This video has a little look at why contradictions aren't as bad as we think and how they can solve a bit of a philosophical conundrum. It's a little look at some of the motivations for paraconsistent logics.

I follow two arguments from Graham Priest, the first argues that contradictions are not explosive in normal language so we shouldn't really be opposed to using them in maths and logic, providing we make new funky kinds of maths and logic. The second proposes that the only way to solve the liar paradox is to claim that it is both true and false, and thus we need contradictions.

The first argument is from Sylvan's Box by Graham Priest. It's possibly my favourite philosophy paper. It's really neat.

The second argument is from In Contradiction, also by Graham Priest. He also goes over that argument in his SEP article on dialetheism.

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