An impossibility theorem demonstrates that a particular problem or set of problems cannot be solved as described in the claim. Such theorems put limits on what is possible to do concerning artificial intelligence, especially the super-intelligent one. As such, these results serve as guidelines, reminders, and warnings to AI safety, AI policy, and governance researchers. These might enable solutions to some long-standing questions in the form of formalizing theories in the framework of constraint satisfaction without committing to one option. This is the most prudent approach to long-term AI safety initiatives. In this paper, impossibility theorems applicable to AI have been categorized into five mechanism-based categories: deduction, indistinguishability, induction, tradeoffs, and intractability. Certain theorems are too specific or have implicit assumptions that limit application. Also, new results (theorems) are added, such as the unfairness of explainability — an inherent strategic inequality in explainability — the first explainability-related result in the induction category. The remaining results deal with misalignment between the clones and put a limit to the self-awareness of agents. Deductive impossibilities deny 100%-guarantees for security. In the end, the paper gives some ideas that hold potential in explainability, controllability, value alignment, ethics, and group decision-making. They can be deepened by further investigation. Since proofs of 100% guarantees of safety can never be obtained, while probabilistic guarantees are attainable, safety work should pursue uncertain inference (impossibilities are a lot less strict when including uncertainty in inference); and keeping a human-in-the-loop — the system being receptive to information from humans — is a necessary attribute of a safe system, complemented by an option to “undo” the system’s actions.
Invest more effort in a more rigorous formalization of alignment. Research the formalization and disentangling of the structure and assumptions of explicit control; advanced forms and notions of control should at least resolve the status of control over oneself. Research the status of controllability and tradeoffs with risk for other forms of control (implicit, aligned, delegated).