When should we draw arrows? Assessing the use of Bayesian networks inphilosophy of science
In this paper I present the criteria under which it is admissible to draw arrows in Bayesian networks. I argue that arrows can be used to represent asymmetric, non-transitive, difference-making relationships in Bayesian networks. Moreover, since these graphs are not heterogeneous, there should be uniformity in what the arrows are representing. That is, a single Bayesian network cannot represent a variety of difference-making relationships. I use this asses two models found in the literature for transferring evidence in intertheoretic reduction. I conclude that these models are either unable to represent the fact that evidence from one theory is evidence for the other
theory, or that they operate with assumptions that contradict the central tenets of intertheoretic reduction. I offer a possible way out of this predicament by proposing heterogeneous graphs that can be condensed into Directed Acyclic Graphs (dags).