Mathematics and Reality
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
OUP Oxford (2010)
Mary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focussed on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. Leng, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized.
|Keywords||Mathematics Philosophy Mathematics Philosophy fiction mathématiques|
|Categories||categorize this paper)|
|Call number||QA8.4.L446 2010|
|External links||This entry has no external links. Add one.|
|Through your library||Configure|
References found in this work BETA
No references found.
Citations of this work BETA
Sam Baron (2013). A Truthmaker Indispensability Argument. Synthese 190 (12):2413-2427.
Frederick Kroon (2011). Fictionalism in Metaphysics. Philosophy Compass 6 (11):786-803.
Jessica Carter (2013). Handling Mathematical Objects: Representations and Context. Synthese 190 (17):3983-3999.
Jeffrey Ketland (2011). Nominalistic Adequacy. Proceedings of the Aristotelian Society 111 (2pt2):201-217.
Sam Baron (2013). Optimisation and Mathematical Explanation: Doing the Lévy Walk. Synthese (3):1-21.
Similar books and articles
Susan Vineberg (1996). Confirmation and the Indispensability of Mathematics to Science. Philosophy of Science 63 (3):263.
J. Frans (2012). The Game of Fictional Mathematics: Review of M. Leng, Mathematics and Reality. [REVIEW] Constructivist Foundations 8 (1):126-128.
Phil Corkum (2012). Aristotle on Mathematical Truth. British Journal for the History of Philosophy 20 (6):1057-1076.
Mary Leng (2005). Platonism and Anti-Platonism: Why Worry? International Studies in the Philosophy of Science 19 (1):65 – 84.
Mark Colyvan (2011). Fictionalism in the Philosophy of Mathematics. In E. J. Craig (ed.), Routledge Encyclopedia of Philosophy.
David Liggins (2008). Quine, Putnam, and the 'Quine-Putnam' Indispensability Argument. Erkenntnis 68 (1):113 - 127.
Russell Marcus (2007). Numbers Without Science. Dissertation, The Graduate School and University Center of the City University of New York
Alan Baker (2009). Mathematical Explanation in Science. British Journal for the Philosophy of Science 60 (3):611-633.
Davide Rizza (2010). Mathematical Nominalism and Measurement. Philosophia Mathematica 18 (1):53-73.
Chris Pincock (2007). A Role for Mathematics in the Physical Sciences. Noûs 41 (2):253-275.
Alan Baker (2003). The Indispensability Argument and Multiple Foundations for Mathematics. Philosophical Quarterly 53 (210):49–67.
Janet Folina (1994). Poincaré's Conception of the Objectivity of Mathematics. Philosophia Mathematica 2 (3):202-227.
Elizabeth Freitas (2013). The Mathematical Event: Mapping the Axiomatic and the Problematic in School Mathematics. [REVIEW] Studies in Philosophy and Education 32 (6):581-599.
Sorry, there are not enough data points to plot this chart.
Added to index2012-01-31
Recent downloads (6 months)0
How can I increase my downloads?