FOM: "The unreasonable effectiveness of mathematics"

[Karlis Podnieks]

-----Original Message-----
From: Solomon Feferman, January 26, 7:59
...

Here are a few quotes from Wigner:
...
"...I would say that mathematics is the science of skillful
operations
with concepts and rules invented just for this purpose.  The
principal
emphasis is on the invention of concepts." (p.2) [SF: This seems
to point to
the subjective origin of mathematical concepts and rules.]

KP> I would say more precisely: mathematics is the science of
skillful operations
with  s e l f - c o n t a i n e d  concepts and rules. I think
this is what makes mathematical concepts  different from
concepts in other branches of science and art.
...
"The miracle of the appropriateness of the language of
mathematics for the
formulation of the laws of physics is a wonderful gift which we
neither
understand nor deserve.  We should be grateful for it and hope
that it
will remain valid in future research ..." (p.14).


KP>  Since self-contained theories can be formalized, i.e.
represented as rather "mechanical" objects of the (real?) world,
their appropriateness for the formulation of the laws of physics
means that in this world some objects/aspects appear to be
"isomorphic" to some other objects/aspects. Does this explain
the mystery?

Best wishes,
K.Podnieks
podnieks at cclu.lv
http://sisenis.com.latnet.lv/~podnieks/
http://www.latnet.lv/LU/MII/Grade/
University of Latvia
Institute of Mathematics and Computer Science