For the past few weeks, the ancient Greek philosopher Plato has been tweeting. His ghostwriter—the author, philosopher and professor Rebecca Newberger Goldstein—has brought him back to life on social media to promote her new book, "Plato at the Googleplex." Sample tweet: "Is tweeting beneath me? Nonsense! Philosophy doesn't live in treatises but in the give & take of many points of view reacting to each other."

In the book, Dr. Goldstein imagines Plato traveling on a speaking tour to places such as...