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. Copyright © 2011 Association for Symbolic Logic.
CITATION STYLE
Ladyman, J., Linnebo, Ø., & Pettigrew, R. (2012). Identity and discernibility in philosophy and logic. Review of Symbolic Logic, 5(1), 162–186. https://doi.org/10.1017/S1755020311000281
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