Moritz Cordes
Universität Regensburg
We argue that the need for commentary in commonly used linear calculi of natural deduction is connected to the “deletion” of illocutionary expressions that express the role of propositions as reasons, assumptions, or inferred propositions. We first analyze the formalization of an informal proof in some common calculi which do not formalize natural language illocutionary expressions, and show that in these calculi the formalizations of the example proof rely on commentary devices that have no counterpart in the original proof. We then present a linear natural deduction calculus that makes use of formal illocutionary expressions in such a way that unique readability for derivations is guaranteed – thus showing that formalizing illocutionary expressions can eliminate the need for commentary.
Keywords Logic  Natural Deduction  Formalization
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DOI 10.12775/LLP.2017.002
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References found in this work BETA

Untersuchungen über das logische Schließen. I.Gerhard Gentzen - 1935 - Mathematische Zeitschrift 35:176–210.
Die Widerspruchsfreiheit der Reinen Zahlentheorie.Gerhard Gentzen - 1936 - Journal of Symbolic Logic 1 (2):75-75.
[Omnibus Review].Dag Prawitz - 1991 - Journal of Symbolic Logic 56 (3):1094-1096.

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Citations of this work BETA

The Constituents of an Explication.Moritz Cordes - 2020 - Synthese 197 (3):983-1010.
Scheinprobleme - Ein explikativer Versuch.Moritz Cordes - 2016 - Dissertation, University of Greifswald

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