The Vacuous Past

Do we always mean past when we use the past tense? Certainly not. Consider the following sentences:

(1) John decided a week ago that in ten days he would say to his mother that they were having their last meal together (Abusch 1988)

(2) John said he would buy a fish that was still alive (Ogihara 1989)

(1) requires for its truth that John decided to say "we are having our last meal together", and (2) requires for its truth that John said he would buy a fish that is alive simultaneously with the buying event. This suggests that the past tense is ambiguous: it may be interpreted either as semantically vacuous or as meaning anteriority with respect to some reference time. The ambiguity thesis nicely explains why we don't need two past tense operators (or past tense quantifiers or whatever) in the logical form of the following sentence:

(3) Mary believed that Nixon was up to no good in the White House.

(3) can be read in two different ways, depending on whether the second occurrence of the past tense is taken to be vacuous. If the second occurrence of the past tense is read as vacuous, then (3) requires for its truth that the time of Mary's believing overlap the time of Nixon's being up to no good in the White House.

References:
Abusch, D. 1988. "Sequence of Tense, Intensionality and Scope". In H. Borer (ed.), Proceedings of WCCFL 7: 1-14.
Ogihara, T. 1989. Temporal Refernece in English and Japanese. Ph. D. Dissertation, University of Texas, Austin.