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 being the lat pushed too far; but has a quite different principle; (maxim), namely placing the end of economy not in the enjoyment of one’s means, but in the mere possession of them, renouncing enjoyment; just as the vice of prodigality is not to be sought in the excessive enjoyment of one’s means, but in the bad maxim which makes the use of them, without regard to their maintenance, the sole end.

For the same reason, no vice can be defined as an excess in the practice of certain actions beyond what is proper (e.g., Prodigalitas est excessus in consumendis opibus); or, as a less exercise of them than is fitting (Avaritia est defectus, etc.).  For since in this way the degree is left quite undefined, and the question whether conduct accords with duty or not, turns wholly on this, such an account is of no use as a definition.

Thirdly.  Ethical virtue must not be estimated by the power we attribute to man of fulfilling the law; but, conversely, the moral power must be estimated by the law, which commands categorically; not, therefore, by the empirical knowledge that we have of men as they are, but by the rational knowledge how, according to the ideas of humanity, they ought to be.  These three maxims of the scientific treatment of ethics are opposed to the older apophthegms: 

{Introduction ^paragraph 170}

1.  There is only one virtue and only one vice.

2.  Virtue is the observance of the mean path between two opposite vices.