Title: Bread Prices and Sea Levels: Interventionism, Monotonicity, and the Problem of Variable Relativity

Abstract: A key challenge for interventionist causal models is to distinguish non-causal probabilistic dependence relations from true causal relations. In this paper, I first argue that causal models can better accomplish this task if they are required to be monotonic in the following sense: the causal relations occurring in a model M would not disappear if further variables were added to M. If causal models must be monotonic, then standard problem cases for the causal modelling approach can be avoided. This is especially true for cases where variables do not stand in causal relations, but are probabilistically related by accident, such as Sober’s famous example of the relationship between bread prices in England and the sea level in Venice. In a second step, I examine the consequences of the monotonicity requirement for the debate on variable relativity, that is, the question of whether a variable can be the cause of another variable relative to a variable set V (constituting a model), but not relative to another variable set V’ (constituting a different model). I argue that the monotonicity requirement is consistent with a benign form of variable relativity, but prevents causal models from being variable relative in a problematic sense.