What embedded counterfactuals tell us about the semantics of attitudes

We discuss German examples where counterfactuals restricting an epistemic modal are embedded under glauben 'believe'. Such sentences raise a puzzle for the analysis of counterfactuals, modals, and belief attributions within possible-worlds semantics. Their truth conditions suggest that the modal's domain is determined exclusively by the subject's belief state, but evaluating the counterfactual separately at each of the subject's doxastic alternatives does not yield the correct quantificational domain: the domain ends up being determined by the facts of each particular world, which include propositions the subject does not believe. We therefore revise the semantics of counterfactuals: counterfactuals still rely on an ordering among worlds that can be derived from a premise set (Kratzer, Angelika. 1978. Semantik der Rede: Kontexttheorie - Modalworter - Konditionalsatze (Monographien Linguistik und Kommunikationswissenschaft 38). Konigstein: Scriptor, 2012 [1981]a. The notional category of modality. In Modals and conditionals (Oxford studies in theoretical linguistics 36), 27-69. Oxford: Oxford University Press), but rather than uniquely characterizing a world, this premise set can be compatible with multiple worlds. In belief contexts, the attitude subject's belief state as a whole determines the relevant ordering. This, in turn, motivates a revision of the semantics of believe: following Yalcin's work on epistemic modals (Yalcin, Seth. 2007. Epistemic modals. Mind 116. 983-1026), we submit that evaluation indices are complex, consisting of a world and an ordering among worlds. Counterfactuals are sensitive to the ordering component of an index. Attitude verbs shift both components, relativizing the ordering to the attitude subject.