Carcinogenesis is a multistep process in which new, parasitic and polymorphic cancer cells evolve from a single, normal diploid cell. This normal cell is converted to a prospective cancer cell, alias "initiated", either by a carcinogen or spontaneously. The initiated cell typically does not have a new distinctive phenotype yet, but evolves spontaneously--over months to decades--to a clinical cancer. The cells of a primary cancer also evolve spontaneously towards more and more malignant phenotypes. The outstanding genotype of initiated and cancer cells is aneuploidy, an abnormal balance of chromosomes, which increases and varies in proportion with malignancy. The driving force of the spontaneous evolution of initiated and cancerous cells to ever more abnormal phenotypes is said to be their "genetic instability". However, since neither the instability of cancer phenotypes nor the characteristically slow kinetics of carcinogenesis are compatible with gene mutation, we propose here that the driving force of carcinogenesis is the inherent instability of aneuploid karyotypes. Aneuploidy renders chromosome structure and segregation error-prone, because it unbalances mitosis proteins and the many teams of enzymes that synthesize and maintain chromosomes. Thus, carcinogenesis is initiated by a random aneuploidy, which is induced either by a carcinogen or spontaneously. The resulting karyotype instability sets off a chain reaction of aneuploidizations, which generate ever more abnormal and eventually cancer-specific combinations and rearrangements of chromosomes. According to this hypothesis the many abnormal phenotypes of cancer are generated by abnormal dosages of thousands of aneuploid, but un-mutated genes.