Abstract
In their recent paper “Do Accelerating Turing Machines Compute the Uncomputable?” Copeland and Shagrir (Minds Mach 21:221–239, 2011) 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 (as well as other computational models) 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.
Similar content being viewed by others
References
Copeland, J. (1996). What is computation? Synthese, 108, 335–359.
Copeland, B. J., & Shagrir, O. (2011). Do accelerating turing machines compute the uncomputable? Minds and Machines, 21, 221–239.
Dresner, E. (2010). Measurement-theoretic representation and computation-theoretic realization. The Journal of Philosophy, 107, 272–292.
Dresner, E., & Rechter, O. (2014). From symbol to 'Symbol': Turing, Hilbert and the Quasi-concreteness of signs. Unpublished manuscript.
Parsons, C. (1983). Mathematics in Philosophy. Ithaca: Cornell University Press.
Rescorla, M. (2014). A theory of computational implementation. Synthese, 191, 1277–1307.
Turing, A. (1936). On computable numbers, with an application to the Entscheudungsproblem. Proceeding of London Mathematical Society, 42(2), 230–265.
Acknowledgments
We would like to thank Jack Copeland and Oron Shagrir for their comments on earlier versions of this paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dresner, E., Rechter, O. From Symbol to ‘Symbol’, to Abstract Symbol: Response to Copeland and Shagrir on Turing-Machine Realism Versus Turing-Machine Purism. Minds & Machines 26, 253–257 (2016). https://doi.org/10.1007/s11023-016-9394-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11023-016-9394-1