Are there algorithms that discover causal structure?

There have been many efforts to infer causation from association by using s tatistical models. Algorithms for automating this process are a more recent innovation. In Humphreys and Freedman [(1996) British Journal for the Phil osophy of Science 47, 113-123] we showed that one such approach, by Spirtes et al., was fatally flawed. Here we put our arguments in a broader context and reply to Korb and Wallace [(1997) British Journal for the Philosophy o f Science 48, 543-553] and to Spirtes et al. [(1997) British Journal for th e Philosophy of Science 48, 555-568]. Their arguments leave our position un changed: claims to have developed a rigorous engine for inferring causation from association are premature at best, the theorems have no implications for samples of any realistic size, and the examples used to illustrate the algorithms are indicative of failure rather than success. The gap between a ssociation and causation has yet to be bridged.