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John R. Lucas (1961). Minds, Machines and Godel.

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  1. A Metasemantic Challenge for Mathematical Determinacy.Jared Warren & Daniel Waxman - forthcoming - Synthese:1-19.
    This paper investigates the determinacy of mathematics. We begin by clarifying how we are understanding the notion of determinacy before turning to the questions of whether and how famous independence results bear on issues of determinacy in mathematics. From there, we pose a metasemantic challenge for those who believe that mathematical language is determinate, motivate two important constraints on attempts to meet our challenge, and then use these constraints to develop an argument against determinacy and discuss a particularly popular approach (...)
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  2. Gödel’s Disjunction: The Scope and Limits of Mathematical Knowledge. [REVIEW]Panu Raatikainen - 2018 - History and Philosophy of Logic 39 (4):401-403.
  3.  13
    Proving That the Mind Is Not a Machine?Johannes Stern - 2018 - Thought: A Journal of Philosophy 7 (2):81-90.
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  4. A Machine That Knows Its Own Code.Samuel A. Alexander - 2014 - Studia Logica 102 (3):567-576.
  5.  12
    Oldest Paradoxes, Future Mathematics and Mysticism.Ulrich Blau - 2014 - Erkenntnis 79 (S7):1-25.
    A direct path that has been missed for 100 years leads from the oldest paradoxes straight to mysticism, via (the concept of) logical and mathematical truth, since the purely formal truth is an absolutely univocal, absolutely timeless and absolutely unbounded reference. I present three theses in passing: (1) logicians fail to fully appreciate the basic mathematical idea of truth and consequently push the semantic paradoxes aside. Otherwise they would have come to adopt the reflexive logic LR* right after Cantor (more (...)
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  6. Fast-Collapsing Theories.Samuel Alexander - 2013 - Studia Logica (1):1-21.
    Reinhardt’s conjecture, a formalization of the statement that a truthful knowing machine can know its own truthfulness and mechanicalness, was proved by Carlson using sophisticated structural results about the ordinals and transfinite induction just beyond the first epsilon number. We prove a weaker version of the conjecture, by elementary methods and transfinite induction up to a smaller ordinal.
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  7. Neural Computation and the Computational Theory of Cognition.Gualtiero Piccinini & Sonya Bahar - 2013 - Cognitive Science 37 (3):453-488.
    We begin by distinguishing computationalism from a number of other theses that are sometimes conflated with it. We also distinguish between several important kinds of computation: computation in a generic sense, digital computation, and analog computation. Then, we defend a weak version of computationalism—neural processes are computations in the generic sense. After that, we reject on empirical grounds the common assimilation of neural computation to either analog or digital computation, concluding that neural computation is sui generis. Analog computation requires continuous (...)
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  8.  47
    Experimental Logics, Mechanism and Knowable Consistency.Martin Kaså - 2012 - Theoria 78 (3):213-224.
    In a paper published in 1975, Robert Jeroslow introduced the concept of an experimental logic as a generalization of ordinary formal systems such that theoremhood is a (or in practice ) rather than . These systems can be viewed as (rather crude) representations of axiomatic theories evolving stepwise over time. Similar ideas can be found in papers by Putnam (1965) and McCarthy and Shapiro (1987). The topic of the present article is a discussion of a suggestion by Allen Hazen, that (...)
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  9. Philosophy of Mind Is (in Part) Philosophy of Computer Science.Darren Abramson - 2011 - Minds and Machines 21 (2):203-219.
    In this paper I argue that whether or not a computer can be built that passes the Turing test is a central question in the philosophy of mind. Then I show that the possibility of building such a computer depends on open questions in the philosophy of computer science: the physical Church-Turing thesis and the extended Church-Turing thesis. I use the link between the issues identified in philosophy of mind and philosophy of computer science to respond to a prominent argument (...)
