[FOM] Are proofs in mathematics based on sufficient evidence?
Monroe Eskew
meskew at math.uci.edu
Tue Jul 13 02:45:55 EDT 2010
Michael,
Can you point me towards a good source that argues for this thesis,
which provides good textual examples/evidence of what you refer to as
the text becoming detached from the original meaning? It is hard for
me to imagine how that would work.
Thanks,
Monroe
On Mon, Jul 12, 2010 at 8:52 PM, Michael Barany
<michael.barany at tellurideassociation.org> wrote:
> Monroe,
>
> Your experiences with Euclid represent one form of a remarkably common
> theme in the history of European mathematics. Of course, there are
> many interpretations of this history, but one I find compelling holds
> that beginning in the late 15th century Euclid's Elements was
> effectively detached from most of the meanings it may have had in
> earlier eras (particularly with respect to truth and rigor) and
> re-appropriated to provide a historical basis for new claims regarding
> the right way to pursue knowledge. The interesting byproduct of this
> transformation was that Euclid's Elements became more rigorous through
> the cascading attempts to translate and teach the text over the
> ensuing centuries. But "rigorous" is always a debatable term, and
> different generations of translators and teachers attached different
> meanings to their prized geometric text. Thus, in the seventeenth
> century Hobbes used one interpretation of Euclid's Elements to claim
> that he had successfully (and rigorously!) doubled the cube while his
> opponents used their version of Euclidean rigor to claim he had done
> no such thing. In the eighteenth century (as Joan Richards and
> several others argue) Euclidean rigor was often seen to be more stale
> and pedantic than a valuable method for mathematics. The early
> nineteenth century saw several waves of reinterpretation of the
> Elements which culminated (for many) in Weierstrass's school of
> analytic rigor, followed by the versions of abstract algebra and logic
> more familiar on this e-list.
>
> It may be interesting to recall that Cauchy himself was a
> mathematician in a family of French lawyers,...
>
> Smiles,
>
> Michael
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