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 import. 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.
Read more about Private Language Argument: Significance, Philosophical Investigations, Kripke's Interpretation
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