The now well-known impossibility results of algorithmic fairness demonstrate that an error-prone predictive model cannot simultaneously satisfy two plausible conditions for group fairness apart from exceptional circumstances where groups exhibit equal base rates. The results sparked, and continue to shape, lively debates surrounding algorithmic fairness conditions and the very possibility of building fair predictive models. This article, first, highlights three underlying points of disagreement in these debates, which have led to diverging assessments of the feasibility of fairness in prediction-based decision-making. (...) Second, the article explores whether and in what sense fairness as defined by the conjunction of the implicated fairness conditions is (un)attainable. Drawing on philosophical literature on the concept of feasibility and the role of feasibility in normative theory, I outline a cautiously optimistic argument for the _diachronic feasibility_ of fairness. In line with recent works on the topic, I argue that fairness can be _made possible_ through collective efforts to eliminate inequalities that feed into local decision-making procedures. (shrink)