Abstract
In this chapter I show, first, what modifications are needed in order to make the design of a Turing machine more suitable for being used as a model of human computation. The result of these modifications is a special kind of TM-inspired computational system, i.e. the Bidimensional Turing machine. Second, I introduce the notion of a Galilean model, namely, a concept of empirical adequacy for cognitive models (Giunti 1995) and I propose to consider Bidimensional Turing machines as a possible Galilean models.
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Notes
- 1.
A full detailed formal definition is in Giunti and Pinna (2016), where BTMs are described as a special case of Algorithmically enhanced Turing Machines (ATMs) with a 2-dimensional external support.
- 2.
These concepts are formulated in Giunti (2010a, b, 2014, 2016, forthcoming).
- 3.
More precisely, Giunti proposes an “Empirical method for investigating the [MTT]-based theory of human computation (Giunti 2009, p. 24)”, where MTT refers to what he calls the methodological version of the Turing thesis. Let BT be a bidimensional Turing machine which models a certain phenomenon of human computation (namely, a cognitive phenomenon involving a human being which executes an algorithm) C, and let \(S_{C}\) be an empirical interpretation of BT on C. Then, the methodological version of the Turing thesis will be the following claim:
For any specific phenomenon C of human computation, there is an appropriate bidimensional Turing machine BT such that \((BT, S_{C})\) turns out to be a Galilean model of C (Giunti 2009, p. 23).
It is quite obvious that a necessary consequence of this claim is the fact that some specific BTM, interpreted on the corresponding algorithmic skills, is an empirically adequate model of those skills, as I assume, for the sake of argument, in the next chapter.
- 4.
See Sect. 2.2 of this book.
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Pinna, S. (2017). Modeling Algorithmic Skills: The Bidimensional Turing Machine. In: Extended Cognition and the Dynamics of Algorithmic Skills. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 35. Springer, Cham. https://doi.org/10.1007/978-3-319-51841-1_4
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