" straight-jacket, and then to further squeeze induction into some variety of deduction is screwed up from the very start. It says a lot about the state of analytic philosophy that this "grue" business is one of the "big issues".
Goodman himself claimed to reject the "old problem" of induction, the worries about induction that analytic philosophers before him had been putting forward, and the attempt to reinterpret induction in terms of deduction. But by raising his "new problem" of induction he nevertheless perpetuated the tired old tradition of questioning non-deductive forms of reasoning.
The "grue" problem itself is just a clever bit of intellectual sleight-of-hand, in which, perhaps, the magician fooled himself as well as his audience. Goodman was careful to define "grue" and "bleen" in such a way that nothing is required to change color at time T in order to be properly called "grue" or "bleen". Thus, a grass blade might actually be both green and "grue" (provided it was examined before time T and was green), despite the fact that blue things examined after time T are also "grue". In other words "grue" and "bleen" are not actually color adjectives, but only slightly complex truth conditionals composed of actual color adjectives and times of observation. Thus there actually is no choice to be made as to whether the grass is colored "either" green "or" grue.
Goodman made it seem like we had to make such a choice (and also that there could not possibly be any basis for such a choice before time T) by giving the complex truth conditional he put forth a name that looks like a color name (and was even derived from other color names). If "grue" actually were a color, then presumably it would be a different color than either green or blue, and it would be reasonable to ask if something were colored green or grue. Furthermore, if "grue" were a color, it would presumably be just as weird for something colored "grue" to change to a different color at some arbitrary time T as it would be for something green to do so. In other words, it would be "just as weird" for something to remain green at arbitrary time T as it would be to suddenly turn blue!
On the one hand Goodman can claim that he is not requiring that anything change its color at some arbitrary time, but on the other hand that is in fact the natural interpretation of the situation if "grue" is viewed as a color. (Then either a green thing changes to a blue thing at time T, or else the thing was not "colored grue" both before and after time T.) His hocus-pocus depends on having it both ways. There would be no plausibility at all to his argument if he did not frame it in terms of the pseudo color adjective "grue" instead of some complex abstact truth condition.
To ask if something is "really" just green, or if it might actually be "grue", is thus in effect to ask how we know that something that is green now will continue to remain green (unless its color is affected by some internal or external development). Or, in other words, it is simply a restatement of the old "doubts" about induction that Goodman supposedly rejected.
The so-called "new riddle of induction" is nothing more than the old, absurd worry that we cannot prove via deduction that things will continue to have the properties they now have (unless there are internal or external forces that cause them to change). In other words, it is really just the same old (supposed) riddle, dressed up in fancy new clothes.
[Kyle Broom sent me a criticism of my previous very brief description of Goodman's "grue" riddle, and—though Mr. Broom may disagree—I think this has helped me improve my discussion of it. However, this is one of those puzzles that can be debated ad infinitum, and it also depends on precisely which definition of "grue" you start with. (There are variations on the theme.) If you think that my dismissal of the problem above is wrong, and that getting to the "true" bottom of a puzzle like this is worth spending a whole lot of time on, then contemporary academic philosophy courses are definitely right for you!]