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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 Fall '07
 DEAR, P
 Archimedes, Euclid, early Greek geometry, solid starting points

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