Nina Haslinger (Göttingen) & Viola Schmitt (Humboldt-Universität zu Berlin)

Belief states as ordered sets of worlds: Evidence from embedded counterfactuals

Much work on attitude verbs within possible-worlds semantics distinguishes between attitude predicates that are sensitive to orderings of worlds, such as *want* or *hope*, and those that are not, such as *believe* (e.g. Heim 1992, following Stalnaker 1984). In this talk, we argue that attitudes of the latter class should be represented in terms of ordered sets of worlds as well, which raises the question whether we ever find quantification over unordered sets of worlds in natural language.

The argument is based on counterfactuals embedded under *believe* and German *vorstellen* 'imagine, suppose'. Counterfactuals are usually thought to be sensitive to an ordering depending on the facts of the evaluation world (e.g. Lewis 1973). We show that this makes wrong predictions for embedded counterfactuals that restrict existential modals. An example with the German modal *möglicherweise* is given in (1).

(1) Anna glaubt, dass sie möglicherweise einen Kaffeekocher bekommen hätte, wenn das Paket nicht gestohlen worden wäre.
'Anna believes she would possibly have received a coffee-maker if the package had not been stolen.'

To get the truth conditions of such sentences right, the counterfactual must be sensitive to a partial ordering determined by the attitude context as a whole (e.g. the subject's belief state as a whole). The relevant ordering for (1) determines how far-fetched a given world is given Anna's beliefs; her standard doxastic alternatives (in the sense of Hintikka 1969 and related work) are the minimal elements of the ordering. The compositional semantics follows Yalcin's (2007) 'domain semantics' for *might*: We take epistemic modals and counterfactuals to be sensitive to an information-state parameter that is shifted by the embedding attitude. Unlike in Yalcin's work, the values of this parameter are partial orderings of worlds rather than unstructured sets.

We further discuss and reject a potential alternative account of the puzzle posed by (1) that relies on the introspection properties of belief, i.e. the assumption that subjects are fully aware of their own belief state. We show that *vorstellen* 'imagine, suppose' interacts with embedded counterfactuals in the same way as *believe*, but crucially lacks the relevant introspection properties.

References:
Heim, Irene. 1992. Presupposition projection and the semantics of attitude verbs. Journal of Semantics 9. 183–221.
Hintikka, Jaakko. 1969. Semantics for Propositional Attitudes. In Models for Modalities. Selected Essays, 87–111. Dordrecht: Reidel.
Lewis, David. 1973. Counterfactuals. Harvard University Press.
Stalnaker, Robert C. 1984. Inquiry. Cambridge, MA: MIT Press.
Yalcin, Seth. 2007. Epistemic Modals. Mind 116. 983–1026.