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Thomson's lamp is dysfunctional

William I. McLaughlin

Synthese 116 (3):281-301 (1998)

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A brief critique of pure hypercomputation.Paolo Cotogno - 2009 - Minds and Machines 19 (3):391-405.details 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 (...) Download Export citation Bookmark 4 citations
A discrete solution for the paradox of Achilles and the tortoise.Vincent Ardourel - 2015 - Synthese 192 (9):2843-2861.details In this paper, I present a discrete solution for the paradox of Achilles and the tortoise. I argue that Achilles overtakes the tortoise after a finite number of steps of Zeno’s argument if time is represented as discrete. I then answer two objections that could be made against this solution. First, I argue that the discrete solution is not an ad hoc solution. It is embedded in a discrete formulation of classical mechanics. Second, I show that the discrete solution cannot (...) be falsified experimentally. (shrink) Download Export citation Bookmark 5 citations
Computation and hypercomputation.Mike Stannett - 2003 - Minds and Machines 13 (1):115-153.details Does Nature permit the implementation of behaviours that cannot be simulated computationally? We consider the meaning of physical computation in some detail, and present arguments in favour of physical hypercomputation: for example, modern scientific method does not allow the specification of any experiment capable of refuting hypercomputation. We consider the implications of relativistic algorithms capable of solving the (Turing) Halting Problem. We also reject as a fallacy the argument that hypercomputation has no relevance because non-computable values are indistinguishable from sufficiently (...) Download Export citation Bookmark 6 citations
Incommensurables and Incomparables: On the Conceptual Status and the Philosophical Use of Hyperreal Numbers.Michael White - 1999 - Notre Dame Journal of Formal Logic 40 (3):420-446.details After briefly considering the ancient Greek and nineteenth-century history of incommensurables (magnitudes that do not have a common aliquot part) and incomparables (magnitudes such that the larger can never be surpassed by any finite number of additions of the smaller to itself), this paper undertakes two tasks. The first task is to consider whether the numerical accommodation of incommensurables by means of the extension of the ordered field of rational numbers to the field of reals is `similar' or analogous to (...) Download Export citation Bookmark 1 citation

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