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 #2 notion of abstraction to shed some light on the notion of an indefinite superposition in quantum mechanics.

The paper is published as: Ellerman, D. (2021). On Abstraction in Mathematics and Indefiniteness in Quantum Mechanics. *Journal of Philosophical Logic*. https://doi.org/10.1007/s10992-020-09586-1

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