9-6-07 - 9/6/07 Deductive Proof and Geometry Generally...

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9/6/07 Deductive Proof and Geometry Generally agreed that Thales did not do the geometrical proofs that we generally associate with the Greeks So much haziness in early Greek geometry because Euclid’s book “Elements” was so comprehensive that people just went strait to it and didn’t need the older texts that he got his info from. This meant that people stopped copying the older books which were his sources and so over time these books were lost really and stopped being studied. Although Proclus is much later than Euclid he claims that he is deriving some of his stuff directly from a history of mathematics written by one of Aristotle's students named Eudemus. Talking about Greek mathematics is synonymous with talking about geometry. They did, however, do some other work. Geometry seemed to be the best idiom within which to talk about mathematics. By the time that Aristotle is writing about geometry he is referring to the way that Greek philosophers talk about the elements. Aristotle on the foundations of Deductive systems: In the posterior analytics he talks about the perfect system of science. He thinks about it in terms of a system where your statements are based on a???? If you want your conclusions to be reliable then they need to be based on solid starting points. The problem, however, is that you can’t prove the soundness of the starting principles. o Have starting statements that are extremely simple, and can not prove them to be true by deducing them because they are the most simple. o Can not pick whatever starting points you would like, need to pick ones that can be generally acceptable starting points. What qualities do these starting points need to have Definitions Include explanations or definitions of the special terms that your science uses. Hypotheses
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9-6-07 - 9/6/07 Deductive Proof and Geometry Generally...

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