Scientific Progress and Changes in Hierarchies of Scientific Disciplines

Abstract

My considerations on the progress of mathematical knowledge arose from historical investigations of the emergence of modern systems of formal logic in the 19th century. Because of the radical changes these processes of development effected, they have been called revolutionary (Gillies 1992). Those portions of formal logic that operated symbolically were removed from the domain of philosophy and inserted into mathematics, where they were utilized in foundations. The fact that today the term “logic” is often identified with “mathematical logic” shows how radical this change has been, as mathematical logic was at first only a further development of a part of traditional logic.