This paper attempts to identify, in a framework deliberately stripped of unnecessary technicalities, some of the basic reasons why adaptive learning may or may not lead to stability and convergence to self-fulfilling expectations in large socioeconomic systems where no agent, or collection of agents, can act to manipulate macroeconomic outcomes. It is shown that if agents are somewhat uncertain about the local stability of the system, and are accordingly ready to extrapolate a large range of regularities (trends) that may show up in past small deviations from equilibrium, including divergent ones, the learning dynamics is locally divergent. On the other hand, if agents are fairly sure of the local stability of the system, and extrapolate only convergent trends out of small past deviations from equilibrium, one may get local stability. This "uncertainty principle" does show up in a wide variety of contexts: smooth or discontinuous, finite or infinite memory learning rules, error learning, recursive least squares, Bayesian learning.