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

Author(s)
Shimada, Junri
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Alternative title
Lebesgue integral approach to existential sentences
Other Contributors
Massachusetts Institute of Technology. Dept. of Linguistics and Philosophy.
Advisor
Danny Fox and Irene Heim.
Terms of use
M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582
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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.
 
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 2009.
 
Cataloged from PDF version of thesis.
 
Includes bibliographical references (p. 165-168).
 
Date issued
2009
URI
http://hdl.handle.net/1721.1/55184
Department
Massachusetts Institute of Technology. Department of Linguistics and Philosophy
Publisher
Massachusetts Institute of Technology
Keywords
Linguistics and Philosophy.

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