Aspect in Ancient Greek - Nijmegen Centre for Semantics

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110 Chapter 4. An analysis of aoristic and imperfective aspectof eventualities happens in a way most compatible with the past course ofeventualities. (137) states that in all these inertia worlds there is an eventualityof which P holds and that temporally includes t. Crucially it does not statethat there is an eventuality of which P holds in the actual world.As before, the time to which the eventuality stands in the specified temporalrelation ends up to be the topic time, due to the semantic contribution oftense. We see this if we apply IMP ′ to (135) (for the full derivation see (223)in Appendix B):(138) PAST(IMP ′ (λwλe d buy(e,w)))= λQ[Q(t TT ) ⊕tTT ≺ n ](λPλt w ′Inert t (w 0 ,w ′ ) → [eτ(e) ·⊃ t ⊕P(w′ )(e)](λwλe d buy(e,w)))≡w ′Inert tTT (w 0 ,w ′ ) →t TT ≺ ned buy(e,w ′ )τ(e) ·⊃ t TT(138) specifies that (135) is true iff in every inertia world w ′ of w 0 at the topictime t TT there is a d buy eventuality e whose runtime τ(e) is a superintervalof the topic time t TT such that t TT is not a final part of τ(e) (note that thetemporal relation is the same as before, with IMP). This is illustrated in Figure4.11. In other words, (135) is true iff in the normal course of eventualities afterthe topic time there is an eventuality of Darius buying the garment. This solvesthe problem of the imperfective paradox since it does not commit itself to theexistence of a buying eventuality in the actual world. 16Recall that every inertia world w ′ of the actual world w 0 at the topic timet TT is identical to w 0 up to and including t TT . Therefore, by making a claim16 The question remains why the natural English translation is wanted to buy rather thanwas buying.
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.
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Aspect in Ancient GreekA semantic a
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viNick Asher, David Beaver, the lat
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Contentsix8 Conclusions and discuss
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2 Chapter 1. Introductiongroundbrea
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4 Chapter 1. Introduction(4) µετ
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6 Chapter 1. Introductionimperfecti
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1.3 Organisation of the thesis 9In
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Chapter 2The interpretations of aor
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2.3 Additional interpretations of t
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2.5 The challenge 21scriptions of h
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24 Chapter 3. Aspect in formal sema
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3.2 The perfective-imperfective dis
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160 Chapter 7. Comparison to theori
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172 Chapter 8. Conclusions and disc
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178 Appendix A: The language of Com
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192 Appendix B: Examples spelled ou
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206 Appendix C: List of abbreviatio
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208 Appendix C: List of abbreviatio
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210 References(Eds.), Cross-linguis
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212 ReferencesGrice, P. (1975). Log
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214 ReferencesLemmon, E. J. (1962).
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216 Referencesvan der Sandt, R. (19
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218 References
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220 Samenvatting (Summary in Dutch)
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222 Samenvatting (Summary in Dutch)
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Aspect in Ancient Greek - Nijmegen Centre for Semantics

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