In this paper it is given a short introduction in a reconsideration about BCC-algebras under the light of Bishop's principled-philosophical orientation. At the first, it is introduced the concept of BCC-algebras into this orientation. Additionally, the consequences of the selected axioms in the determination of BCC-algebras with apartness are analyzed. Also, some substructures in the BCC-algebras with apart-ness that have no counterparts in the classical case and which appear as products of the chosen logical environment such as co-ideals are analyzed. At the end, two different results that can be viewed as the isomorphism theorem in for BCC-algebras are exposed