In On Certainty (1969), Ludwig Wittgenstein writes that certain beliefs make up the ‘inherited background’ against which thinking takes place. Wittgenstein’s phrase can be interpreted as referring to deep, fundamental, or core beliefs that are acquired by being raised in a particular community. This thesis is an exploration of a range of questions concerning rationality and justification that are invited by this idea of an inherited background. I defend the common sense position that the rational response to challenges to one’s inherited core beliefs is to reflect on what justifies those beliefs. In Chapters One and Two I consider certain Wittgensteinian arguments, due to P. F. Strawson and Anthony Kenny, according to which it is not worth engaging in this kind of reflection because our most fundamental beliefs are necessarily unjustifiable. I present several interpretations of these arguments and argue that on each reading they are unsuccessful. In Chapter Three I consider the implications of the fact that some inherited core beliefs – for example in the domains of ethics, politics, and religion – are subject to reasonable disagreement. I argue that the rational response to disagreement is to seek justification for one’s beliefs, and criticise another Wittgensteinian argument, due to Allan Hazlett, that denies this. In Chapters Four and Five I take up the question of whether the fact that one has inherited one’s core beliefs somehow undermines those beliefs. I reject a range of arguments that aim to show that such beliefs are rationally problematic given their origins or ‘genealogy’. I also argue that having inherited one’s core beliefs does not necessarily undermine one’s intellectual autonomy. The rational response to the fact that one has inherited one’s core beliefs is to critically reflect on those beliefs and on how one ended up holding them.