David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
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.
Citations of this work BETA
No citations found.
Similar books and articles
Zvonimir Šikić (1996). What Are Numbers? International Studies in the Philosophy of Science 10 (2):159 – 171.
C. Barry Jay (1989). A Note on Natural Numbers Objects in Monoidal Categories. Studia Logica 48 (3):389 - 393.
Jeremy Gwiazda (2012). On Infinite Number and Distance. Constructivist Foundations 7 (2):126-130.
Zvonimir Šikić (1996). What Are Numbers? International Studies in the Philosophy of Science 10 (2):159-171.
S. W. P. Steen (1972). Mathematical Logic with Special Reference to the Natural Numbers. Cambridge [Eng.]University Press.
Eric Steinhart (2002). Why Numbers Are Sets. Synthese 133 (3):343 - 361.
Jeffrey F. Sicha (1970). Counting and the Natural Numbers. Philosophy of Science 37 (3):405-416.
Friederike Moltmann (forthcoming). The Number of Planets, a Number-Referring Term? In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism. Oxford University Press.
Friederike Moltmann (2013). Reference to Numbers in Natural Language. Philosophical Studies 162 (3):499 - 536.
Added to index2009-01-28
Total downloads176 ( #4,775 of 1,413,357 )
Recent downloads (6 months)17 ( #12,594 of 1,413,357 )
How can I increase my downloads?