Certain aspects of the explainability of AI systems will be critically discussed. This especially with focus on the feasibility of the task of making every AI system explainable. Emphasis will be given to difficulties related to the explainability of highly complex and efficient AI systems which deliver decisions whose explanation defies classical logical schemes of cause and effect. AI systems have provably delivered unintelligible solutions which in retrospect were characterized as ingenious (for example move 37 of the game 2 of AlphaGo). It will be elaborated on arguments supporting the notion that if AI-solutions were to be discarded in advance because of their not being thoroughly comprehensible, a great deal of the potentiality of intelligent systems would be wasted.
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