Suppose everyone had a box with something in it: we call it a “beetle”. No one can look into anyone else’s box, and everyone says he knows what a beetle is only by looking at his beetle. –Here it would be quite possible for everyone to have something different in his box. One might even imagine such a thing constantly changing. –But suppose the word “beetle” had a use in these people’s language? –If so it would not be used as the name of a thing. The thing in the box has no place in the language-game at all; not even as a something: for the box might even be empty. –No, one can ‘divide through’ by the thing in the box; it cancels out, whatever it is.
That is to say: if we construe the grammar of the expression of sensation on the model of ‘object and designation’ the object drops out of consideration as irrelevant.Instead of a box, imagine that we are talking about human bodies, and instead of a beetle, imagine that we are talking about a "soul". Each body's "soul" might be something quite different. Some might change constantly. And some bodies might even be empty, having no soul. But suppose the word "soul" has a use nonetheless? Then it is not used to designate something inside the body (even though, ex hypothesi, "soul" is what we call the thing in the body--presumably calling something something need not involve designating an object, perhaps just as naming a baby or pet is not designating an object). Saying that someone had, or did not have, a soul would then not state a certain, dispassionate kind of fact about that person but would perhaps express an attitude or be a Davidsonian metaphor or something along those lines.
Then what would it mean to say that someone had become a cockroach or beetle? In Kafka's story the inside or soul remains much the same, but the container or body is transformed. I won't interpret this, but it suggests something about people who are regarded as cockroaches, etc. They are treated or thought of or looked at differently than other people, while the dispassionate facts about them are no different from the facts about other people. They still belong to the species homo sapiens, they still bleed when pricked (although that is already starting to shade into a different kind of facts--Shylock is not a mere biologist, which is why the argument from analogy for the existence of other minds seems to work despite also seeming to be an instance of induction from just one case), and so on. Appeal to dispassionate facts won't persuade anyone that a body has a soul attached to it. We cannot shake the box and hear the beetle. This says something, something about facts and imagination and feelings, about the kind of task that Shylock faces in trying to get others to see him as a fellow human being, and about the kind of work that is involved in ethical argument (for instance about the status of animals, or fetuses, or immigrants, or the environment, etc.).
Kafka also suggests a more Sartrean point, that we are what other people see us as being. We are also, Sartre thinks (as I understand him), what we make ourselves through the choices we make. But there is a sense in which we are entirely determined by others. (Perhaps we could say that Sartre believes we are all duck-rabbits, with the duck produced by completely free choices and the rabbit produced completely by forces beyond our control, the views of others. But seeing a duck-rabbit as first a duck and then a rabbit is much easier than seeing yourself as others see you, or seeing someone else as they see themselves. And I imagine Sartre knew this.)
Anyway, as I say, I think it would be a mistake to read too much into the beetle in the box example (although if you want to then see also the entertaining novel Boxer Beetle by Ned Beauman, about a gay Jewish boxer named Roach and fascists who collect beetles). But there is quite a bit already there, not about Antisemitism, but about the relations between mind (or soul) and body, the individual and society, and the subtleties of language. Kafka's story also helps bring these things out, whether he had them in mind or not.