Carnap’s early metatheory: scope and limits

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

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Author Profiles

Erich Reck
University of California, Riverside
Georg Schiemer
University of Vienna
Richard Zach
University of Calgary

Citations of this work

The Church-Turing Thesis.B. Jack Copeland - 2012 - In Ed Zalta, Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford Encyclopedia of Philosophy.
Completeness: From Husserl to Carnap.Víctor Aranda - 2022 - Logica Universalis 16 (1):57-83.
Carnap’s Defense of Impredicative Definitions.Vera Flocke - 2019 - Review of Symbolic Logic 12 (2):372-404.
Projective duality and the rise of modern logic.Günther Eder - 2021 - Bulletin of Symbolic Logic 27 (4):351-384.

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References found in this work

Logic, semantics, metamathematics.Alfred Tarski - 1956 - Oxford,: Clarendon Press. Edited by John Corcoran & J. H. Woodger.
Der Logische Aufbau der Welt.Rudolf Carnap - 1928 - Hamburg: Meiner Verlag.
From Frege to Gödel.Jean Van Heijenoort (ed.) - 1967 - Cambridge,: Harvard University Press.
Der logische Aufbau der Welt.Rudolf Carnap - 1928 - Annalen der Philosophie Und Philosophischen Kritik 8:106-107.

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