(1) How have our ideas about the spiritual changed with the dissolution of the Modernist dream, in which Kandinsky's vision was so deeply embedded?
What dissolution?! The Modernist dream has deepened and magnified.
(2) How has the notion of transcendence changed? Is transcendence still viable in a largely secular, postmodern culture?
Yes. We know much more about the world's cultures. For instance: the phenomenal growth of American Buddhism; our understanding and study of Indian Gurus; and the emergence of current Indian Art.
(3) What might account for the deep suspicion -- or indeed denial -- of the spiritual shared by many artists and intellectuals in our culture?
Postmodernism, cynicism, parody, materialism, suicide. These nihilistic tendencies choose academic study and ritual in an effort subvert our collective spiritual connectivity. Spirituality is perception and clear perception delivers the truth. Krishnamurti delivers the truth. My primary school model was "seek after truth."
(4) How have attitudes toward nature, the material world, and the body changed since Kandinsky?
As art history moves forward artists have branched off into ever more specialized investigations into all things. New and old ideas are explored and enriched. Beauty is found and lost.
(5) In what ways has the rise of digital technology impacted our ideas about the spiritual? Does it present a new vision of transcendence or salvation?
The rise of technology has furthered the methods by which we can explore the spiritual. New dimensions are opened up and new ideas for us to play with. The vision remains the same: truth. Everything else changes around it.
(6) Are the Enlightenment principles championed by Modernity (i.e., rationalism, positivism, materialism, etc.) being superseded by a new, more spiritually-inclined worldview—or is the spiritual being rendered obsolete by a wholly new orientation?
"The spiritual" as a concept is incredibly broad and open. It cannot be rendered obsolete as it is in all things in some language or form in every culture on the Earth.
(7) Does science have a role to play in exploring new approaches to or understandings of the spiritual?
Yes, science has a role to play as does alchemy, in understanding aspects of the transcendent.