Reference to numbers in natural language

Philosophical Studies 162 (3):499 - 536 (2013)
Authors
Friederike Moltmann
Centre National de la Recherche Scientifique
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
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DOI 10.1007/s11098-011-9779-1
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References found in this work BETA

New Work for a Theory of Universals.David Lewis - 1983 - Australasian Journal of Philosophy 61 (4):343-377.
Abstract Objects.Bob Hale - 1988 - Blackwell.

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Citations of this work BETA

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Reply to Critics.Agustín Rayo - 2014 - Inquiry : An Interdisciplinary Journal of Philosophy 57 (4):498-534.
Defusing Easy Arguments for Numbers.Brendan Balcerak Jackson - 2013 - Linguistics and Philosophy 36 (6):447-461.

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