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  10.  53
    Francesco Berto. There's Something About Godel. Malden, Mass., And Oxford: Wiley-Blackwell, 2009. Isbn 978-1-4051-9766-3 (Hbk); 978-1-4051-9767-0 (Pbk). Pp. XX + 233. English Translation of Tutti Pazzi Per Godel! (Rome: Gius, Laterza & Figli, 2008). [REVIEW]V. McGee - 2011 - Philosophia Mathematica 19 (3):367-369.
    There's Something about Gödel is a bargain: two books in one. The first half is a gentle but rigorous introduction to the incompleteness theorems for the mathematically uninitiated. The second is a survey of the philosophical, psychological, and sociological consequences people have attempted to derive from the theorems, some of them quite fantastical.The first part, which stays close to Gödel's original proofs, strikes a nice balance, giving enough details that the reader understands what is going on in the proofs, without (...)
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  11.  13
    Some Limitations to the Psychological Orientation in Semantic Theory.Richmond H. Thomason - 2011 - Journal of Philosophical Logic 40 (1):1 - 14.
    The psychological orientation treats semantics as a matter of idealized computation over symbolic structures, and semantic relations like denotation as relations between linguistic expressions and these structures. I argue that results similar to Gödel's incompleteness theorems and Tarski's theorem on truth create foundational difficulties for this view of semantics.
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  12.  83
    Can Machines Think? An Old Question Reformulated.Achim Hoffmann - 2010 - Minds and Machines 20 (2):203-212.
    This paper revisits the often debated question Can machines think? It is argued that the usual identification of machines with the notion of algorithm has been both counter-intuitive and counter-productive. This is based on the fact that the notion of algorithm just requires an algorithm to contain a finite but arbitrary number of rules. It is argued that intuitively people tend to think of an algorithm to have a rather limited number of rules. The paper will further propose a modification (...)
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  13. Turning the Zombie on its Head.Amir Horowitz - 2009 - Synthese 170 (1):191 - 210.
    This paper suggests a critique of the zombie argument that bypasses the need to decide on the truth of its main premises, and specifically, avoids the need to enter the battlefield of whether conceivability entails metaphysical possibility. It is argued that if we accept, as the zombie argument’s supporters would urge us, the assumption that an ideal reasoner can conceive of a complete physical description of the world without conceiving of qualia, the general principle that conceivability entails metaphysical possibility, and (...)
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  14.  82
    Turing’s Responses to Two Objections.Darren Abramson - 2008 - Minds and Machines 18 (2):147-167.
    In this paper I argue that Turing’s responses to the mathematical objection are straightforward, despite recent claims to the contrary. I then go on to show that by understanding the importance of learning machines for Turing as related not to the mathematical objection, but to Lady Lovelace’s objection, we can better understand Turing’s response to Lady Lovelace’s objection. Finally, I argue that by understanding Turing’s responses to these objections more clearly, we discover a hitherto unrecognized, substantive thesis in his philosophical (...)
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  15.  98
    Consistency, Turing Computability and Gödel’s First Incompleteness Theorem.Robert F. Hadley - 2008 - Minds and Machines 18 (1):1-15.
    It is well understood and appreciated that Gödel’s Incompleteness Theorems apply to sufficiently strong, formal deductive systems. In particular, the theorems apply to systems which are adequate for conventional number theory. Less well known is that there exist algorithms which can be applied to such a system to generate a gödel-sentence for that system. Although the generation of a sentence is not equivalent to proving its truth, the present paper argues that the existence of these algorithms, when conjoined with Gödel’s (...)
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  16.  30
    Closing the Circle: An Analysis of Emil Post's Early Work.Liesbeth de Mol - 2006 - Bulletin of Symbolic Logic 12 (2):267-289.
    In 1931 Kurt Gödel published his incompleteness results, and some years later Church and Turing showed that the decision problem for certain systems of symbolic logic has a negative solution. However, already in 1921 the young logician Emil Post worked on similar problems which resulted in what he called an “anticipation” of these results. For several reasons though he did not submit these results to a journal until 1941. This failure ‘to be the first’, did not discourage him: his contributions (...)
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  17. Open Problems in the Philosophy of Information.Luciano Floridi - 2004 - Metaphilosophy 35 (4):554-582.
