On the Percolation
Theory of Symbolic Systems

Summary

The field of linguistics encompasses a broad range of active research areas, from the evolution of language (Evolinguistics) to the construction of meaning (Cognitive Semantics). At their intersection lies Symbol Emergence Theory, which studies how symbols and meaning systems self-organize and acquire expressive capacity.

The central insight is that expressivity arises when the network of symbols achieves sufficient semantic connectivity. At this point, the definitional graph linking words becomes strongly connected and undergoes percolation, enabling the free composition of meanings. In other words, expressive power emerges once the system crosses a critical threshold of semantic density.

In this paper, we aim to demonstrate mathematically how this phenomenon arises from the perspective of complex physical systems, in the sense articulated by Anderson’s More is Different. Our goal is to construct a formal theory by establishing the necessary and sufficient conditions under which such a system acquires expressive power.