Contemplating Sartre's No Exit
In No Exit, Sartre provides a compelling answer to the problem of other minds through the medium of drama. He puts two women (Inez and Estelle) in one hotel room with one man (Garcin) for all of eternity. This is his concept of hell, and he makes this point in one of the last few lines of the play: "Hell is--other people!" There are no torture racks or red-hot pitchforks in hell because they're after "an economy of man-power--or devil-power if you prefer." Each person is there (in hell) for a specific reason: Garcin because he cheated on and tormented his wife, Estelle because she killed her own child and her lover, then committed suicide, and Inez because she tormented (female) lover until that lover killed both of them. Each person is attracted to someone else: Garcin to Inez, for her strength, vitality (if it's possible to use that word on someone who's dead) and power over him; Inez to Estelle, because Estelle would be, with her weak personality, easily dominated by Inez's strong personality; and Estelle to Garcin, because he is the only man and, as a woman who is weak, she requires a masculine approval to validate her existence.
It is interesting to not that Estelle comes from an extremely poor background and was elevated to the upper classes only through her marriage to a wealthy husband old enough to be her father, who could provide for her and her physically weak and sick younger brother and give them social status. Estelle, however, looks down on Inez, who was only a postal clerk. This is consistent with the way in which Estelle needs others to validate her own existence: she needs Estelle to look down on so that she can value herself by comparison.
Garcin is in a similar situation: he looks down on Estelle for being weak and establishes his own strength by comparison. It is important to note that Garcin's main fear in life was the fear of being cowardly, and this motivated the majority of his actions, e.g. most of his actions were preformed to demonstrate to himself and others that he is/was "manly"; for instance, his conquests of multiple women, his domination and degradation of his wife, and the way he "courted danger at every turn." However, he performed a cowardly action (fled the country when war broke out) which, when he was caught, led to a cowardly death which he defines as merely "a physical lapse."
Additionally, Estelle finds another way to seek approval: she needs Garcin's approval (as the only man there) to establish her superiority over Estelle as an object of desire, by comparison with Inez, the lesbian.
Finally, Inez does the same thing, although in a different form, as Estelle and Garcin. She seeks approval over Estelle as a strong, dominant, hones woman,...