In this talk, I will suggest that cancer is fundamentally a disease of the control on cell differentiation in multicellular organisms, uncontrolled cell proliferation being a mere consequence of blockade, or unbalance, of cell differentiations. Cancer cell populations, that can reverse the sense of differentiations, are extremely plastic and able to adapt without mutations their phenotypes to transiently resist drug insults, which is likely due to the reactivation of ancient, normally silenced, genes. Stepping from mathematical models of non genetic plasticity in cancer cell populations and questions they raise, I will propose an evolutionary biology approach to shed light on this problem, using a description of multicellular organisms in terms of structured cell populations both from a theoretical and partly metaphoric viewpoint, and from a practical point of view oriented towards cancer therapeutics, as cancer is primarily a failure of multicellularity in animals and humans. This joint approach resorts to the emergent field of knowledge named philosophy of cancer and, more classically, to adaptive cell population dynamics and its therapeutic control.