A Gödelian Perspective on Target-Directed Fitness in Cumulative-Selection Models

Many widely used pedagogical models of cumulative selection — including Dawkins’ “weasel” program — define fitness as a monotonic function of distance to a fixed, externally specified target T that the evolving population never directly observes. We prove that any such target-dependent fitness function requires an external oracle supplying d(x, T ) at each generation, and that directed convergence is possible if and only if the algorithm is oracle-augmented. When the entire evolutionary process is idealized as a consistent formal system S powerful enough for arithmetic and T lies outside its axiomatic closure, Gödel’s first incompleteness theorem entails that statements of the form “bit i of x equals bit i of T ” are not uniformly decidable within S; consequently d(x, T ) cannot be computed internally. Experiments with n = 40 bit strings confirm the theoretical dichotomy: with the oracle, convergence is rapid and monotonic; without it, the dynamics reduce to an unbiased random walk. The Gödelian perspective is new; the underlying computational necessity of an oracle follows from the No Free Lunch theorems and has been noted by several authors. The analysis clarifies why target-dependent models, although vivid illustrations of cumulative improvement, cannot serve as non-teleological models of natural evolution, as they violate the causal locality of fitness defended in the propensity interpretation.