John Wilkins has a post at "Evolving Thoughts" on proving a negative. I've discussed the oddity of the slogan that you can't prove a negative myself. My argument was that cases that are supposedly examples of unprovable negatives are really cases of claims whose relevance to any available evidence is unknown, due to vagueness or some such; and thus that the problem is not that they are negative at all. Wilkins has an interesting suggestion that the notion comes from ignoring universes of discourse. I don't think this can be the whole matter, because even if you ignore universes of discourse you can have a theory of proof that allows you to prove negatives, e.g., by allowing you to prove affirmatives that themselves rule out other affirmatives. But it's an interesting suggestion, and probably at least partly true; given how big I am on universes of discourse, I'm surprised it didn't occur to me as a possibility.
UPDATE: I looked for the phrase on Google Book and discovered that (1) philosophers have been pointing out that the slogan is not really true for at least two hundred years; and (2) it's at least possible that the expression grew up in the context of British law courts, and just wandered out into the wide world from there, because the expression appears to have been quite common in discussion of burdens of proof in court.