The Logical Inconsistency of "Sustainable Development": A Lyapunov Stability Perspective

The term sustainable development is widely used across policy design and quantitative modeling, yet it lacks a precise formal interpretation within dynamical systems theory. This paper examines the consistency of the term when sustainability is associated with trajectorybased stability and development is interpreted as directed state transition. We show that, under standard ε–δ stability definitions, these two requirements are formally incompatible with respect to the same reference state. A general incompatibility result is established, its implications for model design are discussed, and the need for greater terminological precision in stability- and transition-oriented modeling is highlighted.