The ability to explain decisions made by AI systems is highly sought after, especially in domains where human lives are at stake such as medicine or autonomous vehicles. While it is often possible to approximate the input-output relations of deep neural networks with a few human-understandable rules, the discovery of the double descent phenomena suggests that such approximations do not accurately capture the mechanism by which deep neural networks work. Double descent indicates that deep neural networks typically operate by smoothly interpolating between data points rather than by extracting a few high level rules. As a result, neural networks trained on complex real world data are inherently hard to interpret and prone to failure if asked to extrapolate. To show how we might be able to trust AI despite these problems we introduce the concept of self-explaining AI. Self-explaining AIs are capable of providing a human-understandable explanation of each decision along with confidence levels for both the decision and explanation. For this approach to work, it is important that the explanation actually be related to the decision, ideally capturing the mechanism used to arrive at the explanation. Finally, we argue it is important that deep learning based systems include a "warning light" based on techniques from applicability domain analysis to warn the user if a model is asked to extrapolate outside its training distribution. For a video presentation of this talk see https://www.youtube.com/watch?v=Py7PVdcu7WY& .