>>76
Of course contradictions are in our own mind - they just show that some of our reasoning or beliefs are wrong and we must re-examine them.
But mathematicians love to "define" contradictions. When I hypothesise that I can move hand into some occupied space, and then fail to do this - that is an invented contradiction. When mathematician proposes that moving hand in some (un)occupied space is a contradiction (by sole definition), that would be a defined contradiction, that has no sense, because it's in strict contrast with senses.