Equatives, Measure Phrases and NPIs

Standard semantic accounts of the equative ascribe it an 'at least' meaning, deriving an 'exactly' reading when necessary via scalar implicature. I argue for a particular formulation of this scalar implicature account which considers that (i) equatives license NPIs in their internal arguments, and (ii) equatives whose internal arguments are measure phrases (MPs) are, in contrast to clausal equatives, ambiguous between 'at most' and 'exactly' interpretations. The analysis employs particular assumptions about MPs, scalar implicature and the notion of set complementation to enable 'at least' readings to be sensitive to the direction of a scale, thereby becoming 'at most' readings in certain constructions.

[1]  R. Nouwen.  Two kinds of modified numerals , 2010 .

[2]  Roger Schwarzschild,et al.  The Semantics of Comparatives and Other Degree Constructions , 2008, Lang. Linguistics Compass.

[3]  Edward L. Keenan,et al.  Formal Semantics of Natural Language , 1975 .

[4]  A. Stechow.  COMPARING SEMANTIC THEORIES OF COMPARISON , 1984 .

[5]  Pieter A. M. Seuren.  THE COMPARATIVE REVISITED , 1984 .

[6]  I. Heim.  Degree Operators and Scope , 2000 .

[7]  Jacob Hoeksema,et al.  TO BE CONTINUED: THE STORY OF THE COMPARATIVE , 1984 .

[8]  J. A. W. Kamp,et al.  Formal semantics of Natural Language: Two theories about adjectives , 1975 .

[9]  Jacob Hoeksema,et al.  Negative polarity and the comparative , 1983 .

[10]  Joan Bresnan,et al.  Syntax of the Comparative Clause Construction in English , 1973 .

[11]  Roger Schwarzschild,et al.  The Role of Dimensions in the Syntax of Noun Phrases , 2006 .

[12]  D. Brubeck,et al.  Take five , 1993, Nature.

[13]  Sally McConnell-Ginet,et al.  Comparative constructions in English : a syntactic and semantic analysis , 1973 .

[14]  H. Cartwright.  Amounts and Measures of Amount , 1975 .

[15]  Roger Schwarzschild,et al.  The Grammar of Measurement , 2002 .

[16]  Ewan Klein,et al.  A semantics for positive and comparative adjectives , 1980 .

[17]  Laurence R. Horn,et al.  On the semantic properties of logical operators in english' reproduced by the indiana university lin , 1972 .

[18]  John Nerbonne,et al.  Nominal comparatives and Generalized Quantifiers , 1995, J. Log. Lang. Inf..

[19]  Irene Heim.  On Quantifiers and NPIs in Comparative Clauses , 2008 .

[20]  H. Kamp.  Two theories about adjectives , 2013 .

[21]  Betty. b. Amy,et al.  Antonymy and Evaluativity , 2009 .