The concept of fitness, central to population genetics and to the synthetic theory of evolution, is discussed. After a historical introduction on the origin of this concept, the current meaning of it in population genetics is examined: a cause of the selective process and its quantification. Several difficulties arise for its exact definition. Three adequacy criteria for such a definition are formulated. It is shown that it is impossible to formulate an adequate definition of fitness respecting these criteria. The propensity (...) definition of fitness is presented and rejected. Finally it is argued that fitness is a conceptual device, a useful tool, only for descriptive purposes of selective processes, changing from case to case, and thus devoid of any substantial physical counterpart. Any attempt to its reification is an apport to the metaphysical load evolutionary theory has inherited from Natural Theology. (shrink)