A Logical Foundation for Potentialist Set Theory

Published by Cambridge University Press. Online Version

Online Appendixes

In this book I advocate a formulation of potentialist set theory that appeals to (a generalization of) the logical possibility operator. I show that, working in this framework, we can justify mathematicians' use of the ZFC axioms from general modal principles which all seem clearly true -- providing slightly more intuitive justification for Replacement than previous approaches.

Looking beyond pure set theory, I also explore how using this generalized logical possibility operator can illuminate topics like:

  • grounding,
  • neo-Carnapian theories of ontological knowledge by convention
  • varieties of (post) Quinean indispensability arguments,
  • and the heterogeneity of applied mathematics.
And I develop a modestly neo-Carnapian approach to general mathematics.

Reader's Guide

Early Draft Version