There are two opposite paradigms to explain aging, here precisely defined as "age-related progressive mortality increase, i.e. fitness decline, in the wild". The first maintains that natural selection is unable to maintain fitness as age increases. The second asserts that, in particular ecological conditions, natural selection favors specific mechanisms for limiting the lifespan. The predictions derived from the two paradigms are quite different and often opposing. A series of empirical data and certain theoretical considerations (non-universality of aging; great inter-specific variation of aging rates; effects of caloric restriction on lifespan; damage of aging for the senescing individual but its advantage in terms of supra-individual selection; existence of fitness decline in the wild; proportion of deaths due to intrinsic mortality inversely related to extrinsic mortality, when various species are compared; impossibility of explaining the age-related fitness decline as a consequence of genes that are harmful at a certain age; age-related progressive decline of cell turnover capacities; on/off cell senescence; gradual cell senescence) are compared with the predictions of the two paradigms and their compatibility with each paradigm is considered. The result is that the abovementioned empirical data and theoretical considerations strongly contradict and falsify in many ways all theories belonging to the first paradigm. On the contrary, they are consistent or compatible with the predictions of the second paradigm.