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

摘要将对等变成身份，但是有两种方法可以实现。给定直线上的等价关系，通过抽象将等价转换为同一性的第一种方法是考虑平行线的等价类。的＃ 2的方法是考虑的抽象概念方向的平行线。本文开发了两种抽象类型的简单数学模型，并举例说明了除普通事件外，如何使用＃ 2抽象作为“叠加事件”来解释有限概率理论。目的是使用抽象的第二个概念来阐明量子力学中不定叠加的概念。