Logic, Metalogic and Neutrality* (penultimate Version)

A natural metametaphysical hope is that logic should be able to act as a neutral arbiter of metaphysical disputes, at least as a framework on which all parties can agree for eliciting the consequences of the rival metaphysical theories. An obvious problem for this hope is the proliferation of alternative logics, many of them motivated by metaphysical considerations. For example, rejection of the law of excluded middle has been based on metaphysical conceptions of the future or of infinity. Quantum mechanics has been interpreted as showing the invalidity of one of the distributive laws. Dialetheists believe that paradoxes about sets or change manifest black holes of contradiction in reality itself. There is no core of universally accepted logical principles. Nevertheless, logic seems to have come of age as a mature science. This paper explores some aspects of the situation just sketched. In particular, it assesses the idea that metalogic is the agreed, scientific part of logic. It takes some comments by Georg Henrik von Wright on the past and future of logic as a convenient starting point.