Carnap’s early metatheory: scope and limits

Synthese 194 (1):33-65 (2017)

Authors
Erich Reck
University of California, Riverside
Richard Zach
University of Calgary
Abstract
In Untersuchungen zur allgemeinen Axiomatik and Abriss der Logistik, 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.
Keywords Carnap  Type theory  Metalogic  Model theory  Consequence  Isomorphism
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DOI 10.1007/s11229-015-0877-z
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References found in this work BETA

Logic, Semantics, Metamathematics.Alfred Tarski - 1956 - Oxford, Clarendon Press.
Collected Works.Kurt Gödel - 1986 - Oxford University Press.
From Frege to Gödel.Jean Van Heijenoort (ed.) - 1967 - Cambridge: Harvard University Press.

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Citations of this work BETA

Carnap’s Defense of Impredicative Definitions.Vera Flocke - 2019 - Review of Symbolic Logic 12 (2):372-404.

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