Intelligence and stupidity, while words oft thrown around -- and I'm no exception to doing so -- are very hard to pin down properties. The current idea I've been toying with is that stupidity, and as a corollary, intelligence, is either a result of, or simply an abundance of, cognitive dissonance and intelligence being the lack thereof.
Cognitive dissonance, for this blissfully unaware enough to know, is when a person holds two mutually exclusive beliefs at the same time. If you speak to someone long enough, you'll often find these. Now, before I start on examples, let us speak of logic for a moment. In logic, if you have a contradiction ,you can prove anything; math is the same way. Since people are more familiar with basic arithmetic than symbolic logic, I'll use a quick math example. If you have 1=0, you can use the rules of math to prove anything. Since 1=0, you can add 1` to one side, and and subtract 0 from the other, since they're equal. 1=0 means any number equals any other number, which means of course, you can mathematically "prove" anything.
Now, I don't believe "beliefs" are logic are analogous. (I'd explain, but that'd take half abook) while not analogous they have similarities. Now, I'm not sure which causes which, is stupidity is the cause of cognitive dissonance, or if cognitive dissonance, once implanted tends to lead to stupidity, but either way there seems to be an undeniable correlation. A person with a large amount of cognitive dissonance is undeniable stupid, because the way they form beliefs results in multiple ones which cannot be sustained together. Any process of belief formulation which results in mutually exclusive beliefs is so flawed that the formulation of accurate beliefs is unlikely, if not impossible and thus the person and their beliefs must be considered stupid.
Let it be noted that, in a logical system, a single contradiction can lead to a proof of anything. In a human mind, the system is far less... proper. It's a tangled mess of evolutionary and social bullshit that leads to a semi-functioning mind. A single case of cognitive dissonance does not imply stupidity as a property, but frequent cases of it cannot be seen as anything else. As an example: I've known, sadly, multiple atheist/agnostic people who have the belief in ghosts. Of course, to have the belief there is no supernatural deity, but to believe there is a sort of personal spirit or soul are two beliefs that are, while not directly mutually exclusive, is extremely close to being so. This is an example of the sort of inane belief structure that makes it difficult for people to render proper beliefs. If you have a structure that conflicts, the structure cannot stand. Now, the most obvious cliche' is religious beliefs. There are a laughable number of cognitive dissonances once you start prying there. But that's not the point, the point is any system which has them results in an unstable system, and any unstable system is without a doubt one that can be called stupidity. (Drunken Rough Draft)