David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 4 (2):124--47 (1996)
One kind of structuralism holds that mathematics is about structures, conceived as a type of abstract entity. Another denies that it is about any distinctively mathematical entities at all—even abstract structures; rather it gives purely general information about what holds of any collection of entities conforming to the axioms of the theory. Of these, pure structuralism is most plausibly taken to enjoy significant advantages over platonism. But in what appears to be its most plausible—modalised—version, even restricted to elementary arithmetic, it requires defence of a very strong possibility claim: that there could be a completed w-sequence of concrete objects. There are very serious epistemological difficulties in the way of providing the requisite defence.
|Keywords||structuralism logicism mathematics WAYS|
|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
Jessica Carter (2008). Structuralism as a Philosophy of Mathematical Practice. Synthese 163 (2):119 - 131.
Charles Parsons (2004). Structuralism and Metaphysics. Philosophical Quarterly 54 (214):56--77.
Robin Jeshion (2014). Intuiting the Infinite. Philosophical Studies 171 (2):327-349.
Similar books and articles
John Forge (2002). Reflections on Structuralism and Scientific Explanation. Synthese 130 (1):109 - 121.
Christopher Menzel (1990). Structuralism and Conceptual Change in Mathematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990:397 - 401.
Jukka Keränen (2001). The Identity Problem for Realist Structuralism. Philosophia Mathematica 9 (3):308--30.
Julian C. Cole (2010). Mathematical Structuralism Today. Philosophy Compass 5 (8):689-699.
Jacob Busch (2003). What Structures Could Not Be. International Studies in the Philosophy of Science 17 (3):211 – 225.
Geoffrey Hellman (2001). Three Varieties of Mathematical Structuralism. Philosophia Mathematica 9 (2):184-211.
Added to index2009-01-28
Total downloads21 ( #81,620 of 1,101,622 )
Recent downloads (6 months)4 ( #81,941 of 1,101,622 )
How can I increase my downloads?