Know what you will answer.

peace
I have a friend with whom I have been arguing for a long time. He claims that it is wrong to say that there are people for whom the law of identity does not apply (he also agrees that it is wrong to believe in logical contradictions, etc., since there is no thought process behind such a claim – and as the rabbi said, but he claims that there may be people for whom it is not a contradiction at all). Is there a way to prove otherwise?