The present paper studies a specific way of addressing the question whether the laws involving the basic constituents of nature are statistical. While most German physicists, above all Planck, treated the issues of determinism and causality within a Kantian framework, the tradition which I call Vienna Indeterminism began from Mach’s reinterpretation of causality as functional dependence. This severed the bond between causality and realism because one could no longer avail oneself of a priori categories as a criterion for empirical reality. (...) Hence, an independent reality criterion had to be sought, a problem which all three physicists to be studied solved in different ways that were mainly conditioned by their different concepts of probability. In order to prevent a dissipation of intuited facts, Mach had to resort to a principle of unique determination as his reality criterion, especially when discussing the Principle of Least Action. Giving theories more independence, Boltzmann understood atomism as property reduction to precisely defined theoretical entities and their interactions. While this served as a relative reality criterion, he also advocated a constructivist one because atomism was already implied by our finitary reasoning power. Finally, Exner contemplated the idea that all apparently deterministic laws are only a macroscopic limit of an irreducible indeterminism, because by adopting the frequency interpretation, observable collectives could be considered as the real basic entities. (shrink)