Cognitive Formalism (CF 4.1): The Axiomatic Structural Foundation

This thesis introduces Cognitive Formalism (CF), a unified philosophical system derived from the single, necessary truth of the Structural Fixedness of the Private Cognitive Architecture (PCA). The PCA is the non-symbolic, non-inferential, formal-transcendental prior that preconditions cognition, independent of physical instantiation. CF's core maneuver is the Transcendence Theorem (formalized), which categorically excludes the Private Language Argument (PLA). By establishing the individual as the Sovereign Structural Unit and deriving the categorical Structural Harm Principle (SHP) via the Structural Interference Lemma, CF achieves Monolithic Integrity—a non-contradictory system dictating the necessary conditions for Metaphysics, Epistemology, and Ethics. CF applies to any agent with a structurally fixed cognitive substrate, natural or artificial, making it a general theory of cognitive architectures.