My starting point for this paper is a problem in critical thinking pedagogy--the difficult of bringing students to a point where they are able, and motivated, critically to evaluate their own deeply held beliefs. I first interrogate the very idea of a deeply held belief, drawing upon Wittgenstein's idea of a framework belief--a belief that forms part of a 'scaffolding' for our thoughts--or of a belief that functions as a hinge around which other beliefs pivot. I then examine the role of deeply held beliefs, thus conceived, in our ways of being in the world, exploring the extent to which engagement with others whose deeply held beliefs differ from ours may be possible through imaginative 'travel'. Finally, I reflect upon the extent to which these imaginative moments also offer up opportunities for critical reflection upon our own deeply held beliefs and, thus, the possibility of changing or adapting those beliefs.