Which philosopher argued that a private language is impossible?

Wittgenstein, in the Philosophical Investigations, published after his death. The argument imagines a language whose words refer to sensations only the speaker can know - and asks what it would mean to use such a word correctly. There is no check: whatever seems right is right, and that, he says, only means we cannot talk about right at all.

The target is a picture of the mind that runs through Descartes and Locke, in which each of us inspects a private inner theatre and language is a set of labels for its contents. If meaning requires the possibility of being wrong, and being wrong requires a standard outside your own impression, then meaning is public from the start - it lives in shared practice, in what he called forms of life.

He had already written one book, the Tractatus, which he believed had solved the problems of philosophy, after which he gave away a large inherited fortune and worked as a village schoolteacher, a gardener and a hospital porter. He came back to Cambridge and spent the rest of his life dismantling his own earlier position. The later book is aphorisms and questions rather than argument, and is quoted by people who reach opposite conclusions from it.