Search results for 'Diagonal' (try it on Scholar)

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  1. Zbigniew Tworak (2006). Analogy and Diagonal Argument. Logic and Logical Philosophy 15 (1):39-66.score: 24.0
    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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  2. John H. Knox, Diagonal Environmental Rights.score: 18.0
    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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  3. Roy A. Sorensen (1986). Was Descartes's Cogito a Diagonal Deduction? British Journal for the Philosophy of Science 37 (3):346-351.score: 18.0
    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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  4. Toby Ord & Tien D. Kieu (2005). The Diagonal Method and Hypercomputation. British Journal for the Philosophy of Science 56 (1):147-156.score: 18.0
    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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  5. I. Antoniou & Z. Suchanecki (1994). The Logic of Quantum Systems with Diagonal Singularities. Foundations of Physics 24 (10):1439-1457.score: 18.0
    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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  6. Longyun Ding & Su Gao (2006). Diagonal Actions and Borel Equivalence Relations. Journal of Symbolic Logic 71 (4):1081 - 1096.score: 18.0
    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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  7. Jordan Zashev (2005). Diagonal Fixed Points in Algebraic Recursion Theory. Archive for Mathematical Logic 44 (8):973-994.score: 18.0
    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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  8. Laureano Luna & Christopher Small (2009). Intentionality and Computationalism. A Diagonal Argument. Mind and Matter 7 (1):81-90.score: 16.0
    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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  9. Keng Meng Ng (2009). On the Degrees of Diagonal Sets and the Failure of the Analogue of a Theorem of Martin. Notre Dame Journal of Formal Logic 50 (4):469-493.score: 16.0
    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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  10. Juan Comesaña (2002). The Diagonal and the Demon. Philosophical Studies 110 (3):249 - 266.score: 15.0
    Reliabilism about epistemic justification – thethesis that what makes a belief epistemicallyjustified is that it was produced by a reliableprocess of belief-formation – must face twoproblems. First, what has been called ``the newevil demon problem'', which arises from the ideathat the beliefs of victims of an evil demonare as justified as our own beliefs, althoughthey are not – the objector claims – reliablyproduced. And second, the problem of diagnosingwhy skepticism is so appealing despite beingfalse. I present a special version ofreliabilism, (...)
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  11. Keith Simmons (1990). The Diagonal Argument and the Liar. Journal of Philosophical Logic 19 (3):277 - 303.score: 15.0
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  12. Keith Simmons (1993). Universality and the Liar: An Essay on Truth and the Diagonal Argument. Cambridge University Press.score: 15.0
    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 his own (...)
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  13. Peter Slezak (1983). Descartes's Diagonal Deduction. British Journal for the Philosophy of Science 34 (March):13-36.score: 15.0
    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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  14. Peter Slezak (1988). Was Descartes a Liar? Diagonal Doubt Defended. British Journal for the Philosophy of Science 39 (3):379-388.score: 15.0
  15. G. Kreisel (1953). The Diagonal Method in Formalized Arithmetic. [REVIEW] British Journal for the Philosophy of Science 3 (12):364-374.score: 15.0
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  16. Gian Aldo Antonelli (1996). Book Review: Keith Simmons. Universality and the Liar: An Essay on Truth and the Diagonal Argument. [REVIEW] Notre Dame Journal of Formal Logic 37 (1):152-159.score: 15.0
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  17. Elisabeth Stöttinger, Stefan Aigner, Klara Hanstein & Josef Perner (2009). Grasping the Diagonal: Controlling Attention to Illusory Stimuli for Action and Perception. Consciousness and Cognition 18 (1):223-228.score: 15.0
  18. R. T. Brady & P. A. Rush (2008). What is Wrong with Cantor's Diagonal Argument? Logique Et Analyse 51 (1):185-219..score: 15.0
    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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  19. Zvonimir Šikić (1992). The Diagonal Argument—A Study of Cases. International Studies in the Philosophy of Science 6 (3):191-203.score: 15.0
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  20. James Cummings & Matthew Foreman (2010). Diagonal Prikry Extensions. Journal of Symbolic Logic 75 (4):1383-1402.score: 15.0
