David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Synthese 116 (3):439-461 (1998)
This paper uses a proof of Gödels theorem, implemented on a computer, to explore how a person or a computer can examine such a proof, understand it, and evaluate its validity. It is argued that, in order to recognize it (1) as Gödel's theorem, and (2) as a proof that there is an undecidable statement in the language of PM, a person must possess a suitable semantics. As our analysis reveals no differences between the processes required by people and machines to understand Gödel's theorem and manipulate it symbolically, an effective way to characterize this semantics is to model the human cognitive system as a Turing Machine with sensory inputs. La logistique n'est plus stérile: elle engendre la contradicion! – Henri Poincaré ‘Les mathematiques et la logique’.
|Keywords||No keywords specified (fix it)|
No categories specified
(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
Taner Edis (1998). How Godel's Theorem Supports the Possibility of Machine Intelligence. Minds and Machines 8 (2):251-262.
Saul A. Kripke (2013). The Church-Turing ‘Thesis’ as a Special Corollary of Gödel’s Completeness Theorem. In B. J. Copeland, C. Posy & O. Shagrir (eds.), Computability: Turing, Gödel, Church, and Beyond. MIT Press.
John R. Lucas (1967). Human and Machine Logic: A Rejoinder. British Journal for the Philosophy of Science 19 (August):155-6.
N. Shankar (1994). Metamathematics, Machines, and Gödel's Proof. Cambridge University Press.
J. J. C. Smart (1961). Godel's Theorem, Church's Theorem, and Mechanism. Synthese 13 (June):105-10.
Francesco Berto (2009). There's Something About Gödel: The Complete Guide to the Incompleteness Theorem. Wiley-Blackwell.
Robert F. Hadley (2008). Consistency, Turing Computability and Gödel's First Incompleteness Theorem. Minds and Machines 18 (1):1-15.
Justin Leiber (2006). Turing's Golden: How Well Turing's Work Stands Today. Philosophical Psychology 19 (1):13-46.
Rosemarie Rheinwald (1991). Menschen, Maschinen Und Gödels Theorem. Erkenntnis 34 (1):1 - 21.
Added to index2009-01-28
Total downloads17 ( #105,410 of 1,140,314 )
Recent downloads (6 months)3 ( #60,710 of 1,140,314 )
How can I increase my downloads?