Synthese

, Volume 194, Issue 1, pp 33–65 | Cite as

Carnap’s early metatheory: scope and limits

S.I.: Carnap on Logic
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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.

Keywords

Carnap Type theory Metalogic  Model theory Consequence Isomorphism 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of ViennaViennaAustria
  2. 2.Munich Center for Mathematical PhilosophyLMU MunichMunichGermany
  3. 3.Department of PhilosophyUniversity of Calgary, 2500 University Drive NWCalgaryCanada
  4. 4.Department of PhilosophyUniversity of California at RiversideRiversideUSA

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