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Scientific knowledge develops in an increasingly fragmentary way. A multitude of scientific disciplines branch out. Curiosity for this development leads into quests for a unifying understanding. To a certain extent, foundational studies provide such unification. There is a tendency, however, also of a fragmentary growth of foundational studies, like in a multitude of disciplinary foundations. We suggest to look at the foundational problem, not primarily as a search for foundations for one discipline in another, as in some reductionist approach, but as a steady revelation of presuppositions for individual scientific theories -- which are bound to meet, sooner or later, in a common language. A decisive point here is our holistic conception of language, as a whole of description-interpretation processes which are entangled (complementary) in the language itself. For every language there is a linguistic complementarity. We suggest this unique form of entanglement as a unifying presupposition, ultimately foundational for all communicable knowledge. Involved is a linguistic realism, in terms of which we critically examine "language-world" problems, as exposed by Wittgenstein, and Russell, about a foundational interdependence of language and reality (world). Throughout, we attach to the development of foundational studies of mathematics, logics, and the natural sciences. In particular, we study the interpretation problem for axioms of infinity in some detail. We emphasize that the holistic concept of language contradicts Carnap’s semiotic fragmentation thesis (thus, no clean cut between syntax, semantics, pragmatics). This is the final, accepted and revised manuscript of this article. Use alternative location to go to the published version. Requires subscription.

Ever since its first conception in 1907 by Bergson, "complementarity" has come to represent extremely wholistic situations, for which fragmentability into parts turn out unsuccessful. In 1927, Bohr used the term complementarity within quantum mechanics, with profound consequences, for a principally unsuccessful fragmentability into independent observability and definability concepts. The paper objectifies language, in a very general understanding, as a complementaristic phenomenon. Language is thereby conceived as a whole of description and interpretation processes, such that fragmentation in these parts is in principle impossible within the language itself, but possible in a metalanguage if one such exists. The linguistic complementarity is an ultimate form to which particular complementarity conceptions can be reduced. In a basic understanding, the linguistic complementarity refers to the impossibility of describing the constituents of a language, its description and interpretation processes, in the language itself. As such, the complementarity obtains for every language, from genetic language over programming and formal languages, to external communication languages. The argument is based on a factual function of every language, namely to admit communication or control, whereby descriptions are bound to be finitely representable and static, whereas the corresponding interpretations may be infinite of any order as well as dynamic. Further understandings of the linguistic complementarity are developed by utilizing specific knowledge of languages. With reference to languages for formal set theories, we develop the complementarity as a tension between describability and interpretability. With reference to a processual function concept, with origins in recursive function theory and lambda calculus, we develop complementarity in terms of the unavoidable partiality of the self-references that a language may permit. The reducibility, to the linguistic complementarity, of the specific complementarity conceptions by Bergson and Bohr is investigated with positive results. For the reducibility of Bohr complementarity, as a tension between definability and observability, to the linguistic complementarity, as a tension between describability and interpretability within a language, we develop observability as interpretability in an observation language. Furthermore, we suggest that the self–reference problem for quantum mechanical measurement be naturally resolved in terms of the linguistic complementarity, thereby pointing at a possibility of developing linguistic models for quantum mechanics, for which mechanistic models do not suffice. It is suggested that the real value in finding entities complementary may not be fully revealed until a reduction is carried out to the complementarity for an embracing language. Not until then, we may know if the complementarity is transcendable or not, and understand the possibilities which correspond to a weighing of describability against interpretability.