Journal Article

On the Possibility, or Otherwise, of Hypercomputation

P. D. Welch

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 55, issue 4, pages 739-746
Published in print December 2004 | ISSN: 0007-0882
Published online December 2004 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/55.4.739
On the Possibility, or Otherwise, of Hypercomputation

More Like This

Show all results sharing these subjects:

  • Philosophy of Science
  • Science and Mathematics

GO

Show Summary Details

Preview

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

Journal Article.  0 words. 

Subjects: Philosophy of Science ; Science and Mathematics

Full text: subscription required

How to subscribe Recommend to my Librarian

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.