GARCIN: What's this?
VALET: Can't you see? An ordinary paper-knife.
GARCIN: Are there books here?
GARCIN: Then what's the use of this? (57-61)
Good question, Garcin. What is going on with that paper-knife, other than providing the opportunity for Estelle to try (and fail) to kill Inez at the end of the play? Actually, the paper-knife is a reference to Sartre’s philosophical treatise, Being and Nothingness. In the philosophical work, Sartre explains the fundamental existential tenet, "Existence precedes essence."
As we discuss in "Genre," existence is the fact of being, whereas essence is definition, function, purpose, or program. For everything in the world except humans, however, essence precedes existence. A paper-knife exists because someone thought, "Hey, I need a pointy object so that I can open letters and/or separate the pages of a book." The essence of the paper-knife (i.e., the reason for its existence, its purpose, its function) came about before someone invented the paper-knife to fulfill this function. Essence came before existence. For humans, though, there is no pre-conceived purpose or plan or program, mostly because there’s no God to conceive of it. Man simply is. Then, AFTER he comes into existence, he defines his own essence (his own purpose, function, definition) through his choices and actions. It’s actually a rather freeing idea, isn’t it? Sartre meant his brand of existentialism to be liberating. There’s nothing you’re supposed to do; you get to decide for yourself.
Sartre uses this example of the paper-knife the same way we just did, in order to explain the difference between existence preceding essence (for humans) and essence preceding existence (for everything else). The reference in No Exit is a little nudge nudge wink wink from the author; you can tell from the context in the passage above that he’s deliberately referring us to his earlier work. Because the paper-knife has a pre-decided essence (to open letters or cut apart the pages of a book), it’s useless when there are no books around. Man, on the other hand, can never be put in this position, since man has no pre-determined essence. So human beings can never be useless, strictly speaking, because they never had a previous defined use.