The Logic and Metaphysics Workshop will meet on May 5th from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Luca Incurvati (ILLC).

Title: On class hierarchies

Abstract: In her seminal article ‘Proper Classes’, Penelope Maddy introduced a theory of classes validating the naïve comprehension rules. The theory is based on a step-by-step construction of the extension and anti-extension of the membership predicate, which mirrors Kripke’s construction of the extension and anti-extension of the truth predicate. Maddy’s theory has been criticized by Øystein Linnebo for its ‘rampant indeterminacy’ and for making identity among classes too fine-grained. In this paper, I present a theory of classes that builds on Maddy’s theory but avoids its rampant indeterminacy and allows for identity among classes to be suitably coarse-grained. For all the systems I discuss, I provide model theories and proof theories (formulated in bilateral natural deduction systems), along with suitable soundness and completeness results.