Results for 'Diagonal'

148 found
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  1.  7
    A Monstrous Inference Called Mahāvidyānumāna and Cantor’s Diagonal Argument.Nirmalya Guha - 2016 - Journal of Indian Philosophy 44 (3):557-579.
    A mahāvidyā inference is used for establishing another inference. Its Reason is normally an omnipresent property. Its Target is defined in terms of a general feature that is satisfied by different properties in different cases. It assumes that there is no case that has the absence of its Target. The main defect of a mahāvidyā inference μ is a counterbalancing inference that can be formed by a little modification of μ. The discovery of its counterbalancing inference can invalidate such an (...)
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  2.  7
    Analogy and Diagonal Argument.Zbigniew Tworak - 2006 - Logic and Logical Philosophy 15 (1):39-66.
    In this paper, I try to accomplish two goals. The first is to provide a general characterization of a method of proofs called — in mathematics — the diagonal argument. The second is to establish that analogical thinking plays an important role also in mathematical creativity. Namely, mathematical research make use of analogies regarding general strategies of proof. Some of mathematicians, for example George Polya, argued that deductions is impotent without analogy. What I want to show is that there (...)
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  3.  46
    The Diagonal Method and Hypercomputation.Toby Ord & Tien D. Kieu - 2005 - British Journal for the Philosophy of Science 56 (1):147-156.
    The diagonal method is often used to show that Turing machines cannot solve their own halting problem. There have been several recent attempts to show that this method also exposes either contradiction or arbitrariness in other theoretical models of computation which claim to be able to solve the halting problem for Turing machines. We show that such arguments are flawed—a contradiction only occurs if a type of machine can compute its own diagonal function. We then demonstrate why such (...)
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  4.  21
    Grasping the Diagonal: Controlling Attention to Illusory Stimuli for Action and Perception.Elisabeth Stöttinger, Stefan Aigner, Klara Hanstein & Josef Perner - 2009 - Consciousness and Cognition 18 (1):223-228.
    Since the pioneering work of [Aglioti, S., DeSouza, J. F., & Goodale, M. A. . Size-contrast illusions deceive the eye but not the hand. Current Biology, 5, 679–685] visual illusions have been used to provide evidence for the functional division of labour within the visual system—one system for conscious perception and the other system for unconscious guidance of action. However, these studies were criticised for attentional mismatch between action and perception conditions and for the fact that grip size is not (...)
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  5.  80
    Was Descartes's Cogito a Diagonal Deduction?Roy A. Sorensen - 1986 - British Journal for the Philosophy of Science 37 (3):346-351.
    Peter Slezak and William Boos have independently advanced a novel interpretation of Descartes's "cogito". The interpretation portrays the "cogito" as a diagonal deduction and emphasizes its resemblance to Godel's theorem and the Liar. I object that this approach is flawed by the fact that it assigns 'Buridan sentences' a legitimate role in Descartes's philosophy. The paradoxical nature of these sentences would have the peculiar result of undermining Descartes's "cogito" while enabling him to "disprove" God's existence.
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  6.  15
    The Logic of Quantum Systems with Diagonal Singularities.I. Antoniou & Z. Suchanecki - 1994 - Foundations of Physics 24 (10):1439-1457.
    The work of the Brussels-Austin groups on irreversibility over the last years has shown that Quantum Large Poincaré systems with diagonal singularity lead to an extension of the conventional formulation of dynamics at the level of mixtures which is manifestly time asymmetric. States with diagonal singularity acquire meaning as linear fractionals over the involutive Banach algebra of operators with diagonal singularity. We show in this paper that the logic of quantum systems with diagonal singularity is not (...)
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  7.  40
    Diagonal Environmental Rights.John H. Knox - manuscript -
    Environmental rights are diagonal if they are held by individuals or groups against the governments of states other than their own. The potential importance of such rights is obvious: governments' actions often affect the environment beyond their jurisdiction, and those who live in and rely upon the environment affected would like to be able to exercise rights against the governments causing them harm. Although international law has not adopted a comprehensive, uniform approach to such rights, human rights law and (...)
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  8.  10
    Diagonal Actions and Borel Equivalence Relations.Longyun Ding & Su Gao - 2006 - Journal of Symbolic Logic 71 (4):1081 - 1096.
    We investigate diagonal actions of Polish groups and the related intersection operator on closed subgroups of the acting group. The Borelness of the diagonal orbit equivalence relation is characterized and is shown to be connected with the Borelness of the intersection operator. We also consider relatively tame Polish groups and give a characterization of them in the class of countable products of countable abelian groups. Finally an example of a logic action is considered and its complexity in the (...)
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  9.  2
    Diagonal Fixed Points in Algebraic Recursion Theory.Jordan Zashev - 2005 - Archive for Mathematical Logic 44 (8):973-994.
