Toward an Ontology Based on Pure Difference and Generativity

Traditional Western metaphysics begins with a fundamental question: “What is being?” and habitually answers with substance. However, this substance ontology faces a fundamental dilemma: it cannot explain how relations are possible, and always reduces relations to subsidiary properties of substances.

Our revolutionary starting point lies in a radical shift in perspective: switching the basic unit of existence from “substance” to “relational event“. This does not deny the stability of phenomena, but rather claims that any seemingly stable “substance” is essentially a stable knot or persistent pattern of dynamic relations.

Saussurean structural linguistics provides a key insight for this turn. Language is “form, not substance,” and the meaning of its elements is entirely defined by difference within the system. “Cat” is “cat” because it is not “dog,” “mouse,” or “animal.” This structure of pure differentiality finds profound echo in Eastern wisdom: the I Ching’s “one yin, one yang—this is called the Dao” reveals that the generation of all things emerges from the interweaving and evolution of the most empty, most abstract binary difference system.

This “pure difference“ is our ontological foundation. Empty of self-nature, possessing no inherent properties, it is pure potentiality—the “Dao” or “meta-language” that generates all things. And mathematical groups provide precisely the most accurate formal expression of this pure difference. In a group G, elements g and h are themselves contentless “empty shells,” existing solely to enter into the relational operation gh. Here occurs an ontological inversion: it is not that g and h exist first and then gh; quite the contrary, it is to express the relational event gh that we retroactively project g and h as convenient symbolic nodes. Relations are ontologically prior to their endpoints.

Further, the multiplication rules of groups—associativity, identity element, inverse element—constitute a pure generative grammar capable of evolving infinitely complex structures from itself. This generativity is not externally imposed but intrinsic to the relational operations themselves. This is the core intuition of what we call “group field theory“: how abstract relational algebra gives rise to the concrete world of our experience through processes of “representation“ or “instantiation.” When we assign abstract group elements a representation space—whether geometric space, social space, or semantic space—concretizing them as transformations within that space, the world manifests.

In sociolinguistics, the fundamental relational event is communication. Social structures, linguistic norms, and individual identities are all stable attractors emerging from the dynamics of countless communicative events (gh operations). Language here is both the object regulated by social structure and the active agent regulating social structure, forming a circular causal dynamic equilibrium. In physics, we might conceive the fundamental relational event as quantum relations, and the continuous spacetime and physical fields we perceive as macroscopic approximations statistically emerging from a deeper, discrete network of quantum relations (modelable as some group structure). This provides a novel pathway for solving the fundamental problem of “the origin of spacetime.”

This framework resonates deeply with constructivism. It reveals that the world we inhabit—from the distinction between “language” and “dialect,” to the borders of nation-states, to our cognition of physical reality—is not passively discovered as given fact, but actively generated as emergent phenomena through the continuous “operation-construction” process of deep, dynamic relational networks. Existence is not the static “what” (what), but the dynamic “how it happens” (how).

We propose that an ontology with pure difference as origin, relational operations as substance, and generativity as primary property is the most powerful paradigm for understanding complexity across different levels—from language and society to physical nature. Group field theory is the mathematical embryo of this paradigm. It invites us to undertake a fundamental revolution in perspective: no longer seeing the world as a collection of objects, but viewing it as a dynamic network woven from relational events—an eternal “dance of relations.”