David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Hungarian Philosophical Review 54 (4):191-203 (2010)
Hermeneutic fictionalism about mathematics maintains that mathematics is not committed to the existence of abstract objects such as numbers. Mathematical sentences are true, but they should not be construed literally. Numbers are just fictions in terms of which we can conveniently describe things which exist. The paper defends Stephen Yablo’s hermeneutic fictionalism against an objection proposed by John Burgess and Gideon Rosen. The objection, directed against all forms of nominalism, goes as follows. Nominalism can take either a hermeneutic form and claim that mathematics, when rightly understood, is not committed to the existence of abstract objects, or a revolutionary form and claim that mathematics is to be understood literally but is false. The hermeneutic version is said to be untenable because there is no philosophically unbiased linguistic argument to show that mathematics should not be understood literally. Against this I argue that it is wrong to demand that hermeneutic fictionalism should be established solely on the basis of linguistic evidence. In addition, there are reasons to think that hermeneutic fictionalism cannot even be defeated by linguistic arguments alone.
|Keywords||mathematics fictionalism hermeneutics Yablo Burgess Rosen metaphor|
|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
B. Armour-Garb (2011). Understanding and Mathematical Fictionalism. Philosophia Mathematica 19 (3):335-344.
Mary Leng (2005). Revolutionary Fictionalism: A Call to Arms. Philosophia Mathematica 13 (3):277-293.
Jason Stanley (2001). Hermeneutic Fictionalism. Midwest Studies in Philosophy 25 (1):36–71.
Chris John Daly (2008). Fictionalism and the Attitudes. Philosophical Studies 139 (3):423 - 440.
Richard Woodward (2008). Why Modal Fictionalism is Not Self-Defeating. Philosophical Studies 139 (2):273 - 288.
Matti Eklund (2005). Fiction, Indifference, and Ontology. Philosophy and Phenomenological Research 71 (3):557-579.
Phil Corkum (2012). Aristotle on Mathematical Truth. British Journal for the History of Philosophy 20 (6):1057-1076.
David Liggins (2008). Modal Fictionalism and Possible-Worlds Discourse. Philosophical Studies 138 (2):151-60.
Matti Eklund (2005). Fiction, Indifference, and Ontology. Philosophy and Phenomenological Research 71 (3):557–579.
Mark Colyvan (2011). Fictionalism in the Philosophy of Mathematics. In E. J. Craig (ed.), Routledge Encyclopedia of Philosophy.
David Liggins (2014). Abstract Expressionism and the Communication Problem. British Journal for the Philosophy of Science 65 (3):599-620.
Alan Baker (2010). No Reservations Required? Defending Anti-Nominalism. Studia Logica 96 (2):127-139.
Mary Leng (2010). Mathematics and Reality. OUP Oxford.
Added to index2011-08-03
Total downloads70 ( #20,793 of 1,102,836 )
Recent downloads (6 months)8 ( #29,592 of 1,102,836 )
How can I increase my downloads?