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Systems of Deduction

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Handbook of Philosophical Logic

Part of the book series: Handbook of Philosophical Logic ((HALO,volume 2))

Abstract

Formal calculi of deduction have proved useful in logic and in the foundations of mathematics, otas well as in metamathematics. Examples of some of these uses are:

  1. 1.

    The use of formal calculi in attempts to give a secure foundation for mathematics, as in the original work of Frege.

  2. 2.

    To generate syntactically an Already given semantical consequence relation, e.g. in some branches of technical modal logic.

  3. 3.

    Formal calculi can serve as heuristic devices for finding metamathematical properties of the consequence relation, as was the case, e.g. in the early development of infinitary logic via the use of cut-free Gentzen sequent calculi.

  4. 4.

    Formal calculi have served as the objects of mathematical study, as in traditional work on Hilbert’s consistency programme.

  5. 5.

    Certain versions of formal calculi have been used in attempts to formulate philosophical insights into the nature of reasoning.

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Author information

Authors and Affiliations

  1. Universiteit Leiden, The Netherlands

    Göran Sundholm

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  1. Göran Sundholm
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Editors and Affiliations

  1. King’s College, London, USA

    D. M. Gabbay

  2. Centrum für Informations- und Sprachverarbeitung, Ludwig-Maximilians-Universität München, Germany

    F. Guenthner

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Sundholm, G. (2001). Systems of Deduction. In: Gabbay, D.M., Guenthner, F. (eds) Handbook of Philosophical Logic. Handbook of Philosophical Logic, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0452-6_1

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  • DOI: https://doi.org/10.1007/978-94-017-0452-6_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5753-2

  • Online ISBN: 978-94-017-0452-6

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