Western knowledge takes being (BE) as its core operator and studies well-founded beings; its precise boundary is the Axiom of Foundation of ZF set theory. The proper classes that axiom excludes — circular, self-nesting structures that presuppose themselves — are where another science begins: the science of generation, whose core operator is generation (shēng).
Object of study
Ontology asks what a being is; such questions presuppose that the being is already there, and before its coming-to-be ontology is silent. The silence is structural. It shows up in five places — consciousness, emergence, self-reference, the generation of life, and the generation of space-time — and in all five the common root is the proper class. Structural inference
Proper class (in this project’s sense): an individual whose existence presupposes itself and forms a cycle. It is excluded by the Axiom of Foundation, and its mathematical home is the terminal coalgebra νF (νF ≅ F(νF)). This is not the NBG sense of a collection too large to be a set.
Theorem Proper classes ↔ the terminal coalgebra νF, together with the bisimulation criterion of identity given by the Anti-Foundation Axiom, is the one theorem-level anchor running through all the texts; in finite cases it is decidable by Paige–Tarjan partition refinement.
Core questions
- How do beings come into being? — a question of generation, not of attributes.
- How do two poles emerge together and define each other? — the question of mutual arising.
- How does a process sustain itself? — the question of the rotor.
Method
The science of generation has no axioms. It replaces axioms with primordial (fixed-point) equations, induction with coinduction, and consistency proofs with bootstrapping demonstrations, and it tests its own legitimacy by two criteria, autologicality and guardedness. The Dao is an operator, not a highest being: it cannot be axiomatised, only operationalised. Structural inference
Relation to the science of being
| Dimension | Science of being | Science of generation |
|---|---|---|
| Root question | What is a being? | How does a being come to be? |
| Core operator | Be (BE) | Generation (Shēng) |
| Objects | Well-founded beings | Proper classes (circular self-nesting individuals) |
| Formal tools | ZF set theory, first-order logic | Yin-yang and Five-Phase theory; links to AFA and νF |
| Epistemology | Sequential recognition, a cognitive origin | Circular recognition, no cognitive origin |
| Inference norm | Truth-preserving | Generation-preserving |
| Direction | Upward abstraction (probabilistic) | Downward deduction (deterministic) |
As concepts, generation and being arise mutually and symmetrically. As systems, the relation is a containment asymmetry: the science of being is the degenerate projection of the science of generation in the limit of existence-independence ι→1. Degenerate does not mean wrong or inferior — the projection is complete and consistent within its domain, and it is where all the success of modern science lies. Structural inference
Structure of the system
Science of Generation is organised by moments of generation rather than by disciplinary branches, in seven parts: Boundary, Dao, Generation, Rotation, Form, Things and Return. Older discipline-style names such as “generative ontology” and “generative logic” survive only as lexical-level correspondences.