David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 9 (1):21-36 (2001)
This paper contains a defense against anti-realism in mathematics in the light both of incompleteness and of the fact that mathematics is a ‘cultural artifact.’. Anti-realism (here) is the view that theorems, say, of aritltmetic cannot be taken at face value to express true propositions about the system of numbers but must be reconstrued to be about somctliiiig else or about nothing at all. A ‘bite-the-bullet’ aspect of the defease is that, adopting new axioms, liitherto independent, is not. a matter of recognizing trutlis wliich had previoasly been unrecognized, but of extending the domain of what is true.
|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
Karin Katz & Mikhail Katz (2012). A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography. Foundations of Science 17 (1):51-89.
Sharon Berry (2014). Malament–Hogarth Machines and Tait's Axiomatic Conception of Mathematics. Erkenntnis 79 (4):893-907.
Similar books and articles
A. S. Troelstra (1975). Axioms for Intuitionistic Mathematics Incompatible with Classical Logic. Mathematisch Instituut.
Penelope Maddy (1991). Philosophy of Mathematics: Prospects for the 1990s. Synthese 88 (2):155 - 164.
Krzysztof Wójtowicz (2006). Independence and Justification in Mathematics. Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):349-373.
Stewart Shapiro (2007). The Objectivity of Mathematics. Synthese 156 (2):337 - 381.
Keith Devlin (2008). A Mathematician Reflects on the Useful and Reliable Illusion of Reality in Mathematics. Erkenntnis 68 (3):359 - 379.
Kenny Easwaran (2008). The Role of Axioms in Mathematics. Erkenntnis 68 (3):381 - 391.
Added to index2009-01-28
Total downloads32 ( #76,453 of 1,696,508 )
Recent downloads (6 months)7 ( #79,559 of 1,696,508 )
How can I increase my downloads?