"Human good turns out to be activity of soul in accordance with excellence" (Nicomachean Ethics, I 7, 1098al6-17).
Can Aristotle show that excellence includes moral virtue?

The essay title's question is quite ambiguous as to its intended focus of interest.  On the one hand, it can be read as inquiring about how Aristotle demonstrates that his concept of the "moral virtues" constituted at least part of his concept of "excellence".  But Aristotle does not attempt to demonstrate this.  Aristotle makes use of a single Greek word (areté) that is translated into English as both "excellence" and as "virtue".  So that excellence includes the virtues as simply a matter of synonymous translation.

On the other hand, the title question can be read as inquiring about how Aristotle demonstrates that his concept of areté includes the particular list of character traits that he considers to be the moral virtues.  But Aristotle does not attempt to demonstrate that his concept of areté includes the moral virtues he identifies.  He makes it very clear that he is examining how his fellow Athenian citizens employ the concept of "a good man".  He takes it as given that his fellow citizens consider the virtues an integral part of what it is to be "a good man".  He does not attempt to show that areté includes those character traits that he identifies. 

Part 1 -- Excellence just IS Virtue

The notion of virtue as excellence was suggested by Socrates/Plato but refined and extended by Aristotle.  Like his predecessor(s), Aristotle held that it is the soul of the person that is virtuous, and that it is virtuous when it attains "the good for man as such."  That is, when the virtuous man achieves a good which is not subordinate to any other good; all other goods being subordinate to it.  So what is the "good for man as such"? 

Aristotle observes that we all agree that it is "eudaimonia."  Note that Aristotle's term "eudaimonia", which has usually been translated as "happiness," means much more than what we normally associate with the English word.  In Aristotle's lexicon, eudaimonia means "living well and faring well."(NE 1.4)  This is quite different from the feeling of well-being that we think of as constituting happiness.  More recent translations of Aristotle have used the phrase "human flourishing" instead because "happiness" is a state of mind, and Aristotle is quite clear that eudaimonia is to be understood as an activity. 

Now, Aristotle does not attempt to "show" (argue, reason, or provide support for a premise) that excellence includes moral virtue.  Rather he stipulates that the moral virtues are those excellences of the activities of the soul that are in accordance with the telos (purpose, function) of Man (qua Man) within the polis.  As indicated above, the very Greek word (areté) that is normally translated into English as "virtue" can also be translated as "excellence".  Hence the title question can be understood as inquiring whether Aristotle shows that excellence includes moral excellence.

But again, the answer to this question is a matter of stipulation.  Aristotle distinguishes two kinds of virtue (NE 1.13): those that pertain to the part of the soul that engages in reasoning (virtues of mind or intellect), and those that pertain to the part of the soul that cannot itself reason but is nonetheless capable of following reason (ethical virtues, virtues of character).  Hence Aristotle is stipulating and not showing that excellence includes moral virtue.
In the text of the Nicomachean Ethics, just preceding the quote in the essay title, Aristotle lays out the reasoning for which the title quote is the conclusion.  All human activity is teleological -- all activity is in pursuit of some goal. 

"Every art and every inquiry, and similarly every action and pursuit, is thought to aim at some good; and for this reason the good has rightly been declared to be that at which all things aim." (NE 1.1) 

There is a hierarchy of these goods at which various activities aim.  Lesser goods are instrumental in the pursuit of (or perhaps partially constitutive of) greater goods. 

"But where such arts fall under a single capacity . . . in all of these the ends of the master arts are to be preferred to all the subordinate ends; for it is for the sake of the former that the latter are pursued." (NE 1.1) 

The top of this hierarchy will be the final or highest goal of human activities -- something which is pursued for its own sake, and not for the sake of any other goal. 

"Since there are evidently more than one end, and we choose some of these . . . for the sake of something else, clearly not all ends are final ends; but the chief good is evidently something final.  Therefore, if there is only one final end, this will be what we are seeking, and if there are more than one, the most final of these will be what we are seeking.  Now we call that which is in itself worthy of pursuit more final than that which is worthy of pursuit for the sake of something else, and that which is never desirable for the sake of something else more final than the things that are desirable both in themselves and for the sake of that other thing, and therefore we call final without qualification that which is always desirable in itself and never for the sake of something else." (NE 1.7)

This final goal Aristotle calls eudaimonia.  Eudaimonia is the one goal that we pursue for itself alone, and not as a means (instrumental or constitutive) of any other end.

"Now such a thing [i.e the highest good] eudaimonia, above all else, is held to be; for this we choose always for itself and never for the sake of something else, but honour, pleasure, reason, and every virtue we choose indeed for themselves (for if nothing resulted from them we should still choose each of them), but we choose them also for the sake of eudaimonia, judging that by means of them we shall be happy.  Eudaimonia, on the other hand, no one chooses for the sake of these, nor, in general, for anything other than itself." (NE 1.7)

Aristotle then proceeds to examine just what this eudaimonia must be if it is the "highest good".  And he approaches this analysis from the starting point of how his fellow Athenian citizens employ the concept "good" in normal conversation. 

