Many authors have argued that the core of evolutionary biology as represented by the catchphrase 'The fittest survive' is tautological. Concerning the fitness concept of population genetics it is easy to rebut this charge by a proper explication of the term 'survival'. In biology and in the philosophy of biology, various fitness concepts over and above that of population genetics have been elaborated. These concepts, which are called 'supervenient' by some philosophers, have a limited usefulness. On some interpretations they do lead to unacceptable tautologies and circular reasoning. The so-called propensity concept of fitness is problematic in this respect. If interpreted in a proper way, supervenient concepts appear not to allow the formulation of highly general explanations and theories; at best they reveal common patterns among diverse non-general explanations and theories. Philosophers cherishing supervenient fitness concepts are apparently motivated by a mistaken search for general theory. The fitness concept of population genetics may play a role in relatively general theories and explanations. Supervenient concepts cannot play such a role. They should rather help us recognize the value of natural history in biology.