People sometimes say they have an experience that words cannot convey. These occasions may be of different kinds. There are trivial cases like Hume's claim that we cannot convey the taste of pineapple to someone who has never tasted it. And there are more dramatic cases as when someone who has lost a child says that it is impossible to convey what the experience is like to someone who has not gone through it.
I would suggest that there is something paradoxical about this notion of words failing us, about the idea of a task to which words are unequal.
The task, for one thing, is undeniably linguistic: conveying experiences is the sort of thing we do with words (unlike feeding people, or keeping them warm - words can't do that either, but we would not call this a shortcoming on the part of words).
In the ordinary kind of case, if I try to give an account of an experience and fail, the failure, as it were, is in the language I use. Speakers may disagree on the right description:
"It wasn't really a chaos, just a roomful of people bustling with activity."
"He didn't really hit you, it was more like a friendly pat on your shoulder."
"The columns may look straight but really they get broader the further up you go."
"It wasn't so much that I felt betrayed as that I was mad at myself because I should have seen it coming."
In these cases, getting the description wrong is a shortcoming on the part of the speaker, not on the part of language. But to say that an experience cannot be conveyed is to claim that language isn't up to it. You can't even attempt to describe it: no proposal is better than any other. Nor can you try to overcome this problem by trying to reform the language. (Cp Wittgenstein, Philosophical Investigations § 610: "James: 'We lack the words.' Then why don't we introduce new ones? What would have to be the case for us to be able to?")
The deficiency, it seems, is not in this language or that, rather here we are up against a limitation of language, of speaking, as such.
We apparently judge how language measures up against something that is not linguistically articulated. But how can this be done? It seems to require that we step outside language and compare it with reality. And this is what seems paradoxical.
Is there some non-paradoxical way (or ways) of understanding such claims?