Believing (n.) means submitting to an authority; once submitted, you cannot question it and then find it convincing again without rebelling.
Believing (n.) taken as an activity going on while we say we believe is something similar to expressing a belief, or the same thing.
Believing (n.) and not believing refer to various differences in different cases, a family, not the presence or absence of one mental state.
Believing (n.) has a grammar worth marvelling at: 'believe', 'hope', 'wish' take every grammatical form that 'eat', 'talk', 'cut' do.
Believing (n.) first done by a child shows when the utterance begins a game he can go on with; how a game suddenly becomes clear, God only knows.