Maximality in the Semantics of Modified Numerals
Brian Buccola
July 2015
 

This thesis develops a new theory of the semantics of modified numerals—a central topic in current linguistic research. The theory arises from a detailed investigation of a new paradigm in the interpretation of modified numerals. Specifically, numerical expressions like "less than n" and "between m and n" sometimes convey maximality, other times minimality, and still other times neither, depending on their linguistic environment. For instance, the sentence "Between five and ten guests arrived late" indicates that the maximum (or total) number of guests who arrived late is between five and ten, whereas the sentence "Between 20 and 30 potatoes can fill that sack" indicates that the minimum number of potatoes that can fill that sack is between 20 and 30. Conversely, the sentence "Between three and five students lifted the piano together" conveys neither maximality nor minimality: it is compatible with, say, a group of two students or a group of seven students having lifted the piano together, just as long as at least one group of three to five students did so too. Building on previous works that deal with similar 'flips' between maximality and minimality (Beck and Rullmann 1999; von Fintel, Fox, and Iatridou 2014), I propose that the lexical semantics of certain numeral modifiers involves an 'informativity'-based maximality component, where the ordering of numbers that maximality operates on is based on how informative they are relative to some property of numbers. The crux of the theory is that, for a number to be maximally informative, sometimes it must be the largest, other times the smallest, and still other times it need not be either. This move to maximal informativity results in a theory that captures the full range of data discussed in the thesis. Along the way, I also propose and examine in detail two fairly standard (but ultimately unsuccessful) analyses of a subset of the paradigmatic data (maximal and non-maximal readings), where maximality is of the 'standard' kind, i.e. based on the natural ordering of numbers. The availability of maximal and non-maximal readings is captured either by flexible scope (on one account) or by the optional presence of the maximality component (on the other account). Both theories, however, face overgeneration problems, and neither theory is able to derive genuinely 'minimal' readings.
Format: [ pdf ]
Reference: lingbuzz/003039
(please use that when you cite this article)
Published in: Ph.D. thesis, McGill University
keywords: quantification, plurality, numerals, modified numerals, monotonicity, distributivity, collectivity, genericity, mereology, semantics
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