Results for 'Proofs and Refutations'

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  1. Proofs and Refutations: The Logic of Mathematical Discovery.Imre Lakatos (ed.) - 1976 - Cambridge and London: Cambridge University Press.
    Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or (...)
  2.  85
    Proofs and Refutations (IV).I. Lakatos - 1963 - British Journal for the Philosophy of Science 14 (56):296-342.
  3.  17
    Proofs and Refutations.Imre Lakatos - 1980 - Noûs 14 (3):474-478.
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  4. Proofs and Refutations (I).Imre Lakatos - 1963 - British Journal for the Philosophy of Science 14 (53):1-25.
  5.  38
    Proofs and Refutations: The Logic of Mathematical Discovery.Imre Lakatos, John Worrall & Elie Zahar (eds.) - 1976 - Cambridge and London: Cambridge University Press.
    Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical (...)
  6.  82
    Proofs and Refutations (III).Imre Lakatos - 1963 - British Journal for the Philosophy of Science 14 (55):221-245.
  7. Proofs and Refutations (II).Imre Lakatos - 1963 - British Journal for the Philosophy of Science 14 (54):120-139.
  8. Proofs and Refutations. The Logic of Mathematical Discovery.I. Lakatos - 1977 - Tijdschrift Voor Filosofie 39 (4):715-715.
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  9. Proofs and Refutations: The Logic of Mathematical Discovery.Imre Lakatos, John Worrall & Elie Zahar - 1977 - Philosophy 52 (201):365-366.
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  10. Proofs and Refutations: The Logic of Mathematical Discovery.Imre Lakatos, John Worrall & Elie Zahar - 1978 - Mind 87 (346):314-316.
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  11.  7
    Proofs and Refutations: The Logic of Mathematical Discovery.Daniel Isaacson - 1978 - Philosophical Quarterly 28 (111):169-171.
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  12. Proofs and Refutations: The Logic of Mathematical Discovery.I. Lakatos, John Worrall & Elie Zahar - 1977 - British Journal for the Philosophy of Science 28 (1):81-82.
     
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  13. Proofs and Refutations: A Reassessment in Imre Lakatos and Theories of Scientific Change.Da Anapolitanos - 1989 - Boston Studies in the Philosophy of Science 111:337-345.
  14.  56
    Proof and Refutation in MALL as a Game.Olivier Delande, Dale Miller & Alexis Saurin - 2010 - Annals of Pure and Applied Logic 161 (5):654-672.
    We present a setting in which the search for a proof of B or a refutation of B can be carried out simultaneously: in contrast, the usual approach in automated deduction views proving B or proving ¬B as two, possibly unrelated, activities. Our approach to proof and refutation is described as a two-player game in which each player follows the same rules. A winning strategy translates to a proof of the formula and a counter-winning strategy translates to a refutation of (...)
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  15.  15
    Proofs and Refutations.Bruce Lercher - 1978 - International Studies in Philosophy 10:192-193.
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    Proofs and Refutations: The Logic of Mathematical Discovery By Imre Lakatos Edited by John Worrall and Elie Zahar Cambridge University Press, 1976, Xii + 174 Pp., £7.50, £1.95 Paper. [REVIEW]I. G. McFetridge - 1977 - Philosophy 52 (201):365-.
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  17. Co-Constructive Logic for Proofs and Refutations.James Trafford - 2014 - Studia Humana 3 (4):22-40.
    This paper considers logics which are formally dual to intuitionistic logic in order to investigate a co-constructive logic for proofs and refutations. This is philosophically motivated by a set of problems regarding the nature of constructive truth, and its relation to falsity. It is well known both that intuitionism can not deal constructively with negative information, and that defining falsity by means of intuitionistic negation leads, under widely-held assumptions, to a justification of bivalence. For example, we do not (...)
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  18. LAKATOS, I. "Proofs and Refutations: The Logic of Mathematical Discovery". Edited by J. Worrall and E. Zahar. [REVIEW]W. D. Hart - 1978 - Mind 87:314.
     
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  19.  41
    From the Method of Proofs and Refutations to the Methodology of Scientific Research Programmes.Gábor Forrai - 1993 - International Studies in the Philosophy of Science 7 (2):161-175.
    Abstract The paper is an attempt to interpret Imre Lakatos's methodology of scientific research programmes (MSRP) on the basis of his mathematical methodology, the method of proofs and refutations (MPR). After sketching MSRP and MPR and analysing their relationship to Popper's and Poly a's work, I argue that MSRP was originally conceived as a methodology in the same sense as MPR. The most conspicuous difference between the two, namely that MSRP is fundamentally backward?looking, whereas MPR is primarily forward?looking, (...)
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  20. LAKATOS, IMRE "Proofs and Refutations: The Logic of Mathematical Discovery". [REVIEW]I. G. Mcfetridge - 1977 - Philosophy 52:365.
     
