Can love, thinking as two, be enough to bond poetry which thinks as "elsewhere" and philosophy which thinks in distinctions?
Despite the dramatic metaphor, in the end there is not a mathematic answer to such a question. Each answers their own way. Love the union of singulars.
Now then, is this poetry? If Badiou's conditions are all redoubled here, poetry on philosophy, philosophy on poetry, etc. then is is too much of a Godel trick to ask? (the Indians wrote their calculus in verse, you know.)
Either transcendental way, and I don't really mind as long as it's transcendental, what I want to say is I think the relationship between philosophy and poetry is like what happens at the real projective plane: various degrees of infinite, like a mobius strip.