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

[Monroe Eskew]

I would still very much like to see direct argument and evidence for
the claim that mathematical standards of rigor have been significantly
shaped by modern-ear juridical standards.  So far I feel we've at most
seen a "penumbral" justification.

Best,
Monroe


On Fri, Jul 16, 2010 at 5:31 PM, Michael Barany
<michael.barany at tellurideassociation.org> wrote:
> Now, for the sticky matter of the lawyers.  While my initial statement
> was meant to be provocative (and of course without a full argument it
> must certainly come off as under-supported), there is an important
> observation at the core which is clearer to grasp.  Mathematics and
> mathematicians have long maintained their epistemological autonomy
> from other forms of knowledge, a split I argue took its present form
> in the early nineteenth century, although it had many prior
> iterations.  However mathematics does not float independently of its
> environs.  The valorization of Euclid in Early Modern Europe had two
> effects: it made the Elements a model for truth in other disciplines
> (see Hobbes) and it led rhetoricians and others to focus on competing
> forms of certainty for those  other disciplines.  As mathematics
> developed, so too did these other models of how to know the right and
> true (as the parent post for this thread encountered on wikipedia).
> As understandings of mathematics and Euclid changed, mathematicians
> had to justify and reinforce their art with reference to the standards
> around them, including juridical standards and the scientific
> standards largely derived from them (see Shapin and Schaffer's famous
> Leviathan and the Air-Pump).  Surely it would be a mistake to argue
> that the laws of deduction formalized around a century ago apply
> purely and retroactively to all of mathematical history---that is the
> main point of my comments.