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Epistemology of quasi-sets

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
Creators:
CreatorsEmailORCID
Sant'Anna, Adonaiadonai@ufpr.br0000-0003-3425-698X
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
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
Date: 2018
URI: http://philsci-archive.pitt.edu/id/eprint/15026

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