You should also read, "How Can We Be Moved by the Fate of Anna Karenina?" by Colin Radford, and the literature that developed in response to it.
This is a great and complex matter. There are a few philosophers of art who come close to an "anything goes" approach to the meaning of a work of literature, but most of us think there are some boundaries in terms of historical context, the intentions of the artists, and most importantly the content of the work of art itself. You might consider a distinction that some find useful between the meaning of a work of art and the significance of a work of art. In terms of significance, a work of literature might have all sorts of features depending on how the work is experienced. Reading Jane Austin might lead me to become a Marxist and someone else to become a Hindu, and so on, but while the book could have such multiple, different significant effects, to get at the meaning of her work we would need to study the plot, characters, England and continental Europe at the time, the English style she used, and so on.... Once we take those factors into account we can see (or I wager we will see) that her work was not meant as Marxist or Hindu literature. Part of this seems to be the sort of thing we can debate objectively (pointing out that Austin died in 1817 whereas Marx wasn't born until 1818, for example) but we might also see how the meaning of a work might contribute to the significant future multiple readings and re-readings of works of literature. In this sense, the meaning of a work such as Sense and Sensibility might remain constant through your life, and yet the work had a radically different significance for you when a young reader than when you re-read it at sixty. I discuss some of these issues in a recent book, Aesthetics: A Beginner's Guide, which you may (or may not!) find of interest. You have certainly raised a central matter that requires far more of a response than I have attempted in this short reply. Good wishes.
Zen and the Art of Motorcycle Maintainance might fit the bill, though it is a bit more oriented to metaphysics than epistemology / the theory of knowledge. I am not sure it is super entertaining, but C.S. Lewis's book Until We Have Faces is terrific; it is a re-telling of an ancient myth. You might also like novels by Hermann Hesse like Sidartha --it is a re-telling of the tale of Buddha's enlightenment, and is quite moving and rich for stimulating philosophical reflection. There is a new book: Alice in Wonderland and Philosophy, raising all sorts of great puzzles (including epistemological ones) and that could be read alongside of reading Lewis Carroll's classics. You might also check out the Ultimate Harry Potter and Philosophy book, which unearths interesting philosophy in connection with Rowling's work. Although not out yet, there is a forthcoming Sherlock Holmes and Philosophy book which might be great to read along side short stories and novels about Holmes. Here is another radical idea: you might try writing some short stories of your own that take up questions / arguments that arise from the Theory of Knowledge. You could begin: George was in the tenth grade in a humanities course when he first encountered Descartes' worry that all our perceptions might be false. He still could not shake the worry when the bell rang and he ran into Chris who had unshakable confidence in his views of the world......
You have asked: who else writes about the mythical dimension of life from a philosophical vantage [point]? Ralph Harper would be good to check out (try his book Sleeping Beauty). He does some interesting philosophical and theological work on fairy tales, but his work does bear on what you might call the mythical (deep use of symbolism that resonates with the kinds of material you would find in the (highly recommended) The Oxford Companion to World Mythology (OUP, 2005)). Richard Wollheim might also be good. His writing is difficult (but not as challenging as Hegel!); you might check out The Thread of Life and The Mind and Its Depths. Jonathan Lear is also a contemporary philosopher who is sensitive to mythology (he combines philosophy and psychoanalysis). The philosopher and novelist Iris Murdoch might also be interesting, as she defends a fairly optimistic, contemporary, secular form of Platonism which may be seen as anti-tragedy. Check out her books The Sovereignty of the Good (1970) and The Fire and the Sun (1977). Actually, Plato himself may be read as replying to Homer (e.g. in the Ion and Republic) and in offering a counter-mythology (the myth of the cave and the myth of er).
Although Mircea Eliade was not a philosopher, two of his books are philosophically very interesting: The Myth of the Eternal Return and Patters of Comparative Religion. There is an interesting Freudian reading of myths in the classic The Uses of Enchantment by Bruno Bettlheim, but this may have the same limitation you note with reference to Freud himself. Though in fairness to Freud, I think he does connect his work on Oedipus and other myths with a bigger picture; this can be seen in his tragic naturalism as outlined in his 1930 book Civilization and its Discontents. Erich Auerbach was also not a philosopher, but what he has to observe in his book Mimesis; The Representation of Reality in Western Literature is quite fascinating philosophically. Have a go with the first essay, "Odysseus' Scar," and if you like it, keep going!
