A Vindication of the Universal Set

(Logic and Philosophy of Mathematics, Englisch)

he 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:

Zeit: 12:00-12:30, 09. September 2022 (Freitag)

Ort: SR 1.006

Alejandro Gracia Di Rienzo

(University of Santiago de Compostela , Spain)

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