[FOM] Psychological basis of Intuitionism

[Steve Stevenson]

“Intuitionism is based on the idea that mathematics is a creation of
the mind. The truth of a mathematical statement can only be conceived
via a mental construction that proves it to be true, and the
communication between mathematicians only serves as a means to create
the same mental process in different minds.”
(http://plato.stanford.edu/entries/intuitionism/)


Now that I'm retired, I would like to research how exactly this plays
out, especially metacognitive processes. The question, simply put, is
“Just how do we do it?”


Some mathematicians who have commented are Poincare, Hadamard, and
Polya. Smullyan's work in refutation starts with the human aspect and
so did Lakatos. I am also familiar with the Craik and Johnson-Laird
mental models view of reasoning.


I would appreciate any comments FOM readers can provide.



--
D. E. (Steve) Stevenson, PhD
Emeritus Associate Professor,
School of Computing, Clemson University

"Those that know, do. Those that understand, teach," Aristotle.