Probability theory asserts the lawfulness of seemingly random events in large populations and seems to be a reasonable approach to a general understanding of the structure and function of the nervous system. The brain, by virtue of the number of its components, the multiplicity of their possible interconnections, and the range and rapidity of their outputs, is almost implausably complex in its over-all design. Probability theory, therefore, is usually applied to (a) descriptions of the behavior of large neuronal populations, (b) statistical analysis of neuronal spike trains, and (c) theoretical models of neuronal interaction. A consideration of each of these subjects is presented, as is a discussion of the most fundamental level of application of the theory to the nervous system: (d) the assertion that the neuron and/or brain is inherently nondeterministic. In practical terms this is shown to be a “nonissue;” the uncertainty principle that follows has rather definite philosophical implications.