In their important paper “Autonomous Agents”, Floridi and Sanders use “levels of abstraction” to argue that computers are or may soon be moral agents. In this paper we use the same levels of abstraction to illuminate differences between human moral agents and computers. In their paper, Floridi and Sanders contributed definitions of autonomy, moral accountability and responsibility, but they have not explored deeply some essential questions that need to be answered by computer scientists who design artificial agents. One such question is, “Can an artificial agent that changes its own programming become so autonomous that the original designer is no longer responsible for the behavior of the artificial agent?” To explore this question, we distinguish between LoA1 (the user view) and LoA2 (the designer view) by exploring the concepts of unmodifiable, modifiable and fully modifiable tables that control artificial agents. We demonstrate that an agent with an unmodifiable table, when viewed at LoA2, distinguishes an artificial agent from a human one. This distinction supports our first counter-claim to Floridi and Sanders, namely, that such an agent is not a moral agent, and the designer bears full responsibility for its behavior. We also demonstrate that even if there is an artificial agent with a fully modifiable table capable of learning* and intentionality* that meets the conditions set by Floridi and Sanders for ascribing moral agency to an artificial agent, the designer retains strong moral responsibility.