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Higher-Order Logic

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Handbook of Philosophical Logic

Part of the book series: Handbook of Philosophical Logic ((HALO,volume 1))

Abstract

What is nowadays the central part of any introduction to logic, and indeed to some the logical theory par excellence, used to be a modest fragment of the more ambitious language employed in the logicist program of Frege and Russell. ‘Elementary’ or ‘first-order’, or ‘predicate logic’ only became a recognized stable base for logical theory by 1930, when its interesting and fruitful meta-properties had become clear, such as completeness, compactness and Löwenheim-Skolem. Richer higher-order and type theories receded into the background, to such an extent that the (re-) discovery of useful and interesting extensions and variations upon first-order logic came as a surprise to many logicians in the sixties.

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  1. University of Amsterdam, The Netherlands

    Johan Van Benthem & Kees Doets

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  1. Johan Van Benthem
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  1. King’s College, London, UK

    D. M. Gabbay

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

    F. Guenthner

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Van Benthem, J., Doets, K. (2001). Higher-Order Logic. In: Gabbay, D.M., Guenthner, F. (eds) Handbook of Philosophical Logic. Handbook of Philosophical Logic, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9833-0_3

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  • DOI: https://doi.org/10.1007/978-94-015-9833-0_3

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