Walter Burley (ca. 1275-after 1344) is the author of a treatise, entitled De primo et ultimo instanti, which is regarded as the most popular medieval work on the problem of assigning first and last instants of being to permanent things. In this paper, however, the author does not deal with this treatise directly. She looks instead at Burley’s Physics commentary to see how he applies the ideas presented in De primo et ultimo instanti to the solution of an Aristotelian puzzle about the ceasing to be (i.e., to exist) of the present instant (Physics IV, 10). In Burley’s interpretation, the relevant question raised by the puzzle is whether the present instant ceases to be when it is or when it is not. While Aristotle’s argument quickly dismisses the first alternative as absurd, Burley defends it by appealing to the ‘expositions’ of sentences about ceasing (desinit). Given that the sentence ‘this instant ceases to be’ has two expositions—(1) ‘this instant now is and immediately afterwards will not be’ (position of the present and negation of the future) or (2) ‘this instant now is not and immediately beforehand was’ (negation of the present and position of the past)—Burley maintains that the sentence is true in exposition (1) but not true in exposition (2), so that an instant ceases to be when it is and not when it is not.