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

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

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  1. The Crisis in the Foundations of Mathematics.J. Ferreiros - 2008 - In T. Gowers (ed.), Princeton Companion to Mathematics. Princeton University Press.
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  • 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.
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  • 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.
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  • 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 (...)
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  • Logic in the 1930s: Type Theory and Model Theory.Georg Schiemer & Erich H. Reck - 2013 - Bulletin of Symbolic Logic 19 (4):433-472.
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  • Von Neumann’s Consistency Proof.Luca Bellotti - 2016 - Review of Symbolic Logic 9 (3):429-455.
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  • Fixed- Versus Variable-Domain Interpretations of Tarski’s Account of Logical Consequence.Paolo Mancosu - 2010 - Philosophy Compass 5 (9):745-759.
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  • 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 (...)
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  • 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 (...)
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