35 found
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  1. Informal Rigour and Completeness Proofs.Georg Kreisel - 1967 - In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. North-Holland. pp. 138--157.
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  2. Interpretation of Analysis by Means of Constructive Functionals of Finite Types.Georg Kreisel - 1959 - In A. Heyting (ed.), Constructivity in Mathematics. Amsterdam: North-Holland Pub. Co.. pp. 101--128.
     
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  3.  47
    Reflection Principles and Their Use for Establishing the Complexity of Axiomatic Systems.Georg Kreisel & Azriel Lévy - 1968 - Zeitschrift für Mathematische Logic Und Grundlagen der Mathematik 14 (1):97--142.
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  4.  45
    Mathematical Logic.Georg Kreisel - 1967 - Journal of Symbolic Logic 32 (3):419-420.
  5.  29
    Hilbert's programme.Georg Kreisel - 1958 - Dialectica 12 (3‐4):346-372.
    Hilbert's plan for understanding the concept of infinity required the elimination of non‐finitist machinery from proofs of finitist assertions. The failure of the original plan leads to a hierarchy of progressively less elementary, but still constructive methods instead of finitist ones . A mathematical proof of this failure requires a definition of « finitist ».—The paper sketches the three principal methods for the syntactic analysis of non‐constructive mathematics, the resulting consistency proofs and constructive interpretations, modelled on Herbrand's theorem, and their (...)
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  6.  19
    Elements of Mathematical Logic: Model Theory.Georg Kreisel - 1967 - Amsterdam: North Holland Pub. Co..
  7. Church's Thesis and the Ideal of Informal Rigour.Georg Kreisel - 1987 - Notre Dame Journal of Formal Logic 28 (4):499-519.
  8.  19
    A Survey of Mathematical Logic.Georg Kreisel - 1966 - Philosophical Review 75 (2):240-244.
  9.  7
    Hilbert's Programme.Georg Kreisel - 1962 - Journal of Symbolic Logic 27 (2):228-229.
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  10.  93
    Mathematical Logic: Tool and Object Lesson for Science.Georg Kreisel - 1985 - Synthese 62 (2):139-151.
    The object lesson concerns the passage from the foundational aims for which various branches of modern logic were originally developed to the discovery of areas and problems for which logical methods are effective tools. The main point stressed here is that this passage did not consist of successive refinements, a gradual evolution by adaptation as it were, but required radical changes of direction, to be compared to evolution by migration. These conflicts are illustrated by reference to set theory, model theory, (...)
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  11.  32
    Finite Definability of Number-Theoretic Functions and Parametric Completeness of Equational Calculi.Georg Kreisel & William W. Tait - 1961 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (1-5):28-38.
  12.  7
    Ensembles Récursivement Mesurable Et Ensembles Récursivement Ouverts Ou Fermés.Georg Kreisel & Daniel Lacombe - 1966 - Journal of Symbolic Logic 31 (1):133-133.
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  13.  21
    Formally Self-Referential Propositions for Cut Free Analysis and Related Systems.Georg Kreisel & Gaisi Takeuti - 1985 - Journal of Symbolic Logic 50 (1):244-246.
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  14.  89
    Collected Works of Kurt Godel 1938-1974.Georg Kreisel, Kurt Godel, Solomon Feferman, John W. Dawson, Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay & Jean van Heijenoort - 1991 - Journal of Symbolic Logic 56 (3):1085.
  15.  2
    Reviews. Kurt Schütte. Beweistheorie. Springer-Verlag, Berlin-Göttingen-Heidelberg 1960, X + 355 pp. [REVIEW]Georg Kreisel - 1960 - Journal of Symbolic Logic 25 (3):243-249.
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  16. Éléments de Logique Mathématique Théorie des Modèles.Georg Kreisel & J. L. Krivine - 1967 - Dunod.
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  17.  7
    Review: Kurt Schutte, Beweistheorie. [REVIEW]Georg Kreisel - 1960 - Journal of Symbolic Logic 25 (3):243-249.
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  18.  43
    Hilary Putnam. Mathematics Without Foundations. The Journal of Philosophy, Vol. 64 , Pp. 5–22.Georg Kreisel - 1972 - Journal of Symbolic Logic 37 (2):402-404.
  19.  22
    Hao Wang. Logic, Computation and Philosophy. L''ge de la Science, Vol. 3 , Pp. 101–115.Georg Kreisel - 1974 - Journal of Symbolic Logic 39 (2):358-359.
  20.  20
    S. Ú. Maslov, G. É. Minc, and V. P. Orévkov. Nérazréšimost′ Ν Konstruktivnom Isčislénii Prédikatov Nékotoryh Klassov Formul, Sodéržaščih Tol′Ko Odnoméstnyé Prédikatnyé Péréménnyé. Doklady Akadémii Nauk, Vol. 163 , Pp. 295–297. - S. Ju. Maslov, G. E. Minc, and V. P. Orevkov. Unsolvability in the Constructive Predicate Calculus of Certain Classes of Formulas Containing Only Monadic Predicate Variables. Translation of the Preceding by E. Mendelson. Soviet Mathematics, Vol. 6 , Pp. 918–920. [REVIEW]Georg Kreisel - 1970 - Journal of Symbolic Logic 35 (1):143-144.
  21.  49
    The Motto of 'Philosophical Investigations' and the Philosophy of Proofs and Rules.Georg Kreisel - 1978 - Grazer Philosophische Studien 6 (1):13-38.
