Measurement that transcends time : a Lebesgue integral approach to existential sentences

Abstract

In the study of natural language semantics, sentences that assert the existence of entities predicated of by noun phrases have traditionally been analyzed with simple usage of the existential quantifier. In this thesis, I challenge this standard approach through discussion of sentences whose semantics cannot be correctly captured in this manner, and develop an alternative, novel approach that employs Lebesgue integration. The first chapter is centered around Musan's (1995) generalization that states that the temporal (situational) interpretation of a non-presuppositional (i.e. existential) noun phrase is obligatorily dependent on that of the main predicate. It defends the view that the situational dependence is obtained by virtue of being in the scope of some operator and argues that in order to obtain the correct interpretation of plural non-presuppositional noun phrases, the numeral part of non-presuppositional noun phrases must be separated and interpreted above the said operator. The second, and last chapter incorporates the result of the former chapter into Krifka's (1990) analysis of the readings of existential sentences which Krifka terms event-related readings. After we observe that Musan's generalization is extended to the situational interpretation of units of measurement, it becomes evident that a proper semantic analysis of sentences that describe continuous production or consumption of mass entities requires the capability of treating infinitesimally small time intervals.

(cont.) This leads to a new theory where the truth conditions of an existential sentence are expressed as a condition on the value of the Lebesgue integral of an appropriate function defined on situations calculated over the set of all situations whose projections onto the time axis are contained in a context time interval. The theory makes a fundamental connection between temporal (situational) interpretation and existential assertion. Furthermore, our natural intuition of a dichotomy between discrete (telic) events and continuous (atelic) events are captured by the decomposition of the measure used in natural language semantics into modified versions of the counting measure and the Lebesgue measure.