Johannes von Kries’s Range Conception, the Method of Arbitrary Functions, and Related Modern Approaches to Probability

Abstract

A conception of probability that can be traced back to Johannes von Kries is introduced: the “Spielraum” or range conception. Its close connection to the so-called method of arbitrary functions is highlighted. Possible interpretations of it are discussed, and likewise its scope and its relation to certain current interpretations of probability. Taken together, these approaches form a class of interpretations of probability in its own right, but also with its own problems. These, too, are introduced, discussed, and proposals in response to them are surveyed, some of which also go back to von Kries.