Aspect in Ancient Greek - Nijmegen Centre for Semantics

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90 Chapter 4. An analysis of aoristic and imperfective aspectThe predicate λe i senator(e)is the translation of the predicate I be a senator.(112) states that (111) is true iff the whole eventuality of the speakerbeing a senator is included in the topic time, which is here the whole life ofthe speaker until the moment of utterance.In sum, the complexive interpretation of the aorist comes about due tothe selectional restriction of the aorist operator for bounded predicates whichinduces a coercion operator if the aorist is confronted with an unboundedpredicate. I have shown that the maximality operator can function as such acoercion operator. This operator yields the complexive interpretation that amaximal eventuality satisfying the predicate is included in the topic time, thetime about which we speak.The complexive interpretation is not the only interpretation of the aoristthat arises with unbounded predicates. This combination can also lead to aningressive interpretation. I claim that this interpretation emerges in a waysimilar to the complexive interpretation. It is also the result of a coercionoperator that solves the mismatch between the selectional restriction of theaorist and the aspectual class of the predicate. This time the relevant coercionoperator is an ingressive operator that maps a set of eventualities in the extensionof a predicate, for example John be king, to a set of begin eventualities ofJohn being king. For this purpose I provisionally propose the operator INGRas defined in (113):(113) INGR = λPλe[¬ [t e ′τ(e) = IB(t)τ(e ′ ) = tt ′ e ′′t ⊂ t ′t ′ = τ(e ′′ )⊕P(e ′′ )]⊕P(e ′ )]A begin eventuality of kind P is formalised as an eventuality e whose runtimeτ(e) is the initial bound (IB) of an interval t that is the runtime of an P eventualitye ′ . 6 The negative condition in (113) furthermore guarantees that noP eventuality starts before an eventuality in the extension of INGR(P). Otherwise,e in Figure 4.8 would count as a starting eventuality of P if P is true ofe ′ but also of e ′′ , contrary to what we want.INGR is only a provisional ingressivity operator. For one thing, it assumesthe existence of eventualities without duration, which may not correspond toour idea of eventualities. 7 A further complication is that, intuitively, whether6 The initial bound function (IB) maps an interval (a convex set of times) t on the latestmoment (a singleton set of times) just before t. See also Dowty (1979:140).7 See Kamp (1980) for a discussion of the logic of change. If one does not accept eventu-
4.5 Aorist and coercion: the ingressive and complexive interpretations 91τ(e) τ(e ′ )τ(e ′′ )Figure 4.8: The contribution of the complex condition in (113)something counts as a begin eventuality of some other eventuality is not justa matter of standing in the right temporal relation to it. We wouldn’t saythat a clock striking in Hong Kong counts as a begin eventuality of Beatrixbeing queen in the Netherlands just because the former happens immediatelybefore the latter. Rather there has to be a causal connection between the twoeventualities. A study of causality, however, goes way beyond this dissertation.Therefore, I will work with INGR, which will do for our purposes since itcaptures the temporal facets of the ingressive interpretation.Let’s look at the effect of the ingressive operator when used as a coercionoperator intervening between the aorist operator and a predicate. In (114),the first sentence of (19), δάκρυσε edakruse ‘weep.aor’ has an ingressiveinterpretation (as is clear from the continuation, see (19)). The logical formof the second clause is given in (115) (again, the full derivation is found inAppendix B (221)):(114) νθατα Ξέρξη̋ ωυτνenthauta ho Xerxēs heōutonthen the.nom Xerxes.nom himself.accalities without duration, one may prefer INGR ′ proposed in Bary and Egg (2007)):e 2τ(e 1 ) ⊃≺ τ(e 2 )e 3¬ [τ(e 3 ) ⊃≺ τ(e 1 ) ⊕P(e 3)](i) INGR ′ = λPλe 1 [¬[e 4 e 5e 4 ⊏ e 1τ(e 4 ) ⊃≺ τ(e 5 )e 6¬ [τ(e 6 ) ⊃≺ τ(e 4 ) ⊕P(e 6)]⊕P(e 5 )]⊕P(e 2 )]INGR ′ resembles Dowty’s (1979:144) BECOME. INGR ′ (P) holds of an eventuality e iff e is thelocally smallest eventuality that does not abut on a preceding P eventuality but abuts on afollowing P eventuality. This operator presupposes three-valued logic.
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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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158 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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