Set-Theoretic Ontology and Fields of Sense: Limits and Interpretations

Markus Gabriel’s reconceptualization of ontology in terms of fields of sense provides a pluralist alternative to monist and more traditional ontological views. Part of the motivation for the shift to fields of sense involves a critique of the use of set theory in ontology. In this paper, I examine some limitations of set-theoretic ontology, consider possible defenses and the difficulties they face. I then critically assess the alternative offered by fields of sense and raise an epistemological concern about them relative to mathematical practice. In conclusion, it seems that, with regard to the foundations of mathematics, fields of sense fail to play a foundational role.