ILL-LOGIC

Among the valuable properties that logical systems can have are:

* Consistency, which means that none of the theorems of the system contradict one another.

* Soundness, which means that the system's rules of proof will never allow a false inference from a true premise. If a system is sound and its axioms are true then its theorems are also guaranteed to be true.

* Completeness, which means that there are no true sentences in the system that cannot, at least in principle, be proved in the system.

From wikipedia

Some stunning examples of the human capacity to think illogically, inconsistently, incompletely, blindly. See them all together here.