The technical possibilities of biomedicine open up the opportunity to intervene in ageing itself with the aim of mitigating, reducing or eliminating it. However, before undertaking these changes or rejecting them outright, it is necessary to ask ourselves if what would be lost by doing so really has much value. This article will analyse the desirability of ageing from an individual point of view, without circumscribing this question to the desirability or undesirability of death. First, we will present the three (...) most widely used arguments to reject biomedical interventions against ageing. We will argue that only the last of these arguments provides a consistent answer to the question of the desirability of ageing. Second, we will show that the third argument falls prey to a conceptual confusion that we will call the paradox of ageing: although ageing entails negative health effects, it leads to a life stage with valuable goods. Both valuations, one positive and the other negative, refer to two different dimensions of ageing: the chronological and the biological. We will defend that, by not adequately distinguishing these two types of ageing, it does not become apparent that all the valuable goods exclusive to ageing derive only from its chronological dimension. Third, we will argue that, if we just conceive ageing biologically, it is undesirable. We will elaborate on the two kinds of undesirable effects biological ageing has: direct and indirect. Finally, we will respond to potential objections by adducing that these are insufficient to weaken our argument. (shrink)