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- Title
The Mereological Foundation of Megethology.
- Authors
Carrara, Massimiliano; Martino, Enrico
- Abstract
In Mathematics is megethology (Lewis (). Philosophia Mathematica, 1(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.
- Subjects
WHOLE &; parts (Philosophy); PRESUPPOSITION (Logic); MATHEMATICS; SET theory; PREDICATE calculus
- Publication
Journal of Philosophical Logic, 2016, Vol 45, Issue 2, p227
- ISSN
0022-3611
- Publication type
Article
- DOI
10.1007/s10992-015-9373-7