Anyone familiar with Matthew Lipman's Community of Inquiry is likely to acknowledge that it cultivates open-mindedness. Even so, bare recognition of this fact is not the same as having a detailed knowledge of what open-mindedness involves and how the Community of Inquiry helps to foster it. To extend our knowledge of these matters, we will conduct a psychological analysis of the dispositions, abilities and skills involved in open-mindedness and show how the Community of Inquiry helps to develop them. Coming to appreciate what is involved in this way deepens our understanding of what we are doing in the Community of Inquiry and enables us to be more attentive to these matters in practice.