[FOM] Psychological basis of Intuitionism

Steve Stevenson steve at clemson.edu
Wed Jun 5 10:42:09 EDT 2013

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.

More information about the FOM mailing list