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  1. Jack Copeland (1999). Beyond the Universal Turing Machine. Australasian Journal of Philosophy 77 (1):46-67.
    We describe an emerging field, that of nonclassical computability and nonclassical computing machinery. According to the nonclassicist, the set of well-defined computations is not exhausted by the computations that can be carried out by a Turing machine. We provide an overview of the field and a philosophical defence of its foundations.
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  2. Jack Copeland (1998). Super Turing-Machines. Complexity 4 (1):30-32.
    The tape is divided into squares, each square bearing a single symbol—'0' or '1', for example. This tape is the machine's general-purpose storage medium: the machine is set in motion with its input inscribed on the tape, output is written onto the tape by the head, and the tape serves as a short-term working memory for the results of intermediate steps of the computation. The program governing the particular computation that the machine is to perform is also stored on the (...)
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  3. Jack Copeland (1997). The Broad Conception of Computation. American Behavioral Scientist 40 (6):690-716.
    A myth has arisen concerning Turing's paper of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine - a myth that has passed into cognitive science and the philosophy of mind, to wide and pernicious effect. This supposed principle, sometimes incorrectly termed the 'Church-Turing thesis', is the claim that the class of functions that can be computed by machines is identical to the class of functions that can be computed by (...)
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  4. Paolo Cotogno (2009). A Brief Critique of Pure Hypercomputation. Minds and Machines 19 (3):391-405.
    Hypercomputation—the hypothesis that Turing-incomputable objects can be computed through infinitary means—is ineffective, as the unsolvability of the halting problem for Turing machines depends just on the absence of a definite value for some paradoxical construction; nature and quantity of computing resources are immaterial. The assumption that the halting problem is solved by oracles of higher Turing degree amounts just to postulation; infinite-time oracles are not actually solving paradoxes, but simply assigning them conventional values. Special values for non-terminating processes are likewise (...)
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  5. Martin Davis (2006). Why There is No Such Discipline as Hypercomputation. Applied Mathematics and Computation, Volume 178, Issue 1, 1.
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  6. Ignazio Licata & Ammar Sakaji (eds.) (2008). Physics of Emergence and Organization. World Scientific.
    This book is a state-of-the-art review on the Physics of Emergence. Foreword v Gregory J. Chaitin Preface vii Ignazio Licata Emergence and Computation at the Edge of Classical and Quantum Systems 1 Ignazio Licata Gauge Generalized Principle for Complex Systems 27 Germano Resconi Undoing Quantum Measurement: Novel Twists to the Physical Account of Time 61 Avshalom C. Elitzur and Shahar Dolev Process Physics: Quantum Theories as Models of Complexity 77 Kirsty Kitto A Cross-disciplinary Framework for the Description of Contextually Mediated (...)
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  7. Manolo Martínez (2013). Ideal Negative Conceivability and the Halting Problem. Erkenntnis 78 (5):979-990.
    Our limited a priori-reasoning skills open a gap between our finding a proposition conceivable and its metaphysical possibility. A prominent strategy for closing this gap is the postulation of ideal conceivers, who suffer from no such limitations. In this paper I argue that, under many, maybe all, plausible unpackings of the notion of ideal conceiver, it is false that ideal negative conceivability entails possibility.
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  8. Aran Nayebi (forthcoming). Practical Intractability: A Critique of the Hypercomputation Movement. [REVIEW] Minds and Machines:1-31.
    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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  9. Brian Rotman (1996). Counting Information: A Note on Physicalized Numbers. [REVIEW] Minds and Machines 6 (2):229-238.
    Existing work on the ultimate limits of computation has urged that the apparatus of real numbers should be eschewed as an investigative tool and replaced by discrete mathematics. The present paper argues for a radical extension of this viewpoint: not only the continuum but all infinitary constructs including the rationals and the potential infinite sequence of whole numbers need to be eliminated if a self-consistent investigative framework is to be achieved.
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