Abstract:We argue that the attempt to build morality into machines is subject to what we call the Interpretation problem, whereby any rule we give the machine is open to infinite interpretation in ways that we might morally disapprove of, and that the interpretation problem in Artificial Intelligence is an illustration of Wittgenstein's general claim that no rule can contain the criteria for its own application. Using games as an example, we attempt to define the structure of normative spaces and argue that any rule-following within a normative space is guided by values that are external to that space and which cannot themselves be represented as rules. In light of this problem, we analyse the types of mistakes an artificial moral agent could make and we make suggestions about how to build morality into machines by getting them to interpret the rules we give in accordance with these external values, through explicit moral reasoning and the presence of structured values, the adjustment of causal power assigned to the agent and interaction with human agents, such that the machine develops a virtuous character and the impact of the interpretation problem is minimised.