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The only real thing I personally believe is existence because it is impredicative. That's true logic.
The rest is hogwash until proven otherwise.
(I do believe in some fringe stuff from personal experience but that probably has a perfectly normal explanation, I just miss the data to explain it for now)
Usually when something appears to violate causality, that doesn't end up being the case. The unexpectedness of the result is caused by our own incomplete understanding of the physics at play. So far none of these have ended up pointing to some supernatural entity secretly judging us.