Actually, Dr. Huxtable IS a scumbag too.
Some people make the argument that Dr. Huxtable is a great guy and totally separate from the bill cosby scumbag.
Actually, that isn't true.
Sondra and Denise are quite obviously of different races than those of Cliff and Claire, and of their other brother and sisters.
Therefore, the only possible explanations are either:
A> Claire committed adultery on Cliff.
B> Cliff committed adultery on Claire.
C> Both Cliff and Claire committed adultery on each other.
...one of the above must be true.
In addition, this point below must also be true:
D> Denise and Sondra are illegitimate children who were not conceived by both Cliff & Claire.
Moreover, given the indisputable adultery committed by either Cliff, Claire, or both Cliff and Claire, one or more of either Theo, Vanessa and Rudy may also be illegitimate children albeit from an adulterous relationship consisting of a partner who was of the same race as Cliff and/or Claire.
The bottom line: by virtue of the otherwise-impossible racial differences between the parents and some of their children and between some the children and their sisters and brother, the show itself proves beyond any doubt that the Huxtables are adulterous scumbags.