The private language argument is a philosophical argument introduced by Ludwig Wittgenstein in his later work, especially in the Philosophical Investigations. The argument was central to philosophical discussion in the second half of the 20th century, and continues to arouse interest. The argument is supposed to show that the idea of a language understandable by only a single individual is incoherent.
In the Investigations Wittgenstein does not present his arguments in a succinct and linear fashion; instead, he describes particular uses of language, and prompts the reader to contemplate the implications of those uses. As a result, there is considerable dispute about both the nature of the argument and its implications. Indeed, it has become common to talk of private language arguments.
Historians of philosophy see precursors of the private language argument in a variety of sources, notably in the work of Gottlob Frege and John Locke. Locke is also a prominent exponent of the view targeted by the argument, since he proposed in his An Essay Concerning Human Understanding that the referent of a word is the idea it stands for.
The private language argument is of central importance to debates about the nature of language. One compelling theory about language is that language maps words to ideas, concepts or representations in each person's mind. On this account, the concepts in my head are distinct from the concepts in your head. But I can match my concepts to a word in our common language, and then speak the word. You then match the word to a concept in your mind. So our concepts in effect form a private language which we translate into our common language and so share. This account is found for example in An Essay Concerning Human Understanding, and more recently in Jerry Fodor's language of thought theory.
Wittgenstein argues, in his later work, that this account of private language is inconsistent. If the idea of a private language is inconsistent, then a logical conclusion would be that all language serves a social function. This would have profound implications for other areas of philosophical and psychological study. For example, if one cannot have a private language, it might not make any sense to talk of private experiences or of private mental states.