    The philosophy of information (PI) is a new area of research with its own field of investigation and methodology. This article, based on the Herbert A. Simon Lecture of Computing and Philosophy I gave at Carnegie Mellon University in 2001, analyses the eighteen principal open problems in PI. Section 1 introduces the analysis by outlining Herbert Simon's approach to PI. Section 2 discusses some methodological considerations about what counts as a good philosophical problem. The discussion centers on Hilbert's famous analysis (...)
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  18.  96
    Mechanism, Truth, and Penrose's New Argument.Stewart Shapiro - 2003 - Journal of Philosophical Logic 32 (1):19-42.
    Sections 3.16 and 3.23 of Roger Penrose's Shadows of the mind (Oxford, Oxford University Press, 1994) contain a subtle and intriguing new argument against mechanism, the thesis that the human mind can be accurately modeled by a Turing machine. The argument, based on the incompleteness theorem, is designed to meet standard objections to the original Lucas-Penrose formulations. The new argument, however, seems to invoke an unrestricted truth predicate (and an unrestricted knowability predicate). If so, its premises are inconsistent. The usual (...)
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  19.  64
    Is Our Universe Deterministic? Some Philosophical and Theological Reflections on an Elusive Topic.Taede A. Smedes - 2003 - Zygon 38 (4):955-979.
    . The question of whether or not our universe is deterministic remains of interest to both scientists and theologians. In this essay I argue that this question can be solved only by metaphysical decision and that no scientific evidence for either determinism or indeterminism will ever be conclusive. No finite being, no matter how powerful its cognitive abilities, will ever be able to establish the deterministic nature of the universe. The only being that would be capable of doing so would (...)
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  20.  5
    A Note on Applicability of the Incompleteness Theorem to Human Mind.Pavel Pudlák - 1999 - Annals of Pure and Applied Logic 96 (1-3):335-342.
  21.  85
    Incompleteness, Mechanism, and Optimism.Stewart Shapiro - 1998 - Bulletin of Symbolic Logic 4 (3):273-302.
  22. On Understanding Understanding.Roger Penrose - 1997 - International Studies in the Philosophy of Science 11 (1):7 – 20.
    It is argued, by use of specific examples, that mathematical understanding is something which cannot be modelled in terms of entirely computational procedures. Our conception of a natural number (a non-negative integer: 0, 1, 2, 3,…) is something which goes beyond any formulation in terms of computational rules. Our ability to perceive the properties of natural numbers depends upon our awareness, and represents just one of the many ways in which awareness provides an essential ingredient to our ability to understand. (...)
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  23.  57
    Consistency, Mechanicalness, and the Logic of the Mind.Qiuen Yu - 1992 - Synthese 90 (1):145-79.
    G. Priest's anti-consistency argument (Priest 1979, 1984, 1987) and J. R. Lucas's anti-mechanist argument (Lucas 1961, 1968, 1970, 1984) both appeal to Gödel incompleteness. By way of refuting them, this paper defends the thesis of quartet compatibility, viz., that the logic of the mind can simultaneously be Gödel incomplete, consistent, mechanical, and recursion complete (capable of all means of recursion). A representational approach is pursued, which owes its origin to works by, among others, J. Myhill (1964), P. Benacerraf (1967), J. (...)
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  24.  76
    On “Seeing” the Truth of the Gödel Sentence.George Boolos - 1990 - Behavioral and Brain Sciences 13 (4):655-656.
  25.  4
    Algorithms and Physical Laws.Franklin Boyle - 1990 - Behavioral and Brain Sciences 13 (4):656-657.
  26.  6
    AI and the Turing Model of Computation.Thomas M. Breuel - 1990 - Behavioral and Brain Sciences 13 (4):657.
  27.  8
    Lucas Revived? An Undefended Flank.Jeremy Butterfield - 1990 - Behavioral and Brain Sciences 13 (4):658.
  28.  88
    Computing the Thinkable.David J. Chalmers - 1990 - Behavioral and Brain Sciences 13 (4):658-659.
