But he did not see, it seems, that it is equally irrelevant to speak of a freedom from a mathematical necessity in such a connexion; although this, as plainly as the other sense of the word, has no conceivable bearing on the point in dispute. If a volition were produced by the omnipotence of God, irresistibly acting on the human mind, still it would not be necessary, in the sense of Leibnitz, since it might and would have been different if God had so willed it; the contrary volition implying no contradiction. Is it not evident, that to suppose the mind may thus be bound to act, and yet be free because the contrary act implies no contradiction, is merely to dream of liberty, and to mistake a shadow for a substance? As the opposite of a volition implies no contradiction, says Leibnitz, so it is free from an absolute necessity; that is to say, it might have been different, nay, it must have been different, from what it is, provided its determining cause had been different. The same thing may be said of the motions of matter. We may say that they are also free, because the opposite motions imply no contradiction; and we only have to vary the force in order to vary the motion. Hence, freedom in this sense of the word is perfectly consistent with the absolute and uncontrolled dominion of causes over the will; for what can be more completely necessitated than the motions of the body? The demand of his own nature, which so strongly impelled Leibnitz to seek and cling to the freedom of the mind, as the basis of moral and accountable agency, could not rest satisfied with so unsubstantial a shadow. After all, he has felt constrained to have recourse to the hypothesis of a preëstablished harmony in order to restore, if possible, the liberty which his scheme of necessity had banished from the universe. It is no part of our intention to examine this obsolete fiction; we merely wish to show how essential Leibnitz regarded it to a solution of the difficulty under consideration. “I come now,” says he, “to show how the action of the will depends on causes; that there is nothing so agreeable to human nature as this dependence of our actions, and that otherwise we should fall into an absurd and insupportable fatality; that is to say, into the _Mohammedan fate_, which is the worst of all, because it does away with foresight and good counsel. However, it is well to explain how this dependency of our voluntary actions does not prevent that there may be at the bottom of things a marvellous spontaneity in us, which in a certain sense renders the mind, in its resolutions, independent of the physical influence of _all other creatures_. This spontaneity, _but little known hitherto_, which raises our empire over our actions as much as it is possible, _is a consequence of the system of preëstablished harmony_.” Thus, in order to satisfy himself that our actions are really free and independent of the physical influence of _other creatures_, he has