In this presentation that partly subsumes and summarises in the form of adapted excerpts some recent articles of which I am author or co-author [2], [3], [11], I suggest that cancer is fundamentally a disease of the control of 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 in order to transiently resist drug insults [10], which is likely due to the reactivation of ancient, normally silenced, genes [5], [7], [12]. Stepping from mathematical models of non genetic plasticity in cancer cell populations [4], [6] and questions they raise, I propose an evolutionary biology approach to shed light on this problem a) from a theoretical viewpoint by a description of multicellular organisms in terms of multi-level structures, which integrate function and matter from lower to upper levels, and b) from a practical point of view by proposing future tracks for cancer therapeutics, as cancer is primarily a failure of multicellularity in animals and humans. This approach resorts to the emergent field of knowledge known as philosophy of cancer [1], [8], [9].