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  1. On Propositional Quantifiers in Provability Logic.Sergei N. Artemov & Lev D. Beklemishev - 1993 - Notre Dame Journal of Formal Logic 34 (3):401-419.
  • On Accelerations in Science Driven by Daring Ideas: Good Messages From Fallibilistic Rationalism.Witold Marciszewski - 2015 - Studies in Logic, Grammar and Rhetoric 40 (1):19-41.
    The first good message is to the effect that people possess reason as a source of intellectual insights, not available to the senses, as e.g. axioms of arithmetic. The awareness of this fact is called rationalism. Another good message is that reason can daringly quest for and gain new plausible insights. Those, if suitably checked and confirmed, can entail a revision of former results, also in mathematics, and - due to the greater efficiency of new ideas - accelerate science’s progress. (...)
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  • What is a Computer? A Survey.William J. Rapaport - 2018 - Minds and Machines 28 (3):385-426.
    A critical survey of some attempts to define ‘computer’, beginning with some informal ones, then critically evaluating those of three philosophers, and concluding with an examination of whether the brain and the universe are computers.
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  • Turing: The Great Unknown.Aurea Anguera, Juan A. Lara, David Lizcano, María-Aurora Martínez, Juan Pazos & F. David de la Peña - 2020 - Foundations of Science 25 (4):1203-1225.
    Turing was an exceptional mathematician with a peculiar and fascinating personality and yet he remains largely unknown. In fact, he might be considered the father of the von Neumann architecture computer and the pioneer of Artificial Intelligence. And all thanks to his machines; both those that Church called “Turing machines” and the a-, c-, o-, unorganized- and p-machines, which gave rise to evolutionary computations and genetic programming as well as connectionism and learning. This paper looks at all of these and (...)
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  • Truth-Conditional Pragmatics: An Overview.Francois Recanati - 2008 - In Richmond Thomason, Paolo Bouquet & Luciano Serafini (eds.), Perspectives on Context. CSLI Stanford. pp. 171-188.
  • Hilbert's Philosophy of Mathematics.Marcus Giaquinto - 1983 - British Journal for the Philosophy of Science 34 (2):119-132.
  • A Renaissance of Empiricism in the Recent Philosophy of Mathematics.Imre Lakatos - 1976 - British Journal for the Philosophy of Science 27 (3):201-223.
  • Da metamatemática para a ciência cognitiva.Henrique de Morais Ribeiro - 1999 - Trans/Form/Ação 21 (1):181-193.
    para o domínio da Ciência Cognitiva funcionalista neurocomputacional. A descrição de tal transição é feita por meio de uma breve análise das idéias de Post, Church, Gödel e Turing sobre a possibilidade de formalização do pensamento criador na matemática, enfatizando as contribuições deste último.
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  • The Modal Argument for Hypercomputing Minds.Selmer Bringsjord - 2004 - Theoretical Computer Science 317.
  • Computing Machines Can't Be Intelligent (...And Turing Said So).Peter Kugel - 2002 - Minds and Machines 12 (4):563-579.
    According to the conventional wisdom, Turing said that computing machines can be intelligent. I don't believe it. I think that what Turing really said was that computing machines –- computers limited to computing –- can only fake intelligence. If we want computers to become genuinelyintelligent, we will have to give them enough “initiative” to do more than compute. In this paper, I want to try to develop this idea. I want to explain how giving computers more ``initiative'' can allow them (...)
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  • On Effective Procedures.Carol E. Cleland - 2002 - Minds and Machines 12 (2):159-179.
    Since the mid-twentieth century, the concept of the Turing machine has dominated thought about effective procedures. This paper presents an alternative to Turing's analysis; it unifies, refines, and extends my earlier work on this topic. I show that Turing machines cannot live up to their billing as paragons of effective procedure; at best, they may be said to provide us with mere procedure schemas. I argue that the concept of an effective procedure crucially depends upon distinguishing procedures as definite courses (...)
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  • Accelerating Turing Machines.B. Jack Copeland - 2002 - Minds and Machines 12 (2):281-300.
