In class last Tuesday, Bill Lycan was discussing the free will debate and the common thought that there is a prima facie incompatibility between free will and determinism. Bill made the following methodological point: prima facie, anything is compatible with anything. For two propositions to be incompatible, there has to be some deductive argument, with one as a premise and the negation of the other as a conclusion. So there should be no such thing as a prima facie incompatibility. Moreover, it's the proponent of the incompatibility who has to establish a necessary truth. So above and beyond the absence of any prima facie incompatibility, the burden of proof is always to prove the incompatibility.
Ignoring the burden of proof argument, I think that prima facie incompatibilities are much better off than Bill gives them credit for being. There's two ways to see this. First, as a psychological fact, you can often guess that you could formulate an argument for a given proposition, and these guesses are better than chance. But if the proposition in question is "the existence of free will entails the falsity of determinism" this guess just is a prima facie incompatibility. This isn't something deviant and isolated either. Much of philosophy (science, math, etc) works like this: you hear a statement and immediately think it's true or false. Then you search for an argument. We do revise our opinions--overturn our prima facie judgments--when the arguments fail to pan out, but that's why it's a prima facie judgment.
Second, most epistemologies compatible with our knowledge of necessary truths would license judgments of prima facie incompatibility. Both Bealer and Sosa's defenses of philosophical intuition hold that a necessary proposition can just seem true to you, and thereby confer justification on that proposition. So the proposition "necessarily not both p&q" can have a prima facie justification. This sort of seeming is prima facie because intuitions are fallible, the canonical example being that the naive comprehension axion of set theory seems true. Lycan's own epistemology endorses of a principle of credulity: at the outset, believe each thing which seems plausible to you. So if you find that you are inclined to think that free will and determinism are incompatible, you have a prima facie justification for believing that they're incompatible.