OPERATORS IN THE PARADOX OF THE KNOWER

Predicates are term-to-sentence devices, and operators are sentence-to -sentence devices. What Kaplan and Montague's Paradox of the Knower de monstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic; they must be treated as opera tors instead. Such is the current wisdom. A number of previous pieces have challenged such a view by showing that a predicative treatment of modalities need not raise the Paradox of the Knower. This paper attem pts to challenge the current wisdom in another way as well: to show th at mere appeal to modal operators in the sense of sentence-to-sentence devices is insufficient to escape the Paradox of the Knower. A family of systems is outlined in which closed formulae can encode other form ulae and in which the diagonal lemma and Paradox of the Knower are the reby demonstrable for operators in this sense.