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  1. Probleme der mathematischen Logik.D. Hilbert - 1920 - In ¸ Iteewald1996. Clarendon Press. pp. 943--946.
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  • (1 other version)From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s.Paolo Mancosu (ed.) - 1997 - Oxford, England: Oxford University Press USA.
    From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920s offers the first comprehensive introduction to the most exciting period in the foundation of mathematics in the twentieth century. The 1920s witnessed the seminal foundational work of Hilbert and Bernays in proof theory, Brouwer's refinement of intuitionistic mathematics, and Weyl's predicativist approach to the foundations of analysis. This impressive collection makes available the first English translations of twenty-five central articles by these important contributors and many others. (...)
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  • Hilbert’s Finitism: Historical, Philosophical, and Metamathematical Perspectives.Richard Zach - 2001 - Dissertation, University of California, Berkeley
    In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...)
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  • Was Sind und was Sollen Die Zahlen?Richard Dedekind - 1888 - Cambridge University Press.
    This influential 1888 publication explained the real numbers, and their construction and properties, from first principles.
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  • (1 other version)Essays on the Theory of Numbers.R. Dedekind - 1903 - The Monist 13:314.
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  • Zur Widerspruchsfreiheit der Zahlentheorie.Wilhelm Ackermann - 1940 - Journal of Symbolic Logic 5 (3):125-127.
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  • Between Vienna and Berlin: The Immediate Reception of Godel's Incompleteness Theorems.Paolo Mancosu - 1999 - History and Philosophy of Logic 20 (1):33-45.
    What were the earliest reactions to Gödel's incompleteness theorems? After a brief summary of previous work in this area I analyse, by means of unpublished archival material, the first reactions in Vienna and Berlin to Gödel's groundbreaking results. In particular, I look at how Carnap, Hempel, von Neumann, Kaufmann, and Chwistek, among others, dealt with the new results.
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  • From Kant to Hilbert: a source book in the foundations of mathematics.William Bragg Ewald (ed.) - 1996 - New York: Oxford University Press.
    This massive two-volume reference presents a comprehensive selection of the most important works on the foundations of mathematics. While the volumes include important forerunners like Berkeley, MacLaurin, and D'Alembert, as well as such followers as Hilbert and Bourbaki, their emphasis is on the mathematical and philosophical developments of the nineteenth century. Besides reproducing reliable English translations of classics works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare, William Ewald also includes selections from Gauss, Cantor, Kronecker, and Zermelo, all translated here for (...)
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  • Remarks on finitism.William Tait - manuscript
    The background of these remarks is that in 1967, in ‘’Constructive reasoning” [27], I sketched an argument that finitist arithmetic coincides with primitive recursive arithmetic, P RA; and in 1981, in “Finitism” [28], I expanded on the argument. But some recent discussions and some of the more recent literature on the subject lead me to think that a few further remarks would be useful.
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  • Completeness before Post: Bernays, Hilbert, and the development of propositional logic.Richard Zach - 1999 - Bulletin of Symbolic Logic 5 (3):331-366.
    Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...)
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  • Numbers and functions in Hilbert's finitism.Richard Zach - 1998 - Taiwanese Journal for History and Philosophy of Science 10:33-60.
    David Hilbert's finitistic standpoint is a conception of elementary number theory designed to answer the intuitionist doubts regarding the security and certainty of mathematics. Hilbert was unfortunately not exact in delineating what that viewpoint was, and Hilbert himself changed his usage of the term through the 1920s and 30s. The purpose of this paper is to outline what the main problems are in understanding Hilbert and Bernays on this issue, based on some publications by them which have so far received (...)
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  • (1 other version)ssays on the Theory of Numbers. [REVIEW]R. Dedekind - 1903 - Ancient Philosophy (Misc) 13:314.
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  • The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel.Ivor Grattan-Guinness - 2011 - Princeton, NJ, USA: Princeton University Press.
    While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913).? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of (...)
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  • Epsilon substitution method for elementary analysis.Grigori Mints, Sergei Tupailo & Wilfried Buchholz - 1996 - Archive for Mathematical Logic 35 (2):103-130.
    We formulate epsilon substitution method for elementary analysisEA (second order arithmetic with comprehension for arithmetical formulas with predicate parameters). Two proofs of its termination are presented. One uses embedding into ramified system of level one and cutelimination for this system. The second proof uses non-effective continuity argument.
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  • (1 other version)From Brouwer to Hilbert: the debate on the foundations of mathematics in the 1920s.Paolo Mancosu (ed.) - 1998 - New York: Oxford University Press.
    From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920s offers the first comprehensive introduction to the most exciting period in the foundation of mathematics in the twentieth century. The 1920s witnessed the seminal foundational work of Hilbert and Bernays in proof theory, Brouwer's refinement of intuitionistic mathematics, and Weyl's predicativist approach to the foundations of analysis. This impressive collection makes available the first English translations of twenty-five central articles by these important contributors and many others. (...)
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  • Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.
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  • Solvable Cases of the Decision Problem.[author unknown] - 1956 - Philosophy 31 (116):92-93.
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  • (1 other version)Grundlagen der Mathematik.S. C. Kleene - 1940 - Journal of Symbolic Logic 5 (1):16-20.
