Before revision:  Building on recent philosophical work on the nature of explanations, I demonstrate the significance of two non-data driven, non-causal explanatory elements: (1) mathematical structures that are the grounds for capturing the decision-making situation; (2) statistical and optimality facts in terms of which the algorithm is designed and implemented. I argue that these elements feature directly in important aspects of AI explainability. I then propose a hierarchical framework that acknowledges the existence of various types of explanation, each of which reveals an aspect of explanation, and answers to a different kind of why-question. The usefulness of this framework will be illustrated by bringing it to bear on some salient normative concerns about the use of AI decision-making systems in society .
After revision:  Building on recent philosophical work on the nature of explanations, I demonstrate the significance of two non-data driven, non-causal explanatory elements: (1) mathematical structures that are the grounds for capturing the decision-making in sensitive contexts have generated lively debates among multiple stakeholders, such as moral and political philosophers, computer scientists, and the public. Yet, the lack of a common language and a conceptual framework for an appropriate bridging of the moral, technical, and political aspects of the debate prevents the discussion to be as effective as it can be. Social scientists and psychologists are contributing to this debate by gathering a wealth of empirical data, yet a philosophical analysis of the social implications of algorithmic decision-making systems in society .