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  21. J. A. Chaldecott (1953). The Zograscope or Optical Diagonal Machine. Annals of Science 9 (4):315-322.score: 15.0
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  22. G. Kreisel (1953). Review: The Diagonal Method in Formalized Arithmetic. [REVIEW] British Journal for the Philosophy of Science 3 (12):364 - 374.score: 15.0
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  23. Moon-Heum Yang (1999). The 'Square Itself' and 'Diagonal Itself' in Republic 510d. Ancient Philosophy 19 (1):31-35.score: 15.0
  24. Stewart D. Clem (2014). Diagonal Advance: Perfection in Christian Theology by Anthony D. Baker (Eugene, OR: Cascade Books, 2011), Xvi + 332 Pp. [REVIEW] Modern Theology 30 (1):169-171.score: 15.0
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  25. Uwe Petersen (2002). Diagonal Method and Dialectical Logic: Tools, Materials, and Groundworks for a Logical Foundation of Dialectic and Speculative Philosophy. Der Andere Verlag.score: 15.0
    bk. 1. Tools for dialectic -- bk. 2. Historical-philosophical background materials -- bk. 3. Groundworks for dialectical logic.
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  26. Laureano Cabanero & C. G. Small (2009). Intentionality and Computationalism: A Diagonal Argument. Mind and Matter 7 (1):81-90.score: 15.0
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  27. Erik Ellentuck (1980). Diagonal Methods in the Theory of Isols. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 26 (13):193-204.score: 15.0
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  28. Andrzej S. Murawski (1995). 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. Bulletin of Symbolic Logic 1:327-339.score: 15.0
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  29. Maurizio Negri (1990). Fixed Points and Diagonal Method. Mathematical Logic Quarterly 36 (4):319-329.score: 15.0
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  30. Lnken Prohl (2000). Martin Repp: Aum Shinrikyô. Ein Kapitel krimineller Religionsgeschichte, Marburg: Diagonal-Verlag, 1997, 132 S. Zeitschrift für Religions- Und Geistesgeschichte 52 (2):182-183.score: 15.0
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  31. José Pedro Ubeda Rives (2011). Diagonal, argumento/Diagonalización/Método diagonal. In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica. Editorial Trotta.score: 15.0
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  32. Sabine Rommevaux (2003). 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. Revue d'Histoire des Sciences 56 (2):401-418.score: 15.0
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  33. Sabine Rommevaux (2003). 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. Revue d'Histoire des Sciences 56 (2):401-418.score: 15.0
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  34. Gerold Stahl (1981). El método diagonal en teoría de conjuntos y metamatemática. Teorema 11 (1):27-35.score: 15.0
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  35. Yehoshua Tsal (1989). Attending to Horizontal, Diagonal, and Vertical Positions in Space. Bulletin of the Psychonomic Society 27 (2):133-134.score: 15.0
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  36. Zvonimir (1992). The Diagonal Argument—a Study of Cases. International Studies in the Philosophy of Science 6 (3):191 – 203.score: 15.0
     
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  37. Andrzej Wiśniewski & Jerzy Pogonowski (2010). Diagonalization in Double Frames. Logica Universalis 4 (1):31-39.score: 10.0
    We consider structures of the form (Φ, Ψ, R ), where Φ and Ψ are non-empty sets and is a relation whose domain is Ψ. In particular, by using a special kind of a diagonal argument, we prove that if Φ is a denumerable recursive set, Ψ is a denumerable r.e. set, and R is an r.e. relation, then there exists an infinite family of infinite recursive subsets of Φ which are not R -images of elements of Ψ. (...)
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  38. Gregory Bochner (2013). The Metasyntactic Interpretation of Two-Dimensionalism. Philosophical Studies 163 (3):611-626.score: 9.0
    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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  39. Vojtěch Kolman (2010). Continuum, Name and Paradox. Synthese 175 (3):351 - 367.score: 9.0
    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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  40. George Boolos (1997). Constructing Cantorian Counterexamples. Journal of Philosophical Logic 26 (3):237-239.score: 9.0
    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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  41. Anne Newstead & Franklin James (2008). On the Reality of the Continuum. Philosophy 83 (01):117-28.score: 9.0
    In a recent article (‘The Continuum: Russell’s Moment of Candour’), Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably infinite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable infinity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-defined’ real numbers as proper objects of (...)
