On causal dynamics without metrisation: Part III

Abstract

A formalisation of heuristic and intuitive ideas about causal dynamical transitions, presented in Part II of this series (this volume, pp. 1–22), is given here. A quotient structure is found to be necessary for any collection of causal dynamical transitions by using arguments employing the Principle of Corporate Agreement. The relevance of the first homotopy group (the fundamental group) to ‘small scale’ phenomena predicted by a theory is pointed out, and the fundamental group is seen to play a wide role in defining the causality, relational and quotient structures of a theory.