Aspect in Ancient Greek - Nijmegen Centre for Semantics

4.9 The conative and likelihood interpretations 111e 1e...................................................................................... 2e 3e 4t TTFigure 4.11: Imperfective aspect intensionalisedabout what happens in the inertia worlds during t TT , a claim is made aboutthe actual world during t TT as well. In this way, the intuition is captured thatthis t TT , which is the topic time, is the time ‘about which we speak’, since itis only as far as t TT is concerned that (by saying something about the inertiaworlds) something is said about the actual world. 17 This nice consequence ofIMP ′ is absent in IMP.Note that this intensionalisation of the imperfective operator does not affectits interpretation with unbounded predicates. For an unbounded predicate Pwe get that if IMP(P) is true of the topic time, and hence in all inertia worldsthere is a P eventuality e of whose runtime τ(e) the topic time is a nonfinalsubset, it is (due to the divisivity of P) probable that in those worldsthere is also a P eventuality e ′ temporally included in the topic time, and thiseventuality takes place in the actual world as well (due to the fact that allthese inertia worlds are identical to the actual world up to and including thetopic time). This is illustrated in Figure 4.12. This result is exactly what wewant, for the imperfective paradox is restricted to bounded predicates.. . . . . . e 1τ(ee...................................................... ′ )................................ 2e 3........................ e 4t TTFigure 4.12: Imperfective aspect intensionalised for unbounded predicatesA possible objection to this intensionalisation of the semantics of imperfectiveaspect may be that as a result imperfective aspect does something completelydifferent from aoristic aspect, (101b). This objection does not hold,17 Admittedly, by saying something about the inertia worlds, we also say something aboutthe actual world before the topic time. The crucial thing, however, is that we don’t saysomething about the actual world after the topic time.