This paper argues that an AI judge is conceptually undesirable and not just something that lies beyond the state of the art in computer science. In a nutshell, even if an AI system could accurately predict how a good human judge would decide a particular case, its prediction would be the product of correlations between such factors as patterns of syntax in bodies of legal texts. This approach of AI systems is insufficient for basing their output on the sort of rationales that are expected of valid judicial decisions in any desirable legal system. Thus, by their very nature, AI systems are incapable of providing valid legal decisions in any such system.