Is trust in science a good thing?

Abstract This paper discusses three different versions of the title question. First, it addresses the question of whether trust, as a special form of shaping interpersonal relationships of reliance, is the right form to aspire to in the case of the relationship of the public to science. Would it be better to strive for plain reliance? Second, when we talk about public trust in democratic politics, distrust is often considered at least as important as trust. Can this be applied to public trust in science? Or are there reasons that make distrust specifically problematic in the epistemic context? Third, while trust has been argued to be indispensable both within science and with regard to the reliance of the public on science, advocates of open science appear to consider this obsolete in light of the replicability debate and the intended changes to improve the odds for replications. Is substituting control for trust a viable path to epistemic improvement?