    Ausgangspunkt dieses Artikels ist die Einsicht, die auch von Wittgenstein und der "schweigenden Mehrheit" geteilt wird, daß die meisten sogenannten fundamentalen Begriffe und Probleme der Philosophie erkenntnistheoretisch unrentabel sind, insbesondere der Begriff der Gültigkeit (von Beweis- und Rechenregeln) und seine traditionelle Problematik. Im Gegensatz zu Wittgenstein wird diese Einsicht aber nicht auf "Sinnlosigkeit", d.h. Präzisionsunfähigkeitjener Problematik, sondern auf ihre Oberflächl d.h. unangemessene Allgemeinheit, zurückgeführt.
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  22.  5
    Finite Definability of Number-Theoretic Functions and Parametric Completeness of Equational Calculi.Georg Kreisel & William W. Tait - 1967 - Journal of Symbolic Logic 32 (2):270-271.
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  23.  14
    N. A. Šanin. On the Constructive Interpretation of Mathematical Judgments. English Translation of XXXI 255 by Elliott Mendelson. American Mathematical Society Translations, Ser. 2 Vol. 23 , Pp. 109–189. - A. A. Markov. On Constructive Functions. English Translation of XXXI 258 by Moshe Machover. American Mathematical Society Translations, Vol. 29 , Pp. 163–195. - S. C. Kleene. A Formal System of Intuitionistic Analysis. The Foundations of Intuitionistlc Mathematics Especially in Relation to Recursive Functions, by Stephen Cole Kleene and Richard Eugene Vesley, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam1965, Pp. 1–89. - S. C. Kleene. Various Notions of Realizability:The Foundations of Intuitionistlc Mathematics Especially in Relation to Recursive Functions, by Stephen Cole Kleene and Richard Eugene Vesley, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam1965, Pp. 90–132. - Richard E. Ve. [REVIEW]Georg Kreisel - 1966 - Journal of Symbolic Logic 31 (2):258-261.
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  24.  13
    Solomon Feferman. Ordinals and Functionals in Proof Theory. Actes du Congrès International des Mathématiciens 1970, Gauthier-Villars, Paris 1971, Vol. 1, Pp. 229–233. [REVIEW]Georg Kreisel - 1975 - Journal of Symbolic Logic 40 (4):625-626.
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  25.  48
    Book Review: Collected Works, Vol. I [Oxford Univ. Press, New York, 1986] by K. Gödel. [REVIEW]Georg Kreisel - 1987 - Notre Dame Journal of Formal Logic 29 (1):160-181.
  26.  9
    Collected Works, Volume II, Publications 1938–1974, by Kurt Gödel, Edited by Solomon Feferman, John W. DawsonJr., Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay, and Jean van Heijenoort, Oxford University Press, New York and Oxford 1990, Xv + 407 Pp. [REVIEW]Georg Kreisel - 1991 - Journal of Symbolic Logic 56 (3):1085-1089.
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  27.  15
    Some Concepts Concerning Formal Systems of Number Theory.Georg Kreisel - 1966 - Journal of Symbolic Logic 31 (1):128-128.
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  28.  15
    Logical Hygiene, Foundations, and Abstractions: Diversity Among Aspects and Options.Georg Kreisel - 2011 - In Matthias Baaz (ed.), Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press. pp. 27.
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  29.  11
    The Motto of 'Philosophical Investigations' and the Philosophy of Proofs and Rules.Georg Kreisel - 1978 - Grazer Philosophische Studien 6 (1):13-38.
    Ausgangspunkt dieses Artikels ist die Einsicht, die auch von Wittgenstein und der "schweigenden Mehrheit" geteilt wird, daß die meisten sogenannten fundamentalen Begriffe und Probleme der Philosophie erkenntnistheoretisch unrentabel sind, insbesondere der Begriff der Gültigkeit und seine traditionelle Problematik. Im Gegensatz zu Wittgenstein wird diese Einsicht aber nicht auf "Sinnlosigkeit", d.h. Präzisionsunfähigkeitjener Problematik, sondern auf ihre Oberflächl d.h. unangemessene Allgemeinheit, zurückgeführt.
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  30.  4
    Formal Rules and Questions of J U S T I F y I N G Mathematical Practice.Georg Kreisel - 1978 - In Kuno Lorenz (ed.), Konstruktionen Versus Positionen: Beiträge Zur Diskussion Um Die Konstruktive Wissenschaftstheorie. Bd 1: Spezielle Wissenschaftstheorie. Bd 2: Allgemeine Wissenschaftstheorie. Paul Lorenzen Zum 60. Geburtstag. De Gruyter. pp. 99-130.
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  31.  13
    Review: Hao Wang, Logic, Computation and Philosophy. [REVIEW]Georg Kreisel - 1974 - Journal of Symbolic Logic 39 (2):358-359.
  32.  2
    Book Review: "Kurt Gödel, Collected Works, Vol. I". [REVIEW]Georg Kreisel - 1987 - Notre Dame Journal of Formal Logic 29:160-181.
  33.  7
    Gödel's Intepretation of Heyting's Arithmetic.Georg Kreisel, G. Kreisel & A. Heyting - 1971 - Journal of Symbolic Logic 36 (1):169-171.
  34.  5
    Review: Solomon Feferman, Ordinals and Functionals in Proof Theory. [REVIEW]Georg Kreisel - 1975 - Journal of Symbolic Logic 40 (4):625-626.
  35. Review: N. A. Sanin, On the Constructive Interpretation of Mathematical Judgments; S. C. Kleene, A Formal System of Intuitionistic Analysis. [REVIEW]Georg Kreisel - 1966 - Journal of Symbolic Logic 31 (2):258-261.