Mainstream work on the semantics of binding has adopted the Tarskian assumptions
in (1) on the basis of an assignment dependent recursive interpretation
(1) a. Assignments are sequences (functions from indices to objects).
b. Bound elements are indices.
I argue that (1) should be replaced with (2):
(2) a. Assignment are sets of objects.
b. Bound elements are definite descriptions.
Initial evidence for the proposal comes from phenomena that argue that
traces and pronouns are definite descriptions, in particular Sauerland
2000 and 2004. Then I show further evidence from agreement licensing and
restrictions on sloppy interpretations in ellipsis.
Sauerland, Uli (2000). "The content of pronouns: Evidence from focus."
Proceedings of SALT 10.
Sauerland, Uli (2004). "The interpretation of traces." Natural