One of the most salient arguments in favor of a semiotic approach, put forward on various occasions among others by Luis Radford, claims that semiotics is most appropriate to treat the interaction between socio-cultural and objective aspects of knowledge problems. But if we want to take such claims seriously, we have to undertake revisions of our basic conceptions about reality, existence, cognition, and cultural development. The semiotic evolutionary realism of Charles S. Peirce provides, or so it appears, an appropriate basis to such intentions. Man is a sign, Peirce had famously said, and "thought is more without us than within. It is we that are in it, rather than it in any of us" (Peirce CP 8.256). And as there is no thought without a sign, we have to accept thoughts, concepts, theories, or works of art as realities "sui generis." Concepts or theories have to be recognized as real before we can ask for their meaning or relevance. This was the problem that concerned critics and protagonists of the "New Math Reform" of the 1960s and 1970s of the twentieth century, like Thom or Bruner.