In this paper, I consider whether the critical rationalist philosophy of science may provide a rationale for trusting scientific knowledge. In the first part, I refer to several insights of Karl Popper's social and political philosophy in order to see whether they may be of help in offsetting the distrust of science spawned by the COVID-19 pandemic. In the second part, I address the more general issue of whether the theoretical principles of the critical rationalist philosophy of science may afford a foundation for building trust in science. Both parts of the discussion, confined for the sake of the argument largely to the repudiation of the concept of good reasons for considering a theory to be true, imply that this question would have to be answered negatively. Against this, I argue that such a conclusion is based on a misconception of the nature of scientific knowledge: critical rationalism views science as a cognitive regime which calls for bold theories and at the same time demands a rigorous and continuous distrust towards them, and it is precisely this attitude that should be adopted as a compelling argument for trusting science.