Many have advocated for engaging publics with science as a way to advance various important goals: democratizing science, increasing social benefits, producing better science, and promoting trust. The enthusiasm for what public engagement can achieve has, however, been mitigated because of several problems. These include conflicts between goals, disagreements between scientists and publics about which of these goals are more important in particular cases, and implementation problems. Here we call attention to a deeper problem that has been neglected: the goals that public engagement is said to seek are ambiguous and can be conceptualized in a variety of distinct ways. We argue that conceptualized in certain ways, some of the goals are worth pursuing and their achievement could help transform knowledge production and further the positive effects on science in society. We show, however, that common engagement strategies are often inadequate as means to attain the goals so understood. Under other conceptualizations, achieving these goals, though not insignificant, is unlikely to produce substantial changes to the relationships between science and society. In these cases, engagement strategies might well constitute appropriate means, but it is not obvious that the benefits would be worth the costs. Finally, some possible conceptualizations of some of these goals would render them undesirable. Although some engagement strategies could achieve them, it is problematic to try to do so. The upshot of our arguments is that without clarifying the meaning of the goal that we hope to achieve by engaging the public with science, we are bound to make incorrect assessments both about the worthiness of the goal and whether it can be accomplished by engaging the public. These challenges do not show that public engagement with science should be abandoned, but they provide further reasons to temper our expectations regarding what public engagement can achieve and when it might be worth doing so.
