Semantic Models

In section 13.8 of Structural Stability and Morphogenesis, René Thom proposes the following definitions and their implications.

Every object, or physical form, can be represented as an attractor of a dynamical system on a space of internal variables.

Such an object is stable, and so can be recognized, only when the corresponding attractor is structurally stable.

All creation or destruction of forms, or morphogenesis, can be described by the disappearance of the attractors representing the initial forms, and their replacement (by capture) by the attractors representing the final forms. This process, called catastrophe, can be described on a space of external variables.

Every structurally stable morphological process is described by a structurally stable catastrophe, or a system of structurally stable catastrophes, on the space of external variables.

Every natural process decomposes into structurally stable islands, the chreods. The set of chreods and the multidimensional syntax controlling their positions constitute the semantic model.

When the chreod is considered as a word of this multidimensional language, the meaning (signification) of this word is precisely that of the global topology of the associated attractor (or attractors) and of the catastrophes that it (or they) undergo. In particular, the signification of a given attractor is defined by the geometry of its domain of existence on the space of external variables and the topology of the regulation catastrophes bounding that domain.

One result of this is that the signification of a form (chreod) manifests itself only by the catastrophes that create or destroy it. This gives the axiom dear to the formal linguists: that the meaning of a word is nothing more than the use of the word; this is also the axiom of the "bootstrap" physicists, according to whom a particle is completely defined by the set of interactions in which it participates.”