The pilot was giving taxi rides to his grandchildren at a private farm strip. Accompanied by two teenage granddaughters, the pilot was observed in the right front seat holding the entry door open while taxiing the aircraft up and down the strip. A witness heard the throttle advance at approximately midfield and saw the aircraft become airborne near the end of the strip. The aircraft climbed in a very high nose-up attitude and then slid backwards in the air, disappearing from view in a tail-down fall. The trim was found in the full nose-up position. None of the occupants were wearing seatbelts. Neither of the passengers had any aeronautical knowledge. The pilot had a medical history of treatment for high blood pressure. A review of his logbook indicated that he discontinued flying while taking medication. He had just started flying again after discontinuing his medication. The pilot's son stated that the pilot had not intended to take off and felt strongly that the pilot became incapacitated while taxiing and became airborne inadvertently.