Interpersonal disagreement happens all the time. How to properly characterize interpersonal disagreement and how to respond to it are important problems, but the existence of such disagreements at least is obvious. The existence of intrapersonal disagreement, however, is another matter. On the one hand, we do change our minds sometimes, especially when new evidence comes in, and so there is a clear enough sense in which we can be characterized as having disagreements with our past selves. But what about synchronic disagreements with ourselves? Are such cases possible, or is there something about the nature of belief that rules out the possibility of knowingly holding beliefs which cannot be rationally held at the same time? In this paper, I argue that there can be cases of intrapersonal synchronic disagreement, and that such disagreements can be deep, in the same way that interpersonal disagreements can be deep. For intrapersonal disagreements, just like interpersonal disagreements, can be grounded in conflicting frameworks for interpreting and reasoning about the world. I also argue that synchronic intrapersonal disagreements are peer disagreements. The paper ends with a discussion of four possible responses to interpersonal deep disagreements, concluding that if those responses are sometimes rational responses in the interpersonal case, then they are also sometimes rational responses in the intrapersonal case.