This paper distinguishes five key interpretations of the argument presented by Wittgenstein in Philosophical Investigations I, §258. I also argue that on none of these five interpretations is the argument cogent. The paper is primarily concerned with the most popular interpretation of the argument: that which that makes it rest upon the principle that one can be said to follow a rule only if there exists a "useable criterion of successful performance" (Pears) or "operational standard of

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... ess" (Glock) for its correct application. This principle, I suggest, is untrue. The private language argument upon which it rests therefore fails. Pears -claim to discern within PI §258 and the surrounding text a powerful argument against the possibility of a necessarily private language. Others dismiss the argument, typically on the grounds that it is verificationist. My aim in this paper is twofold. The first aim is clarity. The dispute over whether the private language argument of PI §258 is cogent has been confused by the fact there are now five main interpretations of PI §258 currently on offer, each interpretation presenting a fundamentally different argument. I will set out and distinguish clearly all five private language arguments. My second aim is to explain why none of these arguments is, as it stands, cogent.