Presentation to the panel, “does mathematics need new axioms?” Asl 2000 meeting, urbana il, June 5, 2000
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
The point of departure for this panel is a somewhat controversial paper that I published in the American Mathematical Monthly under the title “Does mathematics need new axioms?” . The paper itself was based on a lecture that I gave in 1997 to a joint session of the American Mathematical Society and the Mathematical Association of America, and it was thus written for a general mathematical audience. Basically, it was intended as an assessment of Gödel’s program for new axioms that he had advanced most prominently in his 1947 paper for the Monthly, entitled “What is Cantor’s continuum problem?” . My paper aimed to be an assessment of that program in the light of research in mathematical logic in the intervening years, beginning in the 1960s, but especially in more recent years.
|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
Elaine Landry (2011). How to Be a Structuralist All the Way Down. Synthese 179 (3):435 - 454.
Krzysztof Wójtowicz (2006). Independence and Justification in Mathematics. Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):349-373.
Justin Clarke-Doane (2013). What is Absolute Undecidability?†. Noûs 47 (3):467-481.
Penelope Maddy (1984). New Directions in the Philosophy of Mathematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984:427 - 448.
Kenny Easwaran (2008). The Role of Axioms in Mathematics. Erkenntnis 68 (3):381 - 391.
Kurt Gödel (1940). The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory. Princeton University Press;.
Keith Devlin (2008). A Mathematician Reflects on the Useful and Reliable Illusion of Reality in Mathematics. Erkenntnis 68 (3):359 - 379.
Added to index2009-12-04
Total downloads32 ( #129,065 of 1,911,757 )
Recent downloads (6 months)2 ( #322,396 of 1,911,757 )
How can I increase my downloads?