The Constructor-Theoretic Foundation of Mathematical Reality

Constructor theory expresses physical laws in terms of which transformations are possible and which are impossible, rather than as trajectories from initial conditions. I argue that this position finds its deepest justification in the nature of mathematical structure itself. The pattern-randomness dichotomy (that all existence is either patterned or not-patterned (random), both of which are mathematical) is itself a constructor-theoretic principle: it specifies which substrates for physical law are possible (mathematical structures) and which are impossible (non-mathematical "stuff"). This grounds constructor theory's counterfactuals in logical necessity rather than empirical generalization. Furthermore, knowledge (which Deutsch and Marletto identify as a central constructor-theoretic concept) emerges naturally as self-referential mathematical structure that causes itself to remain instantiated. The hard problem of consciousness dissolves: experience is what certain mathematical structures are from the inside. Constructor theory and mathematical monism are mutually reinforcing: constructor theory provides the language, mathematical monism provides the ontology.