The mereological foundation of Megethology

• Autores: Massimiliano Carrara, Enrico Martino
• Localización: Journal of Philosophical Logic, ISSN-e 1573-0433, Vol. 45, Nº. 2, 2016, págs. 227-235
• Idioma: alemán
• Texto completo no disponible (Saber más ...)
• Resumen

  • In Mathematics is megethology (Lewis (1993). 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.