The above clip from the pilot episode of the landmark TV show/sitcom is a microcosm of what the show would be about, the message it would attempt to convey in it's 8 year run.
It has been well-documented that Bill Cosby (Ed.D), along with his main collaborator Dr. Alvin Poussaint wanted to portray in The Huxtable's an idealized family in 1980's/90's America that the entire country could aspire to be like.... In much the same way as the Cleaver's were in the 60's.
The master-stroke was of course was the fact that this particular family was African American, and that this most important aspect of their being was intentionally played-down... It was made to appear almost as an afterthought. That of course was what made the show so effective [at the time].
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