Non-deictic Tenses in Conditionals

This paper is about the interpretation of tenses in conditional sentences. It focuses on a particular cluster of data centering around the observation that tenses in the consequent of a conditional can obtain a non-deictic interpretation. As we will see, there is no need for something very extravagant or new to deal with these observations. We can do with the standard analysis of indicative conditionals using quantification over possible worlds (Kratzer 1979, 1981): a conditional If A, then C is true with respect to a set of possible worlds B if C is true at all, most or few worlds in B at which A is true. This standard analysis will be combined with a similarly well-known approach towards the meaning of the English tenses: a nondeictic, relative semantics, as, for instance, proposed in Abusch (1997) and Stechow (2005). The original contribution of this paper lies primarily in how it spells out the model theory for this standard semantics, particularly in the way it models the asymmetry between closed past and open future. In contrast to the standard position based on work of Kamp (1978), the present paper formalizes the openness of the future by leaving possible worlds generally undefined for the future. This shift in the conception of the future will have consequences for the temporal properties of modal bases B that enter the semantics of modal/conditional constructions. As will be shown below, this affects the interpretation of tenses in modal/conditional constructions. In particular, it will explain the cluster of observations that the paper intends to account for. There are many questions concerning the interpretation of conditional sentences that this paper is silent on (for instance, the interpretation of aspect in conditional constructions, presupposition projection and the issue of how to model counterfactual reasoning). The decision to leave these topics out results from the conviction that these issues are independent from the specific problem the paper does address. This is also the reason for why the present proposal is worked out within a very simple semantic framework. This will enable the reader to easily fit in his/her favored approach to deal with the issues of modal/conditional semantics that (s)he is working on.