These ideas are the bases of mathematical and geometrical theorem construction.
They allow us to explain why some arguments are faulty as a result of incorrect relationships between premises and their conclusions. Aristotle’s rules have had other applications too. For example, in order to evaluate argument, Aristotle classified different types of false reasoning and fallacies. These include reasoning in which argument is swayed by appeals to emotion or by threats. A public demonstration of the rules of argument still survives in the ‘viva voce’ or defence of the PhD thesis, which developed in the Middle Ages.