Sant'Anna, Adonai (2018) Epistemology of quasi-sets. [Preprint]
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Abstract
I briefly discuss the epistemological role of quasi-set theory in mathematics and theoretical physics. Quasi-set theory is a first order theory, based on Zermelo-Fraenkel set theory with Urelemente (ZFU). Nevertheless, quasi-set theory allows us to cope with certain collections of objects where the usual notion of identity is not applicable, in the sense that $x = x$ is not a formula, if $x$ is an arbitrary term. Basically, quasi-set theory offers us some sort of logical apparatus for questioning the need for identity in some branches of mathematics and theoretical physics. I also use this opportunity to discuss a misunderstanding about quasi-sets due mainly to Nicholas J. J. Smith, who argues, in a general way, that sense cannot be made of vague identity.
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Item Type: | Preprint | ||||||
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Additional Information: | forthcoming in Festschrift in honor of Francisco Antonio Doria. | ||||||
Keywords: | quasi-sets, identity, indistinguishability, epistemology | ||||||
Subjects: | Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics |
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Depositing User: | Adonai Sant'Anna | ||||||
Date Deposited: | 13 Sep 2018 00:21 | ||||||
Last Modified: | 13 Sep 2018 00:21 | ||||||
Item ID: | 15026 | ||||||
Subjects: | Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics |
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Date: | 2018 | ||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/15026 |
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