The simplest answer to this mighty question is likely this: a Great Book is a book which causes a reader to confront fundamental questions about the human condition or develops in one the capacity to ask such questions (thanks to Owen Goldin for that addendum). For instance: what is man? What is the basis of morality/are these opposing actions moral? Is man by nature good or evil? Can man learn good or evil (or virtue)? What is the specific nature of man? What is Truth and can it be attained? Etc…A Great Book does not per se have to confront all these questions, but rather during its reading such questions should naturally come up. For instance, during Homer’s Iliad, Achilleus, a young semi-divine warrior has his concubine, which he won through battle, unrightfully stripped from him after a public encounter with the lord of all the Achaians. The reason Achilleus has his concubine stripped from him–who was rightfully his–is that he spoke against Agamemnon in order to have a prophet give forth the reason that the Achaians were being plagued by Apollo, god of plague, archery, etc…So, technically, Achilleus was serving the people and protecting the prophet who would lead the people out of plague. Agamemnon, however, perceived Achilleus as speaking out of turn, and when he heard that he would have to give up his own recently won concubine, Chryseis, he demanded Achilleus’ in turn, Briseis. Achilleus consents to this after considering killing Agamemnon, but in response removes himself from the war. As a result of having his “bride” taken from him, Achilleus begins to ponder the foundations of a glory based society. Why should he, he wonders, ever fight if he and a coward will be held “in a single honor”, and both end up in the same dark and dreary Hades, regardless of deeds. He also considers the foundation of the war–if Menelaos summoned all these men to fight for stolen Helen–is not Agamemnon repeating this offense by stealing Achilleus’ concubine from him? Deep and difficult questions. Questions which challenge and consider the foundations of human relations and society–through the context of external wars and wars of emotion within–these are the questions which make the Iliad great. And questions of similar degree are what make any “Great Book” great.
The second criterion a book must fulfill in order to be “great” is that it must be “timeless”. What timeless, in this context, means is that the values, lessons, and plot of a book must be relatable, connectable, and have some edifying effect on readers. For example, again in the Iliad, Achilleus rightfully questions the valorous heroic code of honor if it used to serve a hypocritical and inglorious (in his opinion) king. However, upon Achilleus’ best friend, Patroklos, being slain by Hektor, Achilleus immediately, without question, makes amends with Agamemnon and seeks vengeance for his departed friend. Now, one may question the relative value or morality of seeking vengeance or retribution as one’s means of justice, and the text certainly allows for that as Achilleus is less and less described as a man, and more and more takes on fire imagery, representing his full consumption by passionate and overpowering Rage. The value, however, which is not questioned is friendship. Achilleus, though he may question leadership, honor-bound society, etc…never once questions what his friend meant to him, and though he may be misguided in how he seeks justice (or he may not), he, like many today might claim, values friendship even over far more abstract principles of loyalty.
The third criterion which a book must fulfill to be “great” is that it must admit of multiple thoughtful and potentially correct interpretations–which may also be mutually exclusive from each other. For instance, if one takes the example above of Achilleus re-entering the Trojan War solely to avenge his fallen friend and kill his friend’s “murderer”, one might rightfully say that Achilleus’ intentions are suspect, and that he is not truly earning himself kleos by serving his emotions rather than a principle of loyalty or friendship. On the other hand, one might equally well say that Achilleus is such a strong adherent to the value of loyalty and friendship that such values require no thought on his part–he lives and feels such values so deeply that he is essentially incapable of questioning them. Having such values ingrained in him provide him with an Archimedean point when questioning other values–like the fabric of the heroic society from above. And from yet a third perspective, one might say that Achilleus is noble in the pursuit of justice for his fallen friend, but he is ignoble in the sense that he has allowed emotions to overpower him (much as they will his cousin Ajax later in the Contest of Arms) where no man ever did so. But then, again, perhaps this perspective just serves to illustrate how ultimately human Achilleus is in the light of his semi-divine heritage and powers. Such lively reflection and debate is the well-spring of thinking, reflection, and what is called “critical thinking”. And such thought is the goal (entelecheia) of reading a “Great Book.”
The fourth piece of the “Great Book” puzzle is that such a work must uphold and question values of human nature and society at the same time. A “Great Book” is therefore the great bridge (pons magnus) in that it is politically progressive in questioning the values of a day while also politically conservative in upholding the very same values, though perhaps under differing conditions. As written above, Achilleus clearly questions the value and nature of Agamemnon’s authority, and in fact he invites the reader to question what the root of authority is: is it physical power derived from divine heritage, or is it simply commanding the largest fleet and most men? However, what Homer does not allow is one to question authority itself as a value–as he clearly demonstrates by having Nestor, wisest and oldest of the Achaians, explicitly tell Achilleus, “Nor, son of Peleus (Achilleus), think to match your strength with the king, since never equal with the rest is the portion of honour of the sceptred king to whom Zeus gives magnificence. Even though you are the stronger man, and the mother who bore you was immortal, yet is this man greater who is lord over more than you rule.”(Iliad, Book I, 277-282, Lattimore tr.). So, all in one scene, one observes the progressive tendency towards questioning the manifestation of an institution, the conservative tendency of upholding the necessity of values, and a third way of both questioning and upholding values based on reflection of the situation as a whole. Such reflection, like in the paragraph above, is the legacy of “Great Books”.