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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 metaontology 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 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 E and
thus of Ω E yield nonclassical, many-valued logics.
Framed this way, ontology suddenly becomes more mathematical: a solid corpus of tech-
niques 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
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: 19 May 2020 20:50
Last Modified: 19 May 2020 20:50
Item ID: 17193
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: May 2020
URI: http://philsci-archive.pitt.edu/id/eprint/17193

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