Compositional Limit

The compositional limit is the theoretical boundary that natural languages approach but never fully reach — the point at which the meaning of every complex expression would be perfectly predictable from the meanings of its parts and their mode of combination. Classical semantics assumes languages exist at this limit. Emergent semantics treats the limit as an asymptote: real languages are always on one side of it, pulled toward compositionality by cognitive and social pressures but constantly perturbed away from it by context, creativity, and the productivity paradox of meaning-making.

The concept is motivated by the observation that natural language is pervasively non-compositional. Idioms, metaphors, pragmatic implicatures, and context-dependent reference are not exceptions to a compositional rule; they are the rule, and compositionality is the exception that emerges under specific conditions. A language approaches the compositional limit when its community of speakers is large, its contexts of use are standardized, and its cognitive demands favor rapid, error-free interpretation. It retreats from the limit when creativity, social differentiation, or technological change introduce new forms of expression that outpace the stabilization of fixed meanings.

The compositional limit is not merely a descriptive claim about language. It is a claim about the observer-indexed nature of semantic properties: what counts as "compositional" depends on the interpreter's capacity to decompose expressions into stable parts. For a neural network, the limit is different than for a human. For a community with shared history, it is different than for strangers.