Operators in the paradox of the knower

Patrick Grim

pp. 409-428

in: Synthese 94 (3), 1993.

Abstract

Predicates are term-to-sentence devices, and operators are sentence-to-sentence devices. What Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic; they must be treated as operators instead. Such is the current wisdom.