The class cannot be a member of itself nor can one of themembers be the class, since the term used for the class is of a different level of abstraction--adifferent Logical Type--from terms used for members. Although in formal logic there is anattempt to maintain this discontinuity between a class and its members, we argue that in thepsychology of real communications this discontinuity is continually and inevitably breached (2),and that a priori we must expect a pathology to occur in the human organism when certainformal patterns of the breaching occur in the communication between mother and child.
The Theory of Logical Types was Russell and Whitehead's attempt to ward off the various paradoxes that were obstructing them and in their quest for an axiomatic foundations for mathematics.
It was an attempt to rid formal systems of self-reference (the supposed source of many paradoxes), an attempt that Gödel later showed was flawed. Turns out you can't keep self-reference out of a system just be banning explicit forms of it.
As far as I can tell, the Double Bind idea is not actually grounded in the Theory of Logical Types in any load bearing way, though depending on your background it is a somewhat illuminating example/connection/comparison.