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Abelian mereology

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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.
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Original languageEnglish
JournalLogic and Logical Philosophy
DOIs
Publication statusPublished - 2015

    Research areas

  • Universalism, Extensionality, Supplementation, Antisymmetry, Mereology, Parthood, Composition

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