Parts, classes and Parts of Classes: an anti-realist reading of Lewisian mereology

This study is in two parts. In the first part, various important principles of classical extensional mereology are derived on the basis of a nice axiomatization involving ‘part of’ and fusion. All results are proved here with full Fregean (and Gentzenian) rigor. They are chosen because they are needed for the second part. In the second part, this natural-deduction framework is used in order to regiment David Lewis’s justification of his Division Thesis, which features prominently in his combination of mereology with class theory. The Division Thesis plays a crucial role in Lewis’s informal argument for his Second Thesis in his book Parts of Classes. In order to present Lewis’s argument in rigorous detail, an elegant new principle is offered for the theory that combines class theory and mereology. The new principle is called the Canonical Decomposition Thesis. It secures Lewis’s Division Thesis on the strong construal required in order for his argument to go through. The exercise illustrates how careful one has ∗To be presented to the SAC conference on David Lewis’s contributions to formal philosophy, to be held in Copenhagen in September 2007; proceedings forthcoming in Synthese. Thanks are owed to Gabriel Uzquiano for helpful correspondence that was a stimulus to this project. Ben Caplan provided detailed comments on an earlier version, which helped avert a formal error. Comments by Kevin Scharp and Nicholaos Jones led to improvements in exposition. Salvatore Florio gave two later versions particularly eagleeyed attention, uncovering errors of composition in some of the formal derivations. Fred Muller kindly provided some LTEX codes for mereological symbols. The author is solely responsible for any errors that remain.