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In classical extensional mereology, composition is idempotent: if x is part of y, then the sum of x and y is identical to y. In this paper, I provide a systematic and coherent formal mereology for which idempotence fails. I first discuss a number of purported counterexamples to idempotence that have been put forward in the literature. I then discuss two recent attempts at sketching non-idempotent formal mereology due to Karen Bennett and Kit Fine. I argue that these attempts are incomplete, however, and there are many open issues left unresolved. I then construct a class of models of a non-idempotent mereology using multiset theory, consider their algebraic structure, and show how these models can shed light on the open issues left from the previous approaches.
Cotnoir , A 2015 , ' Abelian mereology ' Logic and Logical Philosophy . DOI: 10.12775/LLP.2015.006
Logic and Logical Philosophy
Copyright (c) 2015 Logic and Logical Philosophy. This article is covered by a Creative Commons No-Derivatives licence (CC BY-ND). Licence details can be found here: https://creativecommons.org/licenses/by-nd/3.0/
Date of Acceptance: 01/12/2015
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