David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Dialectica 60 (2):115–133 (2006)
Nominalism (the thesis that there are no abstract objects) faces the task of explaining away the ontological commitments of applied mathematical statements. This paper reviews an argument from the philosophy of logic that focuses on this task and which has been used as an objection to certain specific formulations of nominalism. The argument as it is developed in this paper aims to show that nominalism in general does not have the epistemological advantages its defendants claim it has. I distinguish between two strategies that are available to the nominalist: The Evaluation Programme, which tries to preserve the common truth-values of mathematical statements even if there are no mathematical objects, and Fictionalism, which denies that mathematical sentences have significant truth-values. It is argued that the tenability of both strategies depends on the nominalist’s ability to account for the notion of consequence. This is a problem because the usual meta-logical explications of consequence do themselves quantify over mathematical entities. While nominalists of both varieties may try to appeal to a primitive notion of consequence, or, alternatively, to primitive notions of logical or structural possibilities, such measures are objectionable. Even if we are equipped with a notion of either consequence or possibility that is primitive in the relevant sense, it will not be strong enough to account for the consequence relation required in classical mathematics. These examinations are also useful in assessing the possible counter-intuitive appeal of the argument from the philosophy of logic.
|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 Parsons (2008). Mathematical Thought and its Objects. Cambridge University Press.
Otávio Bueno & Edward N. Zalta (2005). A Nominalist's Dilemma and its Solution. Philosophia Mathematica 13 (3):297-307.
Jaakko Hintikka (2009). A Proof of Nominalism: An Exercise in Successful Reduction in Logic. In A. Hieke & H. Leitgeb (eds.), Reduction - Abstraction - Analysis. Ontos.
Davide Rizza (2010). Mathematical Nominalism and Measurement. Philosophia Mathematica 18 (1):53-73.
Charles Sayward (2005). A Wittgensteinian Philosophy of Mathematics. Logic and Logical Philosophy 15 (2):55-69.
Richard Pettigrew (2012). Indispensability Arguments and Instrumental Nominalism. Review of Symbolic Logic 5 (4):687-709.
Mark Colyvan (2011). Fictionalism in the Philosophy of Mathematics. In E. J. Craig (ed.), Routledge Encyclopedia of Philosophy.
Otávio Bueno (2008). Truth and Proof. Manuscrito 31 (1).
David Liggins (2007). Anti-Nominalism Reconsidered. Philosophical Quarterly 57 (226):104–111.
Alan Baker (2010). No Reservations Required? Defending Anti-Nominalism. Studia Logica 96 (2):127-139.
Added to index2009-01-28
Total downloads15 ( #114,321 of 1,102,047 )
Recent downloads (6 months)4 ( #91,864 of 1,102,047 )
How can I increase my downloads?