Barton, Neil (2018) Large Cardinals and the Iterative Conception of Set. [Preprint]
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Abstract
The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. One idea sometimes alluded to is that maximality considerations speak in favour of large cardinal axioms consistent with ZFC, since it appears to be `possible' (in some sense) to continue the hierarchy far enough to generate the relevant transfinite number. In this paper, we argue against this idea based on a priority of subset formation under the iterative conception. In particular, we argue that there are several conceptions of maximality that justify the consistency but falsity of large cardinal axioms. We argue that the arguments we provide are illuminating for the debate concerning the justification of new axioms in iteratively-founded set theory.
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Item Type: | Preprint | ||||||
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Keywords: | Large cardinals, set theory, foundations of mathematics | ||||||
Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics |
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Depositing User: | Dr. Neil Barton | ||||||
Date Deposited: | 06 May 2018 15:33 | ||||||
Last Modified: | 06 May 2018 15:33 | ||||||
Item ID: | 14638 | ||||||
Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics |
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Date: | 2018 | ||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/14638 |
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