In the recent literature on coherence and structural rationality, it is widely assumed that sets of attitudes are coherent just in case they are not incoherent. In particular, the two most popular kinds of views of incoherence—those centered around wide-scope rational requirements and those centered around guaranteed failures of some normatively significant kind—rely on this assumption. We argue that this assumption should be rejected because it fails to capture the difference between positively coherent attitudes and random unrelated ones. We also (...) formulate and defend an alternative support-centric view of coherence and incoherence which captures this difference and has several additional advantages. (shrink)