Attention to epistemological relationships between Indigenous and local knowledges (ILK) and conservation science is increasing. Some approaches for doing so have been developed, but in general, serious engagement between ILK and science still feels experimental and does not have broad uptake. Here we address some of the main issues that arise when considering the epistemological relationships between ILK and conservation or ecological science. A key issue is the relationship between ILK and science that sets the expectations for how they may form dialogues, collaborations, or co-production. After reviewing several perspectives on this relationship, and their limitations, we suggest that a focus on shared meanings within an ‘ethic of equivocation’ is a productive path forward. In an ethic of equivocation, neither ILK nor science validates the other, yet meaning can be created. We explain and develop the concepts of meanings and equivocation in the ILK-science context. We, thus, argue for a broad and rich understanding of the joint roles of ILK and science, which goes beyond treating ILK as a data source. We argue that diverse styles of reasoning exist in science, and scientists may already treat observations, models, and collaborations in the ways that we discuss, providing ready-made analogies for thinking about ILK. We also discuss how to avoid abuses of power while engaging with ILK to co-produce new knowledge.