Aspect in Ancient Greek - Nijmegen Centre for Semantics

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62 Chapter 3. Aspect in formal semanticsKleinimperfectiveperfectivet TTt TTτ(e)τ(e)nnalternativeimperfectiveτ(e)n...................................................τ(e ′ )perfectiveτ(e)nFigure 3.6: Two accounts for the different behaviour of perfective and imperfectiveaspect with respect to n.for aspect cross-linguistically: 29(87) INCLUDED = λPλt∃e[τ(e) ⊇ t ∧P(e)]INCLUDES = λPλt∃e[τ(e) ⊆ t ∧P(e)]POST = λPλt∃e[τ(e) ≺ t ∧P(e)]As before, P is a variable for predicates of eventualities. INCLUDED, INCLUDES,and POST take a predicate of eventualities and return a predicate of times.INCLUDES, for example, maps the set of eventualities in the extension of P ontothe set of times that include the runtime of an eventuality of which P holds.Note that here, in contrast to de Swart’s account, aspect rather than tenseintroduces the existential quantifier that binds the eventuality variable. Thetopic time is rendered as a variable t that ends up free in the semantic composition.It gets its value from the assignment function which is assumed to befixed by the context. This is one of the static ways of rendering intersententialanaphora (see footnote 1). Note that whereas in account of Kamp et al. theanaphoric feature of tense is captured in terms of an anaphoric reference point,in von Stechow et al. it’s the topic time (comparable to the location time of29 Paslawska and von Stechow (2003) adopt the same convention as I do in the presentwork by using e as a variable for eventualities and t for times. In Gerö and von Stechow(2003), on the other hand, e is a variable for both events and times (no distinction is madebetween states and times) and τ maps events and times to times (if e is a time, τ is theidentity mapping).
3.2 The perfective-imperfective distinction 63Kamp et al.) that is treated as an anaphor. I will return to this difference inchapter 6 on discourse.Paslawska and von Stechow (2003) claim that the Russian perfective aspectis ambiguous between INCLUDES and POST. The 2003 paper by Gerö and vonStechow is mainly devoted to the perfect in Ancient Greek, but also discussesGreek aoristic and imperfective aspect. It claims that aoristic aspect in thislanguage corresponds to INCLUDES and imperfective to INCLUDED.Thus far the account of von Stechow et al. basically resembles Klein’s withsome lambda-glue for the semantic composition. Things get fuzzy, however,when it comes to aspectual class. After stating that imperfective aspect inAncient Greek corresponds to INCLUDED, Gerö and von Stechow (2003:263)continue as follows:As a consequence, the embedded Vendlerian Aktionsart must havethe subinterval property. If the VP expresses a state or an activity,this raises no problems. But if it is an accomplishment orachievement, we must stativize it by means of semantic operationssuch as the Progressive, Habituality, Iterativity, or Modality (e.g.,Possibility).In other words, they claim that it follows from the semantics of imperfectiveaspect, that is fromINCLUDED, that imperfective aspect can only combine withunbounded predicates (= predicates that have the ‘subinterval property’). 30This argument is not valid, however. At first sight at least, there is no reasonwhy the runtime of an eventuality that makes a bounded predicate true cannotinclude the topic time. The remainder of the text quoted leads to a secondproblem. Gerö and von Stechow speak of Progressive, Habituality, Iterativityand Modality as if these are coercion operators, i.e. operators that solve amismatch. If this were so, we would expect these operators to come intoexistence only in case of an aspectual clash, that is, with bounded predicates.Crucially, we have seen in section 3.2.3 that this is not the case: we find thehabitual interpretation with bounded as well as unbounded predicates. (Recallthat this was a problem for de Swart’s account, as well.)In a similar way Gerö and von Stechow claim that perfective aspect putsrestrictions on the aspectual class of the predicate it combines with. They claimthat it follows from the semantics of perfective aspect, that is from INCLUDES,that it combines only with bounded predicates. Again, it is not immediatelyclear why this should be the case. Why can’t the runtime of an eventualitythat makes an unbounded predicate true be included in the topic time? Theproposed restriction requires more motivation. Nevertheless, in contrast tothe restriction of imperfective aspect, which made the wrong predictions, this30 In the Vendlerian classification state and activity predicates are unbounded and accomplishmentand achievement predicates are bounded.
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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
Page 21 and 22: Chapter 2The interpretations of aor
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112 Chapter 4. An analysis of aoris
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122 Chapter 5. Aspect and performat
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134 Chapter 6. The temporal structu
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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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Aspect in Ancient Greek - Nijmegen Centre for Semantics

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