Dentamaro, Dario and Loregian, Fosco (2020) Categorical Ontology I - Existence. [Preprint]

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Abstract

The present paper approaches ontology and meta-ontology through Mathematics, and more precisely 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 by means of category theory. For us, an ontology is a mathematical object: it is a category $E$, 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, in the particular case of an elementary topos, is induced by the presence of an object $\Omega_E$ parametrizing the truth values of the internal propositional calculus; such pair $(E,\Omega_E)$ prescribes the modes of existence for the objects of a fixed ontology/category.

This approach resembles, but is more general than, the one leading to fuzzy logics, as most choices of $E$ and thus of $\Omega_E$ 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 the famous Tlön's ``nine copper coins'' paradox, and of other seemingly paradoxical construction in Jorge Luis Borges' literary work.

We conclude with some vistas on the most promising applications of our future work.

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Item Type:	Preprint
Creators:	Creators Email ORCID Dentamaro, Dario dario.dentamaro@stud.unifi.it Loregian, Fosco fosco.loregian@taltech.ee
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
Depositing User:	Dr. Fosco Loregian
Date Deposited:	29 Jul 2020 18:42
Last Modified:	29 Jul 2020 18:42
Item ID:	17679
Subjects:	Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Methodology Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics
Date:	28 July 2020
URI:	https://philsci-archive.pitt.edu/id/eprint/17679

Available Versions of this Item

• Categorical Ontology I - Existence. (deposited 08 May 2020 15:11)
  • Categorical Ontology I - Existence. (deposited 19 May 2020 20:49)
    • Categorical Ontology I - Existence. (deposited 19 May 2020 20:50)
      • Categorical Ontology I - Existence. (deposited 29 Jul 2020 18:42) [Currently Displayed]

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