He begins with a theory of justice, legal and moral, very much on the lines of Hobbes, except that he regards it as up to a certain point _a priori_. Here he is consistent throughout. As in his philosophical account of mathematics and physics, so also in his aesthetics and ethics, he retained, side by side with a strong empirical tendency, belief in certain irreducible _a priori_ forms without which our knowledge cannot be constituted. The pure ethical theory of justice, he says, bears to the political theory the relation of pure to applied mathematics. Injustice he holds to be the positive conception. It means the breaking into the sphere of another person's will to live. The self-affirmation of the will that appears in one individual body is extended to denial of the will that appears in other bodies. Justice consists in non-encroachment. There is a 'natural right,' or 'moral right,' of resistance to injustice by infliction of what, apart from the attempted encroachment, would be wrong. Either force or deception may be used; as either may be the instrument of injustice. The purely ethical doctrine of justice applies only to action; since only the not doing of injustice depends on us. With the State and its laws, the relation is reversed. The object of these is to prevent the suffering of injustice. The State is not directed against egoism, but has sprung out of a rationalised collective egoism. It has for its purpose only to avoid the inconvenient consequences of individual aggressions on others. Outside of the State, there is a right of self-defence against injustice, but no right of punishment. The punishment threatened by the State is essentially a motive against committing wrong, intended to supply the place of ethical motives for those who are insufficiently accessible to them. Actual infliction of it is the carrying out of the threat when it has failed, so that in general the expectation of the penalty may be certain. Revenge, which has a view to the past, cannot be justified ethically: punishment is directed only to the future. There is no right in any one to set himself up as a moral judge and inflict pain; but man has a right to do what is needful for social security. The criminal's acts are of course necessitated; but he cannot justly complain of being punished for them, since it is ultimately from himself, from what he is, that they sprang.