Aristotle

1. Aristotle Aristotle was one of the first people to believe that the world was not flat Philosopher John 12/20/12

2. His Life • Born in 384 B.C. in Stagirus, Greece • Died in 322 B.C. Chalcis, Greece • Father was a medical doctor • Parents died when he was young • Raised by his uncle • In 367 at the age of 17, he became a student of Plato in Athens and eventually a teacher there for 20 years • Left academy when Plato died and moved to Assos • Married Pythias and they had one daughter • Returned to Athens to establish the Lyceum which rivaled the academy

3. Studies • Main areas of study were philosophy, physics, and biological sciences, not mathematics • Not primarily a Mathematician and did not make any new discoveries in mathematics

4. Mathematical Contributions • Wrote a biography of Pythagorus • Wrote history of Geometry with one of his students • Discussed and recorded many mathematical concepts and theorems of his contemporaries and their predecessors • Biggest contribution was the development of the study of logic which he termed “analytics” and is the basis for much of mathematics and deductive reasoning

5. An Example of Logic • Aristotelian syllogistic- an argument consisting of two premises and a conclusion • Every Greek is a person • Every person is mortal • Every Greek is mortal

6. Example- Continuous • Handled mathematical concepts in a philosopher’s style • “The continous is that in which the boundary or limit between two consecutive parts, where they touch, is one and the same…”

7. Example- Infinite • “But my argument does not anyhow rob mathematicians of their study, although it denies the existence of the infinite in the sense of actual existence as something increased to such an extent that it cannot be gone through; for, as it is, they do not need the infinite or use it, but only require that the finite straight line shall be as long as they please. ... Hence it will make no difference to them for the purpose of proofs.”

8. Story Time A philosopher once had the following dream.
First Aristotle appeared, and the philosopher said to him, “Could you give me a fifteen-minute capsule sketch of your entire philosophy?” To the philosopher’s surprise, Aristotle gave him an excellent exposition in which he compressed an enormous amount of material into a mere fifteen minutes. But then the philosopher raised a certain objection which Aristotle couldn’t answer. Confounded, Aristotle disappeared. Then Plato appeared. The same thing happened again, and the philosophers’ objection to Plato was the same as his objection to Aristotle. Plato also couldn’t answer it and disappeared. Then all the famous philosophers of history appeared one-by-one and our philosopher refuted every one with the same objection. After the last philosopher vanished, our philosopher said to himself, “I know I’m asleep and dreaming all this. Yet I’ve found a universal refutation for all philosophical systems! Tomorrow when I wake up, I will probably have forgotten it, and the world will really miss something!” With an iron effort, the philosopher forced himself to wake up, rush over to his desk, and write down his universal refutation. Then he jumped back into bed with a sigh of relief. The next morning when he awoke, he went over to the desk to see what he had written. It was, “That’s what you say.” 

9. Websites • http://worldbookonline.com/student/article?id=ar029880&st=aristotle • http://www-history.mcs.st-and.ac.uk/Biographies/Aristotle.html • http://www.bookrags.com/printfriendly/?=dios@u=aristotle-wom • http://plato.stanford.edu/entries.aristotle-mathematics/