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  1. The Physical Church–Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
    This article defends a modest version of the Physical Church-Turing thesis (CT). Following an established recent trend, I distinguish between what I call Mathematical CT—the thesis supported by the original arguments for CT—and Physical CT. I then distinguish between bold formulations of Physical CT, according to which any physical process—anything doable by a physical system—is computable by a Turing machine, and modest formulations, according to which any function that is computable by a physical system is computable by a Turing machine. (...)
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  • Concrete Digital Computation: What Does It Take for a Physical System to Compute? [REVIEW]Nir Fresco - 2011 - Journal of Logic, Language and Information 20 (4):513-537.
    This paper deals with the question: what are the key requirements for a physical system to perform digital computation? Time and again cognitive scientists are quick to employ the notion of computation simpliciter when asserting basically that cognitive activities are computational. They employ this notion as if there was or is a consensus on just what it takes for a physical system to perform computation, and in particular digital computation. Some cognitive scientists in referring to digital computation simply adhere to (...)
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  • Significance of Models of Computation, From Turing Model to Natural Computation.Gordana Dodig-Crnkovic - 2011 - Minds and Machines 21 (2):301-322.
    The increased interactivity and connectivity of computational devices along with the spreading of computational tools and computational thinking across the fields, has changed our understanding of the nature of computing. In the course of this development computing models have been extended from the initial abstract symbol manipulating mechanisms of stand-alone, discrete sequential machines, to the models of natural computing in the physical world, generally concurrent asynchronous processes capable of modelling living systems, their informational structures and dynamics on both symbolic and (...)
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  • The Dependence of Computability on Numerical Notations.Ethan Brauer - 2020 - Synthese 198 (11):10485-10511.
    Which function is computed by a Turing machine will depend on how the symbols it manipulates are interpreted. Further, by invoking bizarre systems of notation it is easy to define Turing machines that compute textbook examples of uncomputable functions, such as the solution to the decision problem for first-order logic. Thus, the distinction between computable and uncomputable functions depends on the system of notation used. This raises the question: which systems of notation are the relevant ones for determining whether a (...)
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  • Practical Intractability: A Critique of the Hypercomputation Movement. [REVIEW]Aran Nayebi - 2014 - Minds and Machines 24 (3):275-305.
    For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While opponents to the hypercomputation movement provide arguments against the physical realizability of specific models in order to demonstrate this, these arguments lack the generality to be a satisfactory justification against the construction of any information-processing machine that computes beyond the universal Turing machine. To this end, I present a more (...)
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  • Is Church’s Thesis Still Relevant?Jerzy Mycka & Adam Olszewski - 2020 - Studies in Logic, Grammar and Rhetoric 63 (1):31-51.
    The article analyses the role of Church’s Thesis in the context of the development of hypercomputation research. The text begins by presenting various views on the essence of computer science and the limitations of its methods. Then CT and its importance in determining the limits of methods used by computer science is presented. Basing on the above explanations, the work goes on to characterize various proposals of hypercomputation showing their relative power in relation to the arithmetic hierarchy. The general theme (...)
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  • Do Accelerating Turing Machines Compute the Uncomputable?B. Jack Copeland & Oron Shagrir - 2011 - Minds and Machines 21 (2):221-239.
    Accelerating Turing machines have attracted much attention in the last decade or so. They have been described as “the work-horse of hypercomputation”. But do they really compute beyond the “Turing limit”—e.g., compute the halting function? We argue that the answer depends on what you mean by an accelerating Turing machine, on what you mean by computation, and even on what you mean by a Turing machine. We show first that in the current literature the term “accelerating Turing machine” is used (...)
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  • The Philosophy of Computer Science: Introduction to the Special Issue. [REVIEW]Raymond Turner - 2007 - Minds and Machines 17 (2):129-133.