Aspect in Ancient Greek - Nijmegen Centre for Semantics

More documents

Recommendations

Info

98 Chapter 4. An analysis of aoristic and imperfective aspectthe maximality operator.If one assumes with de Swart (1998) and Egg (2005) that a bounded predicaterefers to a set of bounded eventualities and an unbounded predicate toa set of unbounded eventualities, one and the same eventuality cannot be inthe extension of both a bounded and an unbounded predicate. A consequencefor the maximality operator, which is supposed to return bounded predicates,is that no eventuality can be both in the extension of an unbounded predicateP and in the extension of the predicate that results from applying the maximalityoperator to P. In particular, this means that MAX cannot be used asmaximality operator, since the set of eventualities to which MAX(P) refers is asubset of the set of eventualities to which bare P refers.In order to formulate an operator that captures the idea of maximalitybut meets this requirement one often resorts to temporal or spatiotemporalequivalents of eventualities, that is, eventualities that are identical with respectto time or time and space, respectively. The idea is that, whereas it is notpossible for one and the same eventuality to be in the extension of both abounded and an unbounded predicate, it is possible that of two eventualitiesthat are (spatio)temporally identical one is in the extension of a boundedpredicate, and the other in the extension of an unbounded predicate. A naturalcandidate for a maximality operator is then (124), the dynamic equivalent ofEgg’s (2005:95) operator:e ′τ(e) = τ(e ′ )(124) MAX ′ = λPλe[e ′′e ′ ⊏ e ′′ → ¬ [ ⊕P(e ′′ )]⊕P(e ′ )]Here τ is the function that maps eventualities on their (spatio)temporal trace.Note that e is in the extension of MAX ′ (P) and e ′ , its (spatio)temporal equivalent,in that of P.There are two problems with MAX ′ , however, one more serious than theother. First, MAX ′ , in contrast to MAX, is not the identity mapping for boundedpredicates. It is possible that for a bounded predicate P eventualities in theextension ofMAX(P) are not in the extension ofP. This is not too problematic formy enterprise: since the maximality operator functions as a coercion operatorthat comes into play only with unbounded predicates, its effect with boundedpredicates is of no importance. What is more problematic is that MAX ′ , againin contrast to MAX, need not return a bounded predicate.MAX ′ would behave the same asMAX in these two respects if we would assumethat eventualities that coincide spatiotemporally are identical. Note, however,
4.6 Aspectual classes as properties of predicates 99that this is not a way out for those theories which assume that bounded predicatesrefer to a set of bounded eventualities and unbounded ones to a set ofunbounded eventualities (for if two eventualities are identical, they cannot bein different sets). Crucially, it are exactly these theories that need to workwith spatiotemporal equivalents in the first place.Given that this problem is not restricted to the maximality operator, butis observed with many operators that cause a shift in aspectual class, 9 I don’tmake an ontological distinction between bounded and unbounded eventualities,only between bounded and unbounded predicates.As a consequence, on my account no type-theoretic or sortal mismatch isinvolved in the coercion phenomena discussed in this chapter. In this respect Ideviate from de Swart (1998) and Egg (2005), who do model coercion in termsof such a mismatch. In de Swart’s account, the passé simple, for example,requires an input of type 〈l,t〉, with l the type for bounded eventualities andt the type of truth values, that is, a function from bounded eventualities totruth values, or, in other words, a property of bounded eventualities. If theinput candidate is not of this type, coercion comes into play. In my account, onthe other hand, only a mismatch between properties of predicates plays a role.The aorist operator requires predicates with the property of boundedness, andif the predicate does not have this property, we get coercion.One way to explicitly force the mismatch is by incorporating the selectionrestriction of the aorist in its semantics. The result is (125):(125) AOR λPλt[eτ(e) ⊆ t⊕P(e) ⊕ BD(P)] =λPλt[eτ(e) ⊆ t ⊕P(e) ⊕ [e ′ e ′′e ′′ ⊏ e ′ ⊕P(e ′′ )] → ¬ [ ⊕P(e ′′ )]]Now, if P is an unbounded predicate, we get a contradiction: the sentenceDRS, and therefore the sentence it represents, is not true in any model (and afortiori, the DRS that results from merging the sentence DRS with the contextDRS will not be true in any model). Nevertheless, the hearer is willing to makesense of the sentence and reinterprets the predicate as a bounded predicate (byinterpreting it as maximal or as referring to the beginning).It may be more intuitive, however, to assume a short-cut here. Ratherthan completing the whole interpretation process, including the merge of sentenceand context DRS, the hearer detects the inconsistency online. This idea9 For example Egg’s (2005:95) progressive operator (96) in section 3.3.3.
Page 3:
Aspect in Ancient GreekA semantic a
Page 6 and 7:
viNick Asher, David Beaver, the lat
Page 9:
Contentsix8 Conclusions and discuss
Page 12 and 13:
2 Chapter 1. Introductiongroundbrea
Page 14 and 15:
4 Chapter 1. Introduction(4) µετ
Page 16 and 17:
6 Chapter 1. Introductionimperfecti
Page 19 and 20:
1.3 Organisation of the thesis 9In
Page 21 and 22:
Chapter 2The interpretations of aor
Page 23 and 24:
2.3 Additional interpretations of t
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Page 31:
2.5 The challenge 21scriptions of h
Page 34 and 35:
24 Chapter 3. Aspect in formal sema
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
Page 52:
Page 57 and 58: 3.2 The perfective-imperfective dis
Page 77 and 78: 3.3 Aspectual coercion 673.3.1 Aspe
Page 79 and 80: 3.3 Aspectual coercion 69bials ((88
Page 81 and 82: 3.3 Aspectual coercion 71the term c
Page 83 and 84: 3.3 Aspectual coercion 73in the ext
Page 86 and 87: 76 Chapter 4. An analysis of aorist
Page 110 and 111: 100 Chapter 4. An analysis of aoris
Page 132 and 133: 122 Chapter 5. Aspect and performat
Page 144 and 145: 134 Chapter 6. The temporal structu
Page 158 and 159:
148 Chapter 6. The temporal structu
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
158 Chapter 7. Comparison to theori
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
172 Chapter 8. Conclusions and disc
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
178 Appendix A: The language of Com
Page 190 and 191:
Page 192 and 193:
Page 194 and 195:
Page 196 and 197:
Page 198 and 199:
Page 200 and 201:
Page 202 and 203:
192 Appendix B: Examples spelled ou
Page 204 and 205:
Page 206 and 207:
Page 208 and 209:
Page 210 and 211:
Page 212 and 213:
Page 214 and 215:
Page 216 and 217:
206 Appendix C: List of abbreviatio
Page 218 and 219:
208 Appendix C: List of abbreviatio
Page 220 and 221:
210 References(Eds.), Cross-linguis
Page 222 and 223:
212 ReferencesGrice, P. (1975). Log
Page 224 and 225:
214 ReferencesLemmon, E. J. (1962).
Page 226 and 227:
216 Referencesvan der Sandt, R. (19
Page 228 and 229:
218 References
Page 230 and 231:
220 Samenvatting (Summary in Dutch)
Page 232 and 233:
222 Samenvatting (Summary in Dutch)
show all

Aspect in Ancient Greek - Nijmegen Centre for Semantics

Create successful ePaper yourself

Delete template?

Save as template?