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On kinds of indiscernibility in logic and metaphysics

Caulton, Adam and Butterfield, J. (2012) On kinds of indiscernibility in logic and metaphysics. British Journal for the Philosophy of Science, 63 (1). pp. 27-84. ISSN 0007-0882

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Identification Number: 10.1093/bjps/axr007

Abstract

Using the Hilbert–Bernays account as a spring-board, we first define four ways in which two objects can be discerned from one another, using the non-logical vocabulary of the language concerned. (These definitions are based on definitions made by Quine and Saunders.) Because of our use of the Hilbert-Bernays account, these definitions are in terms of the syntax of the language. But we also relate our definitions to the idea of permutations on the domain of quantification, and their being symmetries. These relations turn out to be subtle—some natural conjectures about them are false. We will see in particular that the idea of symmetry meshes with a species of indiscernibility that we will call ‘absolute indiscernibility’. We use these four kinds as a resource for stating four metaphysical theses about identity. Three of these theses articulate two traditional philosophical themes: viz. the principle of the identity of indiscernibles (which will come in two versions), and haecceitism. The fourth is recent. Its most notable feature is that it makes diversity (i.e. non-identity) weaker than what we will call individuality (being an individual): two objects can be distinct but not individuals. For this reason, it has been advocated both for quantum particles and for spacetime points. Finally, we locate this fourth metaphysical thesis in a broader position, which we call structuralism. We conclude with a discussion of the semantics suitable for a structuralist, with particular reference

Item Type: Article
Official URL: http://bjps.oxfordjournals.org/
Additional Information: © 2011 The Author
Divisions: Philosophy, Logic and Scientific Method
Subjects: B Philosophy. Psychology. Religion > B Philosophy (General)
Sets: Departments > Philosophy, Logic and Scientific Method
Date Deposited: 19 Dec 2013 15:33
Last Modified: 20 Jun 2020 01:41
URI: http://eprints.lse.ac.uk/id/eprint/55078

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