Since 1957 many philosophers have pursued H. P. Grice's program of intention-based semantics. A basic aim of this program is to reduce semantic facts to psychological facts, specifically facts involving intentional psychological behavior. Another central aim of this program, at least as understood by proponents sympathetic to physicalism, is to reduce the relevant psychological facts, specifically propositional-attitude facts such as belief-facts, to physical facts. In Remnants of Meaning (Cambridge, Mass.: The MIT Press, 1987), Stephen Schiffer opposes this Gricean program, and presents a novel approach to truths affirming the existence of propositional-attitudes. He calls this approach sentential dualism. I shall show that Schiffer's sentential dualism faces a fatal dilemma. But first I need to outline Schiffer's position on belief-affirming truths. (All subsequent parenthetical page-numbers refer to Remnants of Meaning.)