Lewis on mereology and set theory

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

Abstract

David Lewis in the short monograph Parts of Classes (PC) undertakes a fundamental re-examination of the relationship between mereology, the general theory of parts, and set theory, the general theory of collections. Given Lewis’s theses, to be an element of a set or member of class is just to have a singleton that is a part thereof. Lewis in PC adds a claim of kind of ontological innocence, comparable to that of first-order logic, for mereology. The only substantive assumption of plethynticology is that for any condition there are some things such that they are precisely the things for which the conditions hold. All the alternatives, making do with a single domain of individuals, have in common that they involve the axiom of choice. Restated in Hazen’s terminology rather than Frege’s, the fallback assumption is that there are no more small species than individuals.

Original languageEnglish (US)
Title of host publicationA Companion to David Lewis
Publisherwiley
Pages459-469
Number of pages11
ISBN (Electronic)9781118398593
ISBN (Print)9781118388181
DOIs
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

  • General Arts and Humanities

Keywords

  • Axiom of choice
  • David lewis
  • Mereology
  • Set theory
  • Singletons

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