Hilbert arithmetic as a Pythagorean arithmetic: arithmetic as transcendental

The paper considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis world in Pythagorean manner. unifies foundations mathematics (Peano and set theory), physics (quantum mechanics information), philosophical transcendentalism (Husserl’s phenomenology) into formal theory mathematical structure literally following Husserl’s tracе “philosophy rigorous science”. In pathway to that objective, identifies by itself information related finite sets series quantum referring infinite one both appearing three “hypostases”: correspondingly, mathematical, physical ontological, each which is able generate relevant science area cognition. Scientific falsifiable counterpart transcendentalism. underlying concept totality can be interpreted accordingly also mathematically, consistent completeness, physically, universe defined not empirically or experimentally, but ultimate wholeness containing its externality itself.