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The universal density of measurement

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Abstract

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.

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Authors and Affiliations

  1. Department of Linguistics and Philosophy, MIT, 77 Massachusetts Avenue Bldg. 32-D808, Cambridge, MA, 02139, USA

    Danny Fox

  2. Department of Linguistics and Cognitive Science, MIT and Pomana College, 550 Harvard Ave., Mason Hall 110B, Pomona College, Claremont, CA, 91711, USA

    Martin Hackl

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  1. Danny Fox
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  2. Martin Hackl
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Correspondence to Martin Hackl.

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Fox, D., Hackl, M. The universal density of measurement. Linguistics & Philosophy 29, 537–586 (2006). https://doi.org/10.1007/s10988-006-9004-4

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