More at https://www.philosophytalk.org/shows/true-contradictions.

If you want to tell the truth, you shouldn’t contradict yourself—that’s just common sense. A suspect who was home on the night of the crime can’t have been elsewhere, and whatever the weapon, we can rule out the hypothesis that it was both a candlestick and not a candlestick. But there are philosophers who claim we shouldn’t overgeneralize based on murder mysteries: some contradictions are true. Could a badly written law make the dastardly deed both legal and illegal? Do mathematical paradoxes create weird things that both do and don’t exist? If we embrace contradictions, will we still be able to tell the difference between truth and falsehood? Josh and Ray embrace contradiction with Graham Priest from the City University of New York, author of "Doubt Truth to Be a Liar."