A Second Order Logic of Variable-Binding Operators

Abstract

It is well-known that Frege distinguished between first- and second-level concepts or functions. First-level concepts he associated with properties and relations between objects. These concepts Frege characterized as functions which assigned truth-values (the true or the false) to (n-tuples of) objects. An (n-tuple of) object(s) was said to fall under such a concept if it was assigned the true by that concept. In his Begriffsschrift these concepts were indicated by predicate variables.