Software engineering is a knowledge-intensive process. Consequently, researchers typically understand any lack of knowledge as a problem that must be mitigated by improving, for instance, program comprehension, reverse engineering, community collaboration, or documentation. However, a lack of knowledge may not always be a problem. In fact, several studies in the field of ignorance research have highlighted the diversity of non-knowledge. We argue that non-knowledge can also be a useful concept for software-engineering research to provide a new lens on the domain. In this paper, we provide a brief overview on the research of non-knowledge and ignorance phenomena, and suggest a working definition of non-knowledge for software-engineering research. Then, we sketch how the concept of non-knowledge can benefit future research within this domain and propose three concrete directions to investigate. We envision that non-knowledge contributes a new lens to manage the complexity of intellectual capital and knowledge in modern software engineering. With this paper, we hope to motivate and guide future research into this direction.