Causal relations and causal reasoning have long escaped precise treatment. Since the 1980s, however, this has changed. By combining probability and graph theory, Judea Pearl (2000), Spirtes, Glymour & Scheines (2000) and others were able to successfully formalize different kinds of causal reasoning. Among other things, they developed interesting algorithms for causal discovery (i.e., for inferring causal relations from probabilistic data). Judea Pearl’s IC algorithm certainly is one of the best known. As valuable as IC is, however, it faces several problems (as do many of its likes). Firstly, it presupposes that its input is consistent; i.e. it rules out conflicting (partial) correlations. Both in scientific practice and in every day human reasoning, however, the problem of inconsistency is omnipresent. Secondly and most importantly, the IC algorithm presupposes that its input is complete (relative to some set of variables). It presupposes that for all possible (partial) correlations it is known whether or not they obtain. In scientific practice and in everyday human reasoning, however, the problem of ignorance is even more ubiquitous than is the problem of inconsistency, and there are important pragmatic reasons to deal with it. Here Pearl’s IC algorithm fails. In my paper, I will show how the problem of ignorance can be solved by means of a combined adaptive logic. First I will introduce the theoretical frameworks underlying IC, viz. probability theory, graph theory and their interrelations. Then I will present the IC algorithm and show to what extent it suffers from the problems of inconsistency and ignorance. Finally, I will present the adaptive logic ALIC which properly solves the problem of ignorance and suggest how it might be adapted so as to also solve the problem of inconsistency.