either no valid proof has yet been given, or that there are several distinct duties which have been regarded as one. For all moral proofs, being philosophical, can only be drawn by means of rational knowledge from concepts, not like mathematics, through the construction of concepts. The latter science admits a variety of proofs of one and the same theorem; because in intuition a priori there may be several properties of an object, all of which lead back to the very same principle. If, for instance, to prove the duty of veracity, an argument is drawn first from the harm that a lie causes to other men; another from the worthlessness of a liar and the violation of his own self-respect, what is proved in the former argument is a duty of benevolence, not of veracity, that is to say, not the duty which required to be proved, but a different one. Now, if, in giving a variety of proof for one and the same theorem, we flatter ourselves that the multitude of reasons will compensate the lack of weight in each taken separately, this is a very unphilosophical resource, since it betrays trickery and dishonesty; for several insufficient proofs placed beside one another do not produce certainty, nor even probability. They should advance as reason and consequence in a series, up to the sufficient reason, and it is only in this way that they can have the force of proof. Yet the former is the usual device of the rhetorician. Secondly. The difference between virtue and vice cannot be sought in the degree in which certain maxims are followed, but only in the specific quality of the maxims (their relation to the law). In other words, the vaunted principle of Aristotle, that virtue is the mean between two vices, is false. * For instance, suppose that good management is given as the mean between two vices, prodigality and avarice; then its origin as a virtue can neither be defined as the gradual diminution of the former vice (by saving), nor as the increase of the expenses of the miserly. These vices, in fact, cannot be viewed as if they, proceeding as it were in opposite directions, met together in good management; but each of them has its own maxim, which necessarily contradicts that of the other. {INTRODUCTION ^paragraph 165} * The common classical formulae of ethics- medio tutissimus ibis; omne mimium vertitur in vitium; est modus in rebus, etc., medium tenuere beati; virtus est medium vitiorum et utrinque reductum- ["You will go most safely in the middle" (Virgil); "Every excess develops into a vice"; "There is a mean in all things, etc." (Horace); "Happy they who steadily pursue a middle course"; "Virtue is the mean between two vices and equally removed from either" (Horace).]- contain a poor sort of wisdom, which has no definite principles; for this mean between two extremes, who will assign it for me? Avarice (as a vice) is not distinguished from frugality (as a virtue) by merely