Two-Dimensional Paradox

Two-dimensional accounts of speech and thought make use of so-called ‘diagonal’ propositions. If diagonals are indeed propositions, they can be negated: an ‘anti-diagonal’ is the negation of a diagonal. However, the existence of anti-diagonals is inconsistent with very natural assumptions to which two-dimensionalists like Chalmers and Stalnaker are committed, as shown by an argument that closely resembles more familiar paradoxes