Nicomachean Ethics IX.10

How many friends should one keep? 

Should we, then, make as many friends as possible, or-as in the case of hospitality it is thought to be suitable advice, that one should be 'neither a man of many guests nor a man with none'-will that apply to friendship as well; should a man neither be friendless nor have an excessive number of friends?

To friends made with a view to utility this saying would seem thoroughly applicable; for to do services to many people in return is a laborious task and life is not long enough for its performance. Therefore friends in excess of those who are sufficient for our own life are superfluous, and hindrances to the noble life; so that we have no need of them. Of friends made with a view to pleasure, also, few are enough, as a little seasoning in food is enough. 

Favors to the useful have to be repaid, so you don't want too many of that sort; and those you keep around only for fun can be few in number, since who has time for much fun? The world is full of work to do. 

But as regards good friends, should we have as many as possible, or is there a limit to the number of one's friends, as there is to the size of a city? You cannot make a city of ten men, and if there are a hundred thousand it is a city no longer.

There's an interesting question: are our cities not cities in Aristotle's sense, some of them containing millions? They remain polities of a sort -- a few of them, like Singapore, almost in Aristotle's sense. Hong Kong, perhaps, until the Communists took it back. Have we lost something essential to human community by becoming too many?

In ancient Athens, though it was a great city in its era, at least the key people could all know each other. To some degree that's true in small towns today. It seems as if a better community ought to be possible when we can all get to know one another and, therefore, make adjustments for each other. Yet of course it was that very city that put Socrates to death.

Famously we now have Dunbar's number, which suggests that the average person can maintain not more than about 150 relationships. Presumably Aristotle was trying to work out something similar here.

But the proper number is presumably not a single number, but anything that falls between certain fixed points. So for friends too there is a fixed number perhaps the largest number with whom one can live together (for that, we found, thought to be very characteristic of friendship); and that one cannot live with many people and divide oneself up among them is plain.

How many people can live together? We tend to think of two or three or five, but when we were younger and lived in barracks or dormitories the number was much larger.  

Further, they too must be friends of one another, if they are all to spend their days together; and it is a hard business for this condition to be fulfilled with a large number. It is found difficult, too, to rejoice and to grieve in an intimate way with many people, for it may likely happen that one has at once to be happy with one friend and to mourn with another. Presumably, then, it is well not to seek to have as many friends as possible, but as many as are enough for the purpose of living together; for it would seem actually impossible to be a great friend to many people.

Now another argument for monogamy:  

This is why one cannot love several people; love is ideally a sort of excess of friendship, and that can only be felt towards one person; therefore great friendship too can only be felt towards a few people. This seems to be confirmed in practice; for we do not find many people who are friends in the comradely way of friendship, and the famous friendships of this sort are always between two people. Those who have many friends and mix intimately with them all are thought to be no one's friend, except in the way proper to fellow-citizens, and such people are also called obsequious.

Fafhrd and the Grey Mouser, I suppose; but against that, the Rat Pack as a famous group of friends.  

In the way proper to fellow-citizens, indeed, it is possible to be the friend of many and yet not be obsequious but a genuinely good man; but one cannot have with many people the friendship based on virtue and on the character of our friends themselves, and we must be content if we find even a few such.

Indeed, even a few virtuous friends are a great wealth if one can find them. That is, however, a pragmatic difficulty rather than an answer to the question: shouldn't one want more if one could find them? 

It may be that only pragmatic answers are possible to this question; we are in fact limited by something like Dunbar's number; we can't in fact find very many virtuous friends in any human environ. It may be a limit to us rather than a proof about what ought to be wanted.

Yet that is in keeping with what we were told to expect in I.3: not proofs, which belong to mathematics and strict logic, but arguments about what is most probably true. Ethics often admits of no better than this; it is what we were warned the wise would seek from it, this and no more.