## Generality and Existence 3: Substitution and Identity

#### December 2, 2015

I gave a talk, entitled “Generality and Existence 3: Substitution and Identity” in the Arché Super Special Seminar at the University of St Andrews.

Abstract: In this talk, extend the proof system for free logic to include an identity predicate. Or rather, two different candidate identity predicates allowing for the substitution of a lesser or greater class of predications. I show that the resulting system is well-behaved proof theoretically (the Cut rule is eliminable) and the identity predicates can be well motivated in terms of their defining rules.