Carnap's early metatheory

scope and limits

Georg Schiemer

Richard Zach

Erich Reck

University of California Riverside

pp. 33-65

in: Georg Schiemer (ed), Carnap on logic, Synthese 194 (1), 2017.

Abstract

In Untersuchungen zur allgemeinen Axiomatik (1928) and Abriss der Logistik (1929), Carnap attempted to formulate the metatheory of axiomatic theories within a single, fully interpreted type-theoretic framework and to investigate a number of meta-logical notions in it, such as those of model, consequence, consistency, completeness, and decidability. These attempts were largely unsuccessful, also in his own considered judgment. A detailed assessment of Carnap’s attempt shows, nevertheless, that his approach is much less confused and hopeless than it has often been made out to be. By providing such a reassessment, the paper contributes to a reevaluation of Carnap’s contributions to the development of modern logic.

Cited authors

Carnap Rudolf