Showing papers by "David Bell published in 1981"

The Place of the Grundlagen in Feege’s Development

Abstract: In so far as there exists a traditional account, a received opinion concerning the place occupied by Die Grundlagen der Arithmetik in the development of Frege's philosophical thought, it is, I think, this: the Begriffsschrift of 1879 introduced virtually all of the 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 the logical connectives; an anticipation of the theory of types; the beginnings of a functorial grammar; and a complete formalisation of the first-order predicate calculus with identity. With such technical sophistication, however, Frege combined a relatively naive account of the philosophical foundations of logic, that is, of such concepts as function, argument, judgement, meaning, assertion, identity, predication and the like though the naivety here, it should be said, is relative more to Frege's subsequent writings on such topics than to the pronouncements of his predecessors and contemporaries. In Gl, which appeared some five years later, much of this naivety has disappeared and we meet for the first time "the mature Frege". Virtually all of his subsequent work, we are told, is either propounded or at least adumbrated in Gl: the realism, the anti-psychologism; the sharp distinction between objects and concepts; the 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