Aspect in Ancient Greek - Nijmegen Centre for Semantics

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114 Chapter 4. An analysis of aoristic and imperfective aspectt TT..........................................................................τ(e)tτ(e ′ )................................Figure 4.13: Stacking imperfectivity and progressivity according to Gerö andvon Stechow (2003)We can solve this problem by changing the temporal relations of the progressiveas in (142):(142) PROG ′′ = λPλe w ′Inert τ(e) (w 0 ,w ′ ) → [ e ′τ(e ′ ) ·⊃ τ(e) ⊕P(w′ )(e ′ )]As Figure 4.14 shows, we now get the correct result that the complete crossingthe street eventuality e ′ includes the topic time. This captures the ‘goingon’ interpretation. Furthermore, the analysis is not subject to the imperfectiveparadox, since it does not commit itself to the existence of the completeeventuality in the actual world.t TT..........................................................................τ(e)τ(e ′ )................................Figure 4.14: Adapted version of 4.13The difference between my account and this account is the following. WhereasI do not assume an aspectual class restriction for imperfective aspect andmodify the semantics of imperfective aspect itself to avoid the imperfectiveparadox, Gerö en von Stechow do assume such a restriction and introduce acoercion operator between the imperfective operator and a bounded predicate
4.9 The conative and likelihood interpretations 115to avoid the paradox. Why is it that I prefer my account over theirs?First, it is not clear in Gerö and von Stechow’s account why imperfectiveaspect would be restricted to unbounded predicates, a problem already mentionedin section 3.2.4. They state that this restriction follows from the factthat with imperfective aspect the topic time is included in the eventuality time,but this is not true. It is clear that the restriction to unbounded predicatesis useful for avoiding the imperfective paradox, but without an independentmotivation this restriction is quite ad hoc.Second, in my account the difference between bounded and unboundedpredicates with respect to the imperfective paradox follows from the semanticsof the imperfective itself. The imperfective operator IMP ′ suffices on itsown to account for the fact that (133a) entails (133b), while (134a) does notentail (134b). Gerö and von Stechow’s account, on the other hand, impliesthat something different is going on in (133a) than in (134a), as a coercionoperator is involved in the latter but not the former. Note that apart fromthe imperfective paradox there is no motivation for assuming this coercion operator.We end up with two temporal relations that both intend to capturethe same idea, viz. that an eventuality of the type described by the predicateis going on, whereas IMP ′ shows that we can do with one. 20 We could try toformulate a progressive operator that does not introduce temporal relations ofits own, but it is not clear to me what this operator should look like.20 Although this stacking of imperfectivity and progressitivity is found most explicitly inGerö and von Stechow (2003), we find a similar idea in Kamp and Reyle (1993), de Swart(1998), and Kamp, van Genabith, and Reyle (2005). Let me illustrate it with the lastaccount. The logical form they assign to (i) is roughly (ii) (Kamp et al. 2005:78):(i)(ii)A man was pulling his gun.n s t 1 t 2PROG(λe m pull(e))(s)τ(s) = t 1t 1 ⊇ t 2t 2 ≺ nThey don’t specify what this PROG is, aware of the problem of the imperfective paradox, butit probably contains some temporal relation. (ii) specifies that the runtime of progressivestate t 1 includes the location time (≈ topic time) t 2 . But what reasons do we have to thinkthat this is the correct temporal relation? The natural language sentence (i) seems to giveus only the information that the complete pulling event, rather than the progressive state,includes this time. It gives no information about the relation between the progressive stateand the location time. Since we already have a progressive operator, the inclusion relationbetween eventuality time and location time is superfluous. The source of the problem isthe same as in Gerö and von Stechow (2003): both accounts want to stick to the idea thataspect has to do with the temporal relation between eventuality time and topic time (eitherdirect, as in von Stechow et al., or indirect via aspectual classes, as in Kamp et al.), butwant to avoid the imperfective paradox.
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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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164 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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