Grice, "My Empty Class"

 Start with two vacuous predicates, say ( o: 1) 'is married to a daughter of an English queen and a pope' and ( o: 2) 'is a climber on hands and knees of a  70  Paul Grice  29,000 foot mountain'. (13) If a: 1 and a: 2 are vacuous, then the following predicates are satisfied by the empty set ¢: (13 1) 'is a set composed of daughters of an English queen and a pope', and (13 2) 'is a set composed of climbers on hands and knees of a 29,000 foot mountain'. ( -y) Provided 'R 1' and 'R 2 ' are suitably interpreted, the predicates 13 1 and 132 may be treated as coextensive respectively with the following revised predicates (-y 1) 'Stands in R 1' to a sequence composed of the sets married to, daughters, English queens and popes; and ( -y 2) 'stands in R2 to a sequence composed of the sets climbers, 29,000 foot mountains, and things done on hands and knees'. (o) We may finally correlate with the two initial predicates a: 1 and a: 2 , respectively, the following sequences derived from -y 1 and -y2 : (o 1) the sequence composed of the relation R 1 (taken in extension), the set married to, the set daughters, the set English queens, and the set popes; and (o 2) the sequence composed of the relation R 2 , the set climbers, the set 29,000 foot mountains, and the set things done on hands and knees. These sequences are certainly distinct, and the proposal is that they, rather than the empty set, should be used for determining, in some way yet to be specified, the explanatory potentialities of the vacuous predicates a: 1 and a: 2 . My chief complaint against this proposal is that it involves yet another commission of what I regard as one of the main minimalist sins, that of imposing in advance a limitation on the character of explanations. For it implicitly recognizes it as a condition on the propriety of using vacuous predicates in explanation that the terms in question should be representable as being correlated with a sequence of non-empty sets.