The Bateson Equilibrium: Strategic Ambiguity, Logical Ecology, and the Persistence of Undecidable Propositions

Undecidable propositions, long seen as limits of formal systems, may in fact serve
as equilibrium structures in the ecology of mathematical logic. In this paper, we develop
the Bateson Equilibrium Theorem, a formalization of Gregory Bateson’s insight
that ambiguity and recursive constraints preserve the integrity of complex systems. By
modeling logical foundations as an evolutionary game in which framing strategies coevolve,
we show that undecidability functions analogously to Nash equilibrium: a state
from which no agent can unilaterally deviate without loss. We argue that propositions
such as the Continuum Hypothesis (CH), by remaining undecidable in ZFC, maintain
strategic ambiguity that stabilizes the logical ecosystem and permits diversity of models.
This provides a new framework for understanding the persistence and value of
undecidable statements.