Unless you're dealing with Intuitionistic logic:
Semantically, intuitionistic logic is a restriction of classical logic in which the law of excluded middle and double negation elimination are not admitted as axioms.
In intuitionistic logic, it is still the case that nothing can be both true and false.
I was just wondering. Human minds are messed up in 1001 ways, but are there a few rational principles that most people already have down? Of course, the answers to this question are probably so extremely obvious that I haven't even considered them. But I ask all the same.