Even if we assumed that the position, the direction and the velocity of each atom of cerebral matter are determined at every moment of time, it would not at all follow that our psychic life is subject to the same necessity. For we should first have to prove that a strictly determined psychic state corresponds to a definite cerebral state, and the proof of this is still to be given. As a rule we do not think of demanding it, because we know that a definite vibration of the tympanum, a definite stimulation of the auditory nerve, gives a definite note on the scale, and because the parallelism of the physical and psychical series has been proved in a fairly large number of cases. But then, nobody has ever contended that we were free, under given conditions, to hear any note or perceive any colour we liked. Sensations of this kind, like many other psychic states, are obviously bound up with certain determining conditions, and it is just for this reason that it has been possible to imagine or discover beneath them a system of movements which obey our abstract mechanics. In short, wherever we succeed in giving a mechanical explanation, we observe a fairly strict parallelism between the physiological and the psychological series, and we need not be surprised at it, since explanations of this kind will assuredly not be met with except where the two series exhibit parallel terms. But to extend this parallelism to the series themselves in their totality is to settle _a priori_ the problem of freedom. Certainly this may be done, and some of the greatest thinkers have set the example; but then, as we said at first, it was not for reasons of a physical order that they asserted the strict correspondence between states of consciousness and modes of extension. Leibniz ascribed it to a preestablished harmony, and would never have admitted that a motion could give rise to a perception as a cause produces an effect. Spinoza said that the modes of thought and the modes of extension correspond with but never influence one another: they only express in two different languages the same eternal truth. But the theories of physical determinism which are rife at the present day are far from displaying the same clearness, the same geometrical rigour. They point to molecular movements taking place in the brain: consciousness is supposed to arise out of these at times in some mysterious way, or rather to follow their track like the phosphorescent line which results from the rubbing of a match. Or yet again we are to think of an invisible musician playing behind the scenes while the actor strikes a keyboard the notes of which yield no sound: consciousness must be supposed to come from an unknown region and to be superimposed on the molecular vibrations, just as the melody is on the rhythmical movements of the actor. But, whatever image we fall back upon, we do not prove and we never shall prove by any reasoning that the psychic fact is fatally determined by the molecular