[FOM] Are proofs in mathematics based on sufficient evidence?

[Monroe Eskew]

On Fri, Jul 9, 2010 at 2:43 PM, Michael Barany
<michael.barany at tellurideassociation.org> wrote:
>
> If one goes back 300 years (or even fewer) one finds the very active
> conflation of proofs of different sorts, with juridical proof usually
> taken to be the standard against which others are compared.  The idea
> of scientific proof had significant origins in debates about law and
> rhetoric (see Shapiro, 1986, `To a Moral Certainty': Theories of
> Knowledge and Anglo-American Juries 1600--1850, Hastings Law Journal
> 38:153--193), and the mathematical notion of proof we have today
> certainly has a lot to do with eighteenth and nineteenth century
> adaptations of these ideas.
>

I find this surprising, given the relatively high level of rigor found
in Euclid.  To put it in context, in my high school education, the
most rigorous arguments I encountered were not in the mathematics
classroom but rather in the debate team.  However when I read some
Euclid as a college freshman, I saw a whole new level of care, rigor,
and reliance on first principles.  Of course modern mathematics is a
big step above Euclid, but one gets the impression (both from reading
the math and the history) that its methods are descendants of those of
the ancient Greek mathematicians, rather than modern-era lawyers.

Monroe