Cycles in linguistics and mathematics

Abstract

Within the framework of research in the nineteenth and twentieth centuries it has become increasingly important for scholars to realize that certain relationships form a natural class of objects and that this truth supplies us with the all‐vital notion of theory‐reduction. This paper examines a set of ideas from two worlds of scientific inquiry with a hope that reconciliation of some of the basic similarities can be made. Unfortunately at this time in the scholarship in both areas we have no positive proof for reduction, nor can we perhaps offer any, not because of any sad lack of mechanics in these areas, but because of an overwhelming haziness in questions of human neurology and pricision in brain mechanisms.