No reservations required? Defending anti-nominalism
Studia Logica 96 (2):127-139 (2010)
| Abstract | In a 2005 paper, John Burgess and Gideon Rosen offer a new argument against nominalism in the philosophy of mathematics. The argument proceeds from the thesis that mathematics is part of science, and that core existence theorems in mathematics are both accepted by mathematicians and acceptable by mathematical standards. David Liggins (2007) criticizes the argument on the grounds that no adequate interpretation of “acceptable by mathematical standards” can be given which preserves the soundness of the overall argument. In this discussion I offer a defense of the Burgess-Rosen argument against Liggins’s objection. I show how plausible versions of the argument can be constructed based on either of two interpretations of mathematical acceptability, and I locate the argument in the space of contemporary anti-nominalist views | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,664 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesDavid Liggins (2007). Anti-Nominalism Reconsidered. Philosophical Quarterly 57 (226):104–111.
David Liggins (2006). Is There a Good Epistemological Argument Against Platonism? Analysis 66 (290):135–141.
Gábor Forrai (2010). What Mathematicians' Claims Mean : In Defense of Hermeneutic Fictionalism. Hungarian Philosophical Review 54 (4):191-203.
Torsten Wilholt (2006). Think About the Consequences! Nominalism and the Argument From the Philosophy of Logic. Dialectica 60 (2):115–133.
Richard Pettigrew (forthcoming). Indispensability Arguments and Instrumental Nominalism. Review of Symbolic Logic.
Sorin Ioan Bangu (2008). Inference to the Best Explanation and Mathematical Realism. Synthese 160 (1):13-20.
David Liggins (2008). Quine, Putnam, and the 'Quine-Putnam' Indispensability Argument. Erkenntnis 68 (1):113 - 127.
Mark Balaguer (1998). Platonism and Anti-Platonism in Mathematics. Oxford University Press.
Feng Ye (2007). Indispensability Argument and Anti-Realism in Philosophy of Mathematics. Frontiers of Philosophy in China 2 (4):614-628.
Davide Rizza (2010). Mathematical Nominalism and Measurement. Philosophia Mathematica 18 (1):53-73.
Josh Parsons (1999). There is No 'Truthmaker' Argument Against Nominalism. Australasian Journal of Philosophy 77 (3):325 – 334.
Mary Leng (2005). Platonism and Anti-Platonism: Why Worry? International Studies in the Philosophy of Science 19 (1):65 – 84.
Analytics
Monthly downloads |
Added to index2010-11-17Total downloads24 ( #51,571 of 549,010 )Recent downloads (6 months)1 ( #63,261 of 549,010 )How can I increase my downloads? |
My notes
Discussion
