Aspect in Ancient Greek - Nijmegen Centre for Semantics

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78 Chapter 4. An analysis of aoristic and imperfective aspectfor the data I am concerned with. If an ontological distinction would prove tomake things easier, I would not hesitate to adopt it, but I don’t think it would.On the contrary, and this is my main objection, it makes the formulation ofoperators that cause a shift in aspectual class much more complicated, as wewill see in section 4.6. For these reasons, I will restrict the distinction to thelevel of predicates.As a consequence of restricting aspectual class distinctions to the level ofthe predicate, a mismatch in aspectual class cannot be formalised as a typetheoreticor sortal clash in the way de Swart (1998) and Egg (2005) implementit. Instead we need an alternative way to do this, which I will present in section4.6.4.3 Completed vs. going on: the completiveand processual interpretationsThe evaluation of one-component theories of aspect (theories in which the primarycontribution of aspect is a change in aspectual class) in section 3.2.3 hasdemonstrated that such theories, when adapted to the Ancient Greek data,end up with a vacuous semantics for aoristic and imperfective aspect (on acoercion approach) or are forced to postulate an ambiguity for the two (ona non-coercion approach). Therefore, I propose a two-component theory ofaspect, that is, a theory in which the primary contribution of grammaticalaspect is something different from a change in aspectual class. I follow Klein’s(1994) proposal in positing that grammatical aspect concerns the relation betweenthe time of the eventuality and the topic time. More precisely, I adopta semantics for imperfective and aoristic aspect that is very similar to vonStechow et al.’s INCLUDED and INCLUDES (see (87)), respectively (see below forthe differences). Formulated in terms of DRSs I propose:(101) a. IMP λPλt[b. AOR λPλt[eτ(e) ·⊃ t ⊕P(e)]eτ(e) ⊆ t ⊕P(e)]= IMP= AORThree remarks on the notation. First, as one can see, IMP andIMP are not usedinterchangeably. IMP stands for the imperfective markers (morphemes) usedin natural languages, whereas IMP abbreviates the translation of IMP into ourformal language. Second, ‘τ(e) ·⊃ t’ reads as ‘t is a non-final subset of τ(e)’(see Appendix C.3). Third, whereas it is easiest to keep thinking of e and t asvariables over eventualities and times, respectively, they are actually constants
4.3 Completed vs. going on: the completive and processual interpretations 79for registers for eventualities and times, respectively. This is a consequence ofthe way in which DRT and typed lambda-calculus are fused, following Muskens(1996). For the same reason, P is a variable over dynamic rather than normalstatic predicates of eventualities. The reader is however advised not to paytoo much attention to this as I will continue speaking of e as a variable overeventualities etc. myself as well throughout this thesis, except for Appendix Awhere I provide the formal system.As for the content of (101), the semantics of imperfective and aoristic aspectmaps properties of eventualities onto properties of times. More in particular,the semantics of the imperfective maps properties of eventualities P onto theproperty of being a non-final part of the runtime of an eventuality of which Pholds. Similarly, the semantics of the aorist maps properties of eventualitiesP onto the set of times that include the runtime of an eventuality of which Pholds. After combining (101) with the semantic contribution of tense, the timeto which the eventuality time stands in the specified temporal relation endsup to be the topic time, the time about which we speak (we will see how thisworks in due course). Thus, grammatical aspect concerns the relation betweenthe time of the eventuality and the topic time. A graphic representation of thesemantic contribution of grammatical aspect is given in Figure 4.1.aoristimperfectivetopic timeeventuality time‘completed’‘going on’Figure 4.1: The semantics of aorist and imperfectiveThis semantics of aspect directly yields what Ancient Greek grammarsconsider the basic opposition between imperfective and aoristic aspect: goingon versus completed (see section 2.1). Imperfective aspect indicates thatthe eventuality is going on at the moment about which we speak, that is, theeventuality’s run time includes the topic time. Aoristic aspect, by contrast, indicatesthat the eventuality takes place within the time about which we speak:its runtime is included in the topic time. 1 I labeled these the processual inter-1 Note that both the words ‘completed’ and ‘complete’ can be used to describe the meaningof the aorist on my account. Both ‘the eventuality is completed within the topic time’and ‘the complete eventuality lies within the topic time’ are in accordance with my pro-
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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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26 Chapter 3. Aspect in formal sema
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128 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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