Models of logical systems

Abstract

The purpose of this paper is to show that some of the difficulties confronting logicians are caused by too narrow an interpretation of the function of mathematical logic. I hope to show that very fruitful results can be obtained by considering a much wider range of problems than usually found in the literature. I believe that the function of mathematical logic is to study all logical systems. The problems now considered usually concern some particular system or set of systems. Of course we would have to agree first on what a logical system is. I shall suggest a tentative definition. The rest of my paper will proceed on the assumption that we have agreed on this question. However, it is only necessary for this paper that some definition should be accepted, it is not necessary that it should be the one I suasest.