From Symbol to ‘Symbol’, to Abstract Symbol: Response to Copeland and Shagrir on Turing-Machine Realism Versus Turing-Machine Purism

Minds and Machines 26 (3):253-257 (2016)
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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 course of that presentation opens the door for later purist conceptions. Also, we argue that a purist conception of Turing machines plays an important role not only in the analysis of the computational properties of Turing machines, but also in the philosophical debates over the nature of their realization.



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Ofra Rechter
Tel Aviv University
Eli Dresner
Tel Aviv University

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On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
What is computation?B. Jack Copeland - 1996 - Synthese 108 (3):335-59.
Mathematics in Philosophy.Charles Parsons - 1986 - Philosophy of Science 53 (4):588-606.

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