Why is it that some instances of disagreement appear to be so intractable? And what is the appropriate way to handle such disagreements, especially concerning matters about which there are important practical and political needs for us to come to a consensus? In this paper, I consider an explanation of the apparent intractability of deep disagreement offered by hinge epistemology. According to this explanation, at least some deep disagreements are rationally unresolvable because they concern ‘hinge’ commitments that are unresponsive to rational considerations. This explanation, if correct, seems to have troubling implications for how we should respond to deep disagreement. If my position on a topic is not responsive to rational considerations, then what choice have I but to dogmatically hold to that position, and simply dismiss the views of those with whom I disagree? I address this problem by identifying an attitude of intellectual humility that is appropriate to have towards one's hinge commitments, and suggest that this attitude provides the basis for a non-rational, constructive way to resolve deep disagreement.