While a search for "figure-eight logic" renders many links to NAND logic configurations, it sounds more like Pretzel Logic, which is " is an expression used to describe someone's "twisted reasoning."
That expression has been in existence in the US (as far as I know) since the early 70s.
"Figure-eight" logic seems to be a reference to a figure-skating maneuver in which the skater starts at a single point, draws the pattern of the number 8 in the ice, and ends up finishing at the same place. In other words, a circle with a convolution.
So, a "Figure-eight" logical statement starts with a an questionable declaration, twists it inside-out, and then ends up where it started-- a circular argument that goes nowhere no matter satisfyinghow satisfying it might seem to the gullible.
images courtesy
http://www.elartedeamasar.com/2012/04/pretzel-al-estilo-de-new-york-y-faciles.html