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Identity and Indiscernibility in Quantum MechanicsLogic and Metaphysics of Discernibility

Identity and Indiscernibility in Quantum Mechanics: Logic and Metaphysics of Discernibility [This chapter contains a formal analysis of three most popular variants of discernibility—absolute, relative and weak—together with some basic facts regarding their mutual logical connections. The analysis is done in the framework of standard, first-order logic. We point out that the answer to the question of whether some objects can be discerned may depend on the expressive power of the language in which this discernibility is to be formulated, in particular, on whether this language admits the predicate of numerical identity, or the individual names for all objects in the domain. We also connect the issue of discernibility with the symmetry (permutation invariance) of a language in which objects of the domain are supposed to be discerned. It is proved that only weakly discerning formulas are admitted in such languages. Subsequently, we evaluate the approach to the metaphysics of quantum particles based on the notion of weak discernibility. We argue that all quantum-mechanical relations that are supposed to weakly discern same-type fermions and bosons contain hidden reference to the relation of numerical identity, and thus cannot be used as qualitative grounds for facts of numerical identity/diversity.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Identity and Indiscernibility in Quantum MechanicsLogic and Metaphysics of Discernibility

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References (25)

Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
ISBN
978-3-030-74869-2
Pages
71 –102
DOI
10.1007/978-3-030-74870-8_4
Publisher site
See Chapter on Publisher Site

Abstract

[This chapter contains a formal analysis of three most popular variants of discernibility—absolute, relative and weak—together with some basic facts regarding their mutual logical connections. The analysis is done in the framework of standard, first-order logic. We point out that the answer to the question of whether some objects can be discerned may depend on the expressive power of the language in which this discernibility is to be formulated, in particular, on whether this language admits the predicate of numerical identity, or the individual names for all objects in the domain. We also connect the issue of discernibility with the symmetry (permutation invariance) of a language in which objects of the domain are supposed to be discerned. It is proved that only weakly discerning formulas are admitted in such languages. Subsequently, we evaluate the approach to the metaphysics of quantum particles based on the notion of weak discernibility. We argue that all quantum-mechanical relations that are supposed to weakly discern same-type fermions and bosons contain hidden reference to the relation of numerical identity, and thus cannot be used as qualitative grounds for facts of numerical identity/diversity.]

Published: Jan 3, 2022

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