A detailed analysis of Plato's Gorgias allows to see how the famous debate between Might and Right has been rigged, since Socrates and Callicles agree on everything against the people of Athens. But then, once the moral red herring has been pushed aside, it is still possible to see in the dialog the traces of the conditions of felicity proper to politics and ignored by Socrates' appeal to Reason as well as by Callicles' appeal to Force. The Body Politic made impossible by their settlement, can be made possible again as soon as other definitions of science and politics are provided.