Seminar on History and Philosophy of Science

Friday, November 22, 2013
4:00pm to 5:00pm
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Dabney Hall 110 (Treasure Room)
Representing Order Information in Elementary Geometry: Diagrams vs. Axioms
John Mumma, Philosophy Department, California State University of San Bernardino,
The proofs of Euclid's Elements are often said to contain implicit assumptions about basic geometric facts. Specifically, in contrast to modern theories of elementary geometry, the Elements does not contain axioms for order relations (e.g. lying between, lying inside). Recent analyses of Euclid's arguments have aimed to show that nevertheless a systematic proof method underlies them. The basic idea is that Euclid uses geometric diagrams in a controlled and principled way to record order information. After presenting how on this account Euclid's proof method differs from modern axiomatic approaches to elementary geometry, I examine the account's relevance to broader questions on informal mathematical proofs and axiomatic analyses of them.
For more information, please contact Sinikka Elvington by phone at Ext. 1724 or by email at elvington@hss.caltech.edu.