109 found
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  1. Georg Kreisel (1967). Informal Rigour and Completeness Proofs. In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. North-Holland 138--157.
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  2.  55
    G. Kreisel (1968). A Survey of Proof Theory. Journal of Symbolic Logic 33 (3):321-388.
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  3.  11
    G. Kreisel & A. S. Troelstra (1970). Formal Systems for Some Branches of Intuitionistic Analysis. Annals of Mathematical Logic 1 (3):229-387.
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  4.  19
    Georg Kreisel & Azriel Lévy (1968). Reflection Principles and Their Use for Establishing the Complexity of Axiomatic Systems. Zeitschrift für Mathematische Logic Und Grundlagen der Mathematik 14 (1):97--142.
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  5. Georg Kreisel (1959). Interpretation of Analysis by Means of Constructive Functionals of Finite Types. In A. Heyting (ed.), Constructivity in Mathematics. Amsterdam, North-Holland Pub. Co. 101--128.
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  6.  42
    S. Feferman, G. Kreisel & S. Orey (forthcoming). 1 — Consistency and Faithful Interpretations. Archive for Mathematical Logic.
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  7. G. Kreisel (1958). Wittgenstein's Remarks on the Foundations of Mathematics. [REVIEW] British Journal for the Philosophy of Science 9 (34):135-158.
  8.  45
    G. Kreisel (1974). A Notion of Mechanistic Theory. Synthese 29 (1-4):11 - 26.
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  9.  77
    Georg Kreisel (1987). Church's Thesis and the Ideal of Informal Rigour. Notre Dame Journal of Formal Logic 28 (4):499-519.
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  10.  15
    G. Kreisel (1971). The Collected Papers of Gerhard Gentzen. [REVIEW] Journal of Philosophy 68 (8):238-265.
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  11.  5
    Georg Kreisel (1967). Elements of Mathematical Logic. Amsterdam, North Holland Pub. Co..
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  12. Th Skolem, G. Hasenjaeger, G. Kreisel, A. Robinson, H. Wang, L. Henkin & J. Łoś (eds.) (1971). Mathematical Interpretation of Formal Systems. North-Holland Pub. Co..
     
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  13.  12
    G. Kreisel & Gerald E. Sacks (1965). Metarecursive Sets. Journal of Symbolic Logic 30 (3):318-338.
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  14.  14
    W. A. Howard & G. Kreisel (1966). Transfinite Induction and Bar Induction of Types Zero and One, and the Role of Continuity in Intuitionistic Analysis. Journal of Symbolic Logic 31 (3):325-358.
  15.  3
    Georg Kreisel (1967). Mathematical Logic. Journal of Symbolic Logic 32 (3):419-420.
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  16.  1
    G. Kreisel, R. O. Gandy & C. E. M. Yates (1975). Some Reasons for Generalizing Recursion Theory. Journal of Symbolic Logic 40 (2):230-232.
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  17.  15
    G. Kreisel (1962). On Weak Completeness of Intuitionistic Predicate Logic. Journal of Symbolic Logic 27 (2):139-158.
  18.  27
    Howard Kreisel (1997). Moses Maimonides. In Daniel H. Frank & Oliver Leaman (eds.), History of Jewish Philosophy. Routledge 2--245.
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  19.  5
    G. Kreisel & A. Lévy (1968). Reflection Principles and Their Use for Establishing the Complexity of Axiomatic Systems. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 14 (7-12):97-142.
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  20.  26
    G. Kreisel (1951). On the Interpretation of Non-Finitist Proofs--Part I. Journal of Symbolic Logic 16 (4):241-267.
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  21.  8
    G. Kreisel (1969). Two Notes on the Foundations of Set‐Theory. Dialectica 23 (2):93-114.
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  22.  45
    Georg Kreisel (1991). Review: Kurt Godel, Solomon Feferman, John W. Dawson, Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay, Jean van Heijenoort, Collected Works of Kurt Godel 1938-1974. [REVIEW] Journal of Symbolic Logic 56 (3):1085-1089.
  23.  20
    Heinrich Scholz, G. Kreisel & Leon Henkin (1952). Problems. Journal of Symbolic Logic 17 (2):160.
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  24.  29
    Georg Kreisel (1978). The Motto of 'Philosophical Investigations' and the Philosophy of Proofs and Rules. Grazer Philosophische Studien 6:13-38.
    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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  25.  39
    G. Kreisel (1953). A Variant to Hilbert's Theory of the Foundations of Arithmetic. British Journal for the Philosophy of Science 4 (14):107-129.
    IN Hilbert's theory of the foundations of any given branch of mathematics the main problem is to establish the consistency (of a suitable formalisation) of this branch. Since the (intuitionist) criticisms of classical logic, which Hilbert's theory was intended to meet, never even alluded to inconsistencies (in classical arithmetic), and since the investigations of Hilbert's school have always established much more than mere consistency, it is natural to formulate another general problem in the foundations of mathematics: to translate statements of (...)
