One of the most important and least explained points in Randall Collins' theory in The Sociology of Philosophies is the "law of small numbers." He argues that intellectual development takes place in an argument among a small number of intellectual networks. Almost always, he says, these arguments will resolve into three to six or so positions.
Why three is the minimum I sort of understand. For every position X, there is an opposing anti-X waiting to be filled. Moreover, Collins cleverly sees that in most historical intellectual arguments, there is also a "pox on both your houses" position, which tends to draw people who pose paradoxes, relativize all positions, and often promote distinctive lifestyles.
The upper limit of "about six" or "six to eight" is a little harder to see. My best guess is that that is about the limit of different positions that we can keep track of in opposition to our own. Above that, we tend to think of the various smaller sects as variations on one of the more dominant themes.
Collins keeps reminding us that it takes at least three generations to really get the measure of whether a school of thought has been creative or not. I can well believe that it is almost impossible to maintain an argument of more than eight distinct positions for three generations.
The law of small numbers is a useful, testable idea about how intellectual arguments are carried out.