The idea of a "soul of the world" was dreamed up by Plato in the Timaeus and repeated by countless later thinkers, including many Theosophists in turn-of-the-century Dublin and London.
The anima mundi, as it came to be known, is an essentially religious conception, but Plato offers it less as a doctrinal claim than as a myth—a kind of encouragement to study the metaphysical bases of our world. Joyce may have encountered the idea in more doctrinal forms, however. Gifford suggests that he acquired it from Giordano Bruno, the Italian philosopher and cosmographer whom the Catholic Church burned to death in the Campo dei Fiori in 1600. His claim seems plausible since, as he notes, the young Joyce named him the "father of what is called modern philosophy," and since Joyce later filled A Portrait of the Artist, Ulysses, and Finnegans Wake with admiring references to the Nolan. Bruno uses Aristotelian logical terminology to advance an essentially Neoplatonic metaphysics. He describes the ways in which every part of the material universe is spiritually interconnected with every other part.
A book by Theoharis Constantine Theoharis, Joyce's Ulysses: An Anatomy of the Soul (1988), explores this very systematic Brunonian understanding of the world soul as one of the possible philosophical inspirations for the organization of Ulysses.