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Schiemer, Georg; Zach, Richard; Reck, Erich (2017): Carnap's early metatheory: scope and limits. In: Synthese, Vol. 194, No. 1: pp. 33-65
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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.