Those who despair of the possibility of proving the existence of God tend, naturally, to hold that knowledge of God's existence and of those religious claims that depend upon it can only be had, if it can be had at all, through some direct religious awareness or insight. On this view appeals to authority or to revelation rest on appeals to such insight, if it is agreed that the credentials of the revealing authority cannot be established by the methods of natural theology. It is common for debate between believers and sceptics who share this despair about the possibility of proof to take on an air of hopelessness and unreality because of a fundamental epistemological cleavage: on the one hand the believer has an allegedly cognitive experience and on the other the sceptic lacks and suspects it. I want in this paper to scrutinise some aspects of this division. I shall not do much to mitigate the pessimism of my earlier statements, since I think the division really is, in certain critical ways, an unbridgeable one. But it is worth while to come to a clearer understanding of its nature than I think some philosophers have. What follows has been influenced by reflection on recent controversies about the meaningfulness of religious discourse, but is not intended to be a contribution to them. Some of the best-known contributions, however, seem to me to have made the epistemological cleavage I have referred to seem even worse than it is.