    The relation between least and diagonal fixed points is a well known and completely studied question for a large class of partially ordered models of the lambda calculus and combinatory logic. Here we consider this question in the context of algebraic recursion theory, whose close connection with combinatory logic recently become apparent. We find a comparatively simple and rather weak general condition which suffices to prove the equality of least fixed points with canonical (corresponding to those produced by the (...)
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  10. The Decision Problem of Modal Product Logics with a Diagonal, and Faulty Counter Machines.C. Hampson, S. Kikot & A. Kurucz - 2016 - Studia Logica 104 (3):455-486.
    In the propositional modal treatment of two-variable first-order logic equality is modelled by a ‘diagonal’ constant, interpreted in square products of universal frames as the identity relation. Here we study the decision problem of products of two arbitrary modal logics equipped with such a diagonal. As the presence or absence of equality in two-variable first-order logic does not influence the complexity of its satisfiability problem, one might expect that adding a diagonal to product logics in general is (...)
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  11. The Textuality of Diagonal Ornamentation: Historical Transformations of Signification From the Baltic Perspective.Vytautas Tumėnas - 2014 - Sign Systems Studies 42 (2-3):219.
    This paper deals with textual aspects of the geometric diagonal linear ornamentation that appears on traditional woven Lithuanian bands. Taking into consideration diachronic, local as well as universal perspectives, it aims to determine and classify the basic elements of the ornament that relate to the development of textuality. Previous investigations of Baltic and Lithuanian textile ornaments have been based on a purely geometric analysis of ornamental form, or on creating linguistic inventories of folk pattern denominations. This paper describes a (...)
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  12. The Diagonal and the Demon.Juan Comesaña - 2002 - Philosophical Studies 110 (3):249 - 266.
    Reliabilism about epistemic justification - the thesis that what makes a belief epistemically justified is that it was produced by a reliable process of belief-formation - must face two problems. First, what has been called "the new evil demon problem", which arises from the idea that the beliefs of victims of an evil demon are as justified as our own beliefs, although they are not - the objector claims - reliably produced. And second, the problem of diagnosing why skepticism is (...)
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  13.  2
    Eye Movements During Mental Time Travel Follow a Diagonal Line.Matthias Hartmann, Corinna S. Martarelli, Fred W. Mast & Kurt Stocker - 2014 - Consciousness and Cognition 30:201-209.
  14.  39
    What is Wrong with Cantor's Diagonal Argument?R. T. Brady & P. A. Rush - 2008 - Logique Et Analyse 51 (1):185-219..
    We first consider the entailment logic MC, based on meaning containment, which contains neither the Law of Excluded Middle (LEM) nor the Disjunctive Syllogism (DS). We then argue that the DS may be assumed at least on a similar basis as the assumption of the LEM, which is then justified over a finite domain or for a recursive property over an infinite domain. In the latter case, use is made of Mathematical Induction. We then show that an instance of the (...)
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  15.  21
    Diagonal Methods in the Theory of Isols.Erik Ellentuck - 1980 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 26 (13):193-204.
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  16.  93
    Descartes's Diagonal Deduction.Peter Slezak - 1983 - British Journal for the Philosophy of Science 34 (March):13-36.
    I OFFER AN ANALYSIS OF DESCARTES'S COGITO WHICH IS RADICALLY NOVEL WHILE INCORPORATING MUCH AVAILABLE INSIGHT. BY ENLARGING FOCUS FROM THE DICTUM ITSELF TO THE REASONING OF DOUBT, DREAMING AND DEMON, I DEMONSTRATE A CLOSE PARALLEL TO THE LOGIC OF THE LIAR PARADOX. THIS HELPS TO EXPLAIN FAMILIAR PARADOXICAL FEATURES OF DESCARTES'S ARGUMENT. THE ACCOUNT PROVES TO BE TEXTUALLY ELEGANT AND, MOREOVER, HAS CONSIDERABLE INDEPENDENT PHILOSOPHICAL PLAUSIBILITY AS AN ACCOUNT OF MIND AND SELF.
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  17.  19
    Intentionality and Computationalism. A Diagonal Argument.Laureano Luna & Christopher Small - 2009 - Mind and Matter 7 (1):81-90.
    Computationalism is the claim that all possible thoughts are computations, i.e. executions of algorithms. The aim of the paper is to show that if intentionality is semantically clear, in a way defined in the paper, then computationalism must be false. Using a convenient version of the phenomenological relation of intentionality and a diagonalization device inspired by Thomson's theorem of 1962, we show there exists a thought that canno be a computation.
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  18.  11
    Diagonal Prikry Extensions.James Cummings & Matthew Foreman - 2010 - Journal of Symbolic Logic 75 (4):1383-1402.
