Vector Mereology

Phil Pickering, Sam Baron, John Tanner

Published Jan 15, 2026• 0 citations

Abstract

This paper outlines a notion of parthood for vectors, which has come to the fore in discussions of quantum mechanics. We show that existing accounts fail to generalise in a way that preserves transitivity. We thus present a new more general account that preserves transitivity and is applicable to quantum systems but may have applicability beyond quantum mechanics, including classical vector quantities and waves.

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Vector Parthood

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The goal of this paper is to outline a viable notion of parthood for vectors. The importance of vector parthood has come to the fore in discussions of quantum mechanics, with two accounts existing already. We show that both fail to preserve the transitivity of parthood. We thus present a new account of vector parthood that preserves transitivity and is applicable to quantum systems. We close by suggesting some applications for the notion we present here that go beyond quantum mechanics, including ordinary sinusoidal waves (e.g., water or sound waves).

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