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  1. Jeffrey A. Barrett & Wayne Aitken, On the Physical Possibility of Ordinal Computation (Draft).
    α-recursion lifts classical recursion theory from the first transfinite ordinal ω to an arbitrary admissible ordinal α [10]. Idealized computational models for α-recursion analogous to Turing machine models for classical recursion have been proposed and studied [4] and [5] and are applicable in computational approaches to the foundations of logic and mathematics [8]. They also provide a natural setting for modeling extensions of the algorithmic logic described in [1] and [2]. On such models, an α-Turing machine can complete a θ-step (...)
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  2. Selmer Bringsjord, Computationalism is Dead; Now What?
    In this paper I place Jim Fetzer's esemplastic burial of the computational conceptionof mind within the context of both my own burial and the theory of mind I would put in place of this dead doctrine. My view..
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  3. Selmer Bringsjord, The Impact of Computing on Epistemology: Knowing Gödel's Mind Through Computation.
    I know that those of you who know my mind know that I think I know that we can't know Gödel's mind through computation: ``The Impact : Failing to Know " If computationalism is false, observant philosophers willing to get their hands dirty should be able to find tell-tale signs today: automated theorem proving tomorrow (Eastern APA): robots as zombanimals But let's start with little 'ol me, and literary, not mathematical, creativity: Selmer (samples) vs. Brutus1 (samples again).
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  4. H. C. (2003). Notes on Landauer's Principle, Reversible Computation, and Maxwell's Demon. Studies in History and Philosophy of Science Part B 34 (3):501-510.
    Landauer's principle, often regarded as the basic principle of the thermodynamics of information processing, holds that any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment. Conversely, it is generally accepted that any logically reversible transformation of information can in principle be accomplished by an appropriate physical mechanism operating in a (...)
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  5. 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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  6. 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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  7. 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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  8. 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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  9. Martin Davis (2006). Why There is No Such Discipline as Hypercomputation. Applied Mathematics and Computation, Volume 178, Issue 1, 1.
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  10. Stefan Gruner (2013). Eric Winsberg: Science in the Age of Computer Simulation. [REVIEW] Minds and Machines 23 (2):251-254.
  11. Larry Hauser (2000). Ordinary Devices: Reply to Bringsjord's Clarifying the Logic of Anti-Computationalism: Reply to Hauser. [REVIEW] Minds and Machines 10 (1):115-117.
    What Robots Can and Can't Be (hereinafter Robots) is, as Selmer Bringsjord says "intended to be a collection of formal-arguments-that-border-on-proofs for the proposition that in all worlds, at all times, machines can't be minds" (Bringsjord, forthcoming). In his (1994) "Précis of What Robots Can and Can't Be" Bringsjord styles certain of these arguments as proceeding "repeatedly . . . through instantiations of" the "simple schema".
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  12. Geoffrey Laforte, Pat Hayes & Kenneth M. Ford (1998). Why Godel's Theorem Cannot Refute Computationalism: A Reply to Penrose. Artificial Intelligence 104.
  13. 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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  14. 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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  15. Aran Nayebi (2014). Practical Intractability: A Critique of the Hypercomputation Movement. [REVIEW] 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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  16. 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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  17. Mike Stannett (2003). Computation and Hypercomputation. Minds and Machines 13 (1):115-153.
    Does Nature permit the implementation of behaviours that cannot be simulated computationally? We consider the meaning of physical computation in some detail, and present arguments in favour of physical hypercomputation: for example, modern scientific method does not allow the specification of any experiment capable of refuting hypercomputation. We consider the implications of relativistic algorithms capable of solving the (Turing) Halting Problem. We also reject as a fallacy the argument that hypercomputation has no relevance because non-computable values are indistinguishable from sufficiently (...)
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