SOPhiA 2022

Salzburgiense Concilium Omnibus Philosophis Analyticis

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Programme - Talk

A Vindication of the Universal Set
(Logic and Philosophy of Mathematics, English)

The universal set is the set of absolutely everything. It serves as a domain for absolutely unrestricted quantification and as the extension of the most general concepts, like OBJECT. This notion is metaphysically appealing and useful, but is beset by paradoxes. Quine__s __New Foundations__ (NF) system is the most well-known set theory which admits a universal set as a bona fide and (apparently) paradox-free object. I will defend NF from the common charge that it is unmotivated and artificial. To do this I advance two arguments. First, that NF can be regarded as a development of the __logical__ conception of sets, as opposed to the __iterative__ conception embodied by Zermelo-Fraenkel and related systems. Second, that NF inherits (and actually surpasses) the intuitive motivation of type theory. Both the iterative and the logical conceptions of set, I will maintain, are equally valid notions of set and can coexist peacefully on a pluralist (or more precisely dualist) approach to the philosophy of sets. If this is a cogent view, then the notion of a universal set should not be said to be intrinsically incoherent, and is thereby vindicated as suitable for the aforementioned theoretical roles.

Chair:
Time: 12:00-12:30, 09. September 2022 (Friday)
Location: SR 1.006

Alejandro Gracia Di Rienzo  
(University of Santiago de Compostela , Spain)



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