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On Abstraction in Mathematics and Indefiniteness in Quantum Mechanics

Ellerman, David (2021) On Abstraction in Mathematics and Indefiniteness in Quantum Mechanics. [Preprint]

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Abstract

Abstraction turns equivalence into identity, but there are two ways to do it. Given the equivalence relation of parallelness on lines, the #1 way to turn equivalence into identity by abstraction is to consider equivalence classes of parallel lines. The #2 way is to consider the abstract notion of the direction of parallel lines. This paper developments simple mathematical models of both types of abstraction and shows, for instance, how finite probability theory can be interpreted using #2 abstracts as "superposition events" in addition to the ordinary events. The goal is to use the second #2 notion of abstraction to shed some light on the notion of an indefinite superposition in quantum mechanics.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Ellerman, Daviddavid@ellerman.org0000-0002-5718-618X
Keywords: quantum mechanics, indefiniteness, abstraction
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Physics > Quantum Mechanics
Depositing User: David Ellerman
Date Deposited: 23 Jan 2021 19:18
Last Modified: 23 Jan 2021 19:18
Item ID: 18631
Official URL: https://rdcu.be/cd0N7
DOI or Unique Handle: 10.1007/s10992-020-09586-1
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Physics > Quantum Mechanics
Date: January 2021
URI: http://philsci-archive.pitt.edu/id/eprint/18631

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