On the possibility, or otherwise, of hypercomputation

British Journal for the Philosophy of Science 55 (4):739-746 (2004)
  Copy   BIBTEX

Abstract

We claim that a recent article of P. Cotogno ([2003]) in this journal is based on an incorrect argument concerning the non-computability of diagonal functions. The point is that whilst diagonal functions are not computable by any function of the class over which they diagonalise, there is no ?logical incomputability? in their being computed over a wider class. Hence this ?logical incomputability? regrettably cannot be used in his argument that no hypercomputation can compute the Halting problem. This seems to lead him into a further error in his analysis of the supposed conventional status of the infinite time Turing machines of Hamkins and Lewis ([2000]). Theorem 1 refutes this directly. The diagonalisation misunderstanding Infinite computation Conclusion

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 89,718

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Infinite time Turing machines.Joel David Hamkins & Andy Lewis - 2000 - Journal of Symbolic Logic 65 (2):567-604.
A brief critique of pure hypercomputation.Paolo Cotogno - 2009 - Minds and Machines 19 (3):391-405.
Computation and hypercomputation.Mike Stannett - 2003 - Minds and Machines 13 (1):115-153.
Infinite time Turing machines.Joel David Hamkins - 2002 - Minds and Machines 12 (4):567-604.
The broad conception of computation.Jack Copeland - 1997 - American Behavioral Scientist 40 (6):690-716.
Two dogmas of computationalism.Oron Shagrir - 1997 - Minds and Machines 7 (3):321-44.
The diagonal method and hypercomputation.Toby Ord & Tien D. Kieu - 2005 - British Journal for the Philosophy of Science 56 (1):147-156.

Analytics

Added to PP
2009-01-28

Downloads
32 (#426,604)

6 months
2 (#651,580)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

The Physical Church–Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
SAD computers and two versions of the Church–Turing thesis.Tim Button - 2009 - British Journal for the Philosophy of Science 60 (4):765-792.
A brief critique of pure hypercomputation.Paolo Cotogno - 2009 - Minds and Machines 19 (3):391-405.

Add more citations

References found in this work

Non-Turing Computers and Non-Turing Computability.Mark Hogarth - 1994 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:126-138.
Infinite time Turing machines.Joel David Hamkins & Andy Lewis - 2000 - Journal of Symbolic Logic 65 (2):567-604.
Hypercomputation and the Physical Church‐Turing Thesis.Paolo Cotogno - 2003 - British Journal for the Philosophy of Science 54 (2):181-223.

Add more references