Tiago Aguioncio Vieira

This paper argues that Artificial General Intelligence is not primarily a computational problem but a mathematical, physical, and — most fundamentally — a philosophical one. We prove that any genuinely intelligent system requires a compact global attractor of finite fractal dimension, a structure that Transformers, lacking sectorial dissipation, are structurally incapable of possessing. Catastrophic forgetting is not an implementation defect: it is a theorem. We identify four necessary and sufficient structural conditions (H1–H4) for AGI and connect each, rigorously, to foundational disputes in the history of philosophy: from Aristotle’s teleology to Kant’s transcendental unity, from Searle’s Chinese Room to Chalmers’ hard problem, from Leibniz’s monadology to Wittgenstein’s limits of language. The central claim is that ‘understanding’, ‘purpose’, and ‘consciousness’ admit precise mathematical definitions, and that the current crisis of AI reveals, above all, the philosophical impoverishment of its dominant paradigm.

This paper develops a unified dynamical framework integrating affective and semantic processes in cognition. The Internal State Dynamics Model (ISDM) formalizes emotional regulation as a continuous internal state process governed by energetic constraints and Lyapunov stability, while the Teleological Semantics Model (TSM) formalizes semantic dynamics as a structured flow within a semantic field organized by local transformations and a global teleological operator. By expressing both models as differential dynamical systems, we embed affective and semantic dynamics into a common product space and introduce coupling operators that allow bidirectional interaction without reduction. Emotional states modulate semantic transitions, while semantic structure regulates affective stability, preserving the internal logic of each subsystem. A central result is the demonstration that this coupling does not destabilize the system. Under mild boundedness conditions, a joint Lyapunov functional can be constructed whose monotonic decay establishes global exponential stability of the coupled teleo– affective dynamics. Stability thus emerges not as convergence to a static equilibrium, but as a dynamic pattern of coherence arising from the interplay between energetic regulation and teleological orientation. The framework provides a mathematically minimal yet conceptually robust account of cognitive coherence, offering a non-reductive foundation for the integrated analysis of meaning and affect in both biological and artificial cognitive systems.

Classical formulations of cognitive-affective dynamics, including Lyapunov-based stability frameworks, guarantee convergence to equilibrium: a property appropriate for many engineering applications but insufficient for systems that must learn, evolve, and maintain identity through change. This paper develops quantum foundations for a cognitive-affective architecture comprising three regimes: dynamic evolution (MDEI), stabilization (MCEE), and symbolic measurement (MESN). This paper uniquely introduces the non-Hermitian Hamiltonian Ĥ ef f =Ĥ − iΓ, where the dissipative termΓ models the system's openness to its environment. The central contribution is the derivation of a self-referential floor : for any architecture containing a self-observing module (MESN), the effective dissipation rate is bounded below by an irreducible residue, Γ ef f ≥ ε ∞ > 0. This floor emerges from the back-action inherent to self-measurement-the system cannot observe itself without disturbing itself. Consequently, all bound states have finite lifetime; the system cannot collapse into permanent stasis. Stability, for self-referential systems, is necessarily a pattern of bounded oscillation rather than convergence to rest. This result provides the formal foundation for autopoietic AI and motivates a dual-layer architecture: classical Lyapunov dynamics at the surface for computational efficiency, non-Hermitian quantum dynamics at the core for autopoietic capacity. The operationalization of layer-switching mechanisms and empirical validation constitute the ongoing research agenda.