Dentamaro, Dario and Loregian, Fosco (2020) Categorical Ontology I - Existence. [Preprint]
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Abstract
The present paper is the first piece of a series whose aim is to develop an approach to ontology and metaontology through category theory. We exploit the theory of elementary toposes to claim that a satisfying ``theory of existence'', and more at large ontology itself, can both be obtained through category theory. In this perspective, an ontology is a mathematical object: it is a category, the universe of discourse in which our mathematics (intended at large, as a theory of knowledge) can be deployed. The internal language that all categories possess prescribes the modes of existence for the objects of a fixed ontology/category.
This approach resembles, but is more general than, fuzzy logics, as most choices of $\clE$ and thus of $\Omega_\clE$ yield nonclassical, many-valued logics.
Framed this way, ontology suddenly becomes more mathematical: a solid corpus of techniques can be used to backup philosophical intuition with a useful, modular language, suitable for a practical foundation. As both a test-bench for our theory, and a literary divertissement, we propose a possible category-theoretic solution of Borges' famous paradoxes of Tlön's ``nine copper coins'', and of other seemingly paradoxical construction in his literary work. We then delve into the topic with some vistas on our future works.
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Item Type: | Preprint | |||||||||
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Keywords: | ontology, category theory, metaontology, topos theory, Tlön, Uqbar, Orbis Tertius | |||||||||
Subjects: | Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Methodology Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics |
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Depositing User: | Dr. Fosco Loregian | |||||||||
Date Deposited: | 19 May 2020 20:49 | |||||||||
Last Modified: | 03 Aug 2020 00:54 | |||||||||
Item ID: | 17191 | |||||||||
Subjects: | Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Methodology Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics |
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Date: | May 2020 | |||||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/17191 |
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Categorical Ontology I - Existence. (deposited 08 May 2020 15:11)
- Categorical Ontology I - Existence. (deposited 19 May 2020 20:49) [Currently Displayed]
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