 A hyperintensional concept draws a distinction between necessarily equivalent contents. If the concept is expressed by an operator, \(H\), then \(H\) is hyperintensional insofar as \(HA\) and \(HB\) can differ in truth value in spite of \(A\) and \(B\)’s being necessarily equivalent. Necessary equivalence of claims is standardly understood in terms of possible worlds (ways things could have been): \(A\) and \(B\) are necessarily equivalent when they are true at the same worlds. This is sometimes put in terms of sentences sharing an intension. An extensional operator (e.g., Boolean negation) allows substitution salva veritate of sentences with the same extension, that is, truth value: if \(A\) has the same truth value as \(B\), then also \({\sim}A\) has the same truth value as \({\sim}B\). An intensional operator (e.g., the box of necessity) allows substitution salva veritate of sentences that express necessary equivalents: if \(A\) is necessarily equivalent to \(B\), then \(\Box A\) has the same truth value as \(\Box B\). The expression “hyperintensional” is thus for an \(H\) that defies substitution salva veritate even of expressions with the same intension.