Aristotle now sets himself to find a definition of virtue, per genus et differentiam.  There are three qualities in the Soul—­Passions [Greek:  pathae], as Desire, Anger, Fear, &c., followed by pleasure or pain; Capacities or Faculties [Greek:  dynameis], as our capability of being angry, afraid, affected by pity, &c.; Fixed tendencies, acquirements, or states [Greek:  hexeis].  To which of the three does virtue or excellence belong?  It cannot be a Passion; for passions are not in themselves good or evil, and are not accompanied with deliberate choice [Greek:  prouiresis], will, or intention.  Nor is it a Faculty:  for we are not praised or blamed because we can have such or such emotions; and moreover our faculties are innate, which virtue is not.  Accordingly, virtue, or excellence, must be an acquirement [Greek:  hexis]—­a State (V.).  This is the genus.

Now, as to the differentia, which brings us to a more specific statement of the doctrine of the Mean.  The specific excellence of virtue is to be got at from quantity in the abstract, from which we derive the conceptions of more, less, and equal; or excess, defect, and mean; the equal being the mean between excess and defect.  But in the case of moral actions, the arithmetical mean may not hold (for example, six between two and ten); it must be a mean relative to the individual; Milo must have more food than a novice in the training school.  In the arts, we call a work perfect, when anything either added or taken away would spoil it.  Now, virtue, which, like Nature, is better and more exact than any art, has for its subject-matter, passions and actions; all which are wrong either in defect or in excess.  Virtue aims at the mean between them, or the maximum of Good:  which implies a correct estimation of all the circumstances of the act,—­when we ought to do it—­under what conditions—­towards whom—­for what purpose—­in what manner, &c.  This is the praise-worthy mean, which virtue aspires to.  We may err in many ways (for evil, as the Pythagoreans said, is of the nature of the Infinite, good of the Finite), but we can do right only in one way; so much easier is the path of error.

Combining then this differentia with the genus, as above established, the complete definition is given thus—­’Virtue is an acquirement or fixed state, tending by deliberate purpose (genus), towards a mean relative to us (difference).’  To which is added the following all-important qualification, ’determined by reason [Greek:  logos], and as the judicious man [Greek:  ho Phronimos] would determine.’  Such is the doctrine of the Mean, which combines the practical matter-of-fact quality of moderation, recognized by all sages, with a high and abstract conception, starting from the Pythagorean remark quoted by Aristotle, ’the Infinite, or Indefinite, is evil, the Finite or the Definite is good,’ and re-appearing in Plato