Hartshorne's attack on anthropocentrism is found, most interestingly perhaps, in his "rationalism" and logic. More and more as I read Hartshorne I see him as a speculative philosopher of the future. As I work on my book review of his Creative Experiencing I continue to find this to be so.
Creative Experiencing will be available through SUNY Press in paperback July 2012 (hardcover is available now). The article below is worth taking a look at.
Article: Piotri Gutawski, "Hartshorne's Rationalism" Process Studies, pp.1-9, Vol. 19, Number 1, Spring, 1990.