The Grue Problem

grue emeraldNelson Goodman invented this problem, which he called “the new riddle of induction.” William Poundstone describes it in his book, Labyrinths of Reason.

Colors may be defined and even perceived differently by different cultures. (To see how, check out the page, Which green is different?.) Many cultures do not distinguish between blue and green the way English speakers do. The Himba people of northern Namibia have one word, burou, for vivid blues or greens. The word zoozu includes black and some dark greens and blues, while dumbu includes beige, yellow and some light greens. Thus, an English speaker may say that all emeralds are green, while a Himba-speaking person might say that all emeralds are burou.

Grue and Bleen

Now consider a speaker of Gruebleen, a strange language with a special definition for certain colors. The word grue applies to things that are green before midnight on Dec. 31, 2049, and blue thereafter. The word bleen applies to things that are blue before that same moment, and green thereafter. Thus, a Gruebleen speaker, speaking before the year 2050, would say that all emeralds are grue.

Now ask all three people to make a prediction of what color an emerald will be in the year 2050. The English speaker will say that it will still be green, the Himba speaker will say that it will still be burou, and the Gruebleen speaker will say that it will still be grue. But “grue in the year 2050” means blue!

Grue and bleen seem like unnecessarily complicated concepts to us, but the Gruebleen speaker views our terms the same way. To explain what “green” means, we would have to say that it refers to something that is grue until midnight on Dec. 31, 2049, but then changes to bleen.

The Zero Hour

What makes the terms grue and bleen artificial is the time element they include. A child could be taught that grass is grue and the sky is bleen, but they would not have a full understanding of those terms until the predicted change was explained.

The paradox illustrates the larger problem of induction.(See Hempel’s Raven Paradox.) Even saying, “all emeralds are green” is problematic, because we have not observed all emeralds. True, the ones we have seen are all green, and that is why we feel safe enough using inductive reasoning to conclude that they are all green. But by doing so, we are in a sense predicting the future, suggesting that emeralds of another color will never be found.

Labyrinths of ReasonThe Gruebleen language sheds light on this problem. A Gruebleen speaker would say that every emerald ever found is grue, so it is a fairly safe conclusion that all emeralds are grue. She understands that English speakers have a strange prediction, that in 2050 all grue things will change color to bleen, but she is doubtful.

The only way to find out is to wait for New Year’s Eve, 2049 . If at midnight we see green things suddenly change to blue, we’ll realize that the Gruebleen speakers were right. Our Gruebleen-speaking friend will hold up a blue emerald and say, “See? It was grue all along.” If the change does not occur, we will be the ones saying it was green all along. However, no matter what happens, the Himba speaker will be correct in saying that the emerald stayed burou the whole time.

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