Algorithms and approaches for continual reinforcement learning have gained increasing attention. Much of this early progress rests on the foundations and standard practices of traditional reinforcement learning, without questioning if they are well-suited to the challenges of continual learning agents. We suggest that many core foundations of traditional RL are, in fact, antithetical to the goals of continual reinforcement learning. We enumerate four such foundations: the Markov decision process formalism, a focus on optimal policies, the expected sum of rewards as the primary evaluation metric, and episodic benchmark environments that embrace the other three foundations. Shedding such sacredly held and taught concepts is not easy. They are self-reinforcing in that each foundation depends upon and holds up the others, making it hard to rethink each in isolation. We propose an alternative set of all four foundations that are better suited to the continual learning setting. We hope to spur on others in rethinking the traditional foundations, proposing and critiquing alternatives, and developing new algorithms and approaches enabled by better-suited foundations.