Moore's Problem with Iterated Belief

G.E. Moore's problem is to explain what is odd about sentences such as 'It is raining but I do not believe it'. This sentence is unbelievable whether read commissively as ' p & B ^{˜/sup> p ', or omissively as ' p} & ^{˜/sup> B p '. However, this symmetry is broken when the belief operator is iterated many times. Whereas the commissive ' p & BBBBBBBBBB˜} p ' preserves the oddity Moore first noted, ' p & ^˜BBBBBBBBBB p ' is believable and assertable. The usual explanations of what is odd about Moore's sentences use recursive rules. Hence they uniformly extend the prediction of oddity when the belief operator is iterated. My project is to show how the asymmetry of the iterated version can be respected.