Language and Levels of Abstraction as Criteria for Determining the Status of Systems of Logic

Abstract

1. The of logic. Comparatively recently, Kant's words to the effect that in the two thousand years since Aristotle logic had made a single step forward and, all things considered, it seems to be a fully finished and completed discipline (1) used to be quoted widely and not unsympathetically. Today, however, there are works about logic in which the listing of logical disciplines runs into the dozens. In this regard the attempt by the American logician N. Rescher to compile a diagram or map of in which the list of the branches of logic takes up several pages, is noteworthy. (2) Also characteristic is the following statement by one of the major modern representatives of mathematical logic, S. Kleene: Since the discovery of non-Euclidean geometries by Lobachevsky (1829) and Bolyai (1833), it has become clear that different systems of geometries are conceptually equally possible…. Identically, there are different logics. (3)