How did the Greeks use deductive reasoning?
Although the Greeks, as people today, used deductive reasoning informally in many different ways to apply general principles to specific circumstances, the more technical treatments of deductive reasoning as a formal category really begin with Aristotle. For Aristotle, deductive reasoning could be part of formal or apodeictic demonstration or used as part of rhetorical persuasion. The formal deduction used in demonstrative reasoning was, by Aristotle, termed the "syllogism". Aristotle covers many different forms of syllogism in his Prior Analytics. A second type of deductive reasoning, called the enthymeme, from probable rather than certain premises, was used in rhetoric, and discussed by Aristotle in his Rhetoric.