The Logic of Projection: A Formal Framework for Epistemic Convergence

This paper develops a formal meta-epistemological framework in which knowledge systems are treated as projective operators mapping a non-axiomatic reality into finite cognitive and representational spaces. We argue that the apparent fragmentation of human knowledge—across science, religion, ethics, and aesthetics—arises from a category error: the conflation of projective representations with underlying reality itself. By establishing a formal equivalence between geometric, dynamical, and probabilistic formulations in physics, we demonstrate that no representational language enjoys ontological privilege. Within this framework, Gödelian incompleteness is shown to constrain only static formal systems; when epistemic frameworks are allowed to evolve dynamically, asymptotic convergence remains possible. Truth is therefore redefined not as direct correspondence, but as a stable attractor in conceptual space toward which distinct projections converge under iterative refinement. Finally, we demonstrate a structural morphism between the evolution of human knowledge and optimization dynamics in Artificial Intelligence latent spaces, capturing directional correspondence without assuming structural identity. The result is a rigorous logical foundation for projective pluralism: a unified account of epistemic diversity that avoids both relativism and reductionism, and clarifies the conditions under which heterogeneous knowledge systems can exhibit principled convergence.