The Sage's Empty Purse: An Entropy-Based Theory of Value Formation

Recent work grounds the notion of value in informational entropy, arguing that minds assign dierential probabilities to informational units and that values are simply those units retained with high probability. However, this account remains largely qualitative. This note formalizes value formation as a probability-assignment process over a nite set of informational quanta and proves two elementary propositions: (1) a capacity bound showing that the number of quanta that can simultaneously qualify as values under a xed importance threshold is bounded by the reciprocal of that threshold, and (2) an entropy-reduction theorem showing that any nontrivial departure from uniform probability assignment strictly and measurably lowers informational entropy, quantied exactly by Kullback-Leibler divergence from indierence.