Aspect in Ancient Greek - Nijmegen Centre for Semantics

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.