Specificity is an imprecise but widely used concept in immunology. Usually specificity is described in practical terms, such as the ability of one antibody to bind one and not another member of a family of chemically related substances. Karl Landsteiner's pioneering work "The Specificity of Serological Reactions" set the standard in experimental immunology over 50 years ago. Today, a more general yet precise concept of specificity is needed to describe the behavior of all antigen-specific recognitive components of the immune system. The necessary degree of specificity for antigen recognition in the immune response is determined by evolutionary selection pressures that result in the ridding of pathogens. Potent bio-destructive effector mechanisms are under the direction of specificity-determining elements (e.g. antibodies), and these must accurately distinguish Self (S) components (not to be destroyed) from Nonself (NS) components (to be destroyed). Binding reactions between antigen and antibody are necessary, though not sufficient, for the execution of the protective bio-destructive effector reactions, which, for example, require more than one antibody molecule to be bound before that antigen can be ridded. While the total number of different specificities will determine the precision with which S and NS are distinguished, a concept of relative specificity can be formulated in terms of a Specificity Index (SI), or the ratio of anti-S to anti-NS in the repertoire. A further question concerns whether specificity applies per receptor, or per paratope, when the number of paratopes per receptor is greater than one. The analyses and concepts developed here are based on immunoglobulin structure and function and extrapolated to include the less well studied T cell receptor system.