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Relevant deduction

From solving paradoxes towards a general theory

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Abstract

This paper presents an outline of a new theory of relevant deduction which arose from the purpose of solving paradoxes in various fields of analytic philosophy. In distinction to relevance logics, this approach does not replace classical logic by a new one, but distinguishes between relevance and validity. It is argued that irrelevant arguments are, although formally valid, nonsensical and even harmful in practical applications. The basic idea is this: a valid deduction is relevant iff no subformula of the conclusion is replaceable on some of its occurrences by any other formula salva validitate of the deduction. The paper first motivates the approach by showing that four paradoxes seemingly very distant from each other have a common source. Then the exact definition of relevant deduction is given and its logical properties are investigated. An extension to relevance of premises is discussed. Finally the paper presents an overview of its applications in philosophy of science, ethics, cognitive psychology and artificial intelligence.

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This paper is based on the first part of my habilitation Schurz (1989). For various helps and comments I am indebted to Paul Weingartner. Andrzej Wrónski, Georg Kreisel, David Miller, Kit Fine, Terence Parsons and Peter Woodruff.

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Schurz, G. Relevant deduction. Erkenntnis 35, 391–437 (1991). https://doi.org/10.1007/BF00388295

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