 The objection, presented in Cresswell (2002) against structured propositions and suggested by Stalnaker (1996) against impossible worlds, can be illustrated by focusing on the meaning of negation. Given a statement \(A\), what truth-conditions can we offer for \({\sim}A\)? Plausibly, the truth conditions can be exhausted by specifying that \({\sim}A\) is true when \(A\) is false, and not otherwise. Since this exhausts the meaning of “\({\sim}\)”, it is tempting to identify the proposition \({\sim}A\) as being the proposition with this truth condition. Plausibly, also, the truth conditions for \({\sim}{\sim}A\) will just be the truth conditions for \(A\). (We may even want to derive this second claim from plausible principles about truth, falsehood, and necessity.) Now any theory which allows for distinct necessarily equivalent propositions will fall to the same objection: suppose \(C\) and \(D\) are distinct, necessarily equivalent propositions. Then \({\sim}C\) will be the proposition that is true just in case \(C\) is false, and \({\sim}D\) will be the proposition that is true just in case \(D\) is false: so \({\sim}C\) and \({\sim}D\) will be the same proposition. But then there will be a unique proposition with the truth conditions for \({\sim}{\sim}C (/{\sim}{\sim}D)\), since \({\sim}{\sim}C\) is the negation of \({\sim}C\). So \(C\) and \(D\) must be the same proposition after all. This is a reductio of the hypothesis that there can be a hyperintensional distinction between \(C\) and \(D\): if they are necessarily equivalent, they are identical.