The generality of mathematics

From: Jamie Vicary (jamievicary_at_gmail.com)
Date: 01/30/05 

Date: Sun, 30 Jan 2005 22:30:58 +0000

Dear all,

     Is mathematics completely general? Can all possible algebraic
structures be represented by the mathematical structures which we use
today? It seems to me that modern mathematics is not really very general
at all. Much of algebra is dominated by the notion that objects can be
operated on from the left, and from the right. Why not other
"directions"? Why not conceive of a set of objects which operate on each
other in a much more general sense?

     Most importantly, does there exist a proof that ANY possible
structure between a set of objects is equivalent to some structure that
can be formed using the formalism of modern mathematics? If such a proof
does not exist, why have we not developed a branch of mathematics which
CAN, in principle, deal with all conceivable types of structure between
objects?

         Jamie Vicary.