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 59 (3):499-548 (2008)
We demonstrate that the quantum-mechanical description of composite physical systems of an arbitrary number of similar fermions in all their admissible states, mixed or pure, for all finite-dimensional Hilbert spaces, is not in conflict with Leibniz's Principle of the Identity of Indiscernibles (PII). We discern the fermions by means of physically meaningful, permutation-invariant categorical relations, i.e. relations independent of the quantum-mechanical probabilities. If, indeed, probabilistic relations are permitted as well, we argue that similar bosons can also be discerned in all their admissible states; but their categorical discernibility turns out to be a state-dependent matter. In all demonstrated cases of discernibility, the fermions and the bosons are discerned (i) with only minimal assumptions on the interpretation of quantum mechanics; (ii) without appealing to metaphysical notions, such as Scotusian haecceitas, Lockean substrata, Postian transcendental individuality or Adamsian primitive thisness; and (iii) without revising the general framework of classical elementary predicate logic and standard set theory, thus without revising standard mathematics. This confutes: (a) the currently dominant view that, provided (i) and (ii), the quantum-mechanical description of such composite physical systems always conflicts with PII; and (b) that if PII can be saved at all, the only way to do it is by adopting one or other of the thick metaphysical notions mentioned above. Among the most general and influential arguments for the currently dominant view are those due to Schrödinger, Margenau, Cortes, Dalla Chiara, Di Francia, Redhead, French, Teller, Butterfield, Giuntini, Mittelstaedt, Castellani, Krause and Huggett. We review them succinctly and critically as well as related arguments by van Fraassen and Massimi. Introduction: The Currently Dominant View 1.1 Weyl on Leibniz's principle 1.2 Intermezzo: Terminology and Leibnizian principles 1.3 The rise of the currently dominant view 1.4 Overview Elements of Quantum Mechanics 2.1 Physical states and physical magnitudes 2.2 Composite physical systems of similar particles 2.3 Fermions and bosons 2.4 Physical properties 2.5 Varieties of quantum mechanics Analysis of Arguments 3.1 Analysis of the Standard Argument 3.2 Van Fraassen's analysis 3.3 Massimi's analysis The Logic of Identity and Discernibility 4.1 The language of quantum mechanics 4.2 Identity of physical systems 4.3 Indiscernibility of physical systems 4.4 Some kinds of discernibility Discerning Elementary Particles 5.1 Preamble 5.2 Fermions 5.3 Bosons Concluding Discussion CiteULike Connotea Del.icio.us What's this?
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References found in this work BETA
Robert Merrihew Adams (1979). Primitive Thisness and Primitive Identity. Journal of Philosophy 76 (1):5-26.
R. L. Barnette (1978). Does Quantum Mechanics Disprove the Principle of the Identity of Indiscernibles? Philosophy of Science 45 (3):466-470.
Jeremy Butterfield (1993). Interpretation and Identity in Quantum Theory. Studies in History and Philosophy of Science 24 (3):443--76.
Elena Castellani & Peter Mittelstaedt (2000). Leibniz's Principle, Physics, and the Language of Physics. Foundations of Physics 30 (10):1587-1604.
Alberto Cortes (1976). Leibniz's Principle of the Identity of Indiscernibles: A False Principle. Philosophy of Science 43 (4):491-505.
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.
Don Howard, Bas van Fraassen, Otávio Bueno, Elena Castellani, Laura Crosilla, Steven French & Décio Krause (2011). The Physics and Metaphysics of Identity and Individuality. Metascience 20 (2):225-251.
Adam Caulton & Jeremy Butterfield (2012). On Kinds of Indiscernibility in Logic and Metaphysics. British Journal for the Philosophy of Science 63 (1):27-84.
George Darby (2010). Quantum Mechanics and Metaphysical Indeterminacy. Australasian Journal of Philosophy 88 (2):227-245.
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Federico Laudisa, Relational Quantum Mechanics. Stanford Encyclopedia of Philosophy.
F. A. Muller & M. P. Seevinck (2009). Discerning Elementary Particles. Philosophy of Science 76 (2):179-200.
Michela Massimi (2001). Exclusion Principle and the Identity of Indiscernibles: A Response to Margenau's Argument. British Journal for the Philosophy of Science 52 (2):303--30.
F. A. Muller (2011). Withering Away, Weakly. Synthese 180 (2):223 - 233.
Steven French & Michael Redhead (1988). Quantum Physics and the Identity of Indiscernibles. British Journal for the Philosophy of Science 39 (2):233-246.
Simon Saunders & F. A. Muller (2008). Discerning Fermions. British Journal for the Philosophy of Science 59 (3):499 - 548.
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