 Stalnaker’s account of the necessary a posteriori requires that the proposition semantically expressed by the sentence and the proposition that the sentence semantically expresses a truth hold in different worlds in the context set. And that seems to require that the assumptions shared between the participants of the conversation don’t determine what proposition is semantically expressed by the sentence. It has been argued that that assumption is implausible in some cases of Kripkean a posteriori necessities (Soames 2005, 96–105). Suppose that I point to the desk in my office in broad daylight and say ‘That desk (if it exists) is made of wood.’ Unless the context is highly unusual, the shared assumptions, so the argument goes, uniquely determine what proposition is expressed by the sentence.