The current classification system for breast cancer is based on expression of empirical prognostic and predictive biomarkers. As an alternative, we propose a hypothesis-based ontological breast cancer classification modeled after the taxonomy of species in evolutionary biology. This approach uses normal breast epithelial cell types and differentiation lineages as the gold standard to classify tumors. We show that there are at least eleven previously undefined normal cell types in human breast epithelium and that each breast carcinoma is related to one of these normal cell types. We find that triple negative breast cancers do not have a ‘basal-like’ phenotype. Normal breast epithelial cells conform to four novel hormonal differentiation states and almost all human breast tumors duplicate one of these hormonal differentiation states which have significant survival differences. This ontological classification scheme provides actionable treatment strategies and provides an alternative approach for understanding tumor biology with wide-ranging implications for tumor taxonomy.