Empirical reports in mainstream journals that human cognition extends in ways that challenge the current boundaries of science (anomalous cognition) has been viewed with dismay by many who see it as evidence that science is broken. Here the authors make the case for the value of conducting and publishing well-designed studies investigating anomalous cognition. They distinguish between the criteria that justify entertaining the possibility of anomalous cognition from those required to endorse it as a bona fide phenomenon. In evaluating these 2 distinct thresholds, the authors draw on Bayes’s theorem to argue that scientists may reasonably differ in their appraisals of the likelihood that anomalous cognition is possible. Although individual scientists may usefully vary in the criteria that they hold both for entertaining and endorsing anomalous cognition, we provide arguments for why researchers should consider adopting a liberal criterion for entertaining anomalous cognition while maintaining a very strict criterion for the outright endorsement of its existence. Grounded in an understanding of the justifiability of disparate views on the topic, the authors encourage humility on both the part of those who present evidence in support of anomalous cognition and those who dispute the merit of its investigation.