Abstract

Quantum complementarity is interpreted in terms of duality and opposition. Any two conjugates are considered both as dual and opposite. Thus quantum mechanics introduces a mathematical model of them in an exact and experimental science. It is based on the complex Hilbert space, which coincides with the dual one. The two dual Hilbert spaces model both duality and opposition to resolve unifying the quantum and smooth motions. The model involves necessarily infinity even in any finitely dimensional subspace of the complex Hilbert space being due to the complex basis. Furthermore, infinity is what unifies duality and opposition, universality and openness, completeness and incompleteness in it. The deduced core of quantum complementarity in terms of infinity, duality and opposition allows of resolving a series of various problems in different branches of philosophy: the common structure of incompleteness in Gödel’s (1931) theorems and Enstein, Podolsky, and Rosen’s argument (1935); infinity as both complete and incomplete; grounding and self-grounding, metaphor and representation between language and reality, choice and information, the totality and an observer, the basic idea of philosophical phenomenology. The main conclusion is: Quantum complementarity unifies duality and opposition in a consistent way underlying the physical world.