Minds and Machines 19 (3):391-405 (2009)

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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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DOI 10.1007/s11023-009-9161-7
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References found in this work BETA

Introduction to Metamathematics.Stephen Kleene - 1952 - Princeton, NJ, USA: North Holland.
Systems of Logic Based on Ordinals.Alan Mathison Turing - 1939 - London: Printed by C.F. Hodgson & Son.
Tasks and Supertasks.James Thomson - 1954 - Analysis 15 (1):1--13.
Tasks, Super-Tasks, and the Modern Eleatics.Paul Benacerraf - 1962 - Journal of Philosophy 59 (24):765-784.
Hypercomputation and the Physical Church‐Turing Thesis.Paolo Cotogno - 2003 - British Journal for the Philosophy of Science 54 (2):181-223.

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Citations of this work BETA

Programming Infinite Machines.Anton A. Kutsenko - 2022 - Erkenntnis 87 (1):181-189.
Buttresses of the Turing Barrier.Paolo Cotogno - 2015 - Acta Analytica 30 (3):275-282.

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