David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Dialectica 62 (2: Table of Contents"/> Select):205–222 (2008)
In the course of ten short sections, we comment on Gödel's seminal dialectica paper of fifty years ago and its aftermath. We start by suggesting that Gödel's use of functionals of finite type is yet another instance of the realistic attitude of Gödel towards mathematics, in tune with his defense of the postulation of ever increasing higher types in foundational studies. We also make some observations concerning Gödel's recasting of intuitionistic arithmetic via the dialectica interpretation, discuss the extra principles that the interpretation validates and comment on extensionality and higher order equality. The latter sections focus on the role of majorizability considerations within the dialectica and related interpretations for extracting computational information from ordinary proofs in mathematics.
|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
Patrícia Engrácia (2012). The Bounded Functional Interpretation of Bar Induction. Annals of Pure and Applied Logic 163 (9):1183-1195.
Similar books and articles
Panu Raatikainen (2005). On the Philosophical Relevance of Gödel's Incompleteness Theorems. Revue Internationale de Philosophie 59 (4):513-534.
Francesco Berto (2009). The Gödel Paradox and Wittgenstein's Reasons. Philosophia Mathematica 17 (2):208-219.
Ulrich Kohlenbach (2008). Gödel's Functional Interpretation and its Use in Current Mathematics. Dialectica 62 (2):223–267.
Gabriella Crocco (2003). Gödel, Carnap and the Fregean Heritage. Synthese 137 (1-2):21 - 41.
Justus Diller (2008). Functional Interpretations of Constructive Set Theory in All Finite Types. Dialectica 62 (2):149–177.
Richard Tieszen (2002). Gödel and the Intuition of Concepts. Synthese 133 (3):363 - 391.
Paulo Oliva (2008). An Analysis of Gödel's Dialectica Interpretation Via Linear Logic. Dialectica 62 (2):269–290.
Added to index2009-01-28
Total downloads9 ( #155,519 of 1,098,598 )
Recent downloads (6 months)3 ( #113,599 of 1,098,598 )
How can I increase my downloads?