Conditional 'then' and the QUD-approach to conditional perfection

In this paper, we (re)consider the role of conditional 'then' in bringing about conditional perfection (CP; Geis and Zwicky (1971) and much subsequent work): the pragmatic step from a conditional 'if p, q' to 'if and only if p, q'. Our starting point is von Fintel (2001), according to whom CP depends on the type of question under discussion (QUD) preceding the conditional. Particular attention is devoted to focus placement on conditional 'then' in German ('then_F'), which we argue to come with an exhaustive presupposition (Bassi et al., 2021): 'if p, then_F q' exhaustively presupposes no previously considered antecedent p′ to make the consequent q true. A challenge is raised by cataphoric uses of German 'then_F', where said presupposition does not (always) seem to be triggered.