  An alternative approach, one that is applicable to presuppositions more generally, is to maintain that it is worldly facts which determine whether the presupposition is satisfied or not. Thus for example, ‘John stopped smoking’ suffers from presuppositional failure if and only if John in fact used not to smoke and similarly ‘The thing Jill is thinking about is green’ suffers from presupposition failure if Jill is thinking about the number two, but not if she is thinking about a table. According to a third proposal, one in the spirit of Stalnaker (1973), what matters aren’t the actual facts, but rather which propositions are taken for granted by the participants in conversation. To see how this differs from the ‘worldly’ approach, note that on this Stalnakerian approach to presupposition, ‘John stopped smoking’ would suffer from presupposition failure in a context where participants take it for granted that John never did smoke, even if they are wrong and John in fact used to smoke.