  29.  50
    Is Mathematical Insight Algorithmic?Martin Davis - 1990 - Behavioral and Brain Sciences 13 (4):659-660.
  30.  12
    Betting Your Life on an Algorithm.Daniel C. Dennett - 1990 - Behavioral and Brain Sciences 13 (4):660-661.
  31.  3
    Perceptive Questions About Computation and Cognition.Jon Doyle - 1990 - Behavioral and Brain Sciences 13 (4):661.
  32.  2
    Computations Over Abstract Categories of Representation.Roy Eagleson - 1990 - Behavioral and Brain Sciences 13 (4):661-662.
  33.  7
    Physics of Brain-Mind Interaction.John C. Eccles - 1990 - Behavioral and Brain Sciences 13 (4):662-663.
  34.  1
    Don't Ask Plato About the Emperor's Mind.Alan Gamham - 1990 - Behavioral and Brain Sciences 13 (4):664-665.
  35.  5
    Strong AI and the Problem of “Second-Order” Algorithms.Gerd Gigerenzer - 1990 - Behavioral and Brain Sciences 13 (4):663-664.
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  36.  1
    Where is the Material of the Emperor's Mind?David L. Gilden & Joseph S. Lappin - 1990 - Behavioral and Brain Sciences 13 (4):665-666.
  37.  24
    Why You'll Never Know Whether Roger Penrose is a Computer.Clark Glymour & Kevin Kelly - 1990 - Behavioral and Brain Sciences 13 (4):666-667.
  38.  9
    Penrose's Platonism.James Higginbotham - 1990 - Behavioral and Brain Sciences 13 (4):667-668.
  39.  4
    Selecting for the Con in Consciousness.Deborah Hodgkin & Alasdair I. Houston - 1990 - Behavioral and Brain Sciences 13 (4):668-669.
  40.  21
    A Long Time Ago in a Computing Lab Far, Far Away….Jeffery L. Johnson, R. H. Ettinger & Timothy L. Hubbard - 1990 - Behavioral and Brain Sciences 13 (4):670.
  41.  6
    Parallelism and Patterns of Thought.R. W. Kentridge - 1990 - Behavioral and Brain Sciences 13 (4):670-671.
  42.  6
    Time-Delays in Conscious Processes.Benjamin Libet - 1990 - Behavioral and Brain Sciences 13 (4):672.
  43.  4
    Quantum AI.Rudi Lutz - 1990 - Behavioral and Brain Sciences 13 (4):672-673.
  44.  3
    The Discomforts of Dualism.Bruce MacLennan - 1990 - Behavioral and Brain Sciences 13 (4):673-674.
  45.  5
    Uncertainty About Quantum Mechanics.Mark S. Madsen - 1990 - Behavioral and Brain Sciences 13 (4):674-675.
  46.  3
    Gödel redux.Alexis Manaster-Ramer, Walter J. Savitch & Wlodek Zadrozny - 1990 - Behavioral and Brain Sciences 13 (4):675-676.
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  47.  3
    Computation and Consciousness.Drew McDermott - 1990 - Behavioral and Brain Sciences 13 (4):676-678.
  48.  5
    The Powers of Machines and Minds.Chris Mortensen - 1990 - Behavioral and Brain Sciences 13 (4):678-679.
  49.  5
    Steadfast Intentions.Keith K. Niall - 1990 - Behavioral and Brain Sciences 13 (4):679-680.
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  50.  29
    Precis of the Emperor's New Mind.Roger Penrose - 1990 - Behavioral and Brain Sciences 13 (4):643-705.
    The emperor's new mind (hereafter Emperor) is an attempt to put forward a scientific alternative to the viewpoint of according to which mental activity is merely the acting out of some algorithmic procedure. John Searle and other thinkers have likewise argued that mere calculation does not, of itself, evoke conscious mental attributes, such as understanding or intentionality, but they are still prepared to accept the action the brain, like that of any other physical object, could in principle be simulated by (...)
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