  Marc Alcobé malcobe at gmail.com Tue Jun 8 09:16:34 EDT 2010
> That is why formalising is the goal of mathematics and why >
mathematical rigour is in the blood of all mathematicians > even
when it is not directly seen that it will lead > to so strong
formal tools for our thought.  I would regard that more as a
technical means (hence the word "tools" you use) by which
mathematical goals (the solution of certain problems, and maybe
even only those amenable to formalization) are pursued, rather
than as a goal in itself.  > All you mentioned above
(idealization, abstraction, etc.) is > covered by the phrase >
 formalising our ***thought and intuition*** > but not vice
versa! How abstraction, etc. without assuming > formalisation
would lead to, e.g. the Calculus?  The way I see it, without
those skills, formalization would be something impossible for us
to achieve.  > If formal character of mathematics and
mathematical rigour are > considered only as some additional
feature of mathematical thought > then