 Some algebraic approaches do not take as much advantage of this flexibility as one might expect with respect to hyperintensionality puzzles. Keenan and Faltz (1984)’s algebraic approach identifies necessary equivalents. Bacon (2018) adopts a Boolean account in which the propositions associated with logical equivalents in predicate logic are identified with each other (e.g., the proposition that \({\sim}({\sim}A \lor {\sim}B)\) is identical to the proposition that \((A \land B))\). This leaves room for distinguishing merely necessarily equivalent propositions, e.g., the proposition that \(2+2=4\) and the proposition that it rains if and only if it rains. But it does little to help with cases where we want to discriminate between logical equivalents: if we were to think that \(A\) explains why \({\sim}{\sim}A\), or capture the belief content of the confused man who believes something of the form \((A \land B)\) but does not believe \({\sim}({\sim}A \lor {\sim}B)\). So it is not the algebraic approach per se that yields solutions to particular puzzles about hyperintensionality, but the algebraic approach combined with theoretical choices about the structure of the algebra.