Modern Logic

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Irving H. Anellis - One of the best experts on this subject based on the ideXlab platform.

  • Editor’s Introduction to Jean van Heijenoort, Historical Development of Modern Logic
    Logica Universalis, 2012
    Co-Authors: Irving H. Anellis
    Abstract:

    Van Heijenoort’s account of the historical development of Modern Logic was composed in 1974 and first published in 1992 with an introduction by his former student. What follows is a new edition with a revised and expanded introduction and additional notes.

  • Jean van Heijenoort’s Conception of Modern Logic, in Historical Perspective
    Logica Universalis, 2012
    Co-Authors: Irving H. Anellis
    Abstract:

    I use van Heijenoort’s published writings and manuscript materials to provide a comprehensive overview of his conception of Modern Logic as a first-order functional calculus and of the historical developments which led to this conception of mathematical Logic, its defining characteristics, and in particular to provide an integral account, from his most important publications as well as his unpublished notes and scattered shorter historico-philosophical articles, of how and why the mathematical Logic, whose he traced to Frege and the culmination of its formative period in the incompleteness results of Gödel, became Modern Logic, as distinct from the traditional Logic of Aristotle, and why and how the logistic tradition that led from Frege through Russell, rather than the algebraic tradition that led from De Morgan and Boole through Peirce and Schröder, came, in his view, to define Modern Logic.

  • editor s introduction to jean van heijenoort historical development of Modern Logic
    Logica Universalis, 2012
    Co-Authors: Irving H. Anellis
    Abstract:

    Van Heijenoort’s account of the historical development of Modern Logic was composed in 1974 and first published in 1992 with an introduction by his former student. What follows is a new edition with a revised and expanded introduction and additional notes.

  • jean van heijenoort s conception of Modern Logic in historical perspective
    Logica Universalis, 2012
    Co-Authors: Irving H. Anellis
    Abstract:

    I use van Heijenoort’s published writings and manuscript materials to provide a comprehensive overview of his conception of Modern Logic as a first-order functional calculus and of the historical developments which led to this conception of mathematical Logic, its defining characteristics, and in particular to provide an integral account, from his most important publications as well as his unpublished notes and scattered shorter historico-philosophical articles, of how and why the mathematical Logic, whose he traced to Frege and the culmination of its formative period in the incompleteness results of Godel, became Modern Logic, as distinct from the traditional Logic of Aristotle, and why and how the logistic tradition that led from Frege through Russell, rather than the algebraic tradition that led from De Morgan and Boole through Peirce and Schroder, came, in his view, to define Modern Logic.

Volker Peckhaus - One of the best experts on this subject based on the ideXlab platform.

  • calculus ratiocinator versus characteristica universalis the two traditions in Logic revisited
    History and Philosophy of Logic, 2004
    Co-Authors: Volker Peckhaus
    Abstract:

    It is a commonplace that in the development of Modern Logic towards its actual shape at least two directions or traditions have to be distinguished. These traditions may be called, following the mo...

  • Calculus ratiocinator versus characteristica universalis? The two traditions in Logic, revisited
    History and Philosophy of Logic, 2004
    Co-Authors: Volker Peckhaus
    Abstract:

    It is a commonplace that in the development of Modern Logic towards its actual shape at least two directions or traditions have to be distinguished. These traditions may be called, following the model of Ivor Grattan-Guinness (1988 ), the tradition of the algebra of Logic and the tradition of mathematical Logic. They are represented by the developments going back to the British algebraist George Boole with his The Mathematical Analysis of Logic (1847 ), and, independently, to the German mathematician Gottlob Frege with his Begriffsschrift (1879 ) Closely connected to this distinction is a comparative evaluation of the respective Logical systems, culminating in the question who parented Modern Logic. Some interpreters, among them Boole’s biographer Desmond MacHale (1985, 71–72) or P. L. Heath (in Prior, ed., 1967, 542) have seen Boole as the father of Modern Logic. Others, like Robert Feys (1957 ) call his work the origin of Modern Logic. A few, like Bertrand Russell (1951, 74), even regarded him as the discoverer of pure mathematics (i. e., according to Russell’s Logicism, mathematical Logic). (Those who like Wolfgang Lenzen plead for exchanging Boole with Leibniz (1984, 203) will not concern us here.) Most influential, however, have been those who did not deny that the continuous debate about questions relevant for Modern Logic started with Boole in the middle of the 19th century, but who questioned the scientific value of the algebraic tradition for the actual shape of Logic. Arthur Prior may be named

  • was george boole really the father of Modern Logic
    2000
    Co-Authors: Volker Peckhaus
    Abstract:

    Was George Boole really the ‘father’ of Modern Logic? I confess that I regard this question as rather academic, because it is not possible to answer it convincingly. A typical answer to questions of this kind is: ‘it depends’. In our case it depends on what is meant by the ‘father of a scientific discipline’, it depends on the understanding of Modern Logic, and it even depends on one’s own attitude towards the notion of scientific development.

Paul Schuurman - One of the best experts on this subject based on the ideXlab platform.

Wilfrid Hodges - One of the best experts on this subject based on the ideXlab platform.

  • Traditional Logic, Modern Logic and Natural Language
    Journal of Philosophical Logic, 2009
    Co-Authors: Wilfrid Hodges
    Abstract:

    In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ‘natural Logic’. His paper makes a number of challenging comments on the relationships between traditional Logic, Modern Logic and natural Logic. I respond to his challenge, by drawing what I think are the most significant lines dividing traditional Logic from Modern. The leading difference is in the way Logic is expected to be used for checking arguments. For traditionals the checking is local, i.e. separately for each inference step. Between inference steps, several kinds of paraphrasing are allowed. Today we formalise globally: we choose a symbolisation that works for the entire argument, and thus we eliminate intuitive steps and changes of viewpoint during the argument. Frege and Peano recast the Logical rules so as to make this possible. I comment also on the traditional assumption that Logical processing takes place at the top syntactic level, and I question Johan’s view that natural Logic is ‘natural’.

Mark E. Fuller - One of the best experts on this subject based on the ideXlab platform.

  • Modern Logic 1850-1950, East and West - Modern Logic 1850-1950, East and West
    Studies in Universal Logic, 2016
    Co-Authors: Francine F. Abeles, Mark E. Fuller
    Abstract:

    This book presents diverse topics in mathematical Logic such as proof theory, meta-mathematics, and applications of Logic to mathematical structures. The collection spans the first 100 years of Modern Logic and is dedicated to the memory of Irving Anellis, founder of the journal 'Modern Logic', whose academic work was essential in promoting the algebraic tradition of Logic, as represented by Charles Sanders Peirce. Anellis s association with the Russian Logic community introduced their school of Logic to a wider audience in the USA, Canada and Western Europe. In addition, the collection takes a historical perspective on proof theory and the development of Logic and mathematics in Eastern Logic, the Soviet Union and Russia. The book will be of interest to historians and philosophers in Logic and mathematics, and the more specialized papers will also appeal to mathematicians and Logicians

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