There’s two things that’s exactly right and one thing that’s possibly more questionable about the private language argument posed by Edmund Gordon in his article “Biography in the Twitter age” posted on The Times Literary Supplement on November 14, 2016. Let’s first recount briefly what Wittgenstein — UK’s philosopher of language and logic — said about private languages (see also the post here).
Essentially, Wittgenstein held that the notion that it is possible to generate a language that is truly private is absurd. For instance, in §241 of Philosophical Investigations he notes that,
“So you are saying that human agreement decides what is true and what is false?”—It is what human beings say that is true and false; and they agree in the language they use. That is not agreement in opinions but in form of life.
In what sense are my sensations private? —Well, only I can know whether I am really in pain; another person can only surmise it.—In one way this is wrong, and in another nonsense. If we are using the word “to know” as it is normally used (and how else are we to use it?), then other people very often know when I am in pain.
1. The private has usurped the public
Among the main qualities and duties of contemporary biography is the way it measures the distance between a subject’s public and private selves – and if people don’t regularly take the measure of themselves in writing any more, that may no longer be possible.
If we’re always performing for an external audience, then the distance between our private and public selves will surely shrink.
2. The public has usurped the private
A second sense in which Gordon is right is rendered by recounting the recent politically motivated research into what goes on in the household under the rubric “the private is public.” In this view, it is an oppressive order that maintains the distinction between private and public, and — as the argument goes — it is in the interest of the oppressed to abolish the distinction. There is nothing that goes on in the household that shouldn’t immediately be considered public acts. According to this kind of action research — politically motivated scholarship that seeks to change the order of the world — it is a good thing that, as Gordon notes, “the distance between our private and public selves” have shrunk. In this manner, it will be more challenging for the dominant and oppressive keepers of the household to keep their acts from public view.
The ideal invention here would be the contraption authored by Eric Blair in his momentous 1949 novel, where it is no longer the private citizens who watch television, but the television who observes the private citizens. Nothing — in this rendition of the world — remains private.
3. Is there a truly private language?
Now, let’s finally consider one sense Gordon’s view is a bit more challenging. In order to understand this sense, it is necessary to review the remarks on Wittgenstein above. Given that W asserts how we cannot arrive at a truly private language, it is necessary to make such a language in the presence of some instance that in some way is external to us. Let’s call this instance the Law-Issuing Instance. We can conceivably construct a language under the aegis of such an instance, debating with ourselves — our Law-Issuing Instance — whether or not we have truly encountered that same emotion as when we previously identified a feeling with the inscription of the letter S. However — and this is the crucial point — if this were the case, we would not be truly alone, i.e., in the private, when we made up the language.

“George Berkeley, Bishop of Cloyne,” etching. Courtesy of the Yale University Manuscripts & Archives Digital Images Database, Yale University, New Haven, Connecticut. Public domain.
In fact, would not the true horror scenario be a situation where we would be bereaved of our Law-Issuing Instance? It is such a horror that is suggested — and we believe wrongly — by Gordon’s notion of an evaporation of the boundary between private and public. It is in this sense it is possible to say that there never really was a private writing situation, since each entry in a diary or journal was always accompanied by an instance that — however made up by our selves — remains external to us. The crucial point is that this notion of writing in the presence of an Other does not entail the eradication of the private sphere. It simply means that we are never truly alone: there is always someone there that, as George Berkeley held it, watches over us.