The concept of a dialogue is considered in general terms from the standpoint of its referential presuppositions. The semantics of dialogue implies that dialogue participants must generally have a collective intentionality of agreed-upon references that is minimally sufficient for them to be able to disagree about other things, and ideally for outstanding disagreements to become clearer at successive stages of the dialogue. These points are detailed and illustrated in a fictional dialogue, in which precisely these kinds of referential confusions impede progress in shared understanding. It is only through a continuous exchange of question and answer in this dialogue case study that the meanings of key terms and anaphorical references are disambiguated, and a relevantly complete collective intentionality of shared meaning between dialogue participants is achieved. The importance of a minimally shared referential semantics for the terms entering into reasoning and argument in dialogue contexts broadly construed cannot be over-estimated. Where to draw the line between referential agreement and disagreement within any chosen dialogue, as participants work toward better mutual understanding in clearing up referential incongruities, is sometimes among the dialogue’s main points of dispute.