[FOM] Psychological basis of Intuitionism

[Colin McLarty]

Steve,

I am not sure exactly what you mean by the question.  But could you answer
your question by reading the 18th century mathematicians who actually did
it?

best, Colin

On Wed, Jun 5, 2013 at 10:42 AM, Steve Stevenson <steve at clemson.edu> wrote:

> On Tue, Jun 4, 2013 at 9:41 AM, Andrej Bauer <andrej.bauer at andrej.com>
> wrote:
> >If mathematics is the art of hypothetical reasoning, surely then we must
> > develop mathematics which is open to all possibilities, including the
> one in
> > which mathematics has an independent and objective nature, and moreover
> > allows for existence without construction.
>
> I am asking a different question. Suppose you're an 18th Century
> geometer and want to develop a non-Euclidean geometry. Since there are
> no known such, how do you think about reformulating the parallel line
> axiom? Once you've put a theory together, how do you communicate this
> insight without show your colleagues how to construct such a geometry?
>
> --
> D. E. (Steve) Stevenson, PhD
> Emeritus Associate Professor
> School of Computing, Clemson University
>
> "Those that know, do. Those that understand, teach," Aristotle.
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20130606/bf4b6194/attachment.html>