Mirror notation: Symbol manipulation without inscription manipulation

Journal of Philosophical Logic 28 (2):141-164 (1999)
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Abstract

Stereotypically, computation involves intrinsic changes to the medium of representation: writing new symbols, erasing old symbols, turning gears, flipping switches, sliding abacus beads. Perspectival computation leaves the original inscriptions untouched. The problem solver obtains the output by merely alters his orientation toward the input. There is no rewriting or copying of the input inscriptions; the output inscriptions are numerically identical to the input inscriptions. This suggests a loophole through some of the computational limits apparently imposed by physics. There can be symbol manipulation without inscription manipulation because symbols are complex objects that have manipulatable elements besides their inscriptions. Since a written symbol is an ordered pair of consisting of a shape and the reader's orientation to that inscription, the symbol can be changed by changing the orientation rather than inscription. Although there are the usual physical limits associated with reading the answer, the computation is itself instantaneous. This is true even when the sub-calculations are algorithmically complex, exponentially increasing or even infinite

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Roy Sorensen
University of Texas at Austin

Citations of this work

To Be F Is To Be G.Cian Dorr - 2016 - Philosophical Perspectives 30 (1):39-134.
Accelerating Turing machines.B. Jack Copeland - 2002 - Minds and Machines 12 (2):281-300.
The philosophy of alternative logics.Andrew Aberdein & Stephen Read - 2011 - In Leila Haaparanta (ed.), The development of modern logic. New York: Oxford University Press. pp. 613-723.

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References found in this work

The extended mind.Andy Clark & David J. Chalmers - 1998 - Analysis 58 (1):7-19.
Facts and Propositions.Frank P. Ramsey - 1927 - Aristotelian Society Supplementary Volume 7 (1):153-170.
Defining 'intrinsic'.Rae Langton & David Lewis - 1998 - Philosophy and Phenomenological Research 58 (2):333-345.

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