<?xml:namespace prefix = o />  Many algorithms for inferring causality rely heavily on the faithfulness assumption. The main justification for imposing the faithfulness assumption is that the set of unfaithful distributions has Lebesgue measure zero, since it can be seen as a collection of hypersurfaces. However, due to sampling error the faithfulness condition alone is not sufficient for statistical estimation, and strong-faithfulness has been proposed and assumed to achieve uniform consistency. In contrast to the plain faithfulness assumption, the set of distributions that is not strong-faithful has non-zero Lebesgue measure and in fact, can be surprisingly large as we show in this talk. We study the strong-faithfulness condition from the point of view of real algebraic geometry and give upper and lower bounds on the Lebesgue measure of strong-faithful distributions for various classes of directed acyclic graphs. Our results imply fundamental limitations for algorithms inferring causality based on partial correlations, with the PC-algorithm as its most prominent example.