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It is not the case that Hypercomputation models (Malament-Hogarth spacetimes, Turing's o-machines) permit decision procedures that transcend finite-step termination constraints.
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Reasons For
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Reason for
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1.
No empirical evidence confirms Malament-Hogarth spacetimes exist; general relativity permits them mathematically but not necessarily physically.
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2.
Turing o-machines assume oracles as primitive; this merely relocates computation rather than transcending Church-Turing limits fundamentally.
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3.
Extracting results from hypercomputational processes requires finite observation windows; infinite convergence guarantees collapse under realistic constraints.
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Reasons Against
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Reason against
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1.
Malament-Hogarth spacetimes permit observers to access infinite computation via causal structure without violating local physical laws.
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2.
Turing o-machines formalize oracle access as mathematically coherent, showing transcendence of Turing-computability is logically possible.
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3.
If physical spacetime permits closed timelike curves or naked singularities, finite agents could exploit these to simulate hypercomputational processes.
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