Barton, Neil and Friedman, Sy-David (2018) Set Theory and Structures. [Preprint]
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Abstract
Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a `structural' perspective to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure.
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| Item Type: | Preprint | |||||||||
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| Keywords: | set theory, category theory, urelement, structuralism | |||||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Methodology Specific Sciences > Mathematics |
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| Depositing User: | Dr. Neil Barton | |||||||||
| Date Deposited: | 06 May 2018 15:31 | |||||||||
| Last Modified: | 06 May 2018 15:31 | |||||||||
| Item ID: | 14633 | |||||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Methodology Specific Sciences > Mathematics |
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| Date: | 2018 | |||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/14633 |
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