Grounding Megethology on Plural Reference

Abstract

In Mathematics is megethology (Lewis, Philos Math 1:3---23, 1993) Lewis reconstructs set theory combining mereology with plural quantification. He introduces megethology, a powerful framework in which one can formulate strong assumptions about the size of the universe of individuals. Within this framework, Lewis develops a structuralist class theory, in which the role of classes is played by individuals. Thus, if mereology and plural quantification are ontologically innocent, as Lewis maintains, he achieves an ontological reduction of classes to individuals. Lewis'work is very attractive. However, the alleged innocence of mereology and plural quantification is highly controversial and has been criticized by several authors. In the present paper we propose a new approach to megethology based on the theory of plural reference developed in To be is to be the object of a possible act of choice (Carrara, Stud Log 96: 289---313, 2010). Our approach shows how megethology can be grounded on plural reference without the help of mereology.