Abstract.At the heart of the most radical proposals in Stuart Kauffman's Investigations is his attempt to show that we find in evolutionary biology some configuration spaces—the sets of possible developments for any given system—that (unlike those in traditional physics of Newtonian, relativistic, and quantum stripes) cannot be completely described in advance. We bring Charles Peirce's work on the philosophy of continuity to bear on the problem and discover, first, that Kauffman's arguments do not succeed; second, that Peirce's metaphysics provide new (...) and sounder arguments for the same propositions; third, that Peirce's rigorous but nonstandard treatment of mathematical continuity shows great promise for modeling the unpredictability and growth we find in evolutionary biology; fourth, that it also strengthens a development only hinted at by biologists thus far—the inevitable involvement of the observer's mind in constituting the objects of science. We close with a logical argument for the surprising relevance of metaphysical hypotheses in the natural sciences and with suggestions for future work that will connect these questions to what Kauffman terms the “narrative stance” in biology. (shrink)