Switch to: Citations

References in:

The early development of set theory

Stanford Encyclopedia of Philosophy (web)

Add references

You must login to add references.
  1. (1 other version)Georg Cantor: His Mathematics and Philosophy of the Infinite.Joseph Warren Dauben - 1979 - Hup.
    One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets.
    Download  
     
    Export citation  
     
    Bookmark   62 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   169 citations  
  • Hilbert, logicism, and mathematical existence.José Ferreirós - 2009 - Synthese 170 (1):33 - 70.
    David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following upon Dedekind’s footsteps in his understanding of pure mathematics. This insight makes it possible to throw new light on the evolution of Hilbert’s foundational ideas, including his early contributions to the foundations of geometry and the real number system. The context of Dedekind-style logicism makes it possible to offer a new (...)
    Download  
     
    Export citation  
     
    Bookmark   22 citations  
  • The mathematical development of set theory from Cantor to Cohen.Akihiro Kanamori - 1996 - Bulletin of Symbolic Logic 2 (1):1-71.
    Set theory is an autonomous and sophisticated field of mathematics, enormously successful not only at its continuing development of its historical heritage but also at analyzing mathematical propositions cast in set-theoretic terms and gauging their consistency strength. But set theory is also distinguished by having begun intertwined with pronounced metaphysical attitudes, and these have even been regarded as crucial by some of its great developers. This has encouraged the exaggeration of crises in foundations and of metaphysical doctrines in general. However, (...)
    Download  
     
    Export citation  
     
    Bookmark   19 citations  
  • Understanding the Infinite.Shaughan Lavine - 1994 - Cambridge, Mass.: Harvard University Press.
    How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge.
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • Labyrinth of Thought. A history of set theory and its role in modern mathematics.Jose Ferreiros - 2001 - Basel, Boston: Birkhäuser Verlag.
    Review by A. Kanamori, Boston University (author of The Higher Infinite), review in The Bulletin of Symbolic Logic: “Notwithstanding and braving the daunting complexities of this labyrinth, José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in (...)
    Download  
     
    Export citation  
     
    Bookmark   33 citations  
  • Principia mathematica.Alfred North Whitehead & Bertrand Russell - 1910 - Cambridge,: University Press. Edited by Bertrand Russell.
    This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...)
    Download  
     
    Export citation  
     
    Bookmark   88 citations  
  • Measuring the Size of Infinite Collections of Natural Numbers: Was Cantor’s Theory of Infinite Number Inevitable?Paolo Mancosu - 2009 - Review of Symbolic Logic 2 (4):612-646.
    Cantor’s theory of cardinal numbers offers a way to generalize arithmetic from finite sets to infinite sets using the notion of one-to-one association between two sets. As is well known, all countable infinite sets have the same ‘size’ in this account, namely that of the cardinality of the natural numbers. However, throughout the history of reflections on infinity another powerful intuition has played a major role: if a collectionAis properly included in a collectionBthen the ‘size’ ofAshould be less than the (...)
    Download  
     
    Export citation  
     
    Bookmark   42 citations  
  • From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931.Jean Van Heijenoort (ed.) - 1967 - Cambridge, MA, USA: Harvard University Press.
    Gathered together here are the fundamental texts of the great classical period in modern logic. A complete translation of Gottlob Frege's Begriffsschrift--which opened a great epoch in the history of logic by fully presenting propositional calculus and quantification theory--begins the volume, which concludes with papers by Herbrand and by Gödel.
    Download  
     
    Export citation  
     
    Bookmark   49 citations  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   182 citations  
  • Equivalence: an attempt at a history of the idea.Amir Asghari - 2019 - Synthese 196 (11):4657-4677.
    This paper proposes a reading of the history of equivalence in mathematics. The paper has two main parts. The first part focuses on a relatively short historical period when the notion of equivalence is about to be decontextualized, but yet, has no commonly agreed-upon name. The method for this part is rather straightforward: following the clues left by the others for the ‘first’ modern use of equivalence. The second part focuses on a relatively long historical period when equivalence is experienced (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Einleitung in Die Mengenlehre.Abraham Fraenkel - 1928 - Springer.
    Download  
     
    Export citation  
     
    Bookmark   19 citations  
  • (2 other versions)The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.
    Download  
     
    Export citation  
     
    Bookmark   822 citations  
  • Zermelo and set theory.Akihiro Kanamori - 2004 - Bulletin of Symbolic Logic 10 (4):487-553.
    Ernst Friedrich Ferdinand Zermelo transformed the set theory of Cantor and Dedekind in the first decade of the 20th century by incorporating the Axiom of Choice and providing a simple and workable axiomatization setting out generative set-existence principles. Zermelo thereby tempered the ontological thrust of early set theory, initiated the delineation of what is to be regarded as set-theoretic, drawing out the combinatorial aspects from the logical, and established the basic conceptual framework for the development of modern set theory. Two (...)
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  • Cantorian Set Theory and Limitation of Size.Michael Hallett - 1984 - Oxford, England: Clarendon Press.
    This volume presents the philosophical and heuristic framework Cantor developed and explores its lasting effect on modern mathematics. "Establishes a new plateau for historical comprehension of Cantor's monumental contribution to mathematics." --The American Mathematical Monthly.
    Download  
     
    Export citation  
     
    Bookmark   70 citations  
  • Bernays and set theory.Akihiro Kanamori - 2009 - Bulletin of Symbolic Logic 15 (1):43-69.
    We discuss the work of Paul Bernays in set theory, mainly his axiomatization and his use of classes but also his higher-order reflection principles.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • (1 other version)Gesammelte Abhandlungen: Mathematischen und Philosophischen Inhalts.Georg Cantor, Richard Dedekind & Abraham Adolf Fraenkel - 1932 - Springer.
    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.
    Download  
     
    Export citation  
     
    Bookmark   67 citations  
  • (1 other version)Philosophie mathématique.Jean Cavaillès - 1964 - Les Etudes Philosophiques 19 (3):442-442.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Cohen and set theory.Akihiro Kanamori - 2008 - Bulletin of Symbolic Logic 14 (3):351-378.
    We discuss the work of Paul Cohen in set theory and its influence, especially the background, discovery, development of forcing.
    Download  
     
    Export citation  
     
    Bookmark   23 citations