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Philosophical Studies

, Volume 162, Issue 3, pp 499–536 | Cite as

Reference to numbers in natural language

  • Friederike Moltmann
Article

Abstract

A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets, eight, as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily treated abstract objects, but rather ‘aspects’ of pluralities of ordinary objects, namely number tropes, a view that in fact appears to have been the Aristotelian view of numbers. Natural language moreover provides support for another view of the ontological status of numbers, on which natural numbers do not act as entities, but rather have the status of plural properties, the meaning of numerals when acting like adjectives. This view matches contemporary approaches in the philosophy of mathematics of what Dummett called the Adjectival Strategy, the view on which number terms in arithmetical sentences are not terms referring to numbers, but rather make contributions to generalizations about ordinary (and possible) objects. It is only with complex expressions somewhat at the periphery of language such as the number eight that reference to pure numbers is permitted.

Keywords

Numbers Abstract objects Tropes Frege Referential terms Adjectival Strategy Abstraction 

Notes

Acknowledgments

I would like to thank the audiences of presentations of earlier versions of this paper at the University of St Andrews, the University of Geneva, Hong Kong University, the IHPST (Paris), Kyoto University, Oxford University, the University of Venice, and the University of St Petersburg for very stimulating discussions. The paper has also greatly benefited from comments by Kit Fine, Matti Eklund, Thomas Hofweber, and Richard Kayne. This research was partly supported by the Chaire d’Excellence Semantic Structure and Ontological Structure (Agence Nationale de la Recherche ANR-06-EXC-012-0).

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.IHPST (Paris1/ENS/CNRS)ParisFrance

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