, Volume 78, Issue 3, pp 487–522 | Cite as

Carnap’s Early Semantics

  • Georg Schiemer
Original Paper


This paper concerns Carnap’s early contributions to formal semantics in his work on general axiomatics between 1928 and 1936. Its main focus is on whether he held a variable domain conception of models. I argue that interpreting Carnap’s account in terms of a fixed domain approach fails to describe his premodern understanding of formal models. By drawing attention to the second part of Carnap’s unpublished manuscript Untersuchungen zur allgemeinen Axiomatik, an alternative interpretation of the notions ‘model’, ‘model extension’ and ‘submodel’ in his theory of axiomatics is presented. Specifically, it is shown that Carnap’s early model theory is based on a convention to simulate domain variation that is not identical but logically comparable to the modern account.


Axiom System Background Language Axiomatic Theory Peano Arithmetic Primitive Term 
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Research on this article was partly funded by the Austrian Science Fund (FWF): J3158. Earlier drafts of this paper were presented to the SoCal HPLM Group at UC Irvine, in the Logisches Café - colloquium at the University of Vienna, at GAP.7 in Bremen as well as at Epsa2009 in Amsterdam. I thank the members of the respective audiences for useful comments. I am especially indebted to Michael Friedman, Erich Reck, Steve Awodey, Ilkka Niiniluoto, and Richard Heinrich for helpful discussions and valuable feedback. I also wish to thank two anonymous referees for their comments and suggestions that have substantially improved this paper.


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Munich Center for Mathematical Philosophy (MCMP)Ludwig-Maximilians-Universität (LMU)MunichGermany

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