The Mereological Foundation of Megethology

Journal of Philosophical Logic 45 (2):227-235 (2016)

Authors
Massimiliano Carrara
University of Padua
Abstract
In Mathematics is megethology. Philosophia Mathematica, 1, 3–23) David K. Lewis proposes a structuralist reconstruction of classical set theory based on mereology. In order to formulate suitable hypotheses about the size of the universe of individuals without the help of set-theoretical notions, he uses the device of Boolos’ plural quantification for treating second order logic without commitment to set-theoretical entities. In this paper we show how, assuming the existence of a pairing function on atoms, as the unique assumption non expressed in a mereological language, a mereological foundation of set theory is achievable within first order logic. Furthermore, we show how a mereological codification of ordered pairs is achievable with a very restricted use of the notion of plurality without plural quantification
Keywords Mereology  Megethology  Set theory
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DOI 10.1007/s10992-015-9373-7
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References found in this work BETA

Nominalist Platonism.George Boolos - 1985 - Philosophical Review 94 (3):327-344.
Plural Quantification.Ø Linnebo - 2008 - Stanford Encyclopedia of Philosophy.

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