Abstract: Under the aspect of constructivism evolution generates the varying boundary conditions to which evolution itself then is subject. This applies for organic as well as for cognitive evolution. The currently valid conditions for cognitive evolution we describe as laws of nature brought about by an independent reality. Within the constructivist evolutionary epistemology CEE), however. the regularities we perceive and which we condense to the laws of nature are seen as the invariants of phylogenetically formed cognitive operators. The extension of the inborn operators by means of experimental operators (i.e. by measurement facilities) will lead to the consolidation of the classical world picture if both _are _commutable. Otherwise there will be invariants which cannot be described in classical terms and, which therefore, will require non-classical theories. Likewise mathematical and logical structures can be seen as invariants of cognitive operators. It is shown that the propositions of Gödel would deal with what can be considered as the analogy of non-classical phenomena in physics. To renounce reality as an element of physical metatheory requires some rearrangements of those notions which explicitly refer to reality such as acting and perceiving, learning and adapting, and, partially, language. It turns out that the distinction between acting and perceiving is not unambiguous as it is in the “theory of reality.” Similarly we can see learning as a process of adaptation to the given environment as well as an independent development into something for which an appropriate environment or application still has to be found. It will be shown that both “adaptive” and “initiative” evolution occur in organic as well as in cultural evolution. Within CEE, language is seen as a “generative” theory rather than as a tool to portray independently existing facts. Its competence is based on the fact that it is generated by mechanisms closely related to those generating our physical perceptions. A similar genetically grounded relationship between mental operators enables mathematics to compress empirical data into a generating theory, and then, based on this theory, to extrapolate them (problem of induction). The linguistic equivalent of algorithmic data compression and the subsequent extrapolation is the recognition of a text’s meaning, and the subsequent drawing of conclusions from it, or semantic extrapolation as proposed to say. Accordingly, communication can be defined. Some parallels are discussed between verbal, cultural and genetic communication.