Logical aspects of quantum (non-)individuality

TL;DR

This paper explores the logical and mathematical foundations of quantum entities' identity, proposing a metaphysical view of non-individuals and suggesting a new way to refer to quanta based on collection cardinalities.

Contribution

It introduces a logical framework for understanding quantum non-individuality and proposes referring to quanta via collection cardinalities, offering a novel interpretative approach.

Findings

Logical basis influences concepts of quantum identity

Supports a metaphysics of non-individuals in quantum theory

Suggests using collection cardinalities to refer to quanta

Abstract

In this paper I consider some logical and mathematical aspects of the discussion of the identity and individuality of quantum entities. I shall point out that for some aspects of the discussion, the logical basis cannot be put aside; on the contrary, it leads us to unavoidable conclusions which may have consequences in how we articulate certain concepts related to quantum theory. Behind the discussion, there is a general argument which suggests the possibility of a metaphysics of non-individuals, based on a reasonable interpretation of quantum basic entities. I close the paper with a suggestion that consists in emphasizing that quanta should be referred to by the cardinalities of the collections to which they belong, for which an adequate mathematical framework seems to be possible.