The epistemology of "relativism" that is featured by the theory of radical constructivism is addressed. In particular, I examine several objections, all based on this epistemic position of relativism, that are often raised by critics of the theory: the charge of "reality denial" (which, it is often claimed, must lead ultimately to the epistemically problematic position of "solipsism"), the assertion of "self-referential contradiction" (a theory that rejects the notion of truth cannot itself claim to be true), and the accusation that the theory must lead to a position of "ethical indifference." It is demonstrated that these objections do not hold: they arise, to a large extent, from the failure to distinguish properly between different knowledge domains--specifically, between the notions of cognitive and non-cognitive knowledge. Some concrete examples, specifically pertaining to the conflict between natural science and creationism, are addressed; and their relevance for science education is discussed.