The Review of Symbolic Logic

Research Article

IDENTITY AND DISCERNIBILITY IN PHILOSOPHY AND LOGIC

JAMES LADYMANa1 c1, ØYSTEIN LINNEBOa2 c2 and RICHARD PETTIGREWa3 c3

a1 Department of Philosophy, University of Bristol

a2 Department of Philosophy, Birkbeck College, University of London

a3 Department of Philosophy, University of Bristol

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.

(Received September 22 2011)

Correspondence:

c1 DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BRISTOL 9 WOODLAND ROAD, BRISTOL BS8 1TB, UK E-mail: james.ladyman@bristol.ac.uk

c2 DEPARTMENT OF PHILOSOPHY BIRKBECK COLLEGE, MALET STREET, LONDON WC1E 7HX, UK E-mail: o.linnebo@bbk.ac.uk

c3 DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BRISTOL 9 WOODLAND ROAD, BRISTOL BS8 1TB, UK E-mail: richard.pettigrew@bristol.ac.uk