On Frege’s Begriffsschrift Notation for Propositional Logic: Design Principles and Trade-Offs

History and Philosophy of Logic 39 (1):53-79 (2018)

Authors
Dirk Schlimm
McGill University
Abstract
Well over a century after its introduction, Frege's two-dimensional Begriffsschrift notation is still considered mainly a curiosity that stands out more for its clumsiness than anything else. This paper focuses mainly on the propositional fragment of the Begriffsschrift, because it embodies the characteristic features that distinguish it from other expressively equivalent notations. In the first part, I argue for the perspicuity and readability of the Begriffsschrift by discussing several idiosyncrasies of the notation, which allow an easy conversion of logically equivalent formulas, and presenting the notation's close connection to syntax trees. In the second part, Frege's considerations regarding the design principles underlying the Begriffsschrift are presented. Frege was quite explicit about these in his replies to early criticisms and unfavorable comparisons with Boole's notation for propositional logic. This discussion reveals that the Begriffsschrift is in fact a well thought-out and carefully crafted notation that intentionally exploits the possibilities afforded by the two-dimensional medium of writing like none other.
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DOI 10.1080/01445340.2017.1317429
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The Frege Reader.Gottlob Frege & Michael Beaney (eds.) - 1997 - Blackwell.
Philosophical and Mathematical Correspondence.Gottlob Frege, Gottfried Gabriel, Brian Mcguinness & Hans Kaal - 1982 - Revue Philosophique de la France Et de l'Etranger 172 (1):64-64.
Über Sinn und Bedeutung.Gottlob Frege - 1892 - Zeitschrift für Philosophie Und Philosophische Kritik 100 (1):25--50.
From Frege to Gödel.Jean Van Heijenoort (ed.) - 1967 - Cambridge: Harvard University Press.

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