Comment on Quantifying ethicality of human actions

Wed, 14 Oct 2009 20:25:02 GMT

Take Euclid. He thought that all his conclusions followed deductively from his axioms and that his depictions were just illustrations and played no role in the formal proof. ... But we would still never write, "Euclid sought to describe plane geometry as beginning with a set of axioms and from there, proved propositions about planar figures with the help of undeclared assumptions and visual aids."

Really? Euclid's axiomatic system was only clarified in the late 19th century by Hilbert, and the logic of his visual models is a subject of ongoing research. So this looks like it could be a sensible description of Euclid in an article about how geometrical reasoning might be formalized, since a system which took Euclid's pretenses at face value would face unexpected (and unacceptable) limitations. Now I agree that the OP has other problems, but perhaps this is simply a difference in perspective.

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