A brief critique of pure hypercomputation

Minds and Machines 19 (3):391-405 (2009)
Abstract
Hypercomputation—the hypothesis that Turing-incomputable objects can be computed through infinitary means—is ineffective, as the unsolvability of the halting problem for Turing machines depends just on the absence of a definite value for some paradoxical construction; nature and quantity of computing resources are immaterial. The assumption that the halting problem is solved by oracles of higher Turing degree amounts just to postulation; infinite-time oracles are not actually solving paradoxes, but simply assigning them conventional values. Special values for non-terminating processes are likewise irrelevant, since diagonalization can cover any amount of value assignments. This should not be construed as a restriction of computing power: Turing’s uncomputability is not a ‘barrier’ to be broken, but simply an effect of the expressive power of consistent programming systems.
Keywords Hypercomputation  Turing barrier  Halting problem  Uncomputability
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References found in this work BETA
Paolo Cotogno (2003). Hypercomputation and the Physical Church-Turing Thesis. British Journal for the Philosophy of Science 54 (2):181-223.
Martin Davis (2006). Why There is No Such Discipline as Hypercomputation. Applied Mathematics and Computation, Volume 178, Issue 1, 1.
Solomon Feferman (1992). Turing's\ Oracle": From Absolute to Relative Computability and Back. In Javier Echeverria, Andoni Ibarra & Thomas Mormann (eds.), The Space of Mathematics. De Gruyter. 314--348.

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