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  21.  4
    LAKATOS, I.: "Proofs and Refutations: The Logic of Mathematical Discovery". [REVIEW]W. V. Quine - 1977 - British Journal for the Philosophy of Science 28:81.
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  22. Towards an Evolutionary Account of Conceptual Change in Mathematics: Proofs and Refutations and the Axiomatic Variation of Concepts.Thomas Mormann - 2002 - In G. Kampis, L.: Kvasz & M. Stöltzner (eds.), Appraising Lakatos: Mathematics, Methodology and the Man. Kluwer Academic Publishers. pp. 1--139.
  23.  22
    An Examination of Counterexamples in Proofs and Refutations.Samet Bağçe & Can Başkent - 2009 - Philosophia Scientiae 13 (2):3-20.
    : Lakatos’s seminal work Proofs and Refutations introduced the methods of proofs and refutations by discussing the history and methodological development of Euler’s formula V — E+F = 2 for three dimensional polyhedra. Lakatos considered the history of polyhedra illustrating a good example for his philosophy and methodology of mathematics and geometry. In this study, we focus on the mathematical and topological properties which play a role in Lakatos’s methodological approach. For each example and counterexample given (...)
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  24.  17
    Structuring Co-Constructive Logic for Proofs and Refutations.James Trafford - 2016 - Logica Universalis 10 (1):67-97.
    This paper considers a topos-theoretic structure for the interpretation of co-constructive logic for proofs and refutations following Trafford :22–40, 2015). It is notoriously tricky to define a proof-theoretic semantics for logics that adequately represent constructivity over proofs and refutations. By developing abstractions of elementary topoi, we consider an elementary topos as structure for proofs, and complement topos as structure for refutation. In doing so, it is possible to consider a dialogue structure between these topoi, and (...)
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  25.  52
    Refutations, Proofs, and Models in the Modal Logic K.Tomasz Skura - 2002 - Studia Logica 70 (2):193 - 204.
    In this paper we study the method of refutation rules in the modal logic K4. We introduce refutation rules with certain normal forms that provide a new syntactic decision procedure for this logic. As corollaries we obtain such results for the following important extensions: S4, the provability logic G, and Grzegorczyk''s logic. We also show that tree-type models can be constructed from syntactic refutations of this kind.
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  26.  13
    An Examination of Counterexamples in Proofs and Refutations.Samet Bağçe & Can Başkent - 2009 - Philosophia Scientae 13:3-20.
  27.  8
    Refutations, Proofs, and Models in the Modal Logic K4.Tomasz Skura - 2002 - Studia Logica 70 (2):193-204.
    In this paper we study the method of refutation rules in the modal logic K4. We introduce refutation rules with certain normal forms that provide a new syntactic decision procedure for this logic. As corollaries we obtain such results for the following important extensions: S4, the provability logic G, and Grzegorczyk's logic. We also show that tree-type models can be constructed from syntactic refutations of this kind.
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  28. Truth, Proof and Gödelian Arguments: A Defence of Tarskian Truth in Mathematics.Markus Pantsar - 2009 - Dissertation, University of Helsinki
    One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to (...)
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  29.  29
    Proof and Truth in Lakatos's Masterpiece.James Robert Brown - 1990 - International Studies in the Philosophy of Science 4 (2):117 – 130.
    Abstract Proofs and Refutations is Lakatos's masterpiece. This article investigates some of its central themes, in particular: the nature of proofs ('Proofs do not prove, they improve'); the nature of definitions (real, not nominal); and the consequences of all this for ontology (platonism vs Popper's World Three).
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  30. Proof and Truth. An Anti-Realist Perspective.Luca Tranchini - unknown
    In the first chapter, we discuss Dummett’s idea that the notion of truth arises from the one of the correctness of an assertion. We argue that, in a first-order language, the need of defining truth in terms of the notion of satisfaction, which is yielded by the presence of quantifiers, is structurally analogous to the need of a notion of truth as distinct from the one of correctness of an assertion. In the light of the analogy between predicates in Frege (...)
     
