David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Croatian Journal of Philosophy 11 (3):295-304 (2011)
In his Realism, Mathematics, and Modality, Hartry Field attempted to revitalize the epistemological case against mathematical platontism by challenging mathematical platonists to explain how we could be epistemically reliable with regard to the abstract objects of mathematics. Field suggested that the seeming impossibility of providing such an explanation tends to undermine belief in the existence of abstract mathematical objects regardless of whatever reason we have for believing in their existence. After more than two decades, Field’s explanatory challenge remains among the best available motivations for mathematical nominalism. This paper argues that Field’s explanatory challenge misidentifies the central epistemological problem facing mathematical platonism. Contrary to Field’s suggestion, inexplicability of epistemic reliability does not act as an epistemic defeater. The failure to explain our epistemic reliability with respect to the existence and properties of abstract mathematical objects is simply one aspect of a broader failure to establish that we are epistemically reliable with respect to abstract mathematical objects in the first place. Ultimately, it is this broader failure that is the source of mathematical platonism’s real epistemological problems
|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
Øystein Linnebo (2009). Platonism in the Philosophy of Mathematics. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.
Izabela Bondecka-Krzykowska (2004). Strukturalizm jako alternatywa dla platonizmu w filozofii matematyki. Filozofia Nauki 1.
Justin Clarke-Doane (2012). Morality and Mathematics: The Evolutionary Challenge. Ethics 122 (2):313-340.
Øystein Linnebo (2006). Epistemological Challenges to Mathematical Platonism. Philosophical Studies 129 (3):545-574.
Mary Leng (2005). Platonism and Anti-Platonism: Why Worry? International Studies in the Philosophy of Science 19 (1):65 – 84.
Clevis Headley (1997). Platonism and Metaphor in the Texts of Mathematics: GÃ¶Del and Frege on Mathematical Knowledge. [REVIEW] Man and World 30 (4):453-481.
Mark McEvoy (2012). Platonism and the 'Epistemic Role Puzzle'. Philosophia Mathematica 20 (3):289-304.
David Liggins (2006). Is There a Good Epistemological Argument Against Platonism? Analysis 66 (290):135–141.
Mark Balaguer (1995). A Platonist Epistemology. Synthese 103 (3):303 - 325.
Colin Cheyne (1999). Problems with Profligate Platonism. Philosophia Mathematica 7 (2):164-177.
Mark Balaguer (1998). Non-Uniqueness as a Non-Problem. Philosophia Mathematica 6 (1):63-84.
Charles Parsons (2008). Mathematical Thought and its Objects. Cambridge University Press.
Mark Balaguer (1994). Against (Maddian) Naturalized Platonism. Philosophia Mathematica 2 (2):97-108.
Added to index2012-09-18
Total downloads16 ( #116,466 of 1,410,108 )
Recent downloads (6 months)2 ( #107,970 of 1,410,108 )
How can I increase my downloads?