Norton, John D
(2003)
The Formal Equivalence of Grue and Green and How It Undoes the New Riddle of Induction.
(Unpublished)
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Abstract
The hidden strength of Goodman's ingenious "new riddle of induction" lies in the perfect symmetry of grue/bleen and green/blue. The very same sentence forms used to define grue/bleen in terms of green/blue can be used to define green/blue in terms of grue/bleen by permutation of terms. Therein lies its undoing. In the artificially restricted case in which there are no additional facts that can break the symmetry, grue/bleen and green/blue are merely notational variants of the same facts; or, if they represent different facts, the differences are ineffable, and no account of induction should be expected to pick between them. This still obtains in the more interesting case in which we embed grue/bleen in a grue-ified total science; the grue-ified and regular total sciences are merely equivalent descriptions of the same facts. In the most realistic case, we allow additional facts that break the symmetry and then we can also evade Goodman's new riddle by employing an account of induction rich enough to exploit these facts. Unaugmented enumerative induction is not such an account and it is the primary casualty of Goodman's new riddle.
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