Inconsistency toleration is the phenomenon of working with inconsistent information without threatening one’s rationality. Here I address the role that ignorance plays for the tolerance of contradictions in the empirical sciences. In particular, I contend that there are two types of ignorance that, when present, can make epistemic agents to be rationally inclined to tolerate a contradiction. The first is factual ignorance, understood as temporary undecidability of the truth values of the conflicting propositions. The second is what I call “ignorance (...) of theoretical structure”, which is lack of knowledge of relevant inference patterns within a specific theory. I argue that these two types of ignorance can be explanatory of the scientists’ rational disposition to be tolerant towards contradictions, and I illustrate this with a case study from neutrino physics. (shrink)