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 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, manyvalued 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 testbench for our theory, and a literary divertissement, we propose a possible categorytheoretic 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  

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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 

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://philsciarchive.pitt.edu/id/eprint/17679 
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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)
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Categorical Ontology I  Existence. (deposited 19 May 2020 20:50)

Categorical Ontology I  Existence. (deposited 19 May 2020 20:49)
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