David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Croatian Journal of Philosophy 5 (1):17-29 (2005)
The aim of this paper is to identify some of the motivations that can be found for taking a realist position concerning mathematical entities and to examine these motivations in the light of a case study in contemporary mathematics. The motivations that are found are as follows: (some) mathematicians are realists, mathematical statements are true, and finally, mathematical statements have a special certainty. These claims are compared with a result in algebraic topology stating that a certain sequence, the so-called Mayer-Vietoris sequence, has different properties when placed in different categories. The conclusion is that the before mentioned motivations should be modified and it is suggested that they could also be explained by a position claiming that mathematical entities are introduced by mathematicians.
|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
Jessica Carter (2013). Handling Mathematical Objects: Representations and Context. Synthese 190 (17):3983-3999.
Mark Colyvan (2011). Fictionalism in the Philosophy of Mathematics. In E. J. Craig (ed.), Routledge Encyclopedia of Philosophy.
Jessica Carter (2004). Ontology and Mathematical Practice. Philosophia Mathematica 12 (3):244-267.
Davide Rizza (2011). Magicicada, Mathematical Explanation and Mathematical Realism. Erkenntnis 74 (1):101-114.
Jessica Carter (2008). Categories for the Working Mathematician: Making the Impossible Possible. Synthese 162 (1):1 - 13.
Pieranna Garavaso (1992). The Argument From Agreement and Mathematical Realism. Journal of Philosophical Research 17:173-187.
William J. Melanson (2011). Reassessing the Epistemological Challenge to Mathematical Platonism. Croatian Journal of Philosophy 11 (3):295-304.
Jessica Carter (2008). Structuralism as a Philosophy of Mathematical Practice. Synthese 163 (2):119 - 131.
Mary Leng (2005). Platonism and Anti-Platonism: Why Worry? International Studies in the Philosophy of Science 19 (1):65 – 84.
Michael Kohlhase & Andrea Kohlhase, Reexamining the MKM Value Proposition: From Math Web Search to Math Web Research.
Penelope Maddy (1990). Realism in Mathematics. Oxford University Prress.
Aidan Lyon (2012). Mathematical Explanations Of Empirical Facts, And Mathematical Realism. Australasian Journal of Philosophy 90 (3):559-578.
Davide Rizza (2010). Mathematical Nominalism and Measurement. Philosophia Mathematica 18 (1):53-73.
D. Schlimm (2013). Axioms in Mathematical Practice. Philosophia Mathematica 21 (1):37-92.
Added to index2011-01-09
Total downloads14 ( #246,719 of 1,793,158 )
Recent downloads (6 months)1 ( #463,411 of 1,793,158 )
How can I increase my downloads?