The Axiomatic Nature of Is-ness

Social theoretical discourse remains inadequate, ensnared in intractable dichotomies due to a persistent failure to apprehend the foundational ontological logic and decode the axiomatic kernel of socio-cultural constitution. Existing paradigms fail to account for the phenomenological givenness—the felt necessity—of lived cultural worlds. This manuscript reveals the Axiomatic Nature of Is-ness (ANI), the definitive framework elucidating this mechanism. ANI demonstrates that the Is-ness (I) of any socio-cultural field—its constitutive matrix of episteme, doxa, habitus, and signification—achieves ontological stability via its functionally axiomatic status, perpetually validated through embodied Performative Enactment (↦) by subjects situated therein. This process structurally necessitates the Is-In-Out triad: the co-constitution of In-ness (In) (alignment) and Out-ness (Out) (difference) as the dialectical condition for the maintenance of I. This triad provides the invariant dynamic topology governing all dimensions of social space. By foregrounding the axiomatic self-validation inherent in being-in-culture, ANI transcends prior theoretical limitations, resolving foundational dichotomies and providing a rigorous basis for analyzing, modeling, and predicting the trajectories of cultural persistence, identity formation, power dynamics, systemic transformation (I → I'), and the emergent, yet axiomatically governed, nature of social existence. Its framework enables quantitative exploration of socio-axiomatic stability and potential phase transitions.