In this Letter, we propose a mechanism for driving bioinspired fish swimming locomotion based on proprioceptive sensing. Proprioception provides information about and representation of a body's position, motion, and acceleration in addition to the usual five senses. We hypothesize that a feedback loop based on this "sixth" sense results in an instability, driving the locomotion. In order to test our assumptions, we use a biomimetic robot and compare the experimental results to a simple yet generic model with excellent agreement.