David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophical Studies 162 (3):499 - 536 (2013)
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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References found in this work BETA
David Malet Armstrong (1978). A Theory of Universals. Universals and Scientific Realism Volume Ii. Cambridge University Press.
John Bigelow (1988). The Reality of Numbers: A Physicalist's Philosophy of Mathematics. Oxford University Press.
George Boolos (1984). To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables). Journal of Philosophy 81 (8):430-449.
Berit Brogaard (2007). Number Words and Ontological Commitment. Philosophical Quarterly 57 (226):1–20.
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