I actually started to write this over a year ago and now it's finally complete. It was originally intended to be posted on June 16 (thus the 16 reasons) but that never worked out. It's not meant to be exhaustive or even all that serious, but I think it gets the point across.
1. The simple fact that his writing is beautiful
All good writing strives towards poetry as poetry is the highest form of writing. Joyce started off as a poet and was good enough to receive attention from W.B. Yeats who encouraged Joyce to "turn his mind to unknown arts." This unknown art is a manner of prose in which every word and the flow of the words are considered with precise poetical precision. So Joyce's writing is an original, beautiful gleaming mass that yields gems like this one:
The heaventree of stars hung with humid nightblue fruit.
2. Joyce is to literature what Einstein is to science
In Ulysses Joyce toys with time and space all throughout the book. In the "Proteus" chapter, Stephen Dedalus ruminates and meditates on the nature of Time and Space using Schopenhauer's interesting words Nacheinander (German for "succeeding each other") and Nebeneinander ("beside each other"). The main character Leopold Bloom sells newspaper advertisement space for temporary periods of time. In Richard Ellman's complex exegesis, Ulysses on the Liffey, he argues convincingly that the 18 episodes can be broken into six triads within which the dominant categories of Space, Time, and Space-Time repeat over and over. Relativity (or more specifically what Einstein called "special relativity") also dominates the book, especially in the first six chapters as we follow the movements and thoughts of two different, separate characters at the exact same time of day. Relativity abounds in Bloom's cosmic reflections in the Ithaca episode. Also, Don Gifford's Ulysses Annotated explains how Joyce stretches out time by depicting the events of the day through a "rich mix of clock time, psychological time, and mnemonic time."
We are all aware, for example, that we can think and perceive far more in the course of a few minutes of multi-leveled consciousness than we could spell out in words in as many hours. Joyce variously explores this disparity. (Gifford, pg 3)
Finnegans Wake is also overloaded with the integration of modern relativistic physics into literature. I think of E = mc2 and the discovery of the condensed energy present within every atom when I consider the unbelievable amount of meaning condensed into each sentence, each word of that crazy book. Most words and phrases in the book contain not just double meanings but triple and even quadruple meanings. As Joyce scholar John Bishop explains in his amazing book, the Wake is also written in such a way that it allows and even encourages a style of interpretation called "Sortes Virgilianae" (Latin for "Virgilian fortune-telling") in which the reader opens the book at random and interprets whatever they come across as applicable to their own personal affairs (just like the divination system of reading the I-Ching) and so you can argue that there's nearly infinite meaning compacted into the words of the book.
(An entire post or series of posts could easily be written about Joyce and modern science and there's already an excellent resource about it on the web.)
Joyce was a master of style. It is evident right from the beginning of his career in the short story collection Dubliners which is written in a style meant to subliminally sensitize the reader to the modern day urban paralysis he was depicting. The vocabulary is a limited one since most of the characters endure a meager quality of life and words like "vain", "useless", "tiresome", and "hopeless" recur throughout the different stories. Joyce incrementally expanded on this very modern and original method of writing as he went from the gestation/growth style in A Portrait of the Artist as a Young Man, to the "dance of the hours" in Ulysses (where each hour of the day creates its own style), all the way to a completely new and strange night speech of Finnegans Wake. I think the most exemplary and entertaining example of this method of letting the depicted scene dictate the style is the amazingly musical Sirens episode of Ulysses.
4. The Intersection of Myth and Time
One of the things that's most special about Joyce is how he brings together the real and the mythical. His books (aside from Finnegans Wake) are highly detailed descriptions of the events of everyday life even down to minutely recording the flow of a character's thoughts. But at the same time there's always a sort of mythic, cosmic backdrop to everything brought about by the heavy use of symbolism and mythic correspondences and what this achieves (for me at least) is an experience such that the reader clearly sees their own everyday life as a mythic journey. Richard Aldington once wrote of Ulysses that it "made realism mystic."
