We've all known some people who are stupid and never seen to learn anything. Such people even think they are smarter than average. The stupider they are, the more entrenched they are in the notion that they are competent in anything.
I used to have a boss like that. The guy is not your average stupid. He was so stupid that he thought he had integrity and was honest, even though he lied worse than a politician, and even displayed pride at it. He was so stupid he thought he was good at lying, even though nearly everybody saw through it. He failed at everything he did, and never had a clue why. In fact, he thought he was highly skilled, and he believed his consistent failures were always due to somebody else's shortcomings. He now claims to be a business consultant, providing "expertise" to others on how they should run their businesses. He thinks he is smart. The truth is he's incredibly stupid, but he describes himself like this:
A forward-thinking, entrepreneurial Operations and Business Development Leader with extensive experience in strategic planning, business development, merger/acquisitions, business turnaround/restructuring, organizational development, project management and financial/risk management. Proven capabilities in business planning, new product launches, expanding market share and enhancing shareholder value.
Eventually, this guy got fired, which is what should happen to such frauds (but then frauds like him never should be hired in the first place). By the time he left he had done so much damage I thought he should have been sued for corporate espionage. I've got a few more things to say about morons like him here.
There is an academic article that explores the subject of this kind of stupid person with the inflated ego. Its basic conclusion is that stupid people are stupid, and stay stupid, because they lack the skills to properly evaluate themselves--that is, they are too stupid to know how stupid they are. And of course, being stupid, they think they are brilliant, and they see no need to improve. You can read the article, in PDF form, here.