Although skeptical of the prohibitive power of no-hidden-variables theorems, John Bell was himself responsible for the two most important ones. I describe some recent versions of the lesser known of the two (familiar to experts as the "Kochen-Specker theorem") which have transparently simple proofs. One of the new versions can be converted without additional analysis into a powerful form of the very much better known "Bell's Theorem," thereby clarifying the conceptual link between these two results of Bell.

This heuristic article introduces a generalization of the idea of drawing colored balls from an urn so as to allow mutually incompatible experiments to be represented, thereby providing a device for thinking about quantum logic and other non-classical statistical situations in a concrete way. Such models have proven valuable in generating examples and counterexamples and in making abstract definitions in quantum logic seem more intuitive.