The Modal Statute of Mathematical Objects

Abstract

The article discusses various positions regarding modal ontology and epistemology with the aim of laying the groundwork for a reflection on mathematical objects, particularly focusing on the construction of sets and mathematical structures, while paying particular attention to the modal status of mathematical infinity. All of this is intended to demonstrate that within the realm of mathematical knowledge, there is also room for discussions on the modality of propositions, and how tools like modal logic can shed light on ontological issues in the philosophy of mathematics.