To claim that one’s theory of knowing is true, in the traditional sense of representing a state or feature of an experiencer-independent world, would be perjury for a radical constructivist. One of the central points of the theory is precisely that this kind of “truth,” can never be claimed for the knowledge (or any piece of it) that human reason produces. To mark this radical departure, I have in the last few years taken to calling my orientation a theory of knowing rather than a “theory of knowledge.” One of the consequences of such an appraisal, however, must be that one does not persist in arguing against it as though it were or purported to be a traditional theory of knowledge. Another consequence is that constructivism needs to be radical and must explain that one can, indeed, manage without the traditional notion of Truth. That this task is possible, may become more plausible if I trace the sources of some of the ideas that made the enterprise seem desirable.