The phenomenon of presupposition suspension can be analyzed in terms of explicatures and the corresponding non-presumptive interpretative reasoning underlying it. On the view presented in this paper, the polyphonic articulation of an utterance at different levels can be used to explain cases in which presuppositions are suspended. Presuppositional suspensions indicate that the presumptive reading does not hold and a different interpretation is needed. Utterances can display various types of polyphonic structures, accounting for the speaker’s and the hearer’s commitments. A speaker can be held directly responsible for what he says, but he is committed only indirectly to what he presupposes, i.e. what is uttered by a second voice (the second utterer or enunciator) representing what the common opinion accepts to be true. The reconstruction of the pragmatic structure of an utterance is guided by a complex type of reasoning, which can be represented as an argumentative abductive pattern, grounded on hierarchies of presumptions. By comparing the possible presumptions associated with the explicit meaning and the contextual information, the hearer can find a best possible explanation of the intended effect of the utterance.