    Accelerating Turing machines are Turing machines of a sort able to perform tasks that are commonly regarded as impossible for Turing machines. For example, they can determine whether or not the decimal representation of contains n consecutive 7s, for any n; solve the Turing-machine halting problem; and decide the predicate calculus. Are accelerating Turing machines, then, logically impossible devices? I argue that they are not. There are implications concerning the nature of effective procedures and the theoretical limits of computability. Contrary (...)
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  • Physical Hypercomputation and the Church–Turing Thesis.Oron Shagrir & Itamar Pitowsky - 2003 - Minds and Machines 13 (1):87-101.
    We describe a possible physical device that computes a function that cannot be computed by a Turing machine. The device is physical in the sense that it is compatible with General Relativity. We discuss some objections, focusing on those which deny that the device is either a computer or computes a function that is not Turing computable. Finally, we argue that the existence of the device does not refute the Church–Turing thesis, but nevertheless may be a counterexample to Gandy's thesis.
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  • Super Turing-Machines.B. Jack Copeland - 1998 - Complexity 4 (1):30-32.
  • 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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  • The Necessity of Mathematics.Juhani Yli‐Vakkuri & John Hawthorne - 2018 - Noûs 52.
    Some have argued for a division of epistemic labor in which mathematicians supply truths and philosophers supply their necessity. We argue that this is wrong: mathematics is committed to its own necessity. Counterfactuals play a starring role.
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  • Three Dogmas of First-Order Logic and Some Evidence-Based Consequences for Constructive Mathematics of Differentiating Between Hilbertian Theism, Brouwerian Atheism and Finitary Agnosticism.Bhupinder Singh Anand - manuscript
    We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language. -/- We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'. -/- We then adopt what may (...)
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  • Scanlon’s Contractualism and the Redundancy Objection.Philip Stratton–Lake - 2003 - Analysis 63 (1):70-76.
    Ebbhinghaus, H., J. Flum, and W. Thomas. 1984. Mathematical Logic. New York, NY: Springer-Verlag. Forster, T. Typescript. The significance of Yablo’s paradox without self-reference. Available from http://www.dpmms.cam.ac.uk. Gold, M. 1965. Limiting recursion. Journal of Symbolic Logic 30: 28–47. Karp, C. 1964. Languages with Expressions of Infinite Length. Amsterdam.
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  • Turing's O-Machines, Searle, Penrose and the Brain.B. J. Copeland - 1998 - Analysis 58 (2):128-138.
  • Arithmetical Reflection and the Provability of Soundness.Walter Dean - 2015 - Philosophia Mathematica 23 (1):31-64.
    Proof-theoretic reflection principles are schemas which attempt to express the soundness of arithmetical theories within their own language, e.g., ${\mathtt{{Prov}_{\mathsf {PA}} \rightarrow \varphi }}$ can be understood to assert that any statement provable in Peano arithmetic is true. It has been repeatedly suggested that justification for such principles follows directly from acceptance of an arithmetical theory $\mathsf {T}$ or indirectly in virtue of their derivability in certain truth-theoretic extensions thereof. This paper challenges this consensus by exploring relationships between reflection principles (...)
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  • Beyond the Universal Turing Machine.Jack Copeland - 1999 - 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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  • Naïve Validity.Julien Murzi & Lorenzo Rossi - forthcoming - Synthese:1-23.
    Beall and Murzi :143–165, 2013) introduce an object-linguistic predicate for naïve validity, governed by intuitive principles that are inconsistent with the classical structural rules. As a consequence, they suggest that revisionary approaches to semantic paradox must be substructural. In response to Beall and Murzi, Field :1–19, 2017) has argued that naïve validity principles do not admit of a coherent reading and that, for this reason, a non-classical solution to the semantic paradoxes need not be substructural. The aim of this paper (...)
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  • The Philosophy of Computer Science.Raymond Turner - 2013 - Stanford Encyclopedia of Philosophy.
  • Michael Polanyi: Can the Mind Be Represented by a Machine?Paul Richard Blum - 2010 - Existence and Anthropology.
    On the 27th of October, 1949, the Department of Philosophy at the University of Manchester organized a symposium "Mind and Machine", as Michael Polanyi noted in his Personal Knowledge (1974, p. 261). This event is known, especially among scholars of Alan Turing, but it is scarcely documented. Wolfe Mays (2000) reported about the debate, which he personally had attended, and paraphrased a mimeographed document that is preserved at the Manchester University archive. He forwarded a copy to Andrew Hodges and B. (...)
