In complete absence of any evidence both the statement and its logical negation have equal weight
But there is never "complete absence of any evidence." For example, if I claim to you that I have an invisible flying pig in my backyard, we both have a lifetime of experiences to draw on which are inconsistent with such a claim. e.g. witnessing pigs and similar animals running around but not flying; feeling solid objects which have always been visible in normal light; and so on. So I would bear the burden of proving my claim.
You know the drill - If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
And, while this is an accidental exception, future open threads should start on Mondays until further notice.