Soysal, Zeynep (2017) Why Is the Universe of Sets Not a Set? [Preprint]

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Abstract

According to the iterative conception of sets, standardly formalized by ZFC, there is no set of all sets. But why is there no set of all sets? A simple-minded, though unpopular, "minimal" explanation for why there is no set of all sets is that the supposition that there is contradicts some axioms of ZFC. In this paper, I first explain the core complaint against the minimal explanation, and then argue against the two main alternative answers to the guiding question. I conclude the paper by outlining a close alternative to the minimal explanation, the conception-based explanation, that avoids the core complaint against the minimal explanation.

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Item Type:	Preprint
Creators:	Creators Email ORCID Soysal, Zeynep
Keywords:	Actualism, Potentialism, Iterative conception of set, Universe of sets
Subjects:	Specific Sciences > Mathematics > Foundations
Depositing User:	Dr. Zeynep Soysal
Date Deposited:	03 Aug 2017 12:38
Last Modified:	03 Aug 2017 12:38
Item ID:	13289
Subjects:	Specific Sciences > Mathematics > Foundations
Date:	2017
URI:	https://philsci-archive.pitt.edu/id/eprint/13289

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