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Synthese

, Volume 191, Issue 12, pp 2815–2833 | Cite as

Uniting model theory and the universalist tradition of logic: Carnap’s early axiomatics

  • Iris Loeb
Article

Abstract

We shift attention from the development of model theory for demarcated languages to the development of this theory for fragments of a language. Although it is often assumed that model theory for demarcated languages is not compatible with a universalist conception of logic, no one has denied that model theory for fragments of a language can be compatible with that conception. It thus seems unwarranted to ignore the universalist tradition in the search for the origins and development of model theory. This point is illustrated by Carnap’s early semantics and model theory, which he developed within a type theoretical framework and which stand out both for their universalistic treatment and for certain idiosyncratic technicalities by which the construction is supported. One special property is that individuals are context relative in Carnap’s system. This leads to a model theory in which the model domains are more flexible than has been suggested in the literature.

Keywords

Model theory Universalism Carnap Type theory 

Notes

Acknowledgments

The author would like to thank Arianna Betti and Stefan Roski for valuable feedback on earlier versions of this paper. She is grateful for the opportunity to present her work at the Lunch Lecture series of the Theoretical Philosophy Group at Utrecht University, and would like to thank the audience for their helpful comments. The author was supported through ERC Starting Grant TRANH 203194 until September 2013. All passages from the Rudolf Carnap Papers are quoted by permission of the University of Pittsburgh. All rights reserved.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesVU University AmsterdamAmsterdamThe Netherlands

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