Speaker: Johanna Alstott (MIT)
Title: Trying and failing to count in dense intervals
Time: Wednesday, December 13th, 1pm – 2pm
Location: 32-D461
Abstract: In this LSA practice talk, I offer a semantic analysis of a puzzling restriction on the distribution of ordinal numbers in English: while the temporal adverbials “at first” and “at last” are felicitous, putting any other ordinal in this environment is degraded (#at second, #at sixth). I know of no previous literature that discusses “at first”/”at last” or the unacceptability of #at second, #at third, etc. My analysis of “at first” and “at last” builds on the notion that assertions are relativized to a salient time interval, known in the literature as topic time (Klein 1994). On my semantics, “at first” and “at last” further relativize an assertion to a salient subinterval of the topic time that shares an infimum (first point) or supremum (last point) with it. On the assumption that time-intervals are dense, the infelicity of #at second, #at third, etc. follows from this semantics. Since “at first” and “at last” invoke the infimum and supremum of a time-interval (respectively) on my semantics, #at second will attempt to invoke the second (i.e. second earliest) point of a time-interval. Invoking the infimum or supremum of a (closed) dense interval is coherent, but invoking the second earliest point (the point closer to the infimum than any other) is not. My analysis makes interesting predictions about the interaction of “at first”/”at last” with present tense and with frame adverbials, and it paves the way for an account of why ordinals are forbidden in related “at”-modifiers with superlatives (e.g. at most vs. #at second most).