One intuitively wouldn’t want to have a set of incoherent beliefs. Preferring incoherence is to be frowned upon, for one belief in this set must be false. Any sort of epistemology should then strive for some kind of coherence and mutual support, and if incoherence is found, of finding a way to determine which member of the set is false and which is true.
There are two kinds of coherentism I’m thinking of: the first kind is sort of a nebulous coherentism, that it is better to prefer a set of beliefs that support one another over a set of incoherent beliefs. I would then call myself a ‘weak’ coherentist in a sense, as would most modern epistemologists, but we strive not just for the coherence of our beliefs as indicating its truth, but for the truth of all of our beliefs.
The second kind of coherentism I will call ‘strict coherentism.’ It sees no recourse necessary to any sort of a posteriori examination. This gambit is played, I think, in order to circumnavigate a serious problem for most justificationists: we may be justified in preferring a coherent system over an incoherent system.