A key requirement for seamless human-robot collaboration is for the robot to make its intentions clear to its human collaborator. A collaborative robot's motion must be legible, or intent-expressive. Legibility is often described in the literature as and effect of predictable, unsurprising, or expected motion. Our central insight is that predictability and legibility are fundamentally different and often contradictory properties of motion. We develop a formalism to mathematically define and distinguish predictability and legibility of motion. We formalize the two based on inferences between trajectories and goals in opposing directions, drawing the analogy to action interpretation in psychology. We then propose mathematical models for these inferences based on optimizing cost, drawing the analogy to the principle of rational action. Our experiments validate our formalism's prediction that predictability and legibility can contradict, and provide support for our models. Our findings indicate that for robots to seamlessly collaborate with humans, they must change the way they plan their motion.