David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 16 (3):310-332 (2008)
Philosophers of mathematics agree that the only interpretation of arithmetic that takes that discourse at 'face value' is one on which the expressions 'N', '0', '1', '+', and 'x' are treated as proper names. I argue that the interpretation on which these expressions are treated as akin to free variables has an equal claim to be the default interpretation of arithmetic. I show that no purely syntactic test can distinguish proper names from free variables, and I observe that any semantic test that can must beg the question. I draw the same conclusion concerning areas of mathematics beyond arithmetic. This paper is a greatly extended version of my response to Stewart Shapiro's paper in the conference 'Structuralism in physics and mathematics' held in Bristol on 2–3 December, 2006.
|Keywords||No keywords specified (fix it)|
|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
Fraser MacBride (2003). Speaking with Shadows: A Study of Neo-Logicism. British Journal for the Philosophy of Science 54 (1):103-163.
Citations of this work BETA
Francesca Boccuni (2013). Plural Logicism. Erkenntnis 78 (5):1051-1067.
Stewart Shapiro (2012). An “I” for an I: Singular Terms, Uniqueness, and Reference. Review of Symbolic Logic 5 (3):380-415.
Similar books and articles
H. Jerome Keisler (2006). Nonstandard Arithmetic and Reverse Mathematics. Bulletin of Symbolic Logic 12 (1):100-125.
Christopher Pincock (2009). Towards a Philosophy of Applied Mathematics. In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave Macmillan.
Sergei Tupailo (2001). Realization of Analysis Into Explicit Mathematics. Journal of Symbolic Logic 66 (4):1848-1864.
Stewart Shapiro (2000). Thinking About Mathematics: The Philosophy of Mathematics. Oxford University Press.
Simon Friederich (2010). Structuralism and Meta-Mathematics. Erkenntnis 73 (1):67 - 81.
Mark Balaguer (1998). Platonism and Anti-Platonism in Mathematics. Oxford University Press.
Edward N. Zalta (2007). Reflections on Mathematics. In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
Stewart Shapiro (2005). Categories, Structures, and the Frege-Hilbert Controversy: The Status of Meta-Mathematics. Philosophia Mathematica 13 (1):61-77.
L. Luce (1991). Literalism and the Applicability of Arithmetic. British Journal for the Philosophy of Science 42 (4):469-489.
James Franklin (2011). Aristotelianism in the Philosophy of Mathematics. Studia Neoaristotelica 8 (1):3-15.
Added to index2009-01-28
Total downloads50 ( #39,605 of 1,679,399 )
Recent downloads (6 months)1 ( #183,003 of 1,679,399 )
How can I increase my downloads?