True Sustainability Thinking 107: Placing the critical problem-solving impossibility Theorem and the full critical problem-solving possibility theorem under the degree of externality production framework: Revealing the externality production continuu

The degree of externality production framework treats externality production as a cost externalization continuum ranging from full cost externalization to full no cost externalization. Within this continuum, the critical problem-solving impossibility theorem is structurally admissible only at the endpoint characterized by full cost externalization and a full externality production reduction technology gap. Because producers bear no responsibility for externality costs under this structure, no endogenous incentives exist to eliminate pollution production. As the degree of externality production declines through increasing cost internalization and technological improvement, the structural admissibility of the impossibility theorem progressively weakens. Once the system moves away from the full externalization endpoint, transition conditions emerge under which partial forms of the critical problem-solving possibility theorem become admissible. At the limiting case of no cost externalization and no externality production reduction technology gap, the full critical problem-solving possibility theorem becomes structurally admissible, while the critical problem-solving impossibility theorem becomes fully structurally falsified. As the degree externality production decreases, the critical problem-solving impossibility theorem is progressively relaxed. Consequently, the theorem loses structural admissibility outside the full externality production endpoint, creating the transition conditions under which the critical problem-solving possibility emerges. And this raises important questions such as how to place the critical problem-solving impossibility theorem and the full critical problem-solving possibility theorem under the degree of externality production framework? How can this framework be used to highlight the externality production continuum from full cost externalization to no cost externalization?