In order to walk across the floor, you push backwards on the floor with your foot. Newton's Third Law says that the reaction force to this action force is "floor pushes you forward" (Action: You push floor (backwards). Reaction: floor pushes you (forward).) So, when you walk, it is the floor that pushes you along!
Explanation: The parietal lobe is where the primary somatosensory cortex is located. This cortex is where all tactile stimulation is processed in the brain and allows to you detect/feel someone scratching your back.