CATEGORICALONTOLOGY I - EXISTENCE

DARIO DENTAMARO AND FOSCO LOREGIAN

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 categorytheory. 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 $\mathcal{E}$ and thus of $\Omega_\mathcal{E}$ yield non classical, many-valued logics.

Framed this way, ontology suddenly becomes more mathematical: a solid corpus of techniques can be used to back up 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.