Prior's puzzle is a puzzle about the substitution of certain putatively synonymous or coreferential expressions in sentences. Prior's puzzle is important, because a satisfactory solution to it should constitute a crucial part of an adequate semantic theory for both proposition-embedding expressions and attitudinal verbs. I argue that two recent solutions to this puzzle are unsatisfactory. They either focus on the meaning of attitudinal verbs or content nouns. I propose a solution relying on a recent analysis of that-clauses in linguistics. Our (...) solution is superior, as it not only avoids the problems faced by previous solutions, but it also brings developments in linguistics in line to solve an old puzzle in philosophy. (shrink)