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LOGICAL CONTEXTUALITY IN FREGE

Published online by Cambridge University Press:  26 April 2018

BRICE HALIMI
BRICE HALIMI*
Affiliation:
Department of Philosophy, Université Paris Nanterre
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITÉ PARIS NANTERRE NANTERRE, FRANCE E-mail: [email protected]
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Abstract

Logical universalism, a label that has been pinned on to Frege, involves the conflation of two features commonly ascribed to logic: universality and radicality. Logical universality consists in logic being about absolutely everything. Logical radicality, on the other hand, corresponds to there being the one and the same logic that any reasoning must comply with. The first part of this paper quickly remarks that Frege’s conception of logic makes logical universality prevail and does not preclude the admission of different contexts of discourse. The paper then aims to make it clear how Frege’s universalism can make sense of contextuality. Drawing on a suggestion made by Frege in his discussion of Hilbert, it shows that a properly Fregean notion of model can be devised. Taking up a suggestion from Wilfrid Hodges and William Demopoulos that the non-logical constants of a formal language can be compared to indexicals, this paper shows, pace Hodges and Demopoulos, that such an understanding of non-logical constants is not beyond Frege’s horizon. A formal framework, based on the modern tool of fibrations, is set out to explain and justify this point. This framework allows one to compare Frege and Tarski, by formalizing Frege’s suggestion and by presenting Tarski’s semantics in a generalized setting.

Keywords

03A0501A6003B30Frege“Foundations of Geometry,” logical universalismnon-logical constants as indexicalsFregean model theory
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 1 , March 2018 , pp. 1 - 20
Copyright
Copyright © Association for Symbolic Logic 2018 

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