1. A display device, comprising: a display unit configured to stereoscopically display a display object at an initial position; a detecting unit configured to detect a first object and a second object in a three-dimensional space where the display object is three-dimensionally visible; and a control unit configured to set the display object to a tentatively selected state in response to a detection of a first arrangement in which the display object at the initial position is located between the first object and the second object in the three-dimensional space, maintain the display object, that has been set to the tentatively selected state, at the initial position, when the first object and the second object move from the first arrangement to a second arrangement in which a relative position of the first and second objects to said display object is different from the first arrangement, and then move the display object from the initial position to a position between the first object and the second object, when a distance between the first object and the second object is not widened for a longer period of time than a predetermined time in the second arrangement.