David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
In E. J. Craig (ed.), Routledge Encyclopedia of Philosophy (2011)
Fictionalism in the philosophy of mathematics is the view that mathematical statements, such as ‘8+5=13’ and ‘π is irrational’, are to be interpreted at face value and, thus interpreted, are false. Fictionalists are typically driven to reject the truth of such mathematical statements because these statements imply the existence of mathematical entities, and according to fictionalists there are no such entities. Fictionalism is a nominalist (or anti-realist) account of mathematics in that it denies the existence of a realm of abstract mathematical entities. It should be contrasted with mathematical realism (or Platonism) where mathematical statements are taken to be true, and, moreover, are taken to be truths about mathematical entities. Fictionalism should also be contrasted with other nominalist philosophical accounts of mathematics that propose a reinterpretation of mathematical statements, according to which the statements in question are true but no longer about mathematical entities. Fictionalism is thus an error theory of mathematical discourse: at face value mathematical discourse commits us to mathematical entities and although we normally take many of the statements of this discourse to be true, in doing so we are in error (cf. error theories in ethics).
|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
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Charles Chihara (2010). New Directions for Nominalist Philosophers of Mathematics. Synthese 176 (2):153 - 175.
Torsten Wilholt (2006). Think About the Consequences! Nominalism and the Argument From the Philosophy of Logic. Dialectica 60 (2):115–133.
Charles Sayward (2003). Does Scientific Realism Entail Mathematical Realism? Facta Philosophica 5:173-182.
B. Armour-Garb (2011). Understanding and Mathematical Fictionalism. Philosophia Mathematica 19 (3):335-344.
Feng Ye (2007). Indispensability Argument and Anti-Realism in Philosophy of Mathematics. Frontiers of Philosophy in China 2 (4):614-628.
Sarah Hoffman (2004). Kitcher, Ideal Agents, and Fictionalism. Philosophia Mathematica 12 (1):3-17.
Jessica Carter (2005). Motivations for Realism in the Light of Mathematical Practice. Croatian Journal of Philosophy 5 (1):17-29.
Mary Leng (2010). Mathematics and Reality. OUP Oxford.
Phil Corkum (2012). Aristotle on Mathematical Truth. British Journal for the History of Philosophy 20 (6):1057-1076.
Added to index2009-03-04
Total downloads177 ( #19,017 of 1,792,912 )
Recent downloads (6 months)7 ( #119,751 of 1,792,912 )
How can I increase my downloads?