5. Multiplicity of Meaning
In The Consciousness of Joyce, Richard Ellmann explains that "In Portrait of the Artist, Stephen fears he will always be a shy guest at the feast of the world's culture; in Ulysses Joyce plays host to that culture." The number of different meanings, allusions, and culture that Joyce manages to squeeze into both the macro- and microcosm of Ulysses is simply astounding. Even just in the first chapter, which is probably the easiest section of the book, there are so many things going on amid multiple levels: the naturalistic element is obvious, but Stephen also represents Telemachus and Hamlet at the same time while elements of Dante and Nietzsche are crammed in on almost every page and the entire chapter is a satirical enactment of a mass. This occurs in every chapter of the book, the density of meaning so thick that there are large reference books listing the various allusions and references (and those still don't exhaust all the meanings!).
This method is taken to an unbelievable extreme in Finnegans Wake where one sentence, or even one word, can have four, five, six different meanings. John Bishop gave an example of this in an interesting (though rapidly delivered) lecture. In the introduction to The Cambridge Companion to Joyce, there's a great breakdown of one single paragraph from the Wake in which about 6 or 7 different viable interpretations are unfolded through ten pages and the idea comes up that Joyce could not possibly have purposely included all the different meanings. The response to this is that we can never know for certain that he didn't intentionally include those meanings but also that even if we did know for certain "it need not make any difference, since Joyce has deliberately created a text with the power to generate more meanings than he had in mind." (see #2 above)
6. Architectural Structure
Right from the start, Joyce had an uncanny feel for organizing the macrocosmic structure in his works. His first book, the collection of short stories entitled Dubliners, isn't like most anthologies of stories. The volume was conceived as a book from the beginning, linking multiple stories by theme, technique, subject matter, etc. and the stories are presented through four aspects: childhood, adolescence, maturity, and public life.
I've thoroughly examined the structure of A Portrait of the Artist as a Young Man in a previous post, and the organized structure in both Ulysses and Finnegans Wake is staggering for such enormous texts. I've read a quote from Joyce somewhere describing Ulysses as his Notre Dame and it's not a bad comparison. I'm less familiar with the structural anatomy of the Wake, but it does use Giambattista Vico's four cycles of history as a trellis and, as artist Stephen Crowe recently argued, its structure is even more thoroughly crafted than Ulysses.
7. The Enormous Vocabulary
Ulysses alone contains more vocabulary words (30,030) than the entire Shakespearean canon of thirty-eight plays and 150 sonnets (29,168).
8. The Encyclopedia of Knowledge
Reading Joyce can be very much like reading an encyclopedia. This is not an accident; he sought to make Ulysses a sort of encyclopedia with its tons and tons of references and allusions. There are at least two very large texts that seek to identify and index all the information in Ulysses but (just as with Finnegans Wake) it is often said that we'll never be able to identify all the facts, figures, stories, songs, cartoons, jokes and everything else that's jammed into it. I found my first reading of Ulysses to be extremely rich in learning, all you have to do is wikipedia search some of the stuff mentioned and your historical (or scientific, etc) perspective will be vastly expanded.
10. Finnegans Wake
(these two books alone are enough to make anyone the G.O.A.T.)
11. Affirmation of Life (Yes!)
This is perhaps the ultimate lesson to take from Joyce: the affirmation or saying "Yes" to life. At the end of an immense book that presents in gruesome detail the elements of everyday life, the final chapter is a female explosion of "Yes", the word is repeated over and over throughout the meandering monologue of Molly Bloom. This "Yes" is what keeps the wheel of life spinning. Nietzsche in The Will to Power elaborates:
"If we affirm one moment, we thus affirm not only ourselves but all existence... if our soul has trembled with happiness and sounded like a harp string just once, all eternity was needed to produce this one event---and in this single moment of affirmation all eternity was called good, redeemed, justified, and affirmed."
