 Karttunen’s filters include the binary logical connectives “if then”, “and”, and “or”. The intuition behind the filter metaphor is that these constructions allow only some presuppositions to project, others being caught in the filter, and we have already seen examples of this phenomenon. Thus example (12) showed that sometimes a presupposition in the consequent of a conditional does not project: here the presupposition that there was a knave is filtered out. But the same example includes an occurrence of the definite “the tarts” in the consequent, and the presupposition that there are (or at least were) some tarts projects from the conditional. Karttunen concluded that the consequent of a conditional acts as a hole to some presuppositions, but filters out all those presuppositions which are entailed by the antecedent, or, more generally, by a combination of the antecedent and contextually supplied background information.