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We argue that, to be trustworthy, Computational Intelligence (CI) has to do what it is entrusted to do for permissible reasons and to be able to give rationalizing explanations of its behavior which are accurate and graspable. We support this claim by drawing parallels with trustworthy human persons, and we show what difference this makes in a hypothetical CI hiring system. Finally, we point out two challenges for trustworthy CI and sketch a mechanism which could be used to generate sufficiently accurate as well as graspable rationalizing explanations for CI behavior.