Switch to: References

Citations of:

The development of mathematical logic from Russell to Tarski, 1900-1935

In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press (2009)

Add citations

You must login to add citations.
  1. Mario Pieri’s View of the Symbiotic Relationship Between the Foundations and the Teaching of Elementary Geometry in the Context of the Early Twentieth Century Proposals for Pedagogical Reform.Elena Anne Corie Marchisotto & Ana Millán Gasca - 2021 - Philosophia Scientae 25:157-183.
    Download  
     
    Export citation  
     
    Bookmark  
  • Frege, Peano and the Interplay Between Logic and Mathematics.Joan Bertran-San Millán - 2021 - Philosophia Scientae 25 (1):15-34.
    In contemporary historical studies, Peano is usually included in the logical tradition pioneered by Frege. In this paper, I shall first demonstrate that Frege and Peano independently developed a similar way of using logic for the rigorous expression and proof of mathematical laws. However, I shall then suggest that Peano also used his mathematical logic in such a way that anticipated a formalisation of mathematical theories which was incompatible with Frege’s conception of logic.
    Download  
     
    Export citation  
     
    Bookmark  
  • Frege and the Origins of Model Theory in Nineteenth Century Geometry.Günther Eder - 2019 - Synthese 198 (6):5547-5575.
    The aim of this article is to contribute to a better understanding of Frege’s views on semantics and metatheory by looking at his take on several themes in nineteenth century geometry that were significant for the development of modern model-theoretic semantics. I will focus on three issues in which a central semantic idea, the idea of reinterpreting non-logical terms, gradually came to play a substantial role: the introduction of elements at infinity in projective geometry; the study of transfer principles, especially (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • On Rereading van Heijenoort’s Selected Essays.Solomon Feferman - 2012 - Logica Universalis 6 (3-4):535-552.
    This is a critical reexamination of several pieces in van Heijenoort’s Selected Essays that are directly or indirectly concerned with the philosophy of logic or the relation of logic to natural language. Among the topics discussed are absolutism and relativism in logic, mass terms, the idea of a rational dictionary, and sense and identity of sense in Frege.
    Download  
     
    Export citation  
     
    Bookmark  
  • Beppo Levi’s Analysis of the Paradoxes.Riccardo Bruni - 2013 - Logica Universalis 7 (2):211-231.
    This paper presents and comments the content of a note by Beppo Levi on logical paradoxes. Though the existence of this contribution is known, very little analysis of it is available in the literature. I put the emphasis on Levi’s usage of “elementation procedures” for solving the set-theoretical paradoxes, which is the most original part of Levi’s approach to the topic.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Lingua Characterica and Calculus Ratiocinator: The Leibnizian Background of the Frege-Schröder Polemic.Joan Bertran-San Millán - 2021 - Review of Symbolic Logic 14 (2):411-446.
    After the publication of Begriffsschrift, a conflict erupted between Frege and Schröder regarding their respective logical systems which emerged around the Leibnizian notions of lingua characterica and calculus ratiocinator. Both of them claimed their own logic to be a better realisation of Leibniz’s ideal language and considered the rival system a mere calculus ratiocinator. Inspired by this polemic, van Heijenoort (1967b) distinguished two conceptions of logic—logic as language and logic as calculus—and presented them as opposing views, but did not explain (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • The Crisis in the Foundations of Mathematics.J. Ferreiros - 2008 - In Timothy Gowers (ed.), Princeton Companion to Mathematics. Princeton University Press.
    A general introduction to the celebrated foundational crisis, discussing how the characteristic traits of modern mathematics (acceptance of the notion of an “arbitrary” function proposed by Dirichlet; wholehearted acceptance of infinite sets and the higher infinite; a preference “to put thoughts in the place of calculations” and to concentrate on “structures” characterized axiomatically; a reliance on “purely existential” methods of proof) provoked extensive polemics and alternative approaches. Going beyond exclusive concentration on the paradoxes, it also discusses the role of the (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Kurt Gödel.Juliette Kennedy - 2008 - Stanford Encyclopedia of Philosophy.
    Download  
     
    Export citation  
     
    Bookmark  
  • Carnap’s Early Metatheory: Scope and Limits.Georg Schiemer, Richard Zach & Erich Reck - 2017 - Synthese 194 (1):33-65.
    In Untersuchungen zur allgemeinen Axiomatik and Abriss der Logistik, Carnap attempted to formulate the metatheory of axiomatic theories within a single, fully interpreted type-theoretic framework and to investigate a number of meta-logical notions in it, such as those of model, consequence, consistency, completeness, and decidability. These attempts were largely unsuccessful, also in his own considered judgment. A detailed assessment of Carnap’s attempt shows, nevertheless, that his approach is much less confused and hopeless than it has often been made out to (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Peirce and Diagrams: Two Contributors to an Actual Discussion Review Each Other.Frederik Stjernfelt & Ahti-Veikko Pietarinen - 2015 - Synthese 192 (4):1073-1088.
    The following two review papers have a common origin. Pietarinen’s book Signs of Logic and Stjernfelt’s book Diagrammatology were both published in the same Synthese Library Series being published by Springer. The two books also share the common topic of diagrammatic reasoning in Charles Peirce’s work. Beginning in a conference Applying Peirce held in Helsinki in conjunction with the World Congress of Semiotics in June 2007, two authors have commented upon these books under the headline of Synthese Library Book Session (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • The Role of Universal Language in the Early Work of Carnap and Tarski.Iris Loeb - 2017 - Synthese 194 (1):15-31.
    It is often argued that by assuming the existence of a universal language, one prohibits oneself from conducting semantical investigations. It could thus be thought that Tarski’s stance towards a universal language in his fruitful Wahrheitsbegriff differs essentially from Carnap’s in the latter’s less successful Untersuchungen zur allgemeinen Axiomatik. Yet this is not the case. Rather, these two works differ in whether or not the studied fragments of the universal language are languages themselves, i.e., whether or not they are closed (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Logic in the 1930s: Type Theory and Model Theory.Georg Schiemer & Erich H. Reck - 2013 - Bulletin of Symbolic Logic 19 (4):433-472.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Von Neumann’s Consistency Proof.Luca Bellotti - 2016 - Review of Symbolic Logic 9 (3):429-455.
    Download  
     
    Export citation  
     
    Bookmark  
  • Fixed- Versus Variable-Domain Interpretations of Tarski’s Account of Logical Consequence.Paolo Mancosu - 2010 - Philosophy Compass 5 (9):745-759.
    Download  
     
    Export citation  
     
    Bookmark   13 citations  
  • Paradoxes and Contemporary Logic.Andrea Cantini - 2008 - Stanford Encyclopedia of Philosophy.
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Turing Machines.David Barker-Plummer - 2008 - Stanford Encyclopedia of Philosophy.
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • The Algebra of Logic Tradition.Stanley Burris - 2010 - Stanford Encyclopedia of Philosophy.
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   3 citations