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IDENTITY AND DISCERNIBILITY IN PHILOSOPHY AND LOGIC

Published online by Cambridge University Press:  17 November 2011

JAMES LADYMAN*
Affiliation:
Department of Philosophy, University of Bristol
ØYSTEIN LINNEBO*
Affiliation:
Department of Philosophy, Birkbeck College, University of London
RICHARD PETTIGREW*
Affiliation:
Department of Philosophy, University of Bristol
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BRISTOL 9 WOODLAND ROAD, BRISTOL BS8 1TB, UK E-mail: james.ladyman@bristol.ac.uk
DEPARTMENT OF PHILOSOPHY BIRKBECK COLLEGE, MALET STREET, LONDON WC1E 7HX, UK E-mail: o.linnebo@bbk.ac.uk
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BRISTOL 9 WOODLAND ROAD, BRISTOL BS8 1TB, UK E-mail: richard.pettigrew@bristol.ac.uk

Abstract

Questions about the relation between identity and discernibility are important both in philosophy and in model theory. We show how a philosophical question about identity and discernibility can be ‘factorized’ into a philosophical question about the adequacy of a formal language to the description of the world, and a mathematical question about discernibility in this language. We provide formal definitions of various notions of discernibility and offer a complete classification of their logical relations. Some new and surprising facts are proved; for instance, that weak discernibility corresponds to discernibility in a language with constants for every object, and that weak discernibility is the most discerning nontrivial discernibility relation.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2011

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