12. His works are humorous
Columbia professor William York Tindall has called Finnegans Wake the funniest and dirtiest book ever written. Ulysses contains tons of jokes, hidden or otherwise, and it guarantees a bunch of laugh-out-loud moments. These two books are big, daunting pieces of so-called "highbrow" literature but they're also comedies.
13. His satire and humor often contains his greatest profundities
"One is puzzled to guess where he is teasing, where serious, until at last it begins to dawn that the mode of disorderly burlesque is precisely James Joyce's deepest seriousness," wrote Joseph Campbell. Joyce considered himself a great jokester of the universe. The entirety of Finnegans Wake embodies this, it's all really a big joke, a great comedy filled with puns.
Ulysses has plenty of mockery and satire that Joyce scholars (in my opinion) often misinterpret, for instance his use of Billy Sunday tirades. These little sermons are quite hilarious but they also contain essential messages as in this selection: "Are you a god or a doggone clod?... it's up to you to sense that cosmic force. Have we cold feet about the cosmos? No. Be on the side of the angels. Be a prism. You have that something within, the higher self. You can rub shoulders with a Jesus, a Gautama, an Ingersoll. Are you all in this vibration? I say you are..." (Ulysses pg 507-508)
14. Hidden Messages
It's fun to discover such things as the fact that the first letter of each of the three parts in Ulysses (S, M, and P) corresponds to the focal character in each of those parts (Stephen, Molly, and "Poldy" which is what Molly calls Leopold Bloom), or that the first words of the book ("Stately, plump") are a good physical description of the book itself. Robert Anton Wilson points out that there are 22 words in the first sentence of the book (and the number 22 recurs throughout the book, plus it was published on his birthday 2/2/1922). Finnegans Wake has so much of this stuff that after 50 years of exhaustive study, they probably haven't even scratched the surface. There are actually multiple books examining Joyce's use of the Kabbalah throughout the Wake.
Okay, maybe this kind of thing doesn't make someone a great writer... so I'll add one more:
14a. He "explodotonated" English and created his own style
"James Joyce was probably one of the greatest poets who ever lived on our globe, so abundant in poets, but he did not trouble himself to create within the limits of this or that literary genre. The principle of his writing was the subordination of all existing literary kinds: prose, drama, lyrics, and epics, to one primary aim, which was the most perfect presentation of what he wanted to say." - Maciej Stomczynski
15. Portrayal of Man (Bloom), Woman (Molly), and even himself (Stephen/Shem)
The depiction of Leopold Bloom has often been called the most complete image of a man ever presented in literature. We follow him through an entire day including his bodily functions (pooping/urination/masturbation), eating, interactions in the streets, stores, and pubs, and the whole vast range of his mental travels. The Molly Bloom monologue in the final chapter has been praised by feminists because of its unbelievably accurate look into the flowing thoughts of a woman's mind. And, personally, one of my favorite things about Ulysses and the Wake are the characters that are based on Joyce himself (Stephen Dedalus and Shem the Penman, respectively).
16. He did all of this while living a harsh, often impoverished life
He was born into a middle class family, but his parents kept popping out children until the family was broke. His father drank away any money they had and they eventually had to move from one domicile to the next because they couldn't make the rent. Growing up he lived in at least a dozen different places. His mother died relatively early in his life (when he was around 20) and the household fell into jagged shambles as his father descended into alcoholism.
On top of all that, his beloved daughter Lucia suffered a mental collapse and had to be put in a mental institution where she stayed for the rest of her life. His daughter-in-law suffered the same fate. While all of this was happening he also had terrible eye problems, requiring him to undergo at least 10 operations on his eyes without anesthetics. Somehow, someway (and this is perhaps the thing I find most incredible about Joyce), he battled through all of this to finish his greatest and most immensely enigmatic book, Finnegans Wake. His friend Nino Frank would later write:
"It was as if around the old hero---doesn't Finnegans Wake seem to be man's answer to the sphinx?---some obscure vengeance of the gods was falling."