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  31.  17
    60% Proof: Lakatos, Proof, And Paraconsistency.Graham Priest & Neil Thomason - 2007 - Australasian Journal of Logic 5:89-100.
    Imre Lakatos’ Proofs and Refutations is a book well known to those who work in the philosophy of mathematics, though it is perhaps not widely referred to. Its general thrust is out of tenor with the foundationalist perspective that has dominated work in the philosophy of mathematics since the early years of the 20th century. It seems to us, though, that the book contains striking insights into the nature of proof, and the purpose of this paper is to (...)
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  32.  82
    Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures.James Robert Brown - 2008 - Routledge.
    1. Introduction : the mathematical image -- 2. Platonism -- 3. Picture-proofs and Platonism -- 4. What is applied mathematics? -- 5. Hilbert and Gödel -- 6. Knots and notation -- 7. What is a definition? -- 8. Constructive approaches -- 9. Proofs, pictures and procedures in Wittgenstein -- 10. Computation, proof and conjecture -- 11. How to refute the continuum hypothesis -- 12. Calling the bluff.
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  33. Semantic Epistemology Redux: Proof and Validity in Quantum Mechanics.Arnold Cusmariu - 2016 - Logos and Episteme 7 (3):287-303.
    Definitions I presented in a previous article as part of a semantic approach in epistemology assumed that the concept of derivability from standard logic held across all mathematical and scientific disciplines. The present article argues that this assumption is not true for quantum mechanics (QM) by showing that concepts of validity applicable to proofs in mathematics and in classical mechanics are inapplicable to proofs in QM. Because semantic epistemology must include this important theory, revision is necessary. The one (...)
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  34.  11
    Refutations and Proofs in S4.Tomasz Skura - 1996 - In H. Wansing (ed.), Proof Theory of Modal Logic. Kluwer Academic Publishers.
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  35.  10
    Faith and Knowledge: Kant's Refutation of the Ontological Proof of the Being of God.W. T. Harris - 1881 - Journal of Speculative Philosophy 15 (4):404 - 428.
  36.  1
    Proofs of Prophecy and the Refutation of the Ismāʿīliyya: The Kitāb Ithbāt Nubuwwat Al-Nabī by the Zaydī Al-Muʾayyad Bi-Llāh Al-Hārūnī (D. 411/1020). By Eva-Maria Lika. [REVIEW]Paul E. Walker - 2022 - Journal of the American Oriental Society 140 (3).
    Proofs of Prophecy and the Refutation of the Ismāʿīliyya: The Kitāb Ithbāt nubuwwat al-nabī by the Zaydī al-Muʾayyad bi-llāh al-Hārūnī. By Eva-Maria Lika. Worlds of Islam, vol. 9. Berlin: de Gruyter, 2018. Pp. vii + 177, 152. $149.99, €129.95, £106.99.
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    On the Apodictic Proof and Validation of Kant's Revolutionary Hypothesis.Brett A. Fulkerson-Smith - 2010 - Kantian Review 15 (1):37-56.
    The second edition of the Critique of Pure Reason contains several major and myriad minor emendations. The revision of the mode of presentation is apparent in four sections of the Critique: the Aesthetic; the Doctrine of the Concepts of the Understanding; the Principles of Pure Understanding; and ‘the paralogisms advanced against rational psychology’ . A new refutation of psychological idealism begins at B274. Perhaps most importantly, a new Preface frames the Critique.
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  38. Self-Refutation and Ancient Skepticism.Renata Zieminska - 2011 - Filozofia Nauki 19 (3):151.
    Luca Castagnoli, Ancient Self-Refutation. The Logic and History of the Self- Refutation Argument from Democritus to Augustine, Cambridge: Cambridge University Press 2010, pp. XX+394. Hardback, ISBN 9780521896313. In his book Ancient Self-Refutation L. Castagnoli rightly observes that selfrefutation is not falsification; it overturns the act of assertion but does not prove that the content of the act is false. He argues against the widely spread belief that Sextus Empiricus accepted the self-refutation of his own expressions. Castagnoli also claims that Sextus (...)
     
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  39. Logic: Argument, Refutation, and Proof.Richard L. Purtill - 1979 - New York, NY, USA: Harper & Row.
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  40. Descartes’ Cosmological and Ontological Proofs of God’s Existence: A Refutation of Skepticism?Vijay Mascarenhas - 2002 - Philosophical Investigations 25 (2):190–200.
  41.  8
    Frege Proof System and TNC$^Circ$.Gaisi Takeuti - 1998 - Journal of Symbolic Logic 63 (2):709-738.
    A Frege proof systemFis any standard system of prepositional calculus, e.g., a Hilbert style system based on finitely many axiom schemes and inference rules. An Extended Frege systemEFis obtained fromFas follows. AnEF-sequence is a sequence of formulas ψ1, …, ψκsuch that eachψiis either an axiom ofF, inferred from previous ψuand ψv by modus ponens or of the formq↔ φ, whereqis an atom occurring neither in φ nor in any of ψ1,…,ψi−1. Suchq↔ φ, is called an extension axiom andqa new extension (...)
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  42. Judah Halevi, The Book of Refutation and Proof on Behalf of the Despised Religion, or, The Kuzari.Joshua Parens & Joseph C. Macfarland - 2011 - In Joshua Parens & Joseph C. Macfarland (eds.), Medieval Political Philosophy: A Sourcebook. Cornell University Press.
  43. Frege Proof System and TNC°.Gaisi Takeuti - 1998 - Journal of Symbolic Logic 63 (2):709 - 738.
    A Frege proof systemFis any standard system of prepositional calculus, e.g., a Hilbert style system based on finitely many axiom schemes and inference rules. An Extended Frege systemEFis obtained fromFas follows. AnEF-sequence is a sequence of formulas ψ1, …, ψκsuch that eachψiis either an axiom ofF, inferred from previous ψuand ψv by modus ponens or of the formq↔ φ, whereqis an atom occurring neither in φ nor in any of ψ1,…,ψi−1. Suchq↔ φ, is called an extension axiom andqa new extension (...)
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  44. Classical Logic Through Refutation and Rejection.Achille C. Varzi & Gabriele Pulcini - forthcoming - In Landscapes in Logic (Volume on Philosophical Logics). College Publications.
    We offer a critical overview of two sorts of proof systems that may be said to characterize classical propositional logic indirectly (and non-standardly): refutation systems, which prove sound and complete with respect to classical contradictions, and rejection systems, which prove sound and complete with respect to the larger set of all classical non-tautologies. Systems of the latter sort are especially interesting, as they show that classical propositional logic can be given a paraconsistent characterization. In both cases, we consider Hilbert-style systems (...)
     
