Higher‐order evidence and losing one's conviction

There has been considerable puzzlement over how to respond to higher-order evidence. The existing dilem-mas can be defused by adopting a ‘two-dimensional’ representation of doxastic attitudes which incorporates not only substantive uncertainty about which first-order state of affairs obtains but also the degree of conviction with which we hold the attitude. This makes it possible that in cases of higher-order evidence the evidence sometimes impacts primarily on our conviction, rather than our substantive uncertainty. I argue that such a two-dimensional representation is naturally developed by making use of imprecise probabilities.