How to be really contraction free
type: Item
instance of: scholarly article
title: How to be really contraction free
zbMATH Open document ID: 0793.03003
DOI: 10.1007/BF01057653
author: Greg Restall
published in: Studia Logica
publication date: 1994-08-21T00:00:00Z
review text: It is well known that the inference of contraction (from \(A\to (A\to B)\) to derive \(A\to B\)) is necessary for the deduction of absurdity from paradoxical statements like ``if this is true, then absurdity follows''. If we call this kind of contraction ``2-1 contraction'' (from two uses of the antecedent \(A\) to one use), then the picture generalises. For a logic to resist absurd conclusions from paradoxical statements like these, it must not only be ``2-1 contraction'' free, but also ``\(n-m\) contraction'' free where \(n>m\). This paper shows that no finitely valued logic is \(n-m\) contraction free for each \(n\) and \(m\), and it gives examples of other logics which are \(2-1\) contraction free but not \(n-m\) contraction free.
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03B50
zbMATH DE Number: 488343
zbMATH Keywords: paradox
zbMATH Keywords: finite models
zbMATH Keywords: contraction
zbMATH Keywords: absurdity
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01057653
OpenAlex ID: W1481470750
description: scientific article; zbMATH DE number 488343