What are zigzag theories, and why are they called that? I've encountered the term zigzag theory while randomly clicking my way through the internet. It is given here. I haven't been able to find a clear explanation of what constitutes a zigzag theory. Here, it is said that they have to do with non-Cantorian sets, which, as I understand, are sets that fail to satisfy Cantor's theorem. The article also says that New Foundations is a zigzag theory, but I don't see that it says why exactly that is so. I have gone through the Wikipedia article on New Foundations, and there's nothing about zigzags in it.
So what makes a zigzag theory? And what's zigzagging about it?

As a footnote to Arthur Fischer, here's an additional quote from Michael Potter's Set Theory and its Philosophy:

In 1906, Russell canvassed three forms a solution to the paradoxes might take:
  the no-class theory, limitation of size, and the zigzag theory. It is striking that a century later all of the theories that have been studied in any detail are recognizably descendants of one or other of these. Russell’s no-class theory became the theory of types, and the idea that the iterative conception is interpretable as a cumulative version of the theory of types was explained with great clarity by Gödel in a lecture he gave in 1933, ... although the view that it is an independently motivated notion rather than a device to make the theory more susceptible to metamathematical investigation is hard to find in print before Gödel 1947. The doctrine of limitation of size ... has received rather
  less philosophical attention, but the cumulatively detailed analysis in Hallett
  1984 can be recommended. The principal modern descendants of Russell’s
  zigzag theory -- the idea that a property is collectivizing provided that its syntactic expression is not too complex -- are Quine’s two theories NF and ML.
  Research into their properties has always been a minority sport: for the current
  state of knowledge consult Forster 1995. What remains elusive is a proof
  of the consistency of NF relative to ZF or any of its common strengthenings.

