Suppose I write these phrases on a blackboard:
the sum of the numbers denoted by expressions on the board in Room 213
And suppose I’m in Room 213. It’s clear what the first two phrases denote, but what of the third? If it denotes the quantity k, then k = π + 6 + k, which is absurd. So the third phrase is pathological — it appears to denote a number but it doesn’t.
But if the third phrase doesn’t denote a number, then the sum of the numbers denoted by expressions on the board in Room 213 is π + 6 — and the third phrase has a clear meaning. Asks University of North Carolina professor Keith Simmons, “How can the same phrase be pathological and yet successfully refer?”
(Keith Simmons, “Reference and Paradox,” in JC Beall, ed., Liars and Heaps, 2003)