Abstract: The principle of indifference, which says that the probabilities of two or more events are equal if there is no known reason to think that one will occur rather than any one of the others, appears to give inconsistent results in certain problem cases (the book paradox, Bertrand's chord problem, the perfect cube factory problem, the water-wine paradox). As a result, it is widely held to be false. I will attempt a general solution to the problem, which I hope might go some way towards saving the principle of indifference.