*Abstract*: There is a very natural way to interpret the propositional connectives and quantifiers, relative to the algebra of three semantic values, {0, *i*, 1} where 0 and 1 are understood as the traditional values of falsity and truth, and the third value is some intermediate value. The evaluation clauses do not, by themselves, determine the *logic*, because for *that*, you need to determine how models are used to provide a counterexample to a sequent. If a counterexample is given by a model that assigns every premise the value 1 and assigns every conclusion a value other than 1, the resulting logic is Kleene’s strong three-valued logic, K3. If a counterexample is a model assigning every premise the value 1 or *i* and every conclusion the value 0, the resulting logic is Priest’s logic of paradox, LP. If a counterexample is a model assigning every premise the value 1 and every conclusion the value 0, you get the logic ST of Strict-Tolerant validity. ST is distinctive, in that it *is*, in some sense, *classical logic*—every classically valid sequent in this language is ST-valid—but since it has strictly non-classical models, there are ST theories which are not classical theories.

What does this mean for the logic of *identity* in a three-valued context?

In this talk, I explain how the *classical* logic of identity, when interpreted in ST models, gives us a well-behaved class of three-valued models for identity—much larger than the traditional models for identity, used by afficianados of LP or K3—which can be used to model the distinctive non-classical behaviour of identity statements, with a greater degree of freedom than we might have thought.

The talk is a face-to-face presentation at the Arché Logic and Metaphysics Workshop on the Logic of Identity at the University of St-Andrews.

I’m *Greg Restall*, and this is my personal website. ¶ I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews.

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