Nelson Goodman, in his book 'Fact, Fiction and Forecast', presents a well known problem he calls "The New Riddle of Induction." It seeks to criticize a basic kind of inductive reasoning most notably characterized by the phrase "all emeralds are green." Goodman wants to say that since all the emeralds we have witnessed up to this point have been green, we assume the hypothesis that all future emeralds will also be green. Goodman then introduces the predicate "grue." Something is "grue" if it is green and the time is prior to t (t in this case being 3000 A.D.) or it is blue and the time is not prior to t (3000 A.D.). We can now make a hypothesis that claims "all emeralds are grue" and the problem Goodman wishes to point out is that this proposition has the same amount of inductive support as "all emeralds are green," yet the "grue" claim generates incorrect predictions concerning emeralds in the future (once it becomes 3000 A.D., newly discovered emeralds will not be "grue").
According to Goodman, this is the critical problem of induction. Goodman also creates the word "bleen" which refers to objects that are blue and the time is prior to 3000 A.D., or objects that are green and the time is not prior to 3000 A.D. This allows Goodman to define blue and green according to "grue" and "bleen." S.F. Barker and Peter Achinstein wish to refute Goodman's "grue" problem of induction in an essay they call "On the New Riddle of Induction." They give the "grue" paradox little significance in its attempt to invalidate inductive reasoning, and challenge Goodman's invention of not only these two words, but also his hypothetical alien race brought up to speak the language of 'grue' and 'bleen'.
[...] Barker and Achinstein foresee this possible issue by recreating the previous scenario only this time with Mr. Green. We tell Mr. Green to paint the grass in the first picture green, and the grass in the second picture blue. It is found impossible to show any sort of special power held by Mr. Green. He chooses two different colors of paint, not because of any unobservable phenomenon, but because he was following instructions directing him to the respective colors. Mr. [...]
[...] Grue does embody both statement 1 and statement we are referring to a person who is able to not only note “grueness” at any given time without knowing a date, but he will apply the label to all and only those objects to which speakers of a green/blue language would apply the phrase “green if the date is prior to 3000 A.D. or blue if the date it not prior to 3000 A.D.” In essence, Mr. Grue has special powers and extrasensory perception if he can accomplish these incredible feats. [...]
[...] If we were to repeat the same test with Mr. Green, and told Mr. Green to paint the tympanum blue, Mr. Green could easily complete this task, even before knowing the date of the picture. If we were to tell him the two different dates of our picture, the information would be extraneous and irrelevant. Once again, Goodman is proven incorrect, showing that blue and green are not in fact positional predicates, and therefore making the two languages asymmetrical. While Barker and Achinstein bring up many good ways to refute the problem, and create interesting situations to test their propositions, I found their review of Goodman incomplete and somewhat flawed. [...]
[...] Grue's special skills, he will obviously reach for the blue paint. we tell Mr. Grue, would like a picture of the Holden Chapel in the year 3000. The color of the tympanum never changes due to its immaculate construction.” If Goodman is correct, Mr. Grue will now choose the green paint. Here we see that the only difference between the two pictures is the time period, and this alone caused Mr. Grue to make a color decision. If we had asked him to paint the tympanum without informing him of the time period, he would not know which color to choose. [...]
[...] Grue, there are two possibilities for defining in accordance with the picture: An object in a picture is grue if either: The pigment used is grue pigment. OR Pigment used is either green and the date of the picture is prior to 3000, or pigment used is blue and the date of the picture is not prior to 3000. Looking back at the symmetry issue, statement A conflicts with statement 1 which stated that if the two languages are symmetrical, a “grue/bleen” speaker must understand the grue predicate in such a way that it applies to all and only those objects to which speakers of a green/blue language would apply the phrase “green if the date is prior to the 3000 A.D. [...]
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