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
Keywords Computability  Diagonal  Function  Science  Turing Machines  Cotogno, P
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DOI 10.1093/bjps/55.4.739
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References found in this work BETA

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.
Hypercomputation and the Physical Church‐Turing Thesis.Paolo Cotogno - 2003 - British Journal for the Philosophy of Science 54 (2):181-223.
Infinite Time Turing Machines.Joel Hamkins & Andy Lewis - 2000 - Journal of Symbolic Logic 65 (2):567-604.

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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.
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.

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