  19.  4
    Intentionality and Computationalism: A Diagonal Argument.Laureano Cabanero & C. G. Small - 2009 - Mind and Matter 7 (1):81-90.
    Computationalism is the claim that all possible thoughts are computations, i.e. executions of algorithms. The aim of the paper is to show that if intentionality is semantically clear, in a way defined in the paper, then computationalism must be false. Using a convenient version of the phenomenological relation of intentionality and a diagonalization device inspired by Thomson's theorem of 1962, we show there exists a thought that cannot be a computation.
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  20.  15
    Fixed Points and Diagonal Method.Maurizio Negri - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (4):319-329.
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  21.  39
    The Diagonal Argument and the Liar.Keith Simmons - 1990 - Journal of Philosophical Logic 19 (3):277 - 303.
  22.  52
    Was Descartes a Liar? Diagonal Doubt Defended.Peter Slezak - 1988 - British Journal for the Philosophy of Science 39 (3):379-388.
  23.  17
    The 'Square Itself' and 'Diagonal Itself' in Republic 510d.Moon-Heum Yang - 1999 - Ancient Philosophy 19 (1):31-35.
  24.  6
    I Inverted the Numbers of a Diagonal.Jean Daive & Serge Gavronsky - 1979 - Substance 8 (2/3):51.
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  25.  12
    Martin Repp: Aum Shinrikyô. Ein Kapitel krimineller Religionsgeschichte, Marburg: Diagonal-Verlag, 1997, 132 S.Lnken Prohl - 2000 - Zeitschrift für Religions- Und Geistesgeschichte 52 (2):182-183.
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  26.  33
    Book Review: Keith Simmons. Universality and the Liar: An Essay on Truth and the Diagonal Argument. [REVIEW]Gian Aldo Antonelli - 1996 - Notre Dame Journal of Formal Logic 37 (1):152-159.
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  27.  14
    On the Degrees of Diagonal Sets and the Failure of the Analogue of a Theorem of Martin.Keng Meng Ng - 2009 - Notre Dame Journal of Formal Logic 50 (4):469-493.
    Semi-hyperhypersimple c.e. sets, also known as diagonals, were introduced by Kummer. He showed that by considering an analogue of hyperhypersimplicity, one could characterize the sets which are the Halting problem relative to arbitrary computable numberings. One could also consider half of splittings of maximal or hyperhypersimple sets and get another variant of maximality and hyperhypersimplicity, which are closely related to the study of automorphisms of the c.e. sets. We investigate the Turing degrees of these classes of c.e. sets. In particular, (...)
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  28.  6
    El método diagonal en teoría de conjuntos y metamatemática.Gerold Stahl - 1981 - Teorema: International Journal of Philosophy 11 (1):27-35.
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  29.  2
    Ramsey-Type Graph Coloring and Diagonal Non-Computability.Ludovic Patey - 2015 - Archive for Mathematical Logic 54 (7-8):899-914.
  30.  21
    The Diagonal Method in Formalized Arithmetic. [REVIEW]G. Kreisel - 1953 - British Journal for the Philosophy of Science 3 (12):364-374.
  31.  8
    The Zograscope or Optical Diagonal Machine.J. A. Chaldecott - 1953 - Annals of Science 9 (4):315-322.
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  32.  1
    Universality and the Liar: An Essay on Truth and the Diagonal Argument.Patrick Grim & Keith Simmons - 1995 - Philosophical Review 104 (3):467.
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  33.  2
    L'irrationalité de la Diagonale Et du Côté d'Un Même Carré Dans les Questions de Biaise de Parme Sur le Traité des Rapports de Bradwardine/The Irrationality of the Diagonal with the Side of the Square in Blasius of Parma's Questions on the Treatise on Proportions of Bradwardine.Sabine Rommevaux - 2003 - Revue d'Histoire des Sciences 56 (2):401-418.
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  34.  2
    Fixed Points and Diagonal Method.Maurizio Negri - 1990 - Mathematical Logic Quarterly 36 (4):319-329.
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  35.  6
    The Diagonal Argument—A Study of Cases.Zvonimir Šikić - 1992 - International Studies in the Philosophy of Science 6 (3):191-203.
  36.  2
    Diagonal Advance: Perfection in Christian Theology by Anthony D. Baker , Xvi + 332 Pp. [REVIEW]Stewart D. Clem - 2014 - Modern Theology 30 (1):169-171.
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  37.  3
    Review: The Diagonal Method in Formalized Arithmetic. [REVIEW]G. Kreisel - 1953 - British Journal for the Philosophy of Science 3 (12):364 - 374.
