David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 3 (1):86-102 (1995)
Lucas and Penrose have contended that, by displaying how any characterisation of arithmetical proof programmable into a machine allows of diagonalisation, generating a humanly recognisable proof which eludes that characterisation, Gödel's incompleteness theorem rules out any purely mechanical model of the human intellect. The main criticisms of this argument have been that the proof generated by diagonalisation (i) will not be humanly recognisable unless humans can grasp the specification of the object-system (Benacerraf); and (ii) counts as a proof only on the (unproven) hypothesis that the object system is consistent (Putnam). The present paper argues that criticism (ii) may be met head-on by an intuitionistic proponent of the anti-mechanist argument; and that criticism (i) is simply mistaken. However the paper concludes by questioning the sufficiency of the situation for an interesting anti-mechanist conclusion.
|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
Jon Cogburn & Jason Megill (2010). Are Turing Machines Platonists? Inferentialism and the Computational Theory of Mind. Minds and Machines 20 (3):423-439.
G. Sereny (2011). How Do We Know That the Godel Sentence of a Consistent Theory Is True? Philosophia Mathematica 19 (1):47-73.
Similar books and articles
Paul Benacerraf (1967). God, the Devil, and Godel. The Monist 51 (January):9-32.
Herbert A. Simon & Stuart A. Eisenstadt (1998). Human and Machine Interpretation of Expressions in Formal Systems. Synthese 116 (3):439-461.
J. J. C. Smart (1961). Godel's Theorem, Church's Theorem, and Mechanism. Synthese 13 (June):105-10.
D. King (1996). Is the Human Mind a Turing Machine? Synthese 108 (3):379-89.
Panu Raatikainen (2002). McCall's Gödelian Argument is Invalid. Facta Philosophica 4 (1):167-69.
B. Jack Copeland (2002). Accelerating Turing Machines. Minds and Machines 12 (2):281-300.
Jack Copeland (1998). Turing's o-Machines, Searle, Penrose, and the Brain. Analysis 58 (2):128-138.
Gualtiero Piccinini (2003). Alan Turing and the Mathematical Objection. Minds and Machines 13 (1):23-48.
Added to index2009-01-28
Total downloads32 ( #118,951 of 1,789,998 )
Recent downloads (6 months)1 ( #424,764 of 1,789,998 )
How can I increase my downloads?