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  45.  73
    A Double Edged Sword? Kant's Refutation Of Mendelssohn's Proof Of The Immortality Of The Soul And Its Implications For His Theory Of Matter.Lorne Falkenstein - 1998 - Studies in History and Philosophy of Science Part A 29 (4):561-588.
  46.  39
    Sextan Skepticism and Self-Refutation.Renata Ziemińska - 2012 - Polish Journal of Philosophy 6 (1):89-99.
    Luca Castagnoli, Ancient Self-Refutation. The Logic and History of the Self- Refutation Argument from Democritus to Augustine, Cambridge: Cambridge University Press 2010, pp. XX+394. Hardback, ISBN 9780521896313. -/- Abstract. In his book Ancient Self-Refutation L. Castagnoli rightly observes that selfrefutation is not falsification; it overturns the act of assertion but does not prove that the content of the act is false. He argues against the widely spread belief that Sextus Empiricus accepted the self-refutation of his own expressions. Castagnoli also claims (...)
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  47. Moore’s Proof of an External World and the Problem of Skepticism.Charles Landesman - 1999 - Journal of Philosophical Research 24:21-36.
    Moore’s proof consists of the inference of both “Two hands exist at this moment” and “At least two external objects exist at this moment” from the premise “Here is one hand and here is another.” The paper claims that the proof succeeds in refuting both idealism (“There are no external objects”) and skepticism (“Nobody knows that there are external objects”). The paper defends Moore’s proof against the following objections: Idealism does not deny that there is an external world so Moore’s (...)
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  48.  1
    Proof Compression and NP Versus PSPACE II: Addendum.Lew Gordeev & Edward Hermann Haeusler - 2022 - Bulletin of the Section of Logic 51 (2):197-205.
    In our previous work we proved the conjecture NP = PSPACE by advanced proof theoretic methods that combined Hudelmaier’s cut-free sequent calculus for minimal logic with the horizontal compressing in the corresponding minimal Prawitz-style natural deduction. In this Addendum we show how to prove a weaker result NP = coNP without referring to HSC. The underlying idea is to omit full minimal logic and compress only “naive” normal tree-like ND refutations of the existence of Hamiltonian cycles in given non-Hamiltonian (...)
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  49. A Refutation of Mind-Body Identity.Raziel Abelson - 1970 - Philosophical Studies 21:85-90.
    An elementary mathematical proof is offered that mental states cannot be either intensionally or extensionally identical with brain states. the proof consists in taking a subset of mental states, namely, possible thoughts of integers and showing that this set has the cardinal number aleph null; then taking the largest physically possible set of brain states k and the number of subsets of k which is 2 to the power k, and which, no matter how large, is necessarily finite. it follows (...)
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    Degeneration and Entropy.Eugene Y. S. Chua - 2022 - Kriterion - Journal of Philosophy 36 (2):123-155.
    [Accepted for publication in Lakatos's Undone Work: The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of Science, special issue of Kriterion: Journal of Philosophy. Edited by S. Nagler, H. Pilin, and D. Sarikaya.] Lakatos’s analysis of progress and degeneration in the Methodology of Scientific Research Programmes is well-known. Less known, however, are his thoughts on degeneration in Proofs and Refutations. I propose and motivate two new criteria for degeneration based on the discussion in (...) and Refutations – superfluity and authoritarianism. I show how these criteria augment the account in Methodology of Scientific Research Programmes, providing a generalized Lakatosian account of progress and degeneration. I then apply this generalized account to a key transition point in the history of entropy – the transition to an information-theoretic interpretation of entropy – by assessing Jaynes’s 1957 paper on information theory and statistical mechanics. (shrink)
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