What does the old man's deafness symbolize?
In Hemingway's "A Clean Well-Lighted Place," the fact that the man is deaf indicates that he is even more isolated from people. This deafness and age of the man may also indicate that he is losing some of his other senses as well. So, in his approaching blindness he may seek more light, light that may deter the darkness of death.
In addition to these ideas, the deafness is, perhaps, symbolic of how the other waiter is unconcerned about the old man's wants; he simply cares for himself and wishes to go home. In addition, this unconcern by the waiter is yet a further indication of the alienation of the old man from even the waiter who sees him regularly. For, after the man leaves, the other waiter scolds the younger waiter for his lack of empathy and patience for the lonely old man. Like him, the older waiter is reluctant to return to his lonely room, so he stops in a bar and has a drink.
Certainly, in "A Clean, Well-Lighted Place" the three characters seem isolated from one another in their understanding of the wants of each. They are all three in a disillusioning environment where the only unity is in suffering.