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  • Toward a Formal Philosophy of Hypercomputation.Selmer Bringsjord & Michael Zenzen - 2002 - Minds and Machines 12 (2):241-258.
    Does what guides a pastry chef stand on par, from the standpoint of contemporary computer science, with what guides a supercomputer? Did Betty Crocker, when telling us how to bake a cake, provide an effective procedure, in the sense of `effective' used in computer science? According to Cleland, the answer in both cases is ``Yes''. One consequence of Cleland's affirmative answer is supposed to be that hypercomputation is, to use her phrase, ``theoretically viable''. Unfortunately, though we applaud Cleland's ``gadfly philosophizing'' (...)
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  • Turing's o-Machines, Searle, Penrose, and the Brain.Jack Copeland - 1998 - Analysis 58 (2):128-138.
    In his PhD thesis (1938) Turing introduced what he described as 'a new kind of machine'. He called these 'O-machines'. The present paper employs Turing's concept against a number of currently fashionable positions in the philosophy of mind.
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  • Truth Vs. Provability – Philosophical and Historical Remarks.Roman Murawski - 2002 - Logic and Logical Philosophy 10:93.
  • Reasoning, Logic and Computation.Stewart Shapiro - 1995 - Philosophia Mathematica 3 (1):31-51.
    The idea that logic and reasoning are somehow related goes back to antiquity. It clearly underlies much of the work in logic, as witnessed by the development of computability, and formal and mechanical deductive systems, for example. On the other hand, a platitude is that logic is the study of correct reasoning; and reasoning is cognitive if anything Is. Thus, the relationship between logic, computation, and correct reasoning makes an interesting and historically central case study for mechanism. The purpose of (...)
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  • Turing’s Algorithmic Lens: From Computability to Complexity Theory.Josep Díaz & Carme Torras - 2013 - Arbor 189 (764):a080.
  • On Turing’s Legacy in Mathematical Logic and the Foundations of Mathematics.Joan Bagaria - 2013 - Arbor 189 (764):a079.
  • The Need for Metaphysically-Based Ontologies in Higher-Level Information Fusion Applications.Eric Little - 2006 - In Ingvar Johansson, Bertin Klein & Thomas Roth-Berghofer (eds.), Wspi 2006: Contributions to the Third International Workshop on Philosophy and Informatics. pp. 89.
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  • Informal Versus Formal Mathematics.Francisco Antonio Doria - 2007 - Synthese 154 (3):401-415.
    We discuss Kunen’s algorithmic implementation of a proof for the Paris–Harrington theorem, and the author’s and da Costa’s proposed “exotic” formulation for the P = NP hypothesis. Out of those two examples we ponder the relation between mathematics within an axiomatic framework, and intuitive or informal mathematics.
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  • Godel's Program for New Axioms: Why, Where, How and What?Solomon Feferman - unknown
    From 1931 until late in his life (at least 1970) Godel called for the pursuit of new axioms for mathematics to settle both undecided number-theoretical propositions (of the form obtained in his incompleteness results) and undecided set-theoretical propositions (in particular CH). As to the nature of these, Godel made a variety of suggestions, but most frequently he emphasized the route of introducing ever higher axioms of in nity. In particular, he speculated (in his 1946 Princeton remarks) that there might be (...)
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  • Penrose's Gödelian Argument A Review of Shadows of the Mind by Roger Penrose. [REVIEW]S. Feferman - 1995 - PSYCHE: An Interdisciplinary Journal of Research On Consciousness 2:21-32.
    In his book Shadows of the Mind: A search for the missing science of con- sciousness [SM below], Roger Penrose has turned in another bravura perfor- mance, the kind we have come to expect ever since The Emperor’s New Mind [ENM ] appeared. In the service of advancing his deep convictions and daring conjectures about the nature of human thought and consciousness, Penrose has once more drawn a wide swath through such topics as logic, computa- tion, artificial intelligence, quantum physics (...)
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  • The Machine as Data: A Computational View of Emergence and Definability.S. Cooper - 2015 - Synthese 192 (7):1955-1988.