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  42. Philip D. Welch (2004). On the Possibility, or Otherwise, of Hypercomputation. British Journal for the Philosophy of Science 55 (4):739-746.score: 9.0
    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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  43. Laura Schroeter (2003). Gruesome Diagonals. Philosophers' Imprint 3 (3):1-23.score: 8.0
    Frank Jackson and David Chalmers have suggested that the diagonal intensions defined by their two-dimensional framework can play the two key roles of Fregean senses: they provide a priori accessible extension conditions for a representation and they provide the identity conditions for meanings and thought contents. In this paper, I clarify the nature of the psychological abilities that are needed to underwrite the first role. I then argue that these psychological abilities are not sufficiently stable or cognitively salient to (...)
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  44. Gaetano Chiurazzi (2008). The Diagonalization of Being. Proceedings of the Xxii World Congress of Philosophy 2:13-19.score: 8.0
    Plato’s Theaetetus sets the problem of the definition of science; moreover, what there is in question is the problem of the definition in general. Defining means measuring, referring to definite parameters what is initially indefinite. But it is not a case that the dialogue opens with the discussion about the commensurable and incommensurable numbers: the search for what is common to all sciences is the search for their common measure, for the term to which various elements are or can be (...)
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  45. Dale Jacquette (forthcoming). Computable Diagonalizations and Turing's Cardinality Paradox. Journal for General Philosophy of Science:1-24.score: 8.0
    A. N. Turing’s 1936 concept of computability, computing machines, and computable binary digital sequences, is subject to Turing’s Cardinality Paradox. The paradox conjoins two opposed but comparably powerful lines of argument, supporting the propositions that the cardinality of dedicated Turing machines outputting all and only the computable binary digital sequences can only be denumerable, and yet must also be nondenumerable. Turing’s objections to a similar kind of diagonalization are answered, and the implications of the paradox for the concept of a (...)
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  46. Dilip Raghavan (2010). Almost Disjoint Families and Diagonalizations of Length Continuum. Bulletin of Symbolic Logic 16 (2):240 - 260.score: 8.0
    We present a survey of some results and problems concerning constructions which require a diagonalization of length continuum to be carried out, particularly constructions of almost disjoint families of various sorts. We emphasize the role of cardinal invariants of the continuum and their combinatorial characterizations in such constructions.
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  47. Samuel Alexander (2013). This Sentence Does Not Contain the Symbol X. The Reasoner 7 (9):108.score: 6.0
    A suprise may occur if we use a similar strategy to the Liar's paradox to mathematically formalize "This sentence does not contain the symbol X".
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  48. Cory Juhl (1995). Is Gold-Putnam Diagonalization Complete? Journal of Philosophical Logic 24 (2):117 - 138.score: 6.0
    Diagonalization is a proof technique that formal learning theorists use to show that inductive problems are unsolvable. The technique intuitively requires the construction of the mathematical equivalent of a "Cartesian demon" that fools the scientist no matter how he proceeds. A natural question that arises is whether diagonalization is complete. That is, given an arbitrary unsolvable inductive problem, does an invincible demon exist? The answer to that question turns out to depend upon what axioms of set theory we adopt. The (...)
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  49. Tomek Bartoszynski, Saharon Shelah & Boaz Tsaban (2003). Additivity Properties of Topological Diagonalizations. Journal of Symbolic Logic 68 (4):1254-1260.score: 6.0
    We answer a question of Just, Miller, Scheepers and Szeptycki whether certain diagonalization properties for sequences of open covers are provably closed under taking finite or countable unions.
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  50. Geoff Rayner-Canham (2011). Isodiagonality in the Periodic Table. Foundations of Chemistry 13 (2):121-129.score: 6.0
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