In defense of plural comprehension

Jonathan D. Payton (Bilkent University)

Abstract 

Standard plural logics include a naïve plural comprehension schema (NPC): for any condition Φ, if at least one individual satisfies it then there is a plurality of all and only those individuals which do so. Recently, NPC has come under fire, some denying that it’s a logical truth and some denying that it’s true at all. In this talk, I defend NPC. First, working within a natural deduction system for plural logic, I defend its status as a logical truth. I then turn to the most popular argument against NPC, namely that it conflicts with a plausible universalist principle about sets: for any things, there exists the set of those things. Florio and Linnebo have used this argument to motivate their system of critical plural logic, in which NPC is rejected in favour of some weaker comprehension axioms. I argue that the system is even weaker than Florio and Linnebo realize, and highly unattractive compared to more traditional plural logics. Time permitting, I’ll also argue that universalism about sets isn’t as compelling as it seems.