David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 15 (2):193-226 (2007)
Proofs of Gödel's First Incompleteness Theorem are often accompanied by claims such as that the gödel sentence constructed in the course of the proof says of itself that it is unprovable and that it is true. The validity of such claims depends closely on how the sentence is constructed. Only by tightly constraining the means of construction can one obtain gödel sentences of which it is correct, without further ado, to say that they say of themselves that they are unprovable and that they are true; otherwise a false theory can yield false gödel sentences
|Keywords||Gödel sentences Journal Article Gödel, Kurt. Incompleteness theorem Gödel’s theorem Mathematics Philosophy|
|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
Peter Milne (2007). On Gödel Sentences and What They Say. Philosophia Mathematica 15 (2):193-226.
Neil Thompson (2012). Arithmetic Proof and Open Sentences. Philosophy Study 2 (1):43-50.
Gregor Damschen (2011). Questioning Gödel's Ontological Proof: Is Truth Positive? European Journal for Philosophy of Religion 3 (1):161-169.
Panu Raatikainen (2005). On the Philosophical Relevance of Gödel's Incompleteness Theorems. Revue Internationale de Philosophie 59 (4):513-534.
G. Sereny (2011). How Do We Know That the Godel Sentence of a Consistent Theory Is True? Philosophia Mathematica 19 (1):47-73.
Hirohiko Kushida (2010). The Modal Logic of Gödel Sentences. Journal of Philosophical Logic 39 (5):577 - 590.
Andrzej Mostowski (1952/1982). Sentences Undecidable in Formalized Arithmetic: An Exposition of the Theory of Kurt Gödel. Greenwood Press.
Stewart Shapiro (2002). Incompleteness and Inconsistency. Mind 111 (444):817-832.
Martin K. Solomon (1978). Some Results on Measure Independent Gödel Speed-Ups. Journal of Symbolic Logic 43 (4):667-672.
Francesco Berto (2009). The Gödel Paradox and Wittgenstein's Reasons. Philosophia Mathematica 17 (2):208-219.
Mark Steiner (2001). Wittgenstein as His Own Worst Enemy: The Case of Gödel's Theorem. Philosophia Mathematica 9 (3):257-279.
Zofia Adamowicz & Teresa Bigorajska (2001). Existentially Closed Structures and Gödel's Second Incompleteness Theorem. Journal of Symbolic Logic 66 (1):349-356.
Philip Hugly & Charles Sayward (1989). Can There Be a Proof That an Unprovable Sentence of Arithmetic is True? Dialectica 43 (43):289-292.
Charles Sayward (2001). On Some Much Maligned Remarks of Wittgenstein on Gödel. Philosophical Investigations 24 (3):262–270.
Added to index2011-10-25
Total downloads27 ( #76,690 of 1,692,213 )
Recent downloads (6 months)1 ( #184,284 of 1,692,213 )
How can I increase my downloads?