A Metamodel for Ontologically Heterogeneous Social Dynamics Part I: The Highest Abstract Layer

This is the first paper of a series. It fixes the highest abstract layer, and it goes no further. Dynamical modeling of social systems ordinarily begins by fixing a state space. This is already a commitment, and across domains it is one that cannot be met. The states of a normative order, a power configuration, a value system, and a network of recognition inhabit no common manifold and admit no common metric—and the obstacle is not that such a space is hard to construct but that these are not objects of a kind that admit a common placement. The heterogeneity is ontological, not practical, and it is not answered by better instruments. The proposal here is to begin one layer lower, at a level where change, structure, constraint, and difference are defined but not yet realized. Four axioms are given. The carrier of states is left without structure. The mechanisms acting upon it form a semigroup: associative, without inverses, without an identity. A congruence records what any mechanism is obliged to preserve. And difference is defined—not as a residue, not as a distance—as the set of distinctions a mechanism collapses. From these, four propositions follow that were not assumed: collapse is irreversible; a group of mechanisms has no collapse at all, and hence no history; a mechanism is non-destructive exactly when it is injective modulo the congruence; and collapse accumulates monotonically under composition. The absence of inverses is shown to be the load-bearing commitment. A further consequence concerns the residue: the two traditions with the strongest claim on the notion of a remainder—the economic, for which surplus is a magnitude that could have been returned, and the psychoanalytic, for which the remainder has no place in the order that produced it—disagree about what a remainder is, and any operator returning an element settles that disagreement by notation rather than by argument. Defining difference as a relation leaves both open, and locates the point at which a modeller must choose between them. This paper does not instantiate the metamodel, does not apply it, and derives no substantive result about any particular social system. Those belong to subsequent parts. What is established here is only what a social dynamical system must be able to say, and the price of saying it.