Knowing whether A or B

Can we say that s knows whether A or B when s is only able to rule out A, but remains uncertain about B? We discuss a set of examples put forward by J. Schaffer’s in favour of a contextualist answer to this problem. We present a context-sensitive and dynamic semantics for knowledge attributions, in which those can depend on the alternatives raised by the embedded question, but also on alternatives raised earlier in the context. 1. Alternative questions in epistemic contexts The aim of this paper is to discuss the semantics of knowledge attributions of the form “s knows whether A or B”, which we may symbolize by Ks?(A ∨a B), where ?(A ∨a B) denotes an alternative disjunctive question, like “is John in London, or is Mary in London?”. More specifically, our aim is to provide a dynamic account of the context-sensitivity of such attributions. It is standard in linguistic theory to distinguish polar readings and alternative readings of disjunctive questions (see e.g. Haspelmath 2000, Han and Romero 2003). Under the polar reading, a question of the form “is John or Mary in London?” calls for a yes or no answer. The polar reading can be forced in English by asking “is either John or Mary in London?”. For the alternative reading, by contrast, the question cannot be answered by yes or no and has to be answered by a sentence like “John is London”, or “Mary is not in London”, namely by providing information about the truth and falsity of the respective disjuncts. There is still some debate in the literature about the answerhood conditions of alternative questions, and by way of consequence, about the conditions under which a subject can be said to know whether A or B. In a recent paper (Schaffer 2007), J. Schaffer argues that in a context in which s sees someone on TV, who is actually George Bush, but such that s is not able to discriminate between George Bush and Will Ferrell (because Ferrell is such a good impersonator of Bush), and yet is able to see that it is not Janet Jackson, (1-a) below should be judged false, but (1-b) should count as true: (1) a. s knows whether George Bush or Will Ferrell is on TV b. s knows whether George Bush or Janet Jackson is on TV. The intuition reason for the truth of (1-b), according to Schaffer, is that the question “is Bush or Janet Jackson on TV?” is easier for s to answer than the question “is Bush or Will Ferrell on TV?”. In our view, however, ordinary intuitions are less stable: although (1-a) should be incontrovertibly false in the scenario, the status of (1-b) is much less clear. In our opinion, all that s really knows is that Janet Jackson is not on TV, which need not be sufficient to fully answer the question “is Bush or Janet Jackson on TV?”. More formally, assuming the partition theory of questions of Groenendijk and Stokhof (1984), an answer of the form “Janet Jackson is not on TV” counts only as a partial answer to the question “is Bush or Janet Jackson on TV?”. For s to know the complete answer to the question “is Bush or Janet Jackson on TV”, s should know more, namely that Bush is on TV and that Janet Jackson is not on TV. The partial answer “Janet Jackson is not on TV” would count as complete if one presupposed that exactly one of the two disjuncts had to be true. In principle, however, there is no more reason to think that “s knows whether Bush or Janet Jackson is on TV” is true than there is to think that “s knows whether Ferrell or Janet Jackson is on TV” is true. In other words, s’s ignorance about who exactly is on TV seems to override s’s partial knowledge about who is not on TV. Despite this, we agree with Schaffer that there is a sense in which, if s is allowed to ignore the possibility that Ferrell might be on TV, then s can be said to know whether Bush or Janet Jackson is on TV, simply based on s’s knowledge of that partial answer. 2. Dynamics of knowledge attributions To implement this idea, we propose a question semantics for knowledge in which attributions involving questions can