That feeling of g
But we do fly with input from our posteriors for the feeling of g.
It isn't a normally a primary input for control of the aircraft, and our internal sense of vertical should be only aircraft referenced (that is, it should not be referenced to the outside world attitude).
That little tactile sensation can feed us a lot of information regarding rate of g onset, level of g achieved, and whether or not the rudder is trimmed properly. It is just when we try to infer up and down relative to the earth that we get in trouble by trying to use it.
Dick Rutan recently gave a very interesting briefing regarding his round the world trip in the Voyager aircraft. At high gross weight, the aircraft had a divergent "pogo" type oscillation that required constant pilot intervention to control. He was controlling the oscillation by visual reference to the wing tips, and it occurred to him, "How am I going to control this thing at night when I can't see the wing tips?" Part of his test flying was to prove that he could control the oscillation by seat of the pants. They covered up the windows with quick remove panels and adequate control was maintained-by "seat of the pants" flying. The rest is history.