COLLOQUIUM: "Outline of an Intensional Theory of Truth"
Friday, Apr. 12, 2019, 3pm to 5pm, BEH 217
"Outline of an Intensional Theory of Truth."
Roy Cook, Department of Philosophy, University of Minnesota
In this talk I will extend the fixed-point semantics of (Kripke 1975) via the addition of two unary intensional operators: a paradoxicality operator Π where Π(φ) is true if and only if φ is paradoxical (i.e., if and only if φ receives the third, non-classical value on all fixed-points), and a semi-truth operator ΣT where ΣT(φ) is true if and only if any fixed point can be extended to one on which φ receives the value true. I will sketch proofs of a generalized version of Kripke's fixed-point theorem, guaranteeing the existence of models of this new language, and an expressive completeness result, demonstrating that these new operators allow us to express every allowable (i.e., every monotonic) intensional unary operator. I conclude with an exploration of the significant improvements in expressive power that result from the addition of these new operators, and I precisely identify what still cannot be said on this intensional extension of the Kripkean framework.