In one sense, it impossible to act completely selflessly, because we always can identify rewards for acting selflessly, if nothing more than the reward of being held in high-esteem by ourselves and others.
I think that a distinction might be made between acting selflessly and receiving an appropriate or natural reward and acting with ulterior motives. For example, two men might act lovingly towards a woman, one expecting that he will be loved in return (an appropriate reward) and another because the woman will give him money. The first man’s loving acts are viewed favorably, even though he receive a benefit from his actions. The second is viewed as acting selfishly because he is acting with ulterior motives by seeking something other the natural reward for his affection.
