formulated belief

A distinct belief of that kind, not a vague, pulpy impression, but a formulated belief, exists, we know, in the most unsuspected places, its holders not unfrequently professing Christianity, as at all events the best of the illusions; and it has sunk very far down in the ladder of society.

On Van's part it arose from forlornness mingled with a half formulated belief that he must do something to express his thankfulness that he himself had escaped from the fate that had overtaken the child.