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

Synthese 191 (12):2815-2833 (2014)

Authors
Iris Loeb
VU University Amsterdam
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
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DOI 10.1007/s11229-014-0425-2
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References found in this work BETA

The Logical Syntax of Language.Rudolf Carnap - 1937 - London: K. Paul, Trench, Trubner & Co..
Principia Mathematica.A. N. Whitehead - 1926 - Mind 35 (137):130.
Tarski on Truth and Logical Consequence.John Etchemendy - 1988 - Journal of Symbolic Logic 53 (1):51-79.

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Citations of this work BETA

Hilbert's Axiomatic Method and Carnap's General Axiomatics.Michael Stöltzner - 2015 - Studies in History and Philosophy of Science Part A 53:12-22.

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