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  26.  58
    Georg Kreisel (1985). Mathematical Logic: Tool and Object Lesson for Science. 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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  27.  47
    G. Kreisel (1998). Second Thoughts Around Some of Göde's Writings:. Synthese 114 (1):99-160.
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  28.  2
    G. Kreisel & H. Putnam (1958). Eine Unableitbarkeitsbeweismethode Für den Intuitionistischen Aussagenkalkül. Journal of Symbolic Logic 23 (2):229-229.
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  29.  22
    G. Kreisel (1984). Frege's Foundations and Intuitional Logic. The Monist 67 (1):72-91.
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  30.  2
    G. Kreisel (1965). Foundations of Intuitionistic Logic. Journal of Symbolic Logic 30 (2):243-244.
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  31.  2
    R. O. Gandy, G. Kreisel & W. W. Tait (1962). Set Existence. Journal of Symbolic Logic 27 (2):232-233.
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  32.  4
    David Hilbert, Mary Winston Newsom, Felix E. Browder, Donald A. Martin, G. Kreisel & Martin Davis (1979). Mathematical Problems. Lecture Delivered Before the International Congress of Mathematicians at Paris in 1900. Journal of Symbolic Logic 44 (1):116-119.
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  33.  19
    G. Kreisel (1958). A Remark on Free Choice Sequences and the Topological Completeness Proofs. Journal of Symbolic Logic 23 (4):369-388.
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  34.  4
    Georg Kreisel (1958). Hilbert's programme. 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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  35.  27
    G. Kreisel (1952). On the Interpretation of Non-Finitist Proofs: Part II. Interpretation of Number Theory. Applications. Journal of Symbolic Logic 17 (1):43-58.
  36.  12
    G. Kreisel (1972). Which Number Theoretic Problems Can Be Solved in Recursive Progressions on Π 1/1-Paths Through O? Journal of Symbolic Logic 37 (2):311-334.
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  37.  1
    G. Kreisel, J. Shoenfield & Hao Wang (1966). Number Theoretic Concepts and Recursive Well-Orderings. Journal of Symbolic Logic 31 (3):511-512.
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  38.  8
    G. Kreisel (1954). On a Problem of Henkin's. Journal of Symbolic Logic 19 (3):219-220.
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  39.  8
    Georg Kreisel (2011). Logical Hygiene, Foundations, and Abstractions: Diversity Among Aspects and Options. In Matthias Baaz (ed.), Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press 27.
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  40.  5
    Georg Kreisel & William W. Tait (1961). Finite Definability of Number-Theoretic Functions and Parametric Completeness of Equational Calculi. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (1-5):28-38.
  41.  7
    G. Kreisel (1982). Review: Marian Boykan Pour-El, Ian Richards, A Computable Ordinary Differential Equation with Possesses No Computable Solution; Marian Boykan Pour-El, Ian Richards, The Wave Equation with Computable Initial Data Such That its Unique Solution is Not Computable. [REVIEW] Journal of Symbolic Logic 47 (4):900-902.
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  42.  1
    S. Feferman, G. Kreisel & Solomon Feferman (1972). Persistent and Invariant Formulas Relative to Theories of Higher Order. Journal of Symbolic Logic 37 (4):764-765.
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  43. G. Kreisel (1970). Principles of Proof, Etc. In A. Kino, John Myhill & Richard Eugene Vesley (eds.), Intuitionism and Proof Theory. Amsterdam,North-Holland Pub. Co. 489--5.
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  44.  3
    G. Kreisel & Hao Wang (1956). Some Applications of Formalized Consistency Proofs. Journal of Symbolic Logic 21 (4):404-405.
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  45.  25
    G. Kreisel (1958). Mathematical Significance of Consistency Proofs. Journal of Symbolic Logic 23 (2):155-182.
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  46.  3
    G. Kreisel (1992). On the Idea of Logical Closure. Annals of Pure and Applied Logic 56 (1-3):19-41.
    The article begins and ends with reminiscences and reflections about conversations with Myhill . The topic in the title was never far from these conversations, but remained off stage: questions about the suitability of the focus on logical languages and logical consequence, here meant in contrast to incomparable categories of propositions and proofs. The body of the article goes into cases where this focus has contributed to—and where it has distracted from more rewarding categories for—effective knowledge in mathematics. There are (...)
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  47.  43
    G. Kreisel (1960). Review: Wittgenstein's Theory and Practice of Philosophy. [REVIEW] British Journal for the Philosophy of Science 11 (43):238 - 251.
  48.  1
    G. Kreisel (1970). The Axiom of Choice and the Class of Hyperarithmetic Functions. Journal of Symbolic Logic 35 (2):333-334.
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  49.  42
    G. Kreisel (1956). Some Uses of Mathematics. British Journal for the Philosophy of Science 7 (26):161-173.
  50. G. Kreisel (1967). Reply to Professor Bar-Hillel. In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. Amsterdam, North-Holland Pub. Co. 175--178.
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