Abstract
Abstract The modal‐structural approach is extended to set theory, as an alternative to reifying sets as actual abstract objects, thinking instead of ‘possible results of selection’. Drawing inspiration from Zermelo's important paper of 1930 and suggestions of Putnam, it is shown how to incorporate modality into second‐order Zermelo–Fraenkel set theory, avoiding proper classes and a fixed universe of sets, instead sustaining extendability principles (‘any set‐domain can be part of a larger one’, and strengthenings of this). It is then shown how this naturally leads to important kinds of ‘large cardinals’ (inaccessibles, Mahlo cardinals), motivated ‘from below’ rather than ‘from above’.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
