Studies In Pluralism About Logical Consequence

In the 1930s,Carnap put forward the famous Principle of Tolerance,which was the most influential idea about logical pluralism in the early stage.For Carnap,the reason of pluralism reflected by logic is that we can choose formal languages freely and the number of the languages is infinite.Carnap designed two languages-language I and language ?.In language ?,Carnap set up some constructive restrictions.But in language II there is no such restriction.The two different languages lead to different logics.The idea in the Principle of Tolerance was inherited and developed by Quine in his philosophy of logic.Quine's meaning-variance thesis and the indeterminacy of translation can be summarized as that the apparent conflict of logics can be summed up in the change of meaning of the logical constants,so the different meanings of logical constants lead to different languages.But Quine was a representative monist,which explains from the side that pluralism and monism have something in common on the theoretical root and logicians' choices of positions have some relations to their understandings.In this text,pluralism mainly means the variety of logical systems at the level of formal systems.Susan Haack proposed a theory of global pluralism on the basis of extra-systematic validity which has a profound impact on the philosophy of logics.In this theoretical framework,there are more than one formal arguments for a certain informal argument and different formal arguments may correspond to different informal arguments.On the problem of the rivalry between deviant logics and classical logic,Haack held a view that we can commit the correctness of the them all,and the rivalry only exists at the metalogical level with a moderate nature.Global pluralism by Haack is a summary of the development of the variety of logics in the 1970s.It includes several kinds of pluralism and holds a tolerant attitude to local pluralism.Studies in substructural logics rose in the 1990s,which opened a new world for the development of logical pluralism.Structural reasoning systems can present both classical logic and the variety of distinctive deviant logics in the same language framework,which effectively refutes the pluralism relative to languages supported by Carnap's Principle of Tolerance.It can show clearly that different logics are reasoning in the same language while in different ways,and that different reasoning ways can only be classified by fitness without the standard of good and bad.It leads us to the view of pluralism about logical consequence.Beall and Restall's work Logical Pluralism opened a new situation for the studies of pluralism in the 21st century.On the basis of Generalized Tarski Thesis,they proposed a unified framework combined with the semantics of classical logic,relevant logic and constructive logic,which provide a support for the pluralism about logical consequence.As the most representative contemporary theory of logical pluralism,its theoretical system explains the common view and the divergence of different logical systems reasonably.According to them,even if it seems that there is rivalry,different logical systems represent different ways of precisification of the pre-theoretical concept of logical consequence.Pluralism describes the different ways of reasoning in different logical systems from the angles of proof theory and model theory,and makes a summary about the development of the variety of logics historically.However,there are still some concepts inside the theory needing to be analyzed deeply,and the too broad standard is a problem that can't be ignored.While,the deeper-seated problem is that their pluralism can be understand to be a new logic different from the other logics.Pluralism can't get rid of the suspicion on its own theory.Moreover,after considering some different pluralism,it becomes hard to differentiate the pluralism about logical consequence and the pluralism relative to languages,and queries about adhocness is also a challenge that pluralism needs to face.It may provide more theoretical support for pluralism if we discuss the variety of logics from the angle of application.Otherwise,logical pluralism would be easy to be understood as some kind of monism in the name of pluralism.