Knowledge as Projective Operator: Toward Unified Theory of Human Understanding

This repository contains the author manuscript of the paper: “Knowledge as Projective Operator: Toward a Unified Theory of Human Understanding” The work develops a formal epistemological framework in which all forms of human knowledge — scientific, religious, ethical, aesthetic, etc. — are modeled as projective operators acting on a nonaxiomatic reality. Knowledge is treated as a constrained, non-invertible projection into representational spaces, rather than as a direct description of reality’s intrinsic nature. The central thesis is that long-standing conflicts between epistemic domains arise from a category error: mistaking projections for reality itself. By formalizing knowledge as a family of complementary projective operators, the framework dissolves traditional dichotomies such as realism vs. antirealism, facts vs. values, science vs. religion, and objectivity vs. subjectivity—without collapsing epistemic distinctions or lapsing into relativism. Key contributions include:A mathematical formalization of perspectival epistemology using projective structures and asymptotic convergence.A definition of Truth as a limit and attractor, understood as complete adequacy across all epistemic projections rather than correspondence to unknowable noumena.A rigorous treatment of Gödelian incompleteness as a constraint on static systems only, showing how dynamic epistemic refinement permits convergence.An explicit analysis of representational equivalence across scientific formalisms (geometric, dynamical, quantum).Empirical-historical validation through quantitative analysis of artifact accumulation in Ptolemaic astronomy.A statistical study of long-term religious framework survival, demonstrating objective existential, moral, and social constraints on religious knowledge.A structural morphism between human knowledge evolution and learning in high-dimensional latent spaces, connecting epistemology with modern AI and machine learning theory.