The universal density of measurement

The notion of measurement plays a central role in human cognition. We measure people’s height, the weight of physical objects, the length of stretches of time, or the size of various collections of individuals. Measurements of height, weight, and the like are commonly thought of as mappings between objects and dense scales, while measurements of collections of individuals, as implemented for instance in counting, are assumed to involve discrete scales. It is also commonly assumed that natural language makes use of both types of scales and subsequently distinguishes between two types of measurements. This paper argues against the latter assumption. It argues that natural language semantics treats all measurements uniformly as mappings from objects (individuals or collections of individuals) to dense scales, hence the Universal Density of Measurement (UDM). If the arguments are successful, there are a variety of consequences for semantics and pragmatics, and more generally for the place of the linguistic system within an overall architecture of cognition.

[1]  Godehard Link.  The Logical Analysis of Plurals and Mass Terms: A Lattice‐theoretical Approach , 2008 .

[2]  M. Krifka.  Be brief and vague! And how Bidirectional Optimality Theory allows for verbosity and precision , 2002 .

[3]  Alice G. B. ter Meulen,et al.  The representation of (in)definiteness , 1989 .

[4]  J. Benthem,et al.  Generalized Quantifiers in Natural Language , 1985 .

[5]  P. Unger,et al.  Semantics and Philosophy , 1974 .

[6]  G. Chierchia,et al.  Broaden Your Views: Implicatures of Domain Widening and the Logicality of Language , 2006, Linguistic Inquiry.

[7]  J. Barwise,et al.  Generalized quantifiers and natural language , 1981 .

[8]  Alec Marantz,et al.  A late note on late insertion , 1994 .

[9]  Jeroen Groenendijk,et al.  On the semantics of questions and the pragmatics of answers , 1984 .

[10]  Yo Matsumoto.  The conversational condition on horn scales , 1995 .

[11]  H. Kamp,et al.  Prototype theory and compositionality , 1995, Cognition.

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

[13]  Michael Bennett,et al.  Questions in Montague grammar , 1979 .

[14]  J. Bennett.  A Philosophical Guide to Conditionals , 2003 .

[15]  J. Frampton,et al.  RELATIVIZED MINIMALITY, A REVIEW , 1991 .

[16]  Utpal Lahiri.  Focus and Negative Polarity in Hindi , 1998 .

[17]  Manfred Krifka,et al.  The Semantics and Pragmatics of Weak and Strong Polarity Items in Assertions , 1994 .

[18]  Benjamin Spector.  Aspects de la pragmatique des opérateurs logiques , 2006 .

[19]  Katrin Schulz,et al.  Exhaustive Interpretation of Complex Sentences , 2004, J. Log. Lang. Inf..

[20]  Noam Chomsky.  Language and Problems of Knowledge , 1987 .

[21]  Christopher Kennedy,et al.  Polar Opposition and the Ontology of ‘Degrees’ , 2001 .

[22]  David R. Dowty,et al.  Word Meaning and Montague Grammar , 1979 .

[23]  Paula Menéndez-Benito,et al.  The Grammar of Choice , 2007 .

[24]  Hagit Borer,et al.  Structuring Sense Volume 2: The Normal Course of Events , 2005 .

[25]  Anna Szabolcsi,et al.  Weak islands and an algebraic semantics for scope taking , 1993 .

[26]  L. Rizzi.  Relativized Minimality Effects , 2008 .

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

[28]  Hans-Georg Obenauer.  ON THE IDENTIFICATION OF EMPTY CATEGORIES , 1985 .

[29]  Kai-Uwe Von Fintel,et al.  Restrictions on quantifier domains , 1994 .

[30]  M. Krifka,et al.  The Semantics and Pragmatics of Polarity Items , 2003 .

[31]  Utpal Lahiri,et al.  Questions and Answers in Embedded Contexts , 2002 .

[32]  Ken Turner,et al.  The semantics/pragmatics interface from different points of view , 1999 .

[33]  Irene Heim,et al.  Semantics in generative grammar , 1998 .

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

[35]  James R. Hurford,et al.  Language and Number: The Emergence of a Cognitive System , 1987 .

[36]  Manfred Pinkal.  Die Semantik von Satzkomparativen , 1989 .

[37]  S. Kuno,et al.  Remarks on negative Islands , 1997 .

[38]  David R. Dowty.  Word Meaning and Montague Grammar: The Semantics of Verbs and Times in Generative Semantics and in M , 1979 .

[39]  Gennaro Chierchia,et al.  Topics in the syntax and semantics of infinitives and gerunds : a dissertation , 1984 .

[40]  Elena Guerzoni,et al.  Even-NPIs in YES/NO Questions , 2004 .

[41]  Alessandro Zucchi.  The ingredients of definiteness and the definiteness effect , 1995 .

[42]  Robert Stalnaker.  Context And Content , 1999 .

[43]  A. Bonomi,et al.  Only: Association with focus in event semantics , 1993 .

[44]  M. Krifka.  At least some Determiners aren ’ t Determiners , 1999 .

[45]  Gennaro Chierchia,et al.  Meaning and grammar , 1990 .

[46]  Johan van Benthem,et al.  Semantic Parallels in Natural Language and Computation , 1989 .

[47]  Anthony S. Kroch,et al.  Amount Quantification, Referentiality, and Long Wh-Movement , 1998 .

[48]  Maarten de Rijke,et al.  Logic, Language, and Information , 1997, Relational Methods in Computer Science.

[49]  Dag Westerståhl,et al.  Determiners and Context Sets , 1985 .

[50]  H. Rullmann,et al.  A Flexible Approach to Exhaustivity in Questions , 1999 .

[51]  Hotze Rullmann,et al.  Maximality in the semantics of wh -constructions , 1995 .

[52]  S. Dehaene,et al.  Exact and Approximate Arithmetic in an Amazonian Indigene Group , 2004, Science.

[53]  P. Gordon.  Numerical Cognition Without Words: Evidence from Amazonia , 2004, Science.

[54]  A. Kratzer.  An investigation of the lumps of thought , 1989 .

[55]  Bart Geurts,et al.  The semantics of scalar modifiers , 2007 .

[56]  Adriana Belletti,et al.  Structures and beyond , 2004 .