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Bare Numerals and Scalar Implicatures


Correspondence address: Benjamin Spector, CNRS-ENS-EHESS, Institut Jean Nicod, Pavillon jardin, Ecole Normale Supérieure, 29 rue d'Ulm, 75005 Paris, France. E-mail:


Bare numerals present an interesting challenge to formal semantics and pragmatics: they seem to be compatible between various readings (‘at least’, ‘exactly’, and ‘at most’ readings), and the choice of a particular reading seems to depend on complex interactions between contextual factors and linguistic structure. The goal of this article is to present and discuss some of the current approaches to the interpretation of bare numerals in formal semantics and pragmatics. It discusses four approaches to the interpretation of bare numerals, which can be summarized as follows:

  1. In the neo-Gricean view, the basic, literal meaning of numerals amounts to an ‘at least interpretation’, and the ‘exactly n’ reading results from a pragmatic enrichment of the literal reading, i.e. it is accounted for in terms of scalar implicatures.
  2. In the underspecification view, the interpretation of numerals is ‘underspecified’, with the result that they can freely receive the ‘at least’, ‘exactly’, or ‘at most’ reading, depending on which of these three construals is contextually the most relevant.
  3. In the ‘exactly’-only view, the numerals' basic, literal meaning corresponds to the ‘exactly’ reading, and the ‘at least’ and ‘fewer than n’ readings result from the interaction of this literal meaning with background, non-linguistic knowledge.
  4. In the ambiguity view, numerals are ambiguous between two readings, the ‘at least’ and ‘exactly’ readings.

The article argues that in order to account for all the relevant data, one needs to adopt a certain version of the ambiguity view. But it suggests that numerals should not necessarily be thought of as being lexically ambiguous, but rather as giving rise to ambiguities through their interactions with so-called exhaustivity operators. According to such a view, the ambiguities triggered by numerals are to be explained in terms of a non-Gricean theory of scalar implicatures.