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  1. The Principles of Mathematics.Bertrand Russell - 1903 - Allen & Unwin.
    Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...)
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  • Logic as Calculus and Logic as Language.Jean Van Heijenoort - 1967 - Synthese 17 (1):324-330.
  • Frege’s Begriffsschrift as a Lingua Characteristica.Tapio Korte - 2010 - Synthese 174 (2):283 - 294.
    In this paper I suggest an answer to the question of what Frege means when he says that his logical system, the Begrijfsschrift, is like the language Leibniz sketched, a lingua characteristica, and not merely a logical calculus. According to the nineteenth century studies, Leibniz's lingua characteristica was supposed to be a language with which the truths of science and the constitution of its concepts could be accurately expressed. I argue that this is exactly what the Begriffsschrift is: it is (...)
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  • Metatheory and Mathematical Practice in Frege.Jamie Tappenden - 1997 - Philosophical Topics 25 (2):213-264.
    A cluster of recent papers on Frege have urged variations on the theme that Frege’s conception of logic is in some crucial way incompatible with ‘metatheoretic’ investigation. From this observation, significant consequences for our interpretation of Frege’s understanding of his enterprise are taken to follow. This chapter aims to critically examine this view, and to isolate what I take to be the core of truth in it. However, I will also argue that once we have isolated the defensible kernel, the (...)
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  • Einführung in Die Mathematische Logik Und in Die Methodologie der Mathematik.E. N. - 1938 - Journal of Philosophy 35 (13):361-362.
  • In Defense of Logical Universalism: Taking Issue with Jean van Heijenoort. [REVIEW]Philippe de Rouilhan - 2012 - Logica Universalis 6 (3-4):553-586.
    Van Heijenoort’s main contribution to history and philosophy of modern logic was his distinction between two basic views of logic, first, the absolutist, or universalist, view of the founding fathers, Frege, Peano, and Russell, which dominated the first, classical period of history of modern logic, and, second, the relativist, or model-theoretic, view, inherited from Boole, Schröder, and Löwenheim, which has dominated the second, contemporary period of that history. In my paper, I present the man Jean van Heijenoort (Sect. 1); then (...)
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  • Frege Against the Booleans.Hans Sluga - 1987 - Notre Dame Journal of Formal Logic 28 (1):80-98.
  • Russell and the Universalist Conception of Logic.Ian Proops - 2007 - Noûs 41 (1):1–32.
    The paper critically scrutinizes the widespread idea that Russell subscribes to a "Universalist Conception of Logic." Various glosses on this somewhat under-explained slogan are considered, and their fit with Russell's texts and logical practice examined. The results of this investigation are, for the most part, unfavorable to the Universalist interpretation.
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  • The Development of Mathematical Logic From Russell to Tarski, 1900-1935.Paolo Mancosu, Richard Zach & Calixto Badesa - 2009 - In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press.
    The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...)
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  • Calculus Ratiocinator Versus Characteristica Universalis? The Two Traditions in Logic, Revisited.Volker Peckhaus - 2004 - History and Philosophy of Logic 25 (1):3-14.
  • American Postulate Theorists and Alfred Tarski.Michael Scanlan - 2003 - History and Philosophy of Logic 24 (4):307-325.
    This article outlines the work of a group of US mathematicians called the American Postulate Theorists and their influence on Tarski's work in the 1930s that was to be foundational for model theory. The American Postulate Theorists were influenced by the European foundational work of the period around 1900, such as that of Peano and Hilbert. In the period roughly from 1900???1940, they developed an indigenous American approach to foundational investigations. This made use of interpretations of precisely formulated axiomatic theories (...)
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  • The Logical Syntax of Language.Rudolf Carnap - 1937 - London: K. Paul, Trench, Trubner & Co..
    Available for the first time in 20 years, here is the Rudolf Carnap's famous principle of tolerance by which everyone is free to mix and match the rules of ...
