Emeralds are no chameleons — Why “Grue” is not projectible for induction

Abstract

The model function for induction of Goodmans's composite predicate “Grue” was examined by analysis. Two subpredicates were found, each containing two further predicates which are mutually exclusive (green and blue, observed before and after t). The rules for the inductive processing of composite predicates were studied with the more familiar predicate “blellow” (blue and yellow) for violets and primroses. The following rules for induction were violated by processing “grue”: From two subpredicates only one (blue after t) appears in the conclusion. As a statement about a future and unobserved condition this subpredicate, however, is not projectible for induction whereas the only suitable predicate (green before t) does not show up in the conclusion. In a disjunction “a v b” where “a” is true and “b” false the disjunction is true. When, however, the only true component is dropped, what remains is necessarily false. An analogous mistake may be observed in the processing of “grue”, where the only true component (green) was dropped in the conclusion. — As a potent criterion for correct inductions a check of the necessity of the conclusions is recommended.