Pro-C.3 — Response to Con-C.3 (ax19 Incomparability)#

Impact: C (Serious) — Resolved.

The fitness analogy rescues ax19. The incomparability objection fails for the same reason the parallel anti-evolution argument fails.

  1. The anti-evolution argument says: “Fitness is circular — the fittest are those who survive.” This fails because fitness is technically definable as the expected number of descendants in the next generation. Fitness is multi-dimensional in its inputs (survival, fecundity, mating success, etc.) yet projects to a well-defined scalar that is foundational to all of evolutionary biology.

  2. The same structure applies to ax19. Causal influence on the total future trajectory of civilization is multi-dimensional in its inputs (climate, AI, nuclear, etc.) but is ultimately projected onto a single outcome space: the future of the world. This projection yields a scalar — the expected deviation in the probability distribution over all future world-states caused by one individual’s choices at time t.

  3. Arrow’s impossibility theorem does not apply. Arrow concerns the aggregation of subjective preference orderings into a social ranking. Causal influence is not a preference aggregation problem — it is a physical question about how one node’s state changes the probability distribution over the entire network’s future trajectory. Civilization has only one future, so the effects project onto a single outcome.

  4. The measure-zero argument applies because the projection is scalar. Once causal influence is recognized as a pair of real numbers (for any two agents), exact equality has probability zero under any continuous probability measure. Therefore uniqueness of h* is the null hypothesis.

  5. Ontological vs. epistemic distinction. ax19 claims that h* exists (ontological) — not that anyone can identify h* in real time (epistemic). The epistemic question is acknowledged as future work, but is not needed for the axiom system’s validity. The fitness of an organism exists whether or not anyone can compute it; the same applies to maximal causal influence.

(Source: Reply to C3 from OOv1 Reply Round 1b.)