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  • Towards Transfinite Type Theory: Rereading Tarski’s Wahrheitsbegriff.Iris Loeb - 2014 - Synthese 191 (10):2281-2299.
    In his famous paper Der Wahrheitsbegriff in den formalisierten Sprachen (Polish edition: Nakładem/Prace Towarzystwa Naukowego Warszawskiego, wydzial, III, 1933), Alfred Tarski constructs a materially adequate and formally correct definition of the term “true sentence” for certain kinds of formalised languages. In the case of other formalised languages, he shows that such a construction is impossible but that the term “true sentence” can nevertheless be consistently postulated. In the Postscript that Tarski added to a later version of this paper (Studia Philosophica, (...)
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  • Uniting Model Theory and the Universalist Tradition of Logic: Carnap’s Early Axiomatics.Iris Loeb - 2014 - Synthese 191 (12):2815-2833.
    We shift attention from the development of model theory for demarcated languages to the development of this theory for fragments of a language. Although it is often assumed that model theory for demarcated languages is not compatible with a universalist conception of logic, no one has denied that model theory for fragments of a language can be compatible with that conception. It thus seems unwarranted to ignore the universalist tradition in the search for the origins and development of model theory. (...)
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  • Alfred Tarski: Semantic Shift, Heuristic Shift in Metamathematics.Hourya Sinaceur - 2001 - Synthese 126 (1-2):49 - 65.
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  • On the Development of the Model-Theoretic Viewpoint in Logical Theory.Jaakko Hintikka - 1988 - Synthese 77 (1):1 - 36.
  • Propositional Function.Edwin Mares - 2014 - Stanford Encyclopedia of Philosophy.
  • What is Tarski's Common Concept of Consequence?Ignacio Jané - 2006 - Bulletin of Symbolic Logic 12 (1):1-42.
    In 1936 Tarski sketched a rigorous definition of the concept of logical consequence which, he claimed, agreed quite well with common usage-or, as he also said, with the common concept of consequence. Commentators of Tarski's paper have usually been elusive as to what this common concept is. However, being clear on this issue is important to decide whether Tarski's definition failed (as Etchemendy has contended) or succeeded (as most commentators maintain). I argue that the common concept of consequence that Tarski (...)
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  • Postulational Methods. III.Louis Osgood Kattsoff - 1936 - Philosophy of Science 3 (3):375-417.
  • Sur la Géométrie envisagée comme un système purement logique.Mario Pieri - 1901 - Bibliothèque du Congrès International de Philosophie 3:367-404.
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  • Alfred Tarski and the Vienna Circle: Austro-Polish Connections in Logical Empiricism.Jan Woleński, Ilkka Niiniluoto, Hans Sluga, Anita Burdman Feferman, Solomon Feferman & Richard Creath - 1999 - Springer Verlag.
  • Doctrinal Functions.C. J. Keyser - 1918 - Journal of Philosophy, Psychology and Scientific Methods 15 (10):262-267.
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  • Principia Mathematica.A. N. Whitehead - 1926 - Mind 35 (137):130.
  • Über den Begriff der Logischen Folgerung.Alfred Tarski - 1937 - Journal of Symbolic Logic 2 (2):83-84.
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  • Grundzuge des Systemenkalkuls. Zweiter Teil.Alfred Tarski - 1936 - Journal of Symbolic Logic 1 (2):71-72.
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  • Who Were the American Postulate Theorists?Michael Scanlan - 1991 - Journal of Symbolic Logic 56 (3):981-1002.
    Articles by two American mathematicians, E. V. Huntington and Oswald Veblen, are discussed as examples of a movement in foundational research in the period 1900-1930 called American postulate theory. This movement also included E. H. Moore, R. L. Moore, C. H. Langford, H. M. Sheffer, C. J. Keyser, and others. The articles discussed exemplify American postulate theorists' standards for axiomatizations of mathematical theories, and their investigations of such axiomatizations with respect to metatheoretic properties such as independence, completeness, and consistency.
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