The goal of this talk is to demonstrate that we can systematically translate natural language discourse into appropriate classical truth conditions within one theory, just using a first-order classical logic with dependent types. We do not need a new ontological category of Discourse Structures (Kamp 1981, Kamp&Reyle 1993). Nor do we have to abandon a classical logic for a dynamic theory (Groenendijk and Stokhof 1990, 1991) with a non-classical re-interpretation of the logical quantifiers, or a constructive theory with a non-classical notion of ``proposition'' (Sundholm 1989, Ranta 1991, Ranta 1994, Davila 1994).
Some the formal details of a treatment of singular anaphora in a first-order Property Theory (Turner 1990, 1992) are given, together with a proposal for extending the treatment to some cases of plural anaphora.