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Why Is the Universe of Sets Not a Set?

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:
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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-dev.library.pitt.edu/id/eprint/13289

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