Can we imagine a being who genuinely believes a bald-faced, explicit contradiction (such as that "murder is right, and murder is not right")? Or is there something in the very idea of belief which makes this, not only contingently unlikely, but necessarily impossible?

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I know several people who believe such things, or at least say they do.

One group thinks that there are true contradictions that involve very special cases. The usual example is the so-called liar sentence, "This very sentence is not true". There is a simple argument that the liar sentence is both true and not true, and some people believe just that.

Other people, though, think there are contradictions involving much less special cases. An example would be what are called "borderline cases" of vaguepredicates, like "bald". People often want to say that there are somepeople who aren't bald and aren't not bald either. But the so-called DeMorgan equivalences entail that this is equivalent to saying that theperson is both bald and not-bald (or, strictly, both not-bald andnot-not-bald).

People who hold such views are known as "dialetheists". See this article for more.

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