David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
International Studies in the Philosophy of Science 19 (1):65 – 84 (2005)
This paper argues that it is scientific realists who should be most concerned about the issue of Platonism and anti-Platonism in mathematics. If one is merely interested in accounting for the practice of pure mathematics, it is unlikely that a story about the ontology of mathematical theories will be essential to such an account. The question of mathematical ontology comes to the fore, however, once one considers our scientific theories. Given that those theories include amongst their laws assertions that imply the existence of mathematical objects, scientific realism, when construed as a claim about the truth or approximate truth of our scientific theories, implies mathematical Platonism. However, a standard argument for scientific realism, the 'no miracles' argument, falls short of establishing mathematical Platonism. As a result, this argument cannot establish scientific realism as it is usually defined, but only some weaker position. Scientific 'realists' should therefore either redefine their position as a claim about the existence of unobservable physical objects, or alternatively look for an argument for their position that does establish mathematical Platonism.
|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
Russell Marcus (2013). Intrinsic Explanation and Field's Dispensabilist Strategy. International Journal of Philosophical Studies 21 (2):163 - 183.
Stathis Psillos (2010). Scientific Realism: Between Platonism and Nominalism. Philosophy of Science 77 (5):947-958.
Similar books and articles
Mark Balaguer (1995). A Platonist Epistemology. Synthese 103 (3):303 - 325.
Colin Cheyne (1999). Problems with Profligate Platonism. Philosophia Mathematica 7 (2):164-177.
Greg Restall (2003). Just What is Full-Blooded Platonism? Philosophia Mathematica 11 (1):82--91.
David Liggins (2006). Is There a Good Epistemological Argument Against Platonism? Analysis 66 (290):135–141.
Øystein Linnebo (2009). Platonism in the Philosophy of Mathematics. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.
Øystein Linnebo (2008). The Nature of Mathematical Objects. In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. 205--219.
Mark Balaguer (1998). Platonism and Anti-Platonism in Mathematics. Oxford University Press.
Added to index2009-01-28
Total downloads70 ( #24,160 of 1,413,138 )
Recent downloads (6 months)6 ( #34,975 of 1,413,138 )
How can I increase my downloads?