[FOM] Mathematics ***is*** formalising of our thought and intuition

[Robert Lindauer]

Consider: "Political science is the art and practice of devising and
using conceptual spaces where long sequences of reasoning steps can be
carried out without error"

The problem is that your definition would make mathematics -the only-
science, and that's not reasonable.  Surely mathematics is
foundational in that every science must make some use of mathematical
concepts and procedures, however, it does not follow that the whole
content of those other sciences (e.g. chemistry) is mathematical!

Hegel's definition is classic and correct:

"One could still, however, conceive the thought of a philosophical
mathematics, namely, as a science which would recognise those concepts
which constitute what the conventional mathematical science of the
understanding derives from its presupposed determinations, and
according to the method of the understanding, without concepts. "

Or, think more plainly, pure mathematics is the systematic
consideration of proto-mathematical concepts (space/time, infinite,
finitude, recursion, grouping, shape, etc.) without regard to the
conceptual content (that is, without regard to the concrete concept
itself or the things to which they are to be applied).

Best,

Robbie Lindauer


On Thu, May 27, 2010 at 2:11 PM, Vladimir Sazonov
<vladimir.sazonov at yahoo.com> wrote:

>> Perhaps step back from formalisiation a bit.  Try
>>
>> Mathematics is the art and practice of devising and using conceptual
>> spaces where long sequences of reasoning steps can be carried out
>> without error.
>>