  38.  1
    From a Well-Ordering of the Reals It is Easy (by a Diagonal Argument) to Produce a Non-Determined Set of Reals. However, Large Cardinal Axioms Imply That All Sets of Reals in L (R), and More, Are Determined. See, for Example, Neeman's Papers Optimalproofs of Determinacy.Andrzej S. Murawski - 1995 - Bulletin of Symbolic Logic 1:327-339.
  39. The Diagonal Method in Formalized Arithmetic. "Sentences Undecidable in Formalized Arithmetic: An Exposition of the Theory of Kurt Gödel." By A. Mostowski: Essay. [REVIEW]G. Kreisel - 1952 - British Journal for the Philosophy of Science 3 ([9/12]):364.
  40. Diagonal Method and Dialectical Logic: Tools, Materials, and Groundworks for a Logical Foundation of Dialectic and Speculative Philosophy.Uwe Petersen - 2002 - Der Andere Verlag.
    bk. 1. Tools for dialectic -- bk. 2. Historical-philosophical background materials -- bk. 3. Groundworks for dialectical logic.
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  41. Diagonal, argumento/Diagonalización/Método diagonal.José Pedro Ubeda Rives - 2011 - In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica. Editorial Trotta.
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  42. Thematic Files-the Reception of Euclid's Elements During the Middle Ages and the Renaissance-the Irrationality of the Diagonal with the Side of the Square in Blasius of Parma's Questions on The.Sabine Rommevaux - 2003 - Revue d'Histoire des Sciences 56 (2):401-418.
     
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  43. Introducing Off-Diagonal Elements to Singular Value Matrix in Probabilistic Latent Semantic Indexing.Naoki Shibayama & Hiroshi Nakagawa - 2011 - Transactions of the Japanese Society for Artificial Intelligence 26:262-272.
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  44.  36
    Universality and the Liar: An Essay on Truth and the Diagonal Argument.Keith Simmons - 1993 - Cambridge University Press.
    This book is about one of the most baffling of all paradoxes – the famous Liar paradox. Suppose we say: 'We are lying now'. Then if we are lying, we are telling the truth; and if we are telling the truth we are lying. This paradox is more than an intriguing puzzle, since it involves the concept of truth. Thus any coherent theory of truth must deal with the Liar. Keith Simmons discusses the solutions proposed by medieval philosophers and offers (...)
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  45. Attending to Horizontal, Diagonal, and Vertical Positions in Space.Yehoshua Tsal - 1989 - Bulletin of the Psychonomic Society 27 (2):133-134.
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  46. The Diagonal Argument—a Study of Cases. Zvonimir - 1992 - International Studies in the Philosophy of Science 6 (3):191 – 203.
  47.  17
    On the Possibility, or Otherwise, of Hypercomputation.Philip D. Welch - 2004 - British Journal for the Philosophy of Science 55 (4):739-746.
    We claim that a recent article of P. Cotogno ([2003]) in this journal is based on an incorrect argument concerning the non-computability of diagonal functions. The point is that whilst diagonal functions are not computable by any function of the class over which they diagonalise, there is no ?logical incomputability? in their being computed over a wider class. Hence this ?logical incomputability? regrettably cannot be used in his argument that no hypercomputation can compute the Halting problem. This seems (...)
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  48.  59
    Continuum, Name and Paradox.Vojtěch Kolman - 2010 - Synthese 175 (3):351 - 367.
    The article deals with Cantor's argument for the non-denumerability of reals somewhat in the spirit of Lakatos' logic of mathematical discovery. At the outset Cantor's proof is compared with some other famous proofs such as Dedekind's recursion theorem, showing that rather than usual proofs they are resolutions to do things differently. Based on this I argue that there are "ontologically" safer ways of developing the diagonal argument into a full-fledged theory of continuum, concluding eventually that famous semantic paradoxes based (...)
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  49.  39
    Constructing Cantorian Counterexamples.George Boolos - 1997 - Journal of Philosophical Logic 26 (3):237-239.
    Cantor's diagonal argument provides an indirect proof that there is no one-one function from the power set of a set A into A. This paper provides a somewhat more constructive proof of Cantor's theorem, showing how, given a function f from the power set of A into A, one can explicitly define a counterexample to the thesis that f is one-one.
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  50.  76
    The Metasyntactic Interpretation of Two-Dimensionalism.Gregory Bochner - 2013 - Philosophical Studies 163 (3):611-626.
    Robert Stalnaker contrasts two interpretations, semantic and metasemantic, of the two-dimensionalist framework. On the semantic interpretation, the primary intension or diagonal proposition associated with an utterance is a semantic value that the utterance has in virtue of the actual linguistic meaning of the corresponding sentence, and that primary intension is both what a competent speaker grasps and what determines different secondary intensions or horizontal propositions relative to different possible worlds considered as actual. The metasemantic interpretation reverses the order of (...)
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