   One of the theoretical advantages of thinking of intuitions as intellectual seemings is that we can allow for this mismatch between our intuitions and our beliefs. Just as something can seem perceptually to be a certain way while we don’t believe it is that way, as in Müller-Lyer cases, so a proposition can seem intellectually to be true even though we do not believe it. Since such seemings are not beliefs, this does not commit intuitionists to the view that a conflict between our intuitions and beliefs entails contradictory beliefs.