述語が何であるかについて

Abstract

Frege thought a predicate has some incompleteness, which is shown by the fact that a predicate never occurs in a proposition without a supplementation by a certain subject. Thus such a proposition as "human' is a predicate' is meaningless because it neglects the incompleteness of the predicate 'human'. If this view is correct, however, it seems follow that we cannot speak anything about a predicate. For this reason, Russell, in his early years, rejected this Frege's view and hold that a predicate has exactly the same reference as the corresponding noun phrase. For example, the predicate 'human' has exactly the same reference as the noun 'humanity'. But if we can speak something about a predicate as a subject as though it were an individual, we have no reason to exclude such a 'self-refuting' predicate as 'being not satisfied by itself'. And it leads 'Russell's Paradox'. Russell, in searching for a solution to this difficulty, arrived at the type theory of Principia Mathematica, which makes a sharp contrast between a predicate and an individual. But a predicates remains to be a possible value of some variables and this seems to mean that it must have some being. If so, what is a predicate? Some suggestions will be given.