Citations of:
Do accelerating Turing machines compute the uncomputable?
Minds and Machines 21 (2):221-239 (2011)
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In recent decades, there has been a proliferation among the scientific community of works that focus on Alan Turing’s contributions to the design and development of the modern computer. However, there are significant discrepancies among these studies, to such a point that some of them cast serious doubts on Alan Turing’s work with respect to today’s computer, and there are others that staunchly defend his leading role, as well as other studies that set out more well-balanced opinions. Faced with this (...) |
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In their recent paper “Do Accelerating Turing Machines Compute the Uncomputable?” Copeland and Shagrir draw a distinction between a purist conception of Turing machines, according to which these machines are purely abstract, and Turing machine realism according to which Turing machines are spatio-temporal and causal “notional" machines. In the present response to that paper we concede the realistic aspects of Turing’s own presentation of his machines, pointed out by Copeland and Shagrir, but argue that Turing's treatment of symbols in the (...) |
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The ‘Turing barrier’ is an evocative image for 0′, the degree of the unsolvability of the halting problem for Turing machines—equivalently, of the undecidability of Peano Arithmetic. The ‘barrier’ metaphor conveys the idea that effective computability is impaired by restrictions that could be removed by infinite methods. Assuming that the undecidability of PA is essentially depending on the finite nature of its computational means, decidability would be restored by the ω-rule. Hypercomputation, the hypothetical realization of infinitary machines through relativistic and (...) |
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The received view of computation is methodologically bifurcated: it offers different accounts of computation in the mathematical and physical cases. But little in the way of argument has been given for this approach. This paper rectifies the situation by arguing that the alternative, a unified account, is untenable. Furthermore, once these issues are brought into sharper relief we can see that work remains to be done to illuminate the relationship between physical and mathematical computation. |
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The essays included in the special issue dedicated to the philosophy of computer science examine new philosophical questions that arise from reflection upon conceptual issues in computer science and the insights such an enquiry provides into ongoing philosophical debates. |
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Our limited a priori-reasoning skills open a gap between our finding a proposition conceivable and its metaphysical possibility. A prominent strategy for closing this gap is the postulation of ideal conceivers, who suffer from no such limitations. In this paper I argue that, under many, maybe all, plausible unpackings of the notion of ideal conceiver, it is false that ideal negative conceivability entails possibility. |
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This paper argues that the idea of a computer is unique. Calculators and analog computers are not different ideas about computers, and nature does not compute by itself. Computers, once clearly defined in all their terms and mechanisms, rather than enumerated by behavioral examples, can be more than instrumental tools in science, and more than source of analogies and taxonomies in philosophy. They can help us understand semantic content and its relation to form. This can be achieved because they have (...) |
