The idea that an intimate connection exists between humour and logic is not original with this study. Even before logic had been formalised as an autonomous discipline, humour often appeared in the pseudo-proof of some theory so extravagantly at odds with common-sense notions as to provoke laughter. Some of the epicheirêmata of the pre-Socratic philosopher Zeno of Elea fit this pattern, such as his argument that, given a start, a tortoise could never be overtaken by Achilles. A taste for humorous paradox pervades the work of the fifth-century sophist Gorgias, and persists into the writings of the thirteenth-century Averroist Siger of Brabant, whose six impossibilia included a logical defence of the proposition that the Trojan War was still in progress. Like the Stoics before them, medieval logicians produced numerous syllogisms involving humorous effrontery. For example the thirteenth-century Summulae Logicales of Peter of Spain includes the sophism: ‘Iste canis est tuus et est pater, ergo est tuus pater’. The Middle Ages inherited from classical antiquity such antinomies as that of the barber of the regiment who shaves all the men, and only the men, who do not shave themselves, and is thus unable either to shave or not to shave. It has been suggested that analysis of this paradox might have been better placed in Punch than in the Principia Mathematica, but its appearance in the latter work testifies to the occurrence of comic issues in the most serious of modern treatises on logic.