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  1. 1 Logic and Logical Philosophy

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  1. 1 Cotnoir A. J.

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  1. 1 2015

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Abelian mereology

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Cotnoir A. J.
Logic and Logical Philosophy
|
2015
|
vol. 24
|
issue 4 Mereology and Beyond
429-447
EN
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.
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