"As I have recently written elsewhere, the adjective "great" in the phrase "great books" derives its primary meaning from its use in the phrase "great ideas." There are many other criteria by which people make up diverse lists of the books they wish to honor by calling them "great books." But from the primary significance of the adjustive "great" as applied to the great ideas is derived the significance of that adjective as used in the phrase, "the great conversation."
"In other words, we chose the great books on the basis of their relevance to at least 25 of the 102 great ideas. Many of the great books are relevant to a much larger number of the 102 great ideas, as many as 75 or more great ideas, a few to all 102 great ideas. In sharp contrast are the good books that are relevant to less than 10 or even as few as 4 or 5 great ideas. We placed such books in the lists of Recommended Readings to be found in the last section in each of the 102 chapters of the 'Syntopicon.'"So a Great Book is one full of Great Ideas, and a Great Idea is one that is part of the Great Conversation, and the Great Conversation is the discussion down through the ages of the topics or ideas that have the greatest potential for good or ill when applied in our lives. For example one of the "Great Ideas" listed in the syntopicon is 'Slavery.' The impact of slavery in our world, and the discourse through time on the pros and cons of slavery has been "Great", and thus becomes a "Great Idea". So, although a book within the Great Books series might encourage slavery, even claiming it to be a natural condition for certain people, which I believe is not good or right, the fact remains that it is a "Great idea", an idea that has greatly impacted our world, and can greatly impact me, especially since each work chosen relates to at least 25 great ideas! I hope this helps in your reading and understanding of Great Books.