Pluralism in Mathematics: A New Position in Philosophy of Mathematics

Dordrecht, Netherland: Springer (2013)
  Copy   BIBTEX

Abstract

The pluralist sheds the more traditional ideas of truth and ontology. This is dangerous, because it threatens instability of the theory. To lend stability to his philosophy, the pluralist trades truth and ontology for rigour and other ‘fixtures’. Fixtures are the steady goal posts. They are the parts of a theory that stay fixed across a pair of theories, and allow us to make translations and comparisons. They can ultimately be moved, but we tend to keep them fixed temporarily. Apart from considering rigour of proof as a fixture, I discuss fixed models, invariant notions and fixed information about objects across theories. There are other fixtures, but it is enough to start with these

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,322

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Realism in mathematics.Penelope Maddy - 1990 - New York: Oxford University Prress.
Naturalism in mathematics.Penelope Maddy - 1997 - New York: Oxford University Press.
Mathematics without truth (a reply to Maddy).Hartry Field - 1990 - Pacific Philosophical Quarterly 71 (3):206-222.

Analytics

Added to PP
2015-04-28

Downloads
52 (#299,008)

6 months
8 (#352,434)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Michele Friend
George Washington University

Citations of this work

Maddy On The Multiverse.Claudio Ternullo - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Berlin: Springer Verlag. pp. 43-78.
Definition in mathematics.Carlo Cellucci - 2018 - European Journal for Philosophy of Science 8 (3):605-629.

View all 14 citations / Add more citations

References found in this work

Two Dogmas of Empiricism.W. Quine - 1951 - [Longmans, Green].
Truth and objectivity.Crispin Wright - 1992 - Cambridge, Mass.: Harvard University Press.
The logical basis of metaphysics.Michael Dummett - 1991 - Cambridge, Mass.: Harvard University Press.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
The foundations of arithmetic.Gottlob Frege - 1884/1950 - Evanston, Ill.,: Northwestern University Press.

View all 138 references / Add more references