In his bookMinimal Rationality (1986), Christopher Cherniak draws deep and widespread conclusions from our finitude, and not only for philosophy but also for a wide range of science as well. Cherniak's basic idea is that traditional philosophical theories of rationality represent idealisations that are inaccessible to finite rational agents. It is the purpose of this paper to apply a theory of idealisation in science to Cherniak's arguments. The heart of the theory is a distinction between idealisations that represent reversible, solely quantitative simplifications and those that represent irreversible, degenerate idealisations which collapse out essential theoretical structure. I argue that Cherniak's position is best understood as assigning the latter status to traditional rationality theories and that, so understood, his arguments may be illuminated, expanded, and certain common criticisms of them rebutted. The result, however, is a departure from traditional, formalist theories of rationality of a more radical kind than Cherniak contemplates, with widespread ramifications for philosophical theory, especially philosophy of science itself.