Problem-solving strategies in immunology currently utilize a series of ad hoc, qualitative variations on a foundation of Burnet's formulation of clonal selection theory. These modifications, including versions of two-signal theory, describe how signals regulate lymphocytes to make important decisions governing self-tolerance and changes to their effector and memory states. These theories are useful but are proving inadequate to explain the observable genesis and control of heterogeneity in cell types, the nonlinear passage of cell fate trajectories and how the input from multiple environmental signals can be integrated at different times and strengths. Here, I argue for a paradigm change to place immune theory on a firmer philosophical and quantitative foundation to resolve these difficulties. This change rejects the notion of identical cell subsets and substitutes the concept of a cell as comprised of autonomous functional mechanical components subject to stochastic variations in construction and operation. The theory aims to explain immunity in terms of cell population dynamics, dictated by the operation of cell machinery, such as randomizing elements, division counters, and fate timers. The effect of communicating signals alone and in combination within this system is determined with a cellular calculus. A series of models developed with these principles can resolve logical cell fate and signaling paradoxes and offer a reinterpretation for how self-non-self discrimination and immune response class are controlled.