David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
From 1931 until late in his life (at least 1970) Godel called for the pursuit of new axioms for mathematics to settle both undecided number-theoretical propositions (of the form obtained in his incompleteness results) and undecided set-theoretical propositions (in particular CH). As to the nature of these, Godel made a variety of suggestions, but most frequently he emphasized the route of introducing ever higher axioms of in nity. In particular, he speculated (in his 1946 Princeton remarks) that there might be a uniform (though non-decidable) rationale for the choice of the latter. Despite the intense exploration of the \higher in nite" in the last 30-odd years, no single rationale of that character has emerged. Moreover, CH still remains undecided by such axioms, though they have been demonstrated to have many other interesting set-theoretical consequences.
|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
Sebastian Eberhard (2014). A Feasible Theory of Truth Over Combinatory Algebra. Annals of Pure and Applied Logic 165 (5):1009-1033.
Similar books and articles
Solomon Feferman, Presentation to the Panel, “Does Mathematics Need New Axioms?” Asl 2000 Meeting, Urbana Il, June 5, 2000.
Samuel R. Buss (1994). On Gödel's Theorems on Lengths of Proofs I: Number of Lines and Speedup for Arithmetics. Journal of Symbolic Logic 59 (3):737-756.
Michael Potter (2001). Was Gödel a Gödelian Platonist? Philosophia Mathematica 9 (3):331-346.
Solomon Feferman (2008). Lieber Herr Bernays!, Lieber Herr Gödel! Gödel on Finitism, Constructivity and Hilbert's Program. Dialectica 62 (2: Table of Contents"/> Select):179–203.
Kai Hauser (2006). Gödel's Program Revisited Part I: The Turn to Phenomenology. Bulletin of Symbolic Logic 12 (4):529-590.
Robert F. Hadley (2008). Consistency, Turing Computability and Gödel's First Incompleteness Theorem. Minds and Machines 18 (1):1-15.
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;.
Panu Raatikainen (2005). On the Philosophical Relevance of Gödel's Incompleteness Theorems. Revue Internationale de Philosophie 59 (4):513-534.
Francesco Berto (2009). There's Something About Gödel: The Complete Guide to the Incompleteness Theorem. Wiley-Blackwell.
Katsumi Sasaki (1990). The Simple Substitution Property of Gödel's Intermediate Propositional Logics Sn's. Studia Logica 49 (4):471 - 481.
Louis Narens (1974). Measurement Without Archimedean Axioms. Philosophy of Science 41 (4):374-393.
Raymond M. Smullyan (1987/1988). Forever Undecided: A Puzzle Guide to Gödel. Oxford University Press.
Matthias Baaz (ed.) (2011). Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press.
Added to index2010-12-22
Total downloads15 ( #124,790 of 1,679,378 )
Recent downloads (6 months)1 ( #183,757 of 1,679,378 )
How can I increase my downloads?