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

Keywords

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

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