Axiomatized Theory of Interaction

This paper presents an axiomatized theory of meaning grounded in a single primitive: interaction between systems. A new ontological framework (§0.5) distinguishes ontic existence (the syntactic presupposition of the formal language), relational existence (confirmed through interaction, termed manifestation), and two classes of entities lacking relational existence: constructible class objects (whose introduction produces no contradiction; eliminable by the Razor Principle for parsimony) and inconstructible class objects (whose introduction does; excluded by logical necessity). The theory proceeds in three layers. Layers I–II establish a relational ontology in which manifestation is inherently relational, time direction emerges from the monotonicity of cumulative interaction, and meaning generation is necessarily communal. Layer III introduces purposeful rational systems and derives, as a theorem, that the meta-purpose of any rational system is to maximize its total meaning quantity. Structural results include the minimum existence unit (a pair), the impossibility of self-meaning, the emergence of competition from exclusive interaction in three-system chains, and network-position dependence of meaning-growth rate. The framework extends to composite systems, proving non-conflict of subsystem and composite purposes and formally characterizing rationality failures and system resilience.