Philosophical Thought

Ontological structuralism aims to eliminate fundamental objects from ontology and elevate the status of relations. On the other hand, category theory offers a framework for representing a metaphysical view according to which (possible) worlds lack inner structure, including a domain of fundamental objects. To demonstrate this, we first rule out a naïve approach to category-theoretic structuralism, then examine the preferred approach at two levels of complexity (with respect to sets and relational structures). We establish that category-theoretic structuralism is committed to possible-world realism and, being limited to the resources of category theory, cannot distinguish the actual world in a non-indexical way. Moreover, since the world is emptied of fundamental inner structure and relations are removed from this metaphysical picture along with objects, the resulting view aligns more closely with monism than structuralism. Apparently, structuralists have not fully considered these metaphysical consequences of adopting the category-theoretic framework.