The Place of the Grundlagen in Frege's Development

Abstract

In so far as there exists a traditional account, a received opinion concerning place occupied by Die Grundlagen der Arithmetik in development of Frege's philosophical thought, it is, I think, this: Begriffsschrift of 1879 introduced virtually all of revolutionary technical innovations which were to comprise Frege's lasting contributions to logic.1 These included a notation for expressing multiple generality, using quantifiers and bound variables; a truth-functional account of logical connectives; an anticipation of theory of types; beginnings of a functorial grammar; and a complete formalisation of first-order predicate calculus with identity. With such technical sophistication, however, Frege combined a relatively naive account of philosophical foundations of logic, that is, of such concepts as function, argument, judgement, meaning, assertion, identity, predication and like though naivety here, it should be said, is relative more to Frege's subsequent writings on such topics than to pronouncements of his predecessors and contemporaries. In Gl, which appeared some five years later, much of this naivety has disappeared and we meet for first time the mature Frege. Virtually all of his subsequent work, we are told, is either propounded or at least adumbrated in Gl: realism, anti-psychologism; sharp distinction between objects and concepts; doctrine that numbers are independently existing abstract objects which can be identified with conceptual extensions; and so on. The only doctrines absent from Gl are those which depend