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  • The Reception of Godel's Incompleteness Theorems.John W. Dawson - 1984 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984:253 - 271.
    According to several commentators, Kurt Godel's incompleteness discoveries were assimilated promptly and almost without objection by his contemporaries - - a circumstance remarkable enough to call for explanation. Careful examination reveals, however, that there were doubters and critics, as well as defenders and rival claimants to priority. In particular, the reactions of Carnap, Bernays, Zermelo, Post, Finsler, and Russell, among others, are considered in detail. Documentary sources include unpublished correspondence from Godel's Nachlass.
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  • Hilbert's Programs: 1917–1922.Wilfried Sieg - 1999 - Bulletin of Symbolic Logic 5 (1):1-44.
    Hilbert's finitist program was not created at the beginning of the twenties solely to counteract Brouwer's intuitionism, but rather emerged out of broad philosophical reflections on the foundations of mathematics and out of detailed logical work; that is evident from notes of lecture courses that were given by Hilbert and prepared in collaboration with Bernays during the period from 1917 to 1922. These notes reveal a dialectic progression from a critical logicism through a radical constructivism toward finitism; the progression has (...)
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  • Between Russell and Hilbert: Behmann on the foundations of mathematics.Paolo Mancosu - 1999 - Bulletin of Symbolic Logic 5 (3):303-330.
    After giving a brief overview of the renewal of interest in logic and the foundations of mathematics in Göttingen in the period 1914-1921, I give a detailed presentation of the approach to the foundations of mathematics found in Behmann's doctoral dissertation of 1918, Die Antinomie der transfiniten Zahl und ihre Auflösung durch die Theorie von Russell und Whitehead. The dissertation was written under the guidance of David Hilbert and was primarily intended to give a clear exposition of the solution to (...)
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  • (2 other versions)Grundlagen der Mathematik I.David Hilbert & Paul Bernays - 1968 - Springer.
    Die Leitgedanken meiner Untersuchungen über die Grundlagen der Mathematik, die ich - anknüpfend an frühere Ansätze - seit 1917 in Besprechungen mit P. BERNAYS wieder aufgenommen habe, sind von mir an verschiedenen Stellen eingehend dargelegt worden. Diesen Untersuchungen, an denen auch W. ACKERMANN beteiligt ist, haben sich seither noch verschiedene Mathematiker angeschlossen. Der hier in seinem ersten Teil vorliegende, von BERNAYS abgefaßte und noch fortzusetzende Lehrgang bezweckt eine Darstellung der Theorie nach ihren heutigen Ergebnissen. Dieser Ergebnisstand weist zugleich die Richtung (...)
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  • From Frege to Gödel.Jean Van Heijenoort (ed.) - 1967 - Cambridge,: Harvard University Press.
    The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for ...
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  • (2 other versions)Solvable Cases of the Decision Problem.Paul Bernays - 1957 - Journal of Symbolic Logic 22 (1):68-72.
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  • (1 other version)From Frege to Gödel.Jean van Heijenoort - 1968 - Philosophy of Science 35 (1):72-72.
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  • Grundzüge der theoretischen Logik.D. Hilbert & W. Ackermann - 1928 - Annalen der Philosophie Und Philosophischen Kritik 7:157-157.
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  • Solvable cases of the decision problem.Wilhelm Ackermann - 1954 - Amsterdam,: North-Holland Pub. Co..
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  • Mathematical logic and Hilbert's & symbol.A. C. Leisenring - 1969 - London,: Macdonald Technical & Scientific.
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  • Aus dem briefwechsel wilhelm ackermanns.Hans Richard Ackermann - 1983 - History and Philosophy of Logic 4 (1-2):181-202.
    A selection from the correspondence of the logician Wilhelm Ackermann (1896?1962) is presented in this article. The most significant letters were exchanged with Bernays, Scholz and Lorenzen, from which extensive passages are transcribed. Some remarks from other letters, with quotations, are also included.
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  • Die Grundlagen der Mathematik.David Hilbert, Hermann Weyl & Paul Bernays - 2013 - Springer Verlag.
    Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
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  • The substitution method.W. W. Tait - 1965 - Journal of Symbolic Logic 30 (2):175-192.
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  • Die Widerspruchsfreiheit der reinen Zahlentheorie.Gerhard Gentzen - 1936 - Journal of Symbolic Logic 1 (2):75-75.
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  • Finitism and intuitive knowledge.Charles Parsons - 1998 - In Matthias Schirn (ed.), The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press. pp. 249--270.
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  • Thoralf Skolem and the epsilon substitution method for predicate logic.Grigori Mints - 1996 - Nordic Journal of Philosophical Logic 1 (2):133-146.
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  • (2 other versions)Grundzuge der Theoretischen Logik.W. V. Quine - 1938 - Journal of Symbolic Logic 3 (2):83-84.
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  • Gentzen-type systems and Hilbert’s epsilon substitution method. I.Grigori Efroimovich Mints - 1991 - In Dag Prawitz, Brian Skyrms & Dag Westerståhl (eds.), ¸ Iteprawitz1994. Elsevier. pp. 91--122.
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