The Theory of the Three Angles: a co-emergent metaphysics of Consciousness, Love, and Form, and its categorical formalization

Summary

The Integral System presents a metaphysical framework with three co-emergent dimensions: Consciousness, Love, and Form, derived from the Mother Paradox. Unlike materialism and idealism, which reduce these dimensions to one another, this framework treats them as co-equal. The study provides a formalization of the framework, revealing that the co-emergence of these dimensions is a consequence rather than a postulate. It also discusses its implications for contemporary mathematical consciousness science.

Study at a glance

Abstract

This paper presents the Integral System (Sistema Integral), a metaphysical frameworkpositing three co-emergent fundamental dimensions —Consciousness, Love (relationality),and Form— derived from a single minimal phenomenon, the Mother Paradox (the act ofdistinction that all experience already presupposes).1 Unlike the dominant monopolarframeworks —materialism, which reduces all three to Form, and idealism, which reducesthem to Consciousness— the System holds the three angles to be co-equal and not derivablefrom one another. The paper offers a self-contained presentation of the framework'sfoundations and of its two-layered formalization. The first layer, combinatorial andelementary, derives as theorems the structure of the catalogue: the six angle pathologies as23−2, the four topological modes as a pushout, the fifteen structural pathologies, the fifteensectorial Zero Distances as C(6,2), and the orthogonal movement Eros/Agape as an adjunctioncolim ⊣ Δ with its two canonical natural transformations. The second, more recent layermodels each angle within a single cartesian closed category: Form as an invariant (the limit ofa symmetry, on an ontological reading of Noether's theorem), Love as a relational profile (theYoneda lemma), and Consciousness as the fixed point of a self-representation (Lawvere'stheorem). From this second layer follows the central result: each angle, taken as the solereality, is undermined by the structure of its own central concept, so that co-emergenceceases to be a postulate and becomes a consequence —conditioned on a few explicitlyfalsifiable interpretive bridges. The framework incorporates an in-principle limit (the ceilingof formalization): the indexical first person is located as the residue that no externalobjectification captures, in correspondence with the converse of Lawvere's theorem. Thepaper discusses the relation to contemporary mathematical consciousness science —inparticular Tsuchiya and Saigo's Yoneda-for-qualia programme and the categoricalformalization of Integrated Information Theory— and argues that the System's distinctivecontribution is the combination of three co-equal angles, a derived co-emergence, and aceiling treated as confirmation rather than failure. A scrupulous demarcation betweentheorem, interpretive bridge, and conjecture is maintained throughout.

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