Logic on the Australian plan
type: Item
instance of: scholarly article
title: Logic on the Australian plan
zbMATH Open document ID: 0614.03006
DOI: 10.1007/BF00248574
author: Robert K. Meyer
author: Errol P. Martin
published in: Journal of Philosophical Logic
publication date: 1986-01-01T00:00:00Z
review text: This paper describes the analysis of the negation of relevant logics in terms of the Routley *-operation, and sketches a philosophical underpinning for it. Basic to this is the idea of a dual theory. A theory is a set of sentences closed under entailment. For any theory, T, the dual theory, \(T^*\), is just that theory which asserts what T fails to deny: \(A\in T^*\) iff \(\sim A\not\in T\). The ''truth conditions'' for \(\sim\) now follow simply by contraposition: \(\sim A\in T\) iff \(A\not\in T^*\). In an ''ideal'' situation, where T is maximally consistent, \(T=T^*\), and the familiar truth conditions for negation emerge: \(\sim A\in T\) iff \(A\not\in T\). There are, however, many situations that are not ideal and in which T is non-trivially inconsistent or incomplete. The classical situation is therefore only a special case. A crucial question now is how the theories in question are to be constructed. If theories are taken to be sets of truths, then the view is committed to the possibility that truth may be inconsistent or incomplete. This view the paper categorically rejects. Instead, theories are to be taken to be our theories about something or other. But now the following problems arise: i) It is crucial for this account that there are ''real life'' theories that are inconsistent and incomplete. This is problematic. It may be denied that there are non-trivial inconsistent theories; and though it may be admitted that there are incomplete theories, it may be denied that their duals are theories. The paper points out that we often reason in situations where our data is inconsistent or incomplete; but this does not justify us in thinking of the situations as closed under entailment; for characteristically the reasoning that goes on in these situations is non-monotonic: after a certain amount of deduction we perform some back- tracking and readjust our premises. ii) The paper argues, correctly, against giving an epistemic interpretation of certain semantics of …
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03B45
zbMATH DE Number: 3993532
zbMATH Keywords: negation
zbMATH Keywords: relevant logics
zbMATH Keywords: Routley *-operation
zbMATH Keywords: dual theory
reviewed by: Graham Priest
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00248574
OpenAlex ID: W1966709651
description: scientific article; zbMATH DE number 3993532