Aspect in Ancient Greek - Nijmegen Centre for Semantics

42 Chapter 3. Aspect in formal semanticsWe saw that for (60a) (=(44)) to be true, the whole writing eventuality hasto take place within the Sunday, i.e. at the end of the day there has to be aletter. This does not hold for (60b) (=(43)): it is possible that Mary fell ill onSaturday and recovered on Monday. (60c) behaves the same as (60b) in thisrespect. Recall that Kamp et al. ‘explain’ this difference by postulating thatstates and events engage with the location time by means of different temporalrelations. Krifka does not need to stipulate this (see Krifka 1989b:172-173).If we assume that a time-frame adverbial like on Sunday requires that thereis an eventuality in the extension of the predicate whose runtime is includedin the time denoted by the adverbial (independent of the predicate being telicor atelic), the correct interpretations follow directly from the fact that (60a)has a telic (= quantised) predicate, whereas (60b) and (c) have an atelic (=non-quantised) predicate. Since Mary write a letter is quantised, it is impossiblethat an eventuality in the extension of this predicate (e 1 in the upperpart of Figure 3.3) is part of another eventuality in the extension of the predicate(for otherwise this latter eventuality would have a part (viz., the formereventuality) for which the predicate holds likewise, and, hence, the predicatewould not be quantised). That is to say, eventualities in the extension of atelic predicate are always maximal with respect to this predicate. Therefore,from the fact that there is an eventuality in the extension of Mary write aletter whose runtime is included in the time denoted by on Sunday, it followsthat the maximal eventuality is included in this time, which gives the correctinterpretation for (60a).Mary write or Mary be ill, on the other hand, are non-quantised, andtherefore it is possible that eventualities in the extension of these predicates (e 1in the lower part of Figure 3.3) are parts of eventualities of which the predicateholds as well (e 2 or e 3 ). In other words, eventualities in the extension of anatelic predicate do not have to be maximal with respect to this predicate. So,if it is asserted that there is an eventuality in the extension of Mary be illwhose runtime is included in the time denoted by on Sunday, it is left openwhether this is the maximal illness eventuality or that the maximal eventualityincludes the Sunday. This is exactly what we want.In a similar way, this formalisation of telicity can account for the differentialbehaviour between telic and atelic predicates with respect to narrativeprogression. Consider again (53), repeated for convenience as (61):(61) A man entered the White Hart. He was ill. Bill served him a beer.We only have to assume that eventualities are introduced in the order in whichthey occurred to obtain the correct interpretation. Under this assumption, weget that there is an eventuality of the man being ill (e 2 in Figure 3.4) thatfollows his entrance (e 1 ), but this does not exclude the possibility (due to thefact that the predicate be ill is not quantised) that there is also a larger being