The Positive Differential Argument: Justifying Action When Absolute Probabilities Are Incomputable

Decisions concerning superintelligence face a structural difficulty: the absolute probability that an action improves humanity's survival prospects is incomputable. Takeoff speed, the resulting power structure, the offense–defense balance — for none of the variables that determine the outcome can the parties agree on a probability distribution, and there is no accepted method for identifying one. This is not risk in the ordinary sense but deep uncertainty. This paper presents the Positive Differential Argument, a form of action justification that replaces absolute probabilities with a dominance claim: across an explicitly stated set of regimes, the differential ΔP_r induced by the action is non-negative, and strictly positive for at least one regime (weak dominance). When weak dominance holds, the expected differential is strictly positive under any prior over regimes, so parties who disagree sharply about regime probabilities — one assigning 0.9 to fast takeoff, another 0.01 — can nonetheless agree that the action is justified. The paper specifies, with equal precision, the conditions under which the argument fails: non-dominance, unexamined added risk, and conflation with feasibility. Safeguards against misuse (disciplines R1–R3) and limitations of scope ((i)–(vi)) are built into the argument itself rather than appended to it. Applying the argument to six proposed actions in AI safety and human–AI symbiosis — including the author's own research programs — shows that the verdicts are not uniform: two pass, three pass conditionally, and one fails.