Hostadter attempts, in chapter 2, to define intellect and intellectuals. He draws several contrasts: between intellect and intelligence; between intellect and business; between an intellectual and a "mental technician." In each contrast, the intellectual is characterized by enthusiasm for ideas, their practical value notwithstanding.
the professional man lives off ideas, not for them
As of today's writing, Wikipedia describes intellect as "the ability of the mind to come to correct conclusions about what is true or real, and about how to solve problems", and intelligence as mental abilities that allow people to understand things. (see Intellect) Other dictionaries bring the definitions closer together, defining intellect as the ability for rational thought and abstract reasoning, and intelligence the ability to learn or reason.
Developmental psychology tells us that children learn at least from birth; intelligence, then, is inborn. The same theories of children's development tell us that the ability to reason abstractly develops at or near puberty, as the child's brain matures and develops the connections to allow abstract reasoning and problem solving to happen. By early adulthood, almost everyone has developed some capacity for abstract reasoning and problem solving; that is, by adulthood, nearly everyone has an intellectual capacity. What distinguishes an intellectual, then, is that she routinely uses that capacity for enjoyment, to pursue abstract questions or solve problems to reach an internal and self-determined goal. She may then share the results of that questioning and evaluation, and may even benefit from it, but the primary goal of the endeavor is internal. This is in opposition to the non-intellectual, no matter how intelligent, who uses his capacity for abstract reasoning and problem solving primarily for external reward, for goals he has not personally determined.
This is more or less the same definition that Hofstadter came to.
As a professional, he has acquired a stock of mental skills that are for sale. The skills are highly developed, but we do not think of him as being an intellectual if certain qualities are missing from his work—disinterested intelligence, generalizing power, free speculation, fresh observation, creative novelty, radical criticism.
Expanding my search for definitions, I find the following:
Aaron Swartz, in an essay entitled "What it means to be an intellectual", says:
There’s a social norm that how much we discuss something should be roughly proportional to its importance. [...] There’s just one problem: I enjoy deep discussions of punctuation and other trivialities. [...] What is “this drive”? It’s the tendency to not simply accept things as they are but to want to think about them, to understand them. To not be content to simply feel sad but to ask what sadness means. To not just get a bus pass but to think about the economic reasons getting a bus pass makes sense. I call this tendency the intellectual.
Jonathan Scanlan, in an essay published on blogcritics.org, says:
being an intellectual is not about these details, but rather the practice of reflection and analysis.
(I am inclined to accept Mr. Scanlan's description of himself as an intellectual, for no other reason than that he describes exactly the point I made above regarding nearly everyone having intellectual capacity as a sorites paradox.)
Adding these two additional definitions to our hat, we now have intellect equaling abstract reasoning and problem solving and intellectualism being a practice of reflection and analysis upon a wide variety of ideas, both large and trivial. An intellectual may not agree with the common cultural assessment of the importance of an idea. Thus, Mr. Swartz's desire to debate his friend's disregard of an opinion - a trivial occurrence to his friend - is, in an intellectual light, a moral question: Is it valid to disregard the opinion of someone merely because the subject of the opinion is that person's livelihood?