These are great questions! Some works of art seem quite anchored in the material world. Arguably, a marble statue like the David is in Florence. But poems, plays, novels, musical compositions, and so on do seem more elusive. Some philosophers who might be called Platonists tend to think that poems, plays, and the like are not themselves physical events or objects. On this view, the Iliad may be thought of as an abstract object that can be acted out, recited, written down, remembered, loved or hated, but the epic poem is not itself a physical thing. I am very much drawn to such a position and have defended it (in a short book called Aesthetics; A Beginner's Guide), but many philosophers resist recognizing abstract, non-physical objects. Such philosophers (who might be called nominalists or conceptualists) might have to identify the Iliad as a complex cultural object that has multiple linguistic and social dimensions. For them, the Iliad's status may depend upon an on-going social practice, but for those of us in the Platonic camp, we think that the Iliad still exists even if all records of it fanish. In such conditions, there would still be truths about the Iliad. For example, in such a post-Homeric world, it would still be true that Achilles kills Hector in battle before his beloved city of Troy. Nicholas Wolterstorff has a good book on such topics called (I believe) Works of Art.
Perhaps Professor Greenberg should reply to this, but here goes: I suggest that there are at least two ways of defining a philosophy. On one meaning, to have a philosophy is to have a worldview or a conception of yourself, the world, values, and so on. From this point of view, most people have a philosophy Secondly, "philosophy" can stand for the disciplined reflection on world views or ways of thinking about reality and values. The latter can certainly involve description, clarification, and criticism. Probably Professor Greenberg put such an emphasis on arguments is that while philosophy can involve a great deal of exploration and exposition, a great deal of philosophy addresses questions of justification or evidence. Using these distinctions, I think it likely that Shakespeare the person had a worldview and thus had a philosophy, but in the work attributed to Shakespeare there are multiple philosophies or worldview (Macbeth's philosophy seems different from Prospero's) and it would be hard (but not impossible!) to find straightforward philosophical arguments in the texts that would help us choose which philosophy is better justified.
To speak to your final suggestions, I do think that philosophy need not be seen as so defined by argumentation that this definition becomes a straitjacket. After all, the term "philosophy" come from the Greek philo and sophia and is usually translated the love of wisdom. So, in a sense, loving wisdom can be a philosophical activity, and perhaps a wise person is not always argumentative! As for philosophical work on literature and the arts in general, check out the online site for the American Society for Aesthetics and the British Society for Aesthetics.
Although I agree with most, if not all, of Professor Taliaferro's response to your fascinating question, I want to add a few remarks that may take the discussion in a slightly different direction.
You asked whether Shakespeare was a philosophical genius, and whether philosophers have "deduced a coherent Shakespearean belief system from his works." I think that the two questions should be distinguished. It's not at all clear to me that an author may be a philosophical genius only if a philosophical system can be deduced from his works. Indeed, Wittgenstein, for example, who to my mind at least was certainly a philosophical genius, resisted--at least in his 'later' writings--systematization altogether, so it would be somewhat misguided even to try to deduce a philosophical system from his writings. One might of course respond that Wittgenstein was systematically anti-systematic, and that that in itself constitutes a kind of systematicity. But that seems to me to be a Pickwickian sense of 'systematic'. I propose, therefore, that systematicity not be taken as a criterion of philosophical genius, or even of philosophy. I now turn to the question of whether Shakespeare was a philosophical genius.
One could similarly ask whether Dostoyevsky or Philip K. Dick, was a philosophical genius. Both writers, in certain of their works of fiction--to my knowledge, neither wrote works of philosophy--raise philosophical questions of various sorts, just as Shakespeare certainly does. But does treating an issue of philosophical interest make the treatment of that issue philosophical? I don't believe that it does; I believe that what's distinctive of philosophy is that it makes arguments, and it's not clear to me that works of fiction--or at least the works of fiction by the Dick or Dostoyevsky, or at least their works that I know--themselves make arguments. (Characters in works of fiction make arguments, to be sure, but I would be very wary of identifying the author of a work of fiction with any one of his or her characters; moreover, it's not clear to me that that the point of a work of fiction is to make an argument--although that is not, of course, to say that I know what the point(s) of a work of fiction are, and in fact I would think that that is a matter of interpretation that would need to be settled on a case-by-case basis.) Similarly, despite the recent vogue of treating films as 'doing philosophy', I'm quite suspicious of such an approach to film, although whether some film could be seen as 'doing philosophy'--even if it is granted that what's distinctive of philosophy is advancing arguments--is a question that can only be determined by considering the film in question. (Of course, it might be argued that what I have highlighted as the distinctive feature of philosophy is too restrictive, and perhaps a more catholic conception of philosophy would more readily admit of treating works of literature and films and other art forms, too, for that matter, as philosophical. But could dance, say, be treated as philosophy? Now there's an interesting question, that might reveal something about the nature of the kinds of art that we think could be philosophy...)
