Abstract

The relation between causality and probability is a very complicated matter whose discussion has generated many paradoxes and controversies. In short it is a philosophical minefield. In this paper, I will concentrate on only one aspect of the problem, namely the debates about the Markov, or Screening-Off, Condition. Reichenbach in 1956 proposed a causal model called a conjunctive fork, which satisfied the Markov condition, but later Salmon produced a causal model, called an interactive fork, which did not satisfy this condition. In the 1980s the theory of causal networks was developed in a striking fashion by Pearl and others. Pearl specified that every node in what he called a ‘Bayesian network’ had to satisfy the Markov condition. Yet the Markov condition was criticized in the 1990s by Cartwright, who maintained that the Markov condition is ‘a very special case that holds in unusual circumstances’. In this paper, I will analyse this controversy between Pearl and Cartwright, and then go on to consider the multi-causal forks, which have become common in modern medicine. I will argue that such forks are best handled by a non-Markovian causal model. The paper is designed for anyone with general interests in philosophy of science rather than for specialists in causal modelling. So technical terms such as conjunctive fork, interactive fork, Markov condition, Bayesian network, multi-causal fork, etc. will be fully explained in the course of paper and illustrated by examples.