This paper offers a new theory of donkey anaphora that does not include any dynamic component. Even if the approach is not dynamic, it retains a key aspect of the dynamic tradition, namely the view that information states include not just factual information about the world, but also information about discourse referents, e.g., variables. It also makes crucial use of plural assignment functions (sets of standard assignments, cf. van der Berg 1996; Nouwen 2003; Brasoveanu 2008). Unlike dynamic approaches, sentences are evaluated as true or false relative to a pair (w, G), where w is a possible world and G is a plural assignment, with no reference to contexts or information states, and compositional semantics does not refer in any way to context update or transitions between assignments. In order to predict adequate meanings and felicity conditions, I combine two ingredients that have been used to account for presupposition projection, namely Trivalence (Peters 1979; Beaver and Krahmer 2001) and Schlenker’s Transparency Principle (Schlenker 2007,2008).
Two ideas play a crucial role in the proposal. First, a sentence such as `She_x came' comes with the presupposition that the variable x is `valued' by the assignment function G, which means that every atomic assignment in G maps x to the same value. Second I adopt Mandelkern's (2002) witness condition: an existential statement such as `Someone_x came' is undefi ned in (w;G) if it is classically true in w but G does not map x to a witness of the existential statement. Unde finededness is not equated with Presupposition Failure. Rather, presupposition projection is governed by Schlenker's (2007,2008) Transparency Principle: the presupposition `x is valued' should be redundant in the syntactic position in which `She_x came' occurs.
In the end of the paper, I discuss well-known ambiguities with donkey sentences (weak vs. strong, existential vs. universal readings) and show how they can be addressed in my system.
The theory is presented as a non-standard semantics for fi rst-order logic, rather than a fragment of a natural language. Free variables are the counterparts of syntactically unbound pronouns, and existential quanti fiers those of singular indefi nites.