The paper first presents a short survey of ancient and modern logical, rhetorical and argumentative approaches (e.g. Aristotle, Quintilian, Quine, Anscombre and Ducrot) studying the properties of paradoxical utterances. This survey is followed by a tentative definition of paradoxes as seemingly contradictory utterances triggering conversational implicatures in the sense of Grice. A specific group of paradoxes, namely, persuasive paradoxes, is further characterized by the specific implicatures which they trigger: the implicatures of persuasive paradoxes serve the interest of the (political) speaker (...) because they either convey a sharp criticism of the political opponent(s) or praise the political activities of the speaker in a highly effective way.The second part of the paper takes a corpus of about 80 paradoxical utterances from Cicero's speeches to show how they are used 1. for a devastating criticism of Cicero's political enemies, 2. a milder form of criticism in the case of his friends, when their political activities have failed, 3. a praise of successful policies of Cicero and his political friends and 4. a defense of unsuccessful activities started by Cicero and his friends. (shrink)