What, however, about authors such as Diderot, or Tolstoy, or Camus, or Borges, who wrote both works of fiction and philosophy? Might their works of fiction be philosophy? This, I think, is a subtler and somewhat different matter, but I'm inclined to think that even the fictional works of such authors, although they may be seen as illustrating or exploring certain ideas with which they engaged philosophically, are not themselves instances of philosophy. (War and Peace might be a tricky case for such a view. But I stand by it, at least for the nonce.) But there are of course other authors who wrote both works of fiction and works of philosophy, and here too, I think that in order to adjudicate the issue, one would need to consider each case.
I, too, like your example! Let me add three comments to Charles' response above.
First, we can distinguish between several different interpretative communities. One of these are 'average members of the public' -- consumers of cultural products who have no specialist training in the area. Another would be professionals, those whose career has been devoted to understanding a certain area of cultural production. A professor of literature, for example, or a film critic. A third group, generally rather small, comprises the makers (the scriptwriter and director of your fantasy story, say). Now, we might want to think that these three groups should agree, or should tend towards or strive towards agreement. But there are good reasons to think otherwise. A Hollywood scriptwriter in the 1950s would have had to bury the left-leaning political message of his film under a thoroughly populist and conventional surface. You might even say that in such a case the author’s intention was precisely not to be understood, or at least not by everyone in the same way. Likewise, take a novel like Ulysses. Many people can read it, and enjoy it or get something out of it – but only a very few well-trained people will be able to see the complex and dense web of literary and historical allusions that Joyce uses. Does that mean that the book, and its meaning, ‘belong’ only to professors of literature? By no means. It only suggests that we may be wrong to think that somehow interpretations ought to converge among different consumers.
My second comment is that interpretations of the meaning of something don’t come from nowhere. There is probably nothing to stop someone from thinking that Charles’ dog represents the Baltimore Aquarium. But that person, if asked ‘What makes you think that?’, would probably have to decline to answer. What we are asking for in that question is evidence, a set of references to the conventions of symbolism, or to the author’s biography, laid out in such a way as to make the interpretation compelling. In other words, interpretation of meanings is not a private and spontaneous event, but is rational and communicable. In your example, the problem is that both interpretations seem to be rational. Further debate would have to look at the particular film in more detail: for example, what exactly does this female character do and say? It may be impossible to decide the issue, but that does not mean that there are no generally useful criteria for what counts as evidence of an interpretation.
Third, the search for the ‘meaning’ of something is a relatively recent way of thinking about art or literature. Plato and Aristotle, talking about literature, hardly mention what we would normally call the ‘meaning’. They are concerned about what kind of thing it is, where it comes from (is literature based on knowledge?), or what effect it has on a reader or viewer. It is only within the past century or two that, somehow, we all decided that the main thing to be said about a cultural product was its meaning. Are we sure we are right?
Another panelist should take up this question, but I will start by commending you on appreciating the difficulty of defining 'poetry' given the breadth of sounds and marks that count as poems today. Long gone are the days when 'poetry' could be defined in terms of rhythm, but as we get to the point of having trouble defining boundaries over what is and what is not a poem, we do well to recall that the Greek term (poesis) from which we get in English 'poetry' meant 'to make.' So we may have come full circle. Originally, 'poesis' covered the making of anything; now we may come (sadly or happily) to the same point when almost anything can count as a poem. Even so, there are too alternatives to entertain: define poetry in terms of family resemblence to what is recognized as poetry today. This would mean that a decision whether X (whatever) is a poem is if it resembles the writing of T.S. Eliot, Pound, Edna St. Vincent M, Dylan Thomas (and here follows a long list of poets in the Norton Book of Poetry). This method of definition is sometimes called 'ostensive' and is respectable in different domains: colors have been defined in terms of examples (red, green....) and so have religions (e.g. Y is a religion if it resembles Judaism, Christianity, Islam, Hinduism, Buddhism....). Alternatively, one might try a formal definition. I will leave it to another panelist to do this, except for suggesting that a poem involves language that is about the aesthetic or sonorous character of the words as sounds. To give an example: what makes these lines from the Love Song of Alfred J Prufrock a poem?
"Let us go then, you and I, as the evening is spread out against the sky...."
I think it is not just the referential meeting (someone is asking you to join him or her for a walk at dusk) but this line and those that follow is in some way about the affective (emotively charged) way the language sounds.
Very interesting! Consider two options, among others: one is that great literary works might be (as you suggest) akin to instrumental music. Such music may have emotive features (joy, anger, expressions of longing...) that are difficult to put into words and that is why your friends seem a bit weak in terms of their ability to state these deep truths. But secondly there might be deep truths that are not merely about emotions, but one finds hard to articulate because of a lack of vocabulary. Imagine one finds Tolkien's Lord of the Rings very moving and revealing but one cannot quite say why. Imagine (what seems likely) that Tolkien's trilogy raises questions about the ultimate meaning of life and the possibility of transcendent purpose, but that the reader is completely secular and has no vocabulary or training by which to put these matters into words.