Machine intelligence already helps medical staff with a number of tasks. Ethical decision-making, however, has not been handed over to computers. In this proof-of-concept study, we show how an algorithm based on Beauchamp and Childress' prima-facie principles could be employed to advise on a range of moral dilemma situations that occur in medical institutions. We explain why we chose fuzzy cognitive maps to set up the advisory system and how we utilized machine learning to train it. We report on the difficult task of operationalizing the principles of beneficence, non-maleficence and patient autonomy, and describe how we selected suitable input parameters that we extracted from a training dataset of clinical cases. The first performance results are promising, but an algorithmic approach to ethics also comes with several weaknesses and limitations. Should one really entrust the sensitive domain of clinical ethics to machine intelligence?