 Applying this to intensional transitives is just a matter of assigning appropriate types so that the translations of, say, ‘Lucia seeks Cicero’ and ‘Lucia seeks Tully’, are different propositions (potentially with different truth-values). We need to keep the verb as function, and we already have the types of cicero and tully set to (ip)p. The translations of ‘seeks Cicero’ and ‘seeks Tully’ should be functions capable of accepting inputs of type (ip)p, such as lucia, and producing propositions as output. seeks therefore accepts input of type (ip)p and produces output that accepts input of type (ip)p and produces output of type p. Thus seeks is of type ((ip)p)(((ip)p)p), and we get substitution-failure because seeks(cicero) and seeks(tully) can be different functions of type ((ip)p)p so long as cicero and tully are different functions of type (ip)p (as we already said they should be). seeks(cicero) can therefore map lucia to one proposition while seeks(tully) maps it (not ‘her’) to another; and these propositions can have different  truth-values.[8]