Measuring Causal Specificity

Several authors have argued that causes differ in the degree to which they are 'specific' to their effects. Woodward has used this idea to enrich his influential interventionist theory of causal explanation. Here we propose a way to measure causal specificity using tools from information theory. We show that the specificity of a causal variable is not well defined without a probability distribution over the states of that variable. We demonstrate the tractability and interest of our proposed measure by measuring the specificity of coding DNA and other factors in a simple model of the production of mRNA.