    Turing’s paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure comprehensively hosting causality at the physical level and beyond. On the other, it can give an insight into the way in which higher order information arises and leads to loss of computational control—while demonstrating how the control can be re-established, in special circumstances, via suitable type reductions. (...)
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  • Turing–Taylor Expansions for Arithmetic Theories.Joost Joosten - 2016 - Studia Logica 104 (6):1225-1243.
    Turing progressions have been often used to measure the proof-theoretic strength of mathematical theories: iterate adding consistency of some weak base theory until you “hit” the target theory. Turing progressions based on n-consistency give rise to a \ proof-theoretic ordinal \ also denoted \. As such, to each theory U we can assign the sequence of corresponding \ ordinals \. We call this sequence a Turing-Taylor expansion or spectrum of a theory. In this paper, we relate Turing-Taylor expansions of sub-theories (...)
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  • The Broad Conception of Computation.Jack Copeland - 1997 - 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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  • Chains of Life: Turing, Lebensform, and the Emergence of Wittgenstein’s Later Style.Juliet Floyd - 2016 - Nordic Wittgenstein Review 5 (2):7-89.
    This essay accounts for the notion of _Lebensform_ by assigning it a _logical _role in Wittgenstein’s later philosophy. Wittgenstein’s additions of the notion to his manuscripts of the _PI_ occurred during the initial drafting of the book 1936-7, after he abandoned his effort to revise _The Brown Book_. It is argued that this constituted a substantive step forward in his attitude toward the notion of simplicity as it figures within the notion of logical analysis. Next, a reconstruction of his later (...)
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  • Ideal Negative Conceivability and the Halting Problem.Manolo Martínez - 2013 - 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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  • 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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  • Informal and Absolute Proofs: Some Remarks From a Gödelian Perspective.Gabriella Crocco - 2019 - Topoi 38 (3):561-575.
    After a brief discussion of Kreisel’s notion of informal rigour and Myhill’s notion of absolute proof, Gödel’s analysis of the subject is presented. It is shown how Gödel avoids the notion of informal proof because such a use would contradict one of the senses of “formal” that Gödel wants to preserve. This Gödelian notion of “formal” is directly tied to his notion of absolute proof and to the question of the general applicability of concepts, in a way that overcomes both (...)
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  • The N-R.E. Degrees: Undecidability and Σ1 Substructures.Mingzhong Cai, Richard A. Shore & Theodore A. Slaman - 2012 - Journal of Mathematical Logic 12 (1):1250005-.
    We study the global properties of [Formula: see text], the Turing degrees of the n-r.e. sets. In Theorem 1.5, we show that the first order of [Formula: see text] is not decidable. In Theorem 1.6, we show that for any two n and m with n < m, [Formula: see text] is not a Σ1-substructure of [Formula: see text].
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  • Computability and Recursion.Robert I. Soare - 1996 - Bulletin of Symbolic Logic 2 (3):284-321.
    We consider the informal concept of "computability" or "effective calculability" and two of the formalisms commonly used to define it, "(Turing) computability" and "(general) recursiveness". We consider their origin, exact technical definition, concepts, history, general English meanings, how they became fixed in their present roles, how they were first and are now used, their impact on nonspecialists, how their use will affect the future content of the subject of computability theory, and its connection to other related areas. After a careful (...)
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  • Turing Oracle Machines, Online Computing, and Three Displacements in Computability Theory.Robert I. Soare - 2009 - Annals of Pure and Applied Logic 160 (3):368-399.
    We begin with the history of the discovery of computability in the 1930’s, the roles of Gödel, Church, and Turing, and the formalisms of recursive functions and Turing automatic machines . To whom did Gödel credit the definition of a computable function? We present Turing’s notion [1939, §4] of an oracle machine and Post’s development of it in [1944, §11], [1948], and finally Kleene-Post [1954] into its present form. A number of topics arose from Turing functionals including continuous functionals on (...)
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  • Alan Turing: Person of the XXth Century?José M. Sánchez Ron - 2013 - Arbor 189 (764):a085.
  • Preuves intuitionnistes touchant la première philosophie.Joseph Vidal-Rosset - 2013 - In . Les Cahiers D'Ithaque.
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  • Intuitionism and the Liar Paradox.Nik Weaver - 2012 - Annals of Pure and Applied Logic 163 (10):1437-1445.
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