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Sameness

  • Dag Westerståhl
Chapter
First Online:
Part of the Outstanding Contributions to Logic book series (OCTR, volume 13)

Abstract

I attempt an explication of what it means for an operation across domains to be the same on all domains, an issue that (Feferman, S.: Logic, logics and logicism. Notre Dame J. Form. Log. 40, 31–54 (1999)) took to be central for a successful delimitation of the logical operations. Some properties that seem strongly related to sameness are examined, notably isomorphism invariance, and sameness under extensions of the domain. The conclusion is that although no precise criterion can satisfy all intuitions about sameness, combining the two properties just mentioned yields a reasonably robust and useful explication of sameness across domains.

Keywords

Logical constants Isomorphism invariance Extension Generalized quantifiers 

2010 Mathematics Subject Classification

03B65 03C80 91F20 
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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of PhilosophyStockholm UniversityStockholmSweden

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