A first semantics for <i>at first</i> and <i>at last</i>

Abstract

This paper offers the first ever 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 third). My analysis builds on the notion that assertions are relativized to a salient time interval, known in the literature as reference time or topic time. 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 standard 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 first and last points of a time-interval on my analysis, #at second will attempt to invoke the second (i.e. second earliest) point of a time-interval. Invoking the first and last points of a dense interval is coherent, but invoking the second point (i.e. the point closer to the first point than any other) is not. My analysis makes interesting predictions about the interaction of at first/at last with present tense and frame adverbials, and it opens up several avenues for future research.