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Categorical Ontology I - Existence

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:
CreatorsEmailORCID
Dentamaro, Dariodario.dentamaro@stud.unifi.it
Loregian, Foscofosco.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: http://philsci-archive.pitt.edu/id/eprint/17679

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