For centuries people have been interested in defining and measuring intelligence. The two go hand-in-hand, really, because to measure something requires one to decide what is to be measured. We have a sense of raw, computational intelligence akin to what one might employ in an IQ test. We have theories of multiple intelligences, which include things like emotional intelligence along with verbal and mathematical reasoning. We have memory tests. And, at least in the US, we have the idea of common sense or practical aptitude as a kind of intelligence (think 'how many professors does it take to screw in a lightbulb,' or the TV-show savant who can piece together seemingly unsolvable crimes by means of masterful information processing, but is always pushing with futility on a door you're supposed to pull).
We have plenty of (smart?) people working on how to define and measure these kinds of intelligence, and to quantify and describe intelligence in general; but we're never satisfied with the results. I think this is largely because intelligence is by definition greater than innate ability. Intelligence is inextricably linked with our values. If we lived in a world where everything practical were taken for granted as god-given, it may be painting or poetry that reflects the highest intelligence. If we lived in world where all the matter around us were constantly shifting its properties, it may be the engineer or the physicist who embodies the most formidable genius.
The best definition of intelligence I've come across is from an Oxford 'Short Introduction' to Intelligence that I read some years ago. The author described intelligence as a kind of flashlight. Different flashlights have differing degrees of candle power, such that some have the power to shine light further or brighter than others; but, crucially, it's also important where we point our flashlights. A flashlight with the most brilliant power, pointed continually at the same blank wall (or reality TV show, or futures market) will not achieve the knowledge, enrichment, or results of a dimmer flashlight pointed toward all that is dark, unknown, or underexplored. In other words, computational brain power is a part of intelligence, but so is that inclination or ability to train our brains on things that are diverse and complex and mysterious enough that we can learn and develop and flourish beyond our present selves.
I like this definition not only because it's plausible and accurately descriptive of what I and others empirically observe in our interactions with the world, but also because it allows for the possibility that the intelligence of every person is at least in some part amenable to the will: if we choose, we can all work on pointing our flashlights toward the dark corners in our lives, rather than dwelling complacently in the light of the known world. This is so satisfyingly democratic, despite that, surely, and for whichever reasons, some are more naturally inclined than others to point their flashlights in the right places, and some have the candle power to see so brilliantly anywhere they point.
I bring up intelligence because this, I think, is the crutch upon which modern-day castigation of the intellectual rests. So many--and, it must be said, especially those on the political right--are proudly anti-intellectual. They disdain the idea that someone highly educated or in an elite job in opinion journalism or a senior position at an art gallery, a museum, an opera house, or a scientific research institute might be considered smarter than the average person. The idea that knowing more about something is a form of elitism stems from this understanding of intelligence as fundamentally undemocratic. Rather than seeing people in these elevated 'knowledge' positions as hard workers who pointed their flashlights in uncommon directions, the anti-intellectual sees them as snobs who want to impose a foreign set of 'smart people' values on the commoner. At the same time as the anti-intellectual sees himself as a commoner, however, he also sees himself as intellectually superior, not faffing around with uncommon or unpopular knowledge, but enterprising in the realm of practical knowledge.
This paradoxical mentality of the anti-intellectual forces him into the No True Scotsman fallacy of denying the intelligence that he recognizes as intelligence, and simply renaming it snobbery.
As a consequence of this thinking, 'intellectual' has become a dirty word, signifying not the public good of pointing our flashlights in uncommon and underexplored directions, questioning popular attitudes and ideas, and standing up for knowledge for its own sake, but instead a kind of elitism or frivolity.
I, really, am proud to call myself an intellectual, or to strive to be one, without irony, and without disdain. For me this means leading what is trivially referred to as 'a life of the mind' not in some mythical 'Ivory Tower,' but every day. This means pointing our flashlights toward the darkness and being comfortable with the idea that we might not like what we find, but we'll deal with it as we go along. This means celebrating the freedom of public discourse, delighting in rhetoric, argument, disagreement, skepticism, and uncertainty. This means standing up to the scoffing, checkered-shirted, dark-rimmed tyranny of ironic detachment, and the insouciant consumerism that circumscribes it. This means not being afraid to be wrong or to be mocked for aspiring to something better than what we have.
The intellectual is a modern Don Quixote, a figure who was read as a madman and a buffoon before anyone thought him a visionary.