A Logical Foundation for Potentialist Set Theory
Published by Cambridge University Press. Online Version
Errata and Reader Q&A:
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.
I also develop a modestly neo-Carnapian approach to general mathematics.
This is a Lean formalization of the inference rules and modal operators from my book. It helps clarify how the rules (like modal comprehension and amalgamation) work and includes working examples.