Nominalismo de categorias : teoria das formas esquemáticas e funtorialização da noção de particular paradigmático - Silva, Hendrick Cordeiro Maia e (2018)
The present dissertation shows how Category Theory can be used as a tool to deal with the Problem of Universals. The results developed here allow the Problem of Universals to be viewed from a new and original perspective, that is, of a schematic ontology. In fact, the present study demonstrates how to build schematic forms of sentences. The basic idea is that the justification for applying the same predicate to distinct particulars is given by a schematic relation between schematic forms of sentences; for this, I also define the schematic form of the paradigmatic particular notion. To conclude this idea, I use constructions present in Category Theory. Hence, schematic forms of sentences are formalized as cones, the schematic form of the paradigmatic particular notion is formalized as the limit for a given functor, and the schematic relation between schematic forms of sentences is formalized as the schematic relation factors through. Moreover, I define a category in which the objects are schematic forms of sentences, and the arrows are the schematic relations between these schematic forms of sentences. Finally, I “functorize” the notion of paradigmatic particular, showing that asking about the existence of a schematic form of the notion of paradigmatic particular is asking about the existence of the right adjoint of a given functor. As an example of the Category Nominalism developed in this dissertation, I present a solution to the infinite regress pointed out by Russell in the Resemblance Nominalism. In the conclusion I briefly outline how the theory of schematic forms developed here can be used in problems in the field of the theories of truth and theories of meaning.