The private language argument argues that the idea of a "private language"—i.e., a language that is understandable by only a single individual—is incoherent. It was 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.

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. This technique gives rise to 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 one's head are distinct from the concepts in another's head. One can match their concepts to a word in a common language, and then speak the word to another. The listener can then match the word to a concept in their mind. So the shared concepts, in effect, form a private language that one can translate into a common language and thereby share. This account is found, for example, in Locke's An Essay Concerning Human Understanding and more recently in Jerry Fodor's language of thought theory.

In his later work, Wittgenstein argues 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.

The argument is found in part one of the Philosophical investigations. This part consists of a series of "remarks" numbered sequentially. The core of the argument is generally thought to be presented in §256 and onward, though the idea is first introduced in §243.

If someone were to behave as if they understood a language of which no one else can make sense, we might call this an example of a private language. It is not sufficient here, however, for the language to simply be one that has not yet been translated. In order to count as a private language in Wittgenstein's sense, it must be in principle incapable of translation into an ordinary language – if for example it were to describe those inner experiences supposed to be inaccessible to others. The private language being considered is not simply a language in fact understood by one person, but a language that in principle can only be understood by one person. So the last speaker of a dying language would not be speaking a private language, since the language remains in principle learnable. A private language must be unlearnable and untranslatable, and yet it must appear that the speaker is able to make sense of it.

Wittgenstein sets up a thought experiment in which someone is imagined to associate some recurrent sensation with a symbol by writing S in their calendar when the sensation occurs. Such a case would be a private language in the Wittgensteinian sense. Furthermore, it is presupposed that S cannot be defined using other terms, for example, "the feeling I get when the manometer rises"; for to do so would be to give S a place in our public language, in which case S could not be a statement in a private language.