Abstract: The Logocratic Method, and the Logocratic theory that underwrites it, provide a philosophical explanation of three purposes or goals that arguers have for their arguments: to make arguments that are internally strong (the premises follow from the conclusions, to a greater or lesser degree—greatest degree in valid deductive arguments), or that are dialectically strong (win in some forum of argument competition, as for example in litigation contests of plaintiffs or prosecutors on the one hand, and defendants, on the other), or that are rhetorically strong (effective at persuading a targeted audience). This article presents the basic terms and methods of Logocratic analysis and then uses a case study to illustrate the Logocratic explanation of arguments. Highlights of this explanation are: the use of a (non-moral) virtue (and vice) framework to explicate the three strengths and weaknesses of arguments that are of greatest interest to arguers in many contexts (including but not limited to the context of legal argument), the Logocratic explication of the structure of abduction generally and of legal abduction specifically, the concept of a system of arguments, and the concept of the dynamic interactive virtue (and vice) of arguments—a property of systems of arguments in which the system of arguments as a whole (for example, the set of several arguments typically offered by a plaintiff or by a defendant) is as virtuous (or vicious) as are the component arguments that comprise the system. This is especially important since, according to Logocratic theory (and as illustrated in detail in this paper), some arguments, such as abduction and analogical argument, are themselves comprised of different logical forms (for example, abduction always plays a role within analogical argument, and either deduction or defeasible modus ponens, always plays a role within legal abduction).