, Volume 190, Issue 4, pp 709-742
Date: 07 Nov 2012

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

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Abstract

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 when setting up the details of an adequate foundational theory of parts and classes. The main aim behind this investigation is to determine whether an anti-realist, inferentialist theorist of meaning has the resources to exhibit Lewis’s argument for his Second Thesis—which is central to his marriage of class theory with mereology—as a purely conceptual one. The formal analysis shows that Lewis’s argument, despite its striking appearance to the contrary, can be given in the constructive, relevant logic IR. This is the logic that the author has argued, elsewhere, to be the correct logic from an anti-realist point of view. The anti-realist is therefore in a position to regard Lewis’s argument as purely conceptual.

This paper was accepted for presentation at the SAC conference on David Lewis’s contributions to formal philosophy, held in Copenhagen in September 2007, but, in the event, the author was unable to attend. The paper was submitted for the proceedings immediately after the conference was held; this is its first publication. The author offers this study as a tribute to the legacy of David’s unfailingly rigorous but catholic intellect, and in grateful memory of particularly helpful and encouraging philosophical conversations with David during his annual visits to Australia in the late eighties and early nineties. 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 eagle-eyed attention, uncovering errors of composition in some of the formal derivations. Fred Muller kindly provided some \({\text{\LaTeX}}\) codes for mereological symbols. The author is solely responsible for any errors that remain.