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John Lucas (2003). Minds, Machines and Gödel.

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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.  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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  5.  27
    Beyond Physics? On the Prospects of Finding a Meaningful Oracle.Taner Edis & Maarten Boudry - 2014 - Foundations of Science 19 (4):403-422.
    Certain enterprises at the fringes of science, such as intelligent design creationism, claim to identify phenomena that go beyond not just our present physics but any possible physical explanation. Asking what it would take for such a claim to succeed, we introduce a version of physicalism that formulates the proposition that all available data sets are best explained by combinations of “chance and necessity”—algorithmic rules and randomness. Physicalism would then be violated by the existence of oracles that produce certain kinds (...)
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  6. On Some Properties of Humanly Known and Humanly Knowable Mathematics.Jason L. Megill, Tim Melvin & Alex Beal - 2014 - Axiomathes 24 (1):81-88.
    We argue that the set of humanly known mathematical truths (at any given moment in human history) is finite and so recursive. But if so, then given various fundamental results in mathematical logic and the theory of computation (such as Craig’s in J Symb Log 18(1): 30–32(1953) theorem), the set of humanly known mathematical truths is axiomatizable. Furthermore, given Godel’s (Monash Math Phys 38: 173–198, 1931) First Incompleteness Theorem, then (at any given moment in human history) humanly known mathematics must (...)
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  7. 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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  8. 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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  9.  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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  10. 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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  11.  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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  12.  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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  13.  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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  14. 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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  15.  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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  16.  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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  17.  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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  18. 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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  19.  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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  20.  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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  21. The Turing Test: The First Fifty Years.Robert French - 2000 - Trends in Cognitive Sciences 4 (3):115-121.
    The Turing Test, originally proposed as a simple operational definition of intelligence, has now been with us for exactly half a century. It is safe to say that no other single article in computer science, and few other articles in science in general, have generated so much discussion. The present article chronicles the comments and controversy surrounding Turing's classic article from its publication to the present. The changing perception of the Turing Test over the last fifty years has paralleled the (...)
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  22.  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.
  23.  85
    Incompleteness, Mechanism, and Optimism.Stewart Shapiro - 1998 - Bulletin of Symbolic Logic 4 (3):273-302.
  24. Is the Human Mind a Turing Machine?D. King - 1996 - Synthese 108 (3):379-89.
    In this paper I discuss the topics of mechanism and algorithmicity. I emphasise that a characterisation of algorithmicity such as the Turing machine is iterative; and I argue that if the human mind can solve problems that no Turing machine can, the mind must depend on some non-iterative principle — in fact, Cantor's second principle of generation, a principle of the actual infinite rather than the potential infinite of Turing machines. But as there has been theorisation that all physical systems (...)
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  25.  32
    Simulating Convesations: The Communion Game. [REVIEW]Stephen J. Cowley & Karl MacDorman - 1995 - AI and Society 9 (2-3):116-137.
    In their enthusiasm for programming, computational linguists have tended to lose sight of what humansdo. They have conceived of conversations as independent of sound and the bodies that produce it. Thus, implicit in their simulations is the assumption that the text is the essence of talk. In fact, unlike electronic mail, conversations are acoustic events. During everyday talk, human understanding depends both on the words spoken and on fine interpersonal vocal coordination. When utterances are analysed into sequences of word-based forms, (...)
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  26.  52
    Computationalism.Stuart C. Shapiro - 1995 - Minds and Machines 5 (4):467-87.
    Computationalism, the notion that cognition is computation, is a working hypothesis of many AI researchers and Cognitive Scientists. Although it has not been proved, neither has it been disproved. In this paper, I give some refutations to some well-known alleged refutations of computationalism. My arguments have two themes: people are more limited than is often recognized in these debates; computer systems are more complicated than is often recognized in these debates. To underline the latter point, I sketch the design and (...)
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  27.  27
    Minds, Machines and Self-Reference.Peter Slezak - 1984 - Dialectica 38 (1):17-34.
    SummaryJ.R. Lucas has argued that it follows from Godel's Theorem that the mind cannot be a machine or represented by any formal system. Although this notorious argument against the mechanism thesis has received considerable attention in the literature, it has not been decisively rebutted, even though mechanism is generally thought to be the only plausible view of the mind. In this paper I offer an analysis of Lucas's argument which shows that it derives its persuasiveness from a subtle confusion. In (...)
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