So now we have seen the influence of the two first aspects of the die—the causes, and the number and indifference of the sides—and have learned how they give a push to our thought, and divide that push into as many parts as there are sides. We must now look into the effects of •the third factor, namely the figures inscribed on the sides. Obviously, where several sides have the same figure inscribed on them, they must work together in their influence on the mind, bringing to bear on one image or idea of the figure all those divided pushes that were scattered over the several sides that have that figure on them. If we were asking ‘Which side will fall uppermost?’, all the sides would be perfectly equal, and no-one could have any advantage over any other. But the question is ‘Which figure will fall uppermost?’; and as the same figure is exhibited by more than one side, it is obvious that the pushes belonging to all those sides must come together on that one figure, and become stronger and more forcible by their union. In our example, four sides have a circle, two have a square. The pushes on the circle are therefore more numerous than the pushes on the square. But as the outcomes are contrary—it can’t happen that circle and square both turn up in a single throw—the pushes likewise become contrary; the weaker force destroys the stronger as far as it has strength to do so; ·and what remains of the stronger one after the weaker has expended itself is the mind’s probabilityjudgment about the outcome·. The liveliness of the idea is always proportional to the degrees of the push or tendency to make the transition; and according to my doctrine that liveliness of the idea is belief.