"For just as for a flute-player, a sculptor, or an artist, and, in general, for all things that have a function or activity, the 'good' and the 'well' is thought to reside in the function, so would it seem to be for man, if he has a function." (NE 1.7)

In sharp contrast with the modern understanding of the "ethical good", Aristotle is setting up a clearly functional concept.  To be properly called a "good flute-player" one must fulfill with excellence the function of a flute-player.  And by analogy, Aristotle concludes that to be properly called a "good man" one must fulfill with excellence the function of a man (if he has one).  The two key observations to note here are: (i) the word that Aristotle actually employs in this passage is "areté"; and (ii) he is taking his cue from the standard linguistic practice of his community. 

In its ancient Greek usage, the concept of "areté" was closely linked with the notion of the fulfillment of purpose or function: the act of performing up to one's full potential.  Hence a flute player who fulfilled his function, who lived up to his full potential as a flute-player would, in common linguistic practice, be labelled "areté".  Likewise, an axe that performed up to its full potential would also be labelled "areté".  Aristotle is arguing that analogously a man who fulfills his function (if he has one), who lives and performs up to his full potential as a man, should also properly be labelled "areté".

Aristotle next explores what might be the proper function ("ergon") of man.  For various reasons we need not go into at this point, he concludes that the proper function of man is "life of the rational element".  (In order to address the specific question of the essay title, we need not explore here the plausibility of Aristotle's choice of man's proper function.) 

"Now if the function of man is an activity of soul which follows or implies a rational principle, and if we say 'a so-and-so' and 'a good so-and-so' have a function which is the same in kind, . . . eminence in respect of goodness being added to the name of the function . . . : if this is the case, and we state the function of man to be a certain kind of life, and this to be an activity or actions of the soul implying a rational principle, and the function of a good man to be the good and noble performance of these, and if any action is well performed when it is performed in accordance with the appropriate excellence: if this is the case, human good turns out to be activity of soul in accordance with virtue, and if there are more than one virtue, in accordance with the best and most complete." (NE 1.7)

Notice particularly how Aristotle sets up his reasoning in this last quote:

IF the ergon (proper function) of man is an activity of soul which follows or implies
            a rational principle;
and
IF standard linguistic practice is that eminence in respect of areté (excellence / virtue)
            is added to the name of the ergon;
and
IF any action is well performed when it is performed in accordance with the standards
            of areté appropriate to the particular ergon;
THEN human good turns out to be activity of soul in accordance with the appropriate
            standards of "goodness", "excellence", or "virtue".

In other words, on one possible reading, the question that is the focus of the essay title is based on a misunderstanding of the English translations of Aristotle.  In the ancient Greek in which Aristotle wrote, "excellence" just is "virtue".  And the moral virtues are those excellences that are excellences of soul simply as a consequence of the then common usages of those words.

Part 2 -- Excellence in a Social Context

Aristotle's analysis is based on an examination of how his fellow Athenian speakers of Greek, people with whom he is familiar, actually employ the concept of a "good man".  He is not attempting to provide an a priori analysis, or an ex cathedra declaration of how we ought to employ the label of a "good man".  Hence his starting point is an examination of how his fellow Greek citizens actually do, in fact, employ the label.  So it is quite understandable that he would conclude in his concept of the appropriate standards of "goodness", "excellence", or "virtue" those elements of character that would be admired, respected, and commended by the cognoscenti of his local polis.  Hence, those character traits that Aristotle labelled "moral virtues" are character traits that people living in a particular community actually did hold in high regard as positively contributing to the welfare of that community. 

"We do not mean that which is sufficient for a man by himself, for one who lives a solitary life, but also for parents, children, wife, and in general for his friends and fellow citizens, since man is born for citizenship." (NE 1.7) 

For Aristotle, man derives his sense of identity, his purpose, from his role as part of an existing community -- including friends, customs, institutions, and laws.  Aristotle does not conceive of the individual as prior to or independent of the community.  Thus, moral virtues -- the excellences of soul we are seeking -- are essentially social and political in nature.  For Aristotle, his study of ethics starts with the actual moral judgments of his community, before he can approach the formulation of general principles

Aristotle does not explore, and hence offers no reply to, the many challenges that philosophers since his time have offered to the effect that "human good" is not to be so analyzed.  Similarly, Aristotle does not explore, and hence offers no rebuttal to, the many challenges raised by philosophers since his time of, the possibility that man (qua man) has other "proper functions" than the one that Aristotle elects as his foundation.

Hence, given his purpose and starting point, it is quite understandable that for Aristotle, it is not a matter of showing that the standards of excellence by which we judge that a man is a "good man" include the moral virtues, or that the moral virtues include those socially valued character traits he does in fact pick out.  For Aristotle, the socially esteemed character traits just are those standards of excellence that apply when his fellow Athenian speakers of Greek identify a man as "good".

References

Aristotle, The Nicomachean Ethics, Translated and introduced by David Ross, revised by J.L. Ackrill and J.O. Urmson;  Oxford University Press, Oxford, England. 1980.  ISBN 0-19-283407-x

Cooper, John M., Reason and Human Good in Aristotle, Hackett Publishing Company, Indianapolis, Indiana, 1986. ISBN 0-87200-022-1.

Hughes, Gerard J., Routledge Philosophy Guidebook to Aristotle on Ethics, Routledge (The Taylor & Frances Group), New York, New York, 2001. ISBN 0-415-22187-0.

Kraut, Richard, "Aristotle's Ethics", The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.), URL=<http://plato.stanford.edu/archives/fall2009/entries/aristotle-ethics/>.

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