The opposite of the Illuminati, who take pride in their high level of knowledge and learning. An Illiterati takes pride in the fact that they are ignorant and refuse to learn (adjust their paradigm)often to the severe detriment of those around them.
Many examples abound, from the liberal screaming out News Media sound Bites to the clergy who says trust their judgment while molestation lawsuits rain upon them.
Not so secret society of people who seemingly know something about Every subject, but somehow never grasped the basic concepts of the English language.
The illiterati have many 'good ideals' about how to make the world a better place.