Does he say what is "up to the job"? Does he offer a methothodology that produces better theories to explain the fossil record, consistent with the physical evidence?
Rosen suggests that mathematics can give us insights into the structure of reality. IMHO, he like Einstein was a mathematical physicist of the Platonist type. His main mathematical tools were number theory, set theory, and category theory. His aim was to explore and understand complex living systems in nature by reasoning according to the logical dicta of these mathematical structures.
At least that is the basic understanding I have of his work, though I haven't read all his books yet.
Does he offer a methothodology that produces better theories to explain the fossil record, consistent with the physical evidence?
Jeepers, tacticalogic, but I don't think Rosen gave a tinker's dam about the fossil record. That type of evidence is simply irrelevant to understanding what makes biological organisms tick.