I was inspired to write this post after seeing a post by Hammurabi Rubio (a guest post for Romaric Jannel) with a fun revisiting of Wittgenstein’s “beetle in the box” metaphor for language:
“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 they know what a beetle is only by looking at their beetle. — Here it would be quite possible for everyone to have something different in their box. Or even for everyone to have something that constantly changes. — 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 doesn’t belong to the language-game at all; not even as a something: for the box might even be empty.” (Philosophical Investigations, 1969, p. 100)
Wittgenstein’s point is valid as far as it goes, but it goes only as far as classical language (which I’ll make more specific shortly). His argument on the limitations of classical language has been universally overgeneralized in an unwarranted slide to irreducibly observer-dependent antirealism (the claim that the box is empty). In short, the basic mistakes in the slide to antirealism are (1) equating epistemology (the study of knowledge) to ontology (the study of what exists), enabled by (2) the assumption that whatever exists must be describable in classical language. An instructive analogy is the Blind Men and the Elephant:
There is indeed an Elephant, but the only way the Blind Men can gain knowledge of the Elephant is through specific kinds of interactions–“opening the box”. Each man’s access only reveals a certain partial truth about the Elephant, and that partial truth is the only thing that can be rendered in classical language. But the interactions are real contact with the Elephant, as are the Blind Men’s interactions with one another indirectly through their differing accounts in their “classical languages”.
If one or more Blind Men look at the larger picture of the way those differing accounts fit together, they are indeed able to develop a theory of the Elephant that is NOT “classical language” but is the mathematical structure of the Elephant itself. The latter is not subject to Wittgenstein’s “beetle in the box” claim that language must always be disconnected from “what is.”
The Blind Man referred to above is Werner Heisenberg, and what he stumbled on when he went beyond “classical language” is quantum theory. In this way, quantum theory can be considered an authentic invariant description of the Elephant (underlying the ‘beetle in the box’). It is a “language”, though not “classical language”.
The point is that the ‘beetle in the box’ can indeed be connected through (non-classical) language if one looks at the way all the “classical languages” fit together in interactions with the ‘beetle’. Even when the ‘beetle’ changes (which is just the time-dependent Schrodinger equation).
The bottom line: quantum theory can indeed be considered a language describing reality (the Elephant) in an invariant respect across different “boxes” (analogous to Blind Men). Thus it is a mistake to conclude that there is no Elephant (what Bohr asserted, see https://arxiv.org/abs/1601.07545 ) or that the each person’s “beetle” can have no connection to language. For it is interactions with the beetle that determine the structure of our theory (language) which enables us to predict (within well-defined statistical boundaries, i.e. the Born Rule) what anyone’s beetle is going to look like the next time they open the box.
Overgeneralization of Wittegenstein’s argument to slide into antirealism is based on neglecting the fact that one can unify these differing modes of description in an invariant way, and that this unification is highly constrained, not arbitrary. That is an argument for the existence of a real Elephant/beetle; something real that exists whether or not anyone “opens the box.” Wittgenstein’s “beetles” are only the locally available aspects of the Elephant, conditioned by each individual observer’s capacities. And in this way, the Elephant is indeed connected to the language of quantum theory. It just isn’t a classical language.
Transactional Interpretation 