The philosopher Wittengstein has something to say about this, in part of a discussion of formal logic. He says contradictions are not as bad as you might think

The philosopher Wittengstein has something to say about this, in part of a discussion of formal logic. He says contradictions are not as bad as you might think. "Or suppose that there is a contradiction in the statutes of a particular country. There might be a statute that on feast days the vice-president had to sit next to the president, and another statute that he had to sit between two ladies. This contradiction may remain unnoticed for some time, if he is constantly ill on feast-days. But one day a feast comes and he is not ill. Then what do we do? I may say 'We must get rid of this contradiction.' All right, but does that vitiate what we did before? Not at all. [...] When a contradiction appears, then there is time to eliminate it. We may even put a ring round the second rule and say 'This is obsolete.'"