The syllogism is a form of logical argument invented by the Greek philosopher Aristotle (384-322 B.C.). Aristotle was the first philosopher to put forward a formal system of logic (see Aristotelian logic), a system which would stand virtually unchanged and unchallenged for more than 2000 years after his death. For Aristotle, logic was the primary tool for discourse about any of the sciences. At the heart of Aristotle's logic was the syllogism. To illustrate the form that a syllogism takes, here is one that Aristotle used: "All humans are mortal. Socrates is a human. Therefore, Socrates is mortal." This has the more general form "All B is A. Some C is B. Therefore, some C is A." The first sentence in the syllogism is called the major premise. The second sentence is called the minor premise. The third sentence is called the conclusion. All...