A workshop group developed the concept of a "polyspecific" TCR/BCR in the framework of today's consensus model. They argue that the individual TCR/BCR combining site is composed of a packet of specificities randomly plucked from the repertoire, hence it is "polyspecific." This essay analyzes the conclusions of the workshop and suggests an alternative. "Polyspecificity" must be dissected into its two component parts, specificity and degeneracy. The TCR and the BCR must be treated differently because the TCR recognizes allele-specifically the MHC-encoded restricting element (R) that serves as the platform presenting peptide (P). Only the anti-P paratope of the TCR behaves analogously to the BCR paratope. The two paratopes are selected to recognize a shape-determinant referred to as an epitope or ligand. The paratope is functionally unispecific in recognition, not polyspecific, with respect to shape; it is degenerate in recognition with respect to chemistry. The recognized shape-determinant can be the product of many chemically different substances, peptide, carbohydrate, lipid, steroid, nucleic acid, etc. Such a degenerate set is functionally treated by the paratope as one shape/epitope/ligand and, in no sense, can a paratope recognizing such a degenerate set be described as "polyspecific." Degeneracy and specificity are concepts that must be distinguished. The two positions are analyzed in this essay, the experiments used to support the view that the paratope of the TCR/BCR is polyspecific, are reinterpreted, and an alternative framework with its accompanying nomenclature, is presented.