From an analytic point of view, this article deals with different attempts, based on the appeal to mental experiments, to prove or refute the Principle of Identity of Indiscernibles (PII). The text begins with a study of the Principle's conditions of validity, and then the positions of Black, O'Connor, Hacking, Godwin, and Wittgenstein are e xamined. Fina lly, the aut hor presents a solution to t he problem of indiscernibles drawing from Godwin and Wittgenstein's analysis.