Contextual Emergence of Deterministic and Stochastic Descriptions

Abstract

Hans Primas laid the groundwork for contextual emergence and also had a long-standing interest in issues of stochasticity and determinism and their consequences. In this contribution we describe contextual emergence and then turn to the question of whether determinism and stochasticity could be regarded as contextually emergent notions. In a first step we demonstrate that the conventional concept of determinism is not fully contained in the fundamental description of dynamical systems but requires some contextual stability condition for the emergence of unique trajectories. Second, we discuss mathematical dilation techniques of deterministic systems for the contextual emergence of stochastic descriptions. Finally, the emergence of deterministic “mean field” descriptions from stochastic Markov processes illustrates another contextual aspect of the nature of determinism. We discuss our results regarding contextual determinism and stochasticity in the framework of relative onticity and indicate its potential relevance for the freewill-determinism debates.