What Is Logical Pluralism? (J.C. Beall’s and Greg Restall’s Standpoint)
Abstract
C. Beall and Greg Restall are advocates of a comprehensive pluralist approach to logic, which they call Logical Pluralism (LP). According to LP, there is not one correct logic, but many equally acceptable logical systems. The authors share Tarski’s conviction and follow the mainstream in thinking about logic as the discipline that investigates the notion of logical consequence. LP is the pluralism about logical consequence – a pluralist maintains that there is more than one relation of logical consequence. According to LP, classical, intuitionistic and relevant logics are not rivals, but they all are equally correct, they all count as genuine logics.
The purpose of this paper is to present some remarks concerning J.C. Beall’s and Greg Restall’s exposition of LP. At the beginning, the definition of the relation of logical consequence, which is central to their proposal, is shown. According to Beall and Restall, argument is valid if, and only if, in every case when the premisses are true, then the conclusion is, too. They argue that by considering different types of cases the logical pluralist obtains different logics.
The paper—apart from presenting LP—also gives a critical discussion of this approach. It seems, that the thesis of LP is far from being clear. It is even unclear what exactly LP is and where is stops. It is unclear what “equally good”, “equally correct”, “equally true” mean. It is not clear, how to explain, in scope of logic, that the system of logic, is a model of real logical connections.
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