According to Matthew Lipman, one of the founders of the Philosophy for Children (P4C) programme, critical thinking improves reasonableness and the exercise of good judgement, both of which Lipman takes to be necessary to sustaining a democratic society. Against his view, I argue that although critical thinking can be done well or badly, it does not necessarily lead to the exercise of good judgement given that the value of judgements is not purely a matter of mere algorithmic calculation or instrumental means/end reasoning. The fact that Lipman's critical thinking approach does not justify the values that guide the community of inquiry may potentially lead to epistemic injustice within the community. One way to avoid this threat is to justify the programme's meta-philosophical assumptions by articulating and seeking to justify its epistemological foundations. I discuss different attempts to do this, arguing that none of the epistemological foundations offered can support P4C's basic assumption that critical thinking entails good judgement (where this is conceived of as a constitutively normative ability that meets the standards of ‘practical wisdom’ or moral virtue). Given these inconsistencies and lacunae, I offer a new perspective on how the process of inquiry could be conceived. Developing ideas outlined by Gilbert Ryle and Ludwig Wittgenstein, I argue that the process of inquiry may be valuable if conceived of as conceptual analysis that aims at perspicuous representations.