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Quantifying over indiscernibles

Krause, Décio (2022) Quantifying over indiscernibles. [Preprint]

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Abstract

One of the main criticisms of the theory of collections of in- discernible objects is that once we quantify over one of them, we are quantifying over all of them since they cannot be dis- cerned from one another. In this way, we would call the collapse of quantifiers: ‘There exists one x such as P ’ would entail ‘All x are P’. In this paper we argue that there are situations (quantum theory is the sample case) where we do refer to a certain quantum entity, saying that it has a certain property, even without committing all other indistinguishable entities with the considered property. Mathematically, within the realm of the the- ory of quasi-sets Q, we can give sense to this claim. We show that the above-mentioned ‘collapse of quantifiers’ depends on the interpretation of the quantifiers and on the mathematical background where they are ranging. In this way, we hope to strengthen the idea that quantification over indiscernibles, in particular in the quantum domain, does not conform with quantification in the standard sense of classical logic.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Krause, Déciodeciokrause@gmail.com0000-0003-0463-2796
Keywords: quantification, quantum logic, indiscernibility, iden- tity, in- discernible objects.
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Physics > Quantum Mechanics
Depositing User: Décio Krause
Date Deposited: 12 Sep 2022 16:28
Last Modified: 12 Sep 2022 16:28
Item ID: 21153
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Physics > Quantum Mechanics
Date: 12 September 2022
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/21153

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