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

Carnap’s early metatheory: scope and limits

  • Georg SchiemerEmail author
  • Richard Zach
  • Erich Reck
S.I.: Carnap on Logic


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.


Carnap Type theory Metalogic  Model theory Consequence Isomorphism 



Georg Schiemer’s research was supported by the Austrian Science Fund, projects J3158–G17 and P–27718. Richard Zach’s research was supported by the Social Sciences and Humanities Research Council of Canada. We are grateful to A. W. Carus and an anonymous referee for their detailed and thoughtful comments on earlier drafts of this paper. We would also like to thank the audiences at the 2013 workshop Carnap on Logic at the Munich Center for Mathematical Philosophy, the Minnesota Center for Philosophy of Science, the 2014 Spring Meeting of the ASL, and the 2014 Society for the Study of the History of Analytic Philosophy Annual Meeting. Richard Zach acknowledges the generous support of the Calgary Institute for the Humanities and the Department of Philosophy at McGill University.


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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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