When the Harvard historian James T. Kloppenberg decided to write about the influences that shaped President Obama’s view of the world, he interviewed the president’s former professors and classmates, combed through his books, essays, and speeches, and even read every article published during the three years Mr. Obama was involved with the Harvard Law Review (“a superb cure for insomnia,” Mr. Kloppenberg said). What he did not do was speak to President Obama.

“He would have had to deny every word,” Mr. Kloppenberg said with a smile. The reason, he explained, is his conclusion that President Obama is a true intellectual — a word that is frequently considered an epithet among populists with a robust suspicion of Ivy League elites.

In New York City last week to give a standing-room-only lecture about his forthcoming intellectual biography, “Reading Obama: Dreams, Hopes, and the American Political Tradition,” Mr. Kloppenberg explained that he sees Mr. Obama as a kind of philosopher president, a rare breed that can be found only a handful of times in American history....