The fracture in the emerging discipline of biosemiotics when the code biologist Marcello Barbieri claimed that Peircian biosemiotics is not genuine science raises anew the question: What is science? When it comes to radically new approaches in science, there is no simple answer to this question, because if successful, these new approaches change what is understood to be science. This is what Galileo, Darwin and Einstein did to science, and with quantum theory, opposing interpretations are not merely about what theory is right, but what is real science. Peirce's work, as he acknowledged, is really a continuation of efforts of Schelling to challenge the heritage of Newtonian science for the very good reason that the deep assumptions of Newtonian science had made sentient life, human consciousness and free will unintelligible, the condition for there being science. Pointing out the need for such a revolution in science has not succeeded as a defence of Peircian biosemiotics, however. In this paper, I will defend the scientific credentials of Peircian biosemiotics by relating it to the theoretical biology of the bio-mathematician, Robert Rosen. Rosen's relational biology, focusing on anticipatory systems and giving a place to final causes, should also be seen as a rigorous development of the Schellingian project to conceive nature in such a way that the emergence of sentient life, mind and science are intelligible. Rosen has made a very strong case for the characterization of his ideas as a real advance not only in science, but in how science should be understood, and I will argue that it is possible to provide a strong defence of Peircian biosemiotics as science through Rosen's defence of relational biology. In the process, I will show how biosemiotics can and should become a crucial component of anticipatory systems theory.