This paper offers a reading of Theaetetus 171a-b in the context of Plato’s critique of Protagorean relativism. It analyses the structure and philosophical significance of the so-called "self-refutation" (peritropê) argument, following the interpretations of Burnyeat and Erginel. It aims to show that Plato’s argument is not a mere logical paradox but a dialectical refutation revealing the impossibility for the relativist to defend their own position rationally: by acknowledging the truth of the belief that relativism is false, the relativist undermines the validity of their own doctrine. This dialectical impossibility exposes a constitutive weakness of relativism, which cannot be formulated, communicated, or sustained without presupposing a shared space of discourse and common criteria of truth. The final section draws a parallel between this Platonic analysis and contemporary phenomena of post-truth and populist demagogy, both grounded in the dissolution of the common world and the replacement of facts by convictions. Plato thus appears not as the defender of archaic dogmatism but as the thinker of the very conditions of rational disagreement and a shared world.