Abelian mereology

A. J. Cotnoir

DOI: http://dx.doi.org/10.12775/LLP.2015.006

Abstract


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.

Keywords


universalism; extensionality; supplementation; antisymmetry; mereology; parthood; composition

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References


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ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

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