David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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British Journal for the Philosophy of Science 63 (1):27-84 (2012)
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 to physical theories as well as elementary model theory
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References found in this work BETA
Tim Button (2006). Realistic Structuralism's Identity Crisis: A Hybrid Solution. Analysis 66 (3):216–222.
Steven French & Michael Redhead (1988). Quantum Physics and the Identity of Indiscernibles. British Journal for the Philosophy of Science 39 (2):233-246.
Jeffrey Ketland (2006). Structuralism and the Identity of Indiscernibles. Analysis 66 (292):303–315.
James Ladyman (2005). Mathematical Structuralism and the Identity of Indiscernibles. Analysis 65 (287):218–221.
Hannes Leitgeb & James Ladyman (2008). Criteria of Identity and Structuralist Ontology. Philosophia Mathematica 16 (3):388-396.
Citations of this work BETA
James Ladyman, Øystein Linnebo & Richard Pettigrew (2012). Identity and Discernibility in Philosophy and Logic. Review of Symbolic Logic 5 (1):162-186.
Adam Caulton & Jeremy Butterfield (2012). Symmetries and Paraparticles as a Motivation for Structuralism. British Journal for the Philosophy of Science 63 (2):233-285.
Øystein Linnebo & F. A. Muller (2013). On Witness-Discernibility of Elementary Particles. Erkenntnis 78 (5):1133-1142.
Adam Caulton (2013). Discerning “Indistinguishable” Quantum Systems. Philosophy of Science 80 (1):49-72.
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