From Aristotle's doctrine of the mean

Missing the mark is possible in a virtually indefinite number of ways. A person aiming at a target can miss to the right, to the left, above, below; a crooked shot can glance off the target, etc. To hit the mark one must land a shot within a relatively small, more or less precisely defined, area. Just so, Aristotle suggests, what is excellent and commendable to do is definite and limited. There is a correspondingly vast, relatively unlimited, area for wrongs and shots that miss the mark:

Missing the mark is possible in many ways (for badness is a form of the indefinite, to use Pythagorean terms, and goodness a form of the definite), while success can be had only one way (which is why it is easy to err and hard to succeed -- easy to miss the mark and hard to hit it). (1106b29-33)

Now while hitting the mark is in this sense a much more precise matter than missing it, there is still room for variation within the shots that hit the mark. More than one shot can hit the bulls-eye of a good-sized target, and all such hits are scored the same. And a shot need not hit the exact center of the bulls-eye to be an excellent one. In the same way, Aristotle's simile suggests, virtue rarely demands a single precisely determined act, or an emotional reaction of a particular intensity, duration, frequency, etc. It rather demands that one's acts or emotions fall somewhere within a more or less precisely delineated range.


For example, the person who flees from every danger is cowardly; the person who does not flee from anything is rash. What is courageous, then, falls somewhere between these extremes; courage is "preserved by the observance of the mean" (1104a26). The same is true of temperance; what is temperate lies in a mean between the extremes of excessive enjoyment of sensual pleasures and deficient enjoyment of such pleasures. Similar things, Aristotle thinks, can be said for each virtue. There are important differences among the dispositions Aristotle calls virtues, of course; but each virtue involves the observance of a mean between extremes. One extreme consists in some sort of excess; another in some sort of deficiency, though (as I shall argue) this way of talking can mislead. Our task in trying to be good is to find these means and avoid these opposed extremes.
The means in question are "relative to us." What are we to make of this? Aristotle explains:

By the mean of a thing I mean what is equally distant from either extreme, which is one and the same for everyone; by the mean relative to us what is neither too much nor too little, and this is not the same for everyone. For instance, if ten are many and two few, we take the mean of the the thing if we take six; since it exceeds and is exceeded by the same amount; this then is the mean according to arithmetic proportion. But we cannot arrive thus at the mean relative to us. Let ten lbs. of food be a large portion for someone and two lbs. a small portion; it does not follow that a trainer will prescribe six lbs., for maybe even this amount will be a large portion, or a small one, for the particular athlete who is to receive it.... In the same way then one with understanding in any matter avoids excess and deficiency, and searches out and chooses the mean -- the mean, that is, not of the thing itself but relative to us. (1106a29-b8; cf. EE II.5, 1222a23-37)

"The mean according to arithmetic proportion" is a point, a fixed and determinate amount. We cannot arrive at the mean relative to us by this method, for at least four reasons. First, the mean relative to us need not be equidistant from two opposed extremes the way an arithmetic mean is. Secondly, unlike an arithmetic mean, the mean relative to us is "of considerable range and not indivisible" (On Generation and Corruption 334b26-30); by this Aristotle means that it is not an extensionless point. Thirdly, as we have seen, Aristotle's target simile suggests that there is room for variation among shots all of which hit the target. What virtue or excellence demands is not a fixed and determinate act or emotional response on a particular occasion, but that our acts and emotions fall within a certain more or less precisely delineated range. Aristotle himself points out that in practical matters the arithmetic mean is not particularly useful (see, e.g., Topics139b21, 149a35-b4; On the Heavens 312b2). Fourthly, each of us is different; the mean relative to us will consequently also be different, and cannot be determined without close attention to features of the persons to whom such means are relative and the circumstances in which those persons are placed. The importance of this will become clear when I turn in section II to discussing particular Aristotelian virtues.
Seen one way, then, the possibilities for error are indefinitely various. Any shot that misses the mark in any direction qualifies. There is a sense, then, in which the remark Aristotle quotes at 1106b35 -- "there is but one way to act nobly, many ways to act basely" -- is true. Seen another way, however, the recipe for such error is absolutely precise: any shot that lands anywhere beyond the fixed edge of the target counts. This comports well with what Aristotle says earlier about excellence of character, that there is nothing fixed and invariable about matters of excellent or virtuous conduct (1104a4-12); the excellent thing to do is anything which falls within a certain range. What is excellent depends upon circumstances, just as the appropriate amount of food or exercise does. It cannot be determined with arithmetic precision (1104a1-6).