There is an increasing awareness that designers play a pivotal role in the ethical implications of their designs. Accounting for these implications is challenging, as designers are often confronted with a variety of stakeholders, with different interests, and different underlying moral values and standpoints. In order to make informed design choices, a moral inquiry is needed to reveal the relevant moral values and standpoints in a specific design context. Designers require methods to perform such inquiry. Socratic dialogue is a method in which a group of participants jointly finds an answer to a philosophical question. Socratic dialogue is mostly used in education and training. This abstract argues that Socratic dialogue can also be used to support moral inquiry in design and research contexts. The basic elements of a Socratic dialogue are described, and its use as a method for moral inquiry in design and the larger field of Human-Computer Interaction (HCI) is examined.