 because, for instance, \(\llbracket\)‘three’\(\rrbracket = \{w_3, w_4\}\). A literal interpreter, who is otherwise oblivious to contextual factors, would respond to every message by choosing any true interpretation with equal probability. So, for instance, if the literal interpreter hears ‘three’, he would choose \(w_3\) or \(w_4\), each with probability \(½\). But that means that an optimal choice of expression for a speaker who wants to communicate that the actual world is \(w_3\) would be ‘three’, because this maximizes the chance that the literal interpreter selects \(w_3\). Concretely, if the speaker chooses ‘one’, the chance that the literal listener chooses \(w_3\) is ¼; for ‘two’ it’s ⅓; for ‘three’ it’s \(½\), and for ‘four’ it’s zero, because \(w_3\) is not an element of \(\llbracket\)‘three’\(\rrbracket\). So, a rational Gricean speaker selects \(\llbracket\)‘three’\(\rrbracket\) in \(w_3\) and nowhere else, as is easy to see by a parallel argument for all other states. But that means that a Gricean interpreter who hears ‘three’ will infer that the actual world must be \(w_3\).