This paper presents the beginnings of an analysis of Double Access readings (Smith, 1975) as being due to imprecision.
(1) John said Mary is sick.
conveys: John said at t that Mary-sick at t
conveys(?): Mary is sick now.
Double Access readings have long been an intransigent problem for theories of embedded tense. The second inference of (1) is not only mysterious in origin, but there is not even a consensus as to how it should be characterized in the first place. (The paraphrase given is actually wrong for a variety of reasons which I’ll explain.)
I argue that (1) has the meaning it does because the embedded clause, whose literal meaning identifies Mary’s sickness time with speech time, is interpreted imprecisely. This accounts for a variety of facts related to (1), including its apparent violation of the Upper Limit Constraint (e.g., Abusch 1997). Importantly, this requires interpreting the embedded clause imprecisely before composing it with the matrix clause, making this a case of embedded implicature.