This article investigates the semantics and pragmatics of the ‘hortative’ aorist (the aorist indicative in questions with τί οὐ ‘why don't …’) and the ‘tragic’ or ‘performative’ aorist (for example ὤμοσα ‘I swear’). Lloyd argued in 1999 that the tragic aorist is a more polite alternative for the corresponding present (ὄμνυμι ‘I swear’). Recently, he has extended this view to the hortative aorist, suggesting that, for example, τί οὐκ ἐκαλέσαμεν; is a polite alternative for τί οὐ καλοῦμεν; Lloyd argues that the politeness value of the aorist derives from its being a past tense, comparing the so-called ‘attitudinal’ past (as in I wanted to ask you something instead of I want to ask you something). The present article, building on work by Colvin, Bary and Nijk, argues instead that the semantic value of the aorist is purely aspectual in these cases: the hortative and tragic aorists serve to construe the designated event as bounded, while the corresponding present forms serve to construe the designated event as unbounded. An extensive discussion of the evidence for the hortative aorist and present is presented, as well as a case study concerning the aspectual behaviour of the verb ὄμνυμι. Moreover, I argue that the proposed semantic account of the hortative and tragic aorists in terms of aspect can be unified with Lloyd's pragmatic account in terms of politeness: the difference in tone between the present and the aorist can be derived from their respective aspectual values, rather than from their temporal values.