We develop theories and build models in science and engineering in order to visualize, explain, and predict physico-chemical phenomena.  As such, theories and models are intricate parts of the scientific method, which is the cyclical process whereby new phenomena are predicted and tested, until the prediction fails.  At the point of failure, the theory (i.e., the basis of the model) is modified and the process continues until failure again occurs.  Eventually, no amount of non-ad hoc modification can make the model succeed.  At that point, a new theory must be formulated, a model for that theory must be developed, and the whole process must begin anew.  While the distinction between a “theory” and a “model” is seldom sharp, and in many cases is so blurred that the two are often indistinguishable, the old adage that a theory “explains” and a model “calculates” is usually a reliable classification tool.  Another useful, distinguishing property is that a (physical) model must possess a theoretical basis, but a theory need not necessarily yield a model or to calculate.  Thus, while the theory of evolution certainly “explains”, it has no facility for predicting the rates at which species evolve.  On the other hand, the theory and model are often melded into one; this being so in the case of the Theory of Relativity, for example.  Recognizing that all theories, upon which the derived models are based, are merely our perceptions of reality, and are not reality itself, it is evident that all theories and models are ultimately wrong or at least are incomplete and the scientific method is nothing more or less than the mechanism by which theories and models are nudged toward reality or obsolescence.  Compounded on this is the fact that we observe systems and behavior through imperfect senses and we interpret the results through imperfect intellect.  It is little wonder, then, that the scientific literature is littered with models of various forms and different degrees of determinism versus empiricism.
    We review development of deterministic theories and models in corrosion science and engineering from a philosophical viewpoint.  Our principal goal is the answer the question: What are the essential components of a model that can predict the accumulation of damage deterministically?  This subject is much too broad to be done justice in a single presentation, but, by limiting the scope, the authors wish to illustrate the essential elements of theory- and deterministic model-building.  The case selected, the prediction of crack growth rate via the Coupled Environment Fracture Model, been chosen because these models have been successful in quantitatively predicting the growth of pits and cracks in a variety of systems.  Much of the material is derived from a graduate course titled “Theories and Models in Science and Engineering” that one of the authors (DDM) presents in the Department of Materials Science and Engineering at the Pennsylvania State University.  The course traces the development of scientific philosophy from the introduction of the concept of causality by Aristotle in 350 BC until the current time.