Wittgenstein considered that the notion of a private language rested on two fundamental mistakes: one about the nature of experience, and one about the nature of language. The former is the belief that experience is private; the latter is the belief that words can acquire meaning by ostensive definition. The so-calledp: private language argument" establishes that the speaker of the language would be left with no way to distinguish between seeming right and being right; i.e, nobody other than the speaker could understand it and nothing could be recognized as a word of such a language to refer to a thing. In this paper, we first discuss 243-258 of the Philosophical Investigations in order to find a comprehensive and truthful reading of the argument. Then we present a comparative discussion of some of his commentator's explanations. Our discussion shows that Kenny's reading of Wittgenstein should be seen as the most reliable and coherent readings.