Philosophy of Mathematics seminar

James Studd, Oxford

Contingentist sets as potentialist properties  

Philosophers who take being to be contingent face a problem involving sets of possibilia. Semantic reflection gives contingentists a powerful motivation to posit sets with non-actual members or even sets with incompossible members. On the other hand, good metaphysics assures us that there are no such sets. This talk outlines an interpretation of set theory based on a potentialist theory of properties that permits ‘sets’ with non-actual or incompossible members. This provides a way, I argue, for contingentists to meet the needs of semantics without resorting to bad metaphysics.