Authors
Toby Ord
Oxford University
Abstract
The diagonal method is often used to show that Turing machines cannot solve their own halting problem. There have been several recent attempts to show that this method also exposes either contradiction or arbitrariness in other theoretical models of computation which claim to be able to solve the halting problem for Turing machines. We show that such arguments are flawed—a contradiction only occurs if a type of machine can compute its own diagonal function. We then demonstrate why such a situation does not occur for the methods of hypercomputation under attack, and why it is unlikely to occur for any other serious methods. Introduction Issues with specific hypermachines Conclusions for hypercomputation.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/phisci/axi108
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 69,114
Through your library

References found in this work BETA

On Computable Numbers, with an Application to the N Tscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers.Piergiorgio Odifreddi - 1989 - Sole Distributors for the Usa and Canada, Elsevier Science Pub. Co..
Classical Recursion Theory.Peter G. Hinman - 2001 - Bulletin of Symbolic Logic 7 (1):71-73.
Hypercomputation.B. Jack Copeland - 2002 - Minds and Machines 12 (4):461-502.
Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.

View all 10 references / Add more references

Citations of this work BETA

The Physical Church–Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
A Brief Critique of Pure Hypercomputation.Paolo Cotogno - 2009 - Minds and Machines 19 (3):391-405.
On TAE Machines and Their Computational Power.Apostolos Syropoulos - 2019 - Logica Universalis 13 (2):165-170.

View all 7 citations / Add more citations

Similar books and articles

Accelerating Turing Machines.B. Jack Copeland - 2002 - Minds and Machines 12 (2):281-300.
Hypercomputation: Computing More Than the Turing Machine.Toby Ord - 2002 - Dissertation, University of Melbourne
Quantum Hypercomputation.Tien D. Kieu - 2002 - Minds and Machines 12 (4):541-561.
Computation and Hypercomputation.Mike Stannett - 2003 - Minds and Machines 13 (1):115-153.
A Brief Critique of Pure Hypercomputation.Paolo Cotogno - 2009 - Minds and Machines 19 (3):391-405.
What Turing Did After He Invented the Universal Turing Machine.Diane Proudfoot & Jack Copeland - 2000 - Journal of Logic, Language and Information 9:491-509.
Hypercomputation.B. Jack Copeland - 2002 - Minds and Machines 12 (4):461-502.
On the Possibility, or Otherwise, of Hypercomputation.Philip D. Welch - 2004 - British Journal for the Philosophy of Science 55 (4):739-746.

Analytics

Added to PP index
2009-01-28

Total views
138 ( #83,613 of 2,499,248 )

Recent downloads (6 months)
1 ( #418,195 of 2,499,248 )

How can I increase my downloads?

Downloads

My notes