The Rule of Law is a foundational value of the modern democratic state. It contains within its most influential conceptualizations key legal principles to reduce arbitrariness in the exercise of power, and in doing so promoting legal certainty and individual autonomy, while protecting against despotism. A growing body of research points to the potential for AI to undermine Rule of Law values, especially when implemented in the exercise of public power. This contribution attempts to approach these concerns through four critical dichotomies. These dichotomies are intended to assist in underpinning a theoretical foundation for a critical analysis of AI, assisting in structuring previously diverse explorations into Rule of Law concerns along more fundamental analytical lines.