Re: A quiet query from a visitor

angus wrote:

On Tue, 21 Aug 2007 14:21:34 +0200, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> wrote:

Angus Rodgers wrote:

Hey, leave me out of this! I admit to discomfort
with the
usual presentation of ZFC as a foundation for
mathematics.

Alas. That alone makes you already kind of a
"dissident", in my highly
personal and biased classification. Please, read the
disclaimer below.

Disclaimer. The above lists are only an
approximation of the reality in
'sci.math' and highly relflect the author's
opinion and experience.

I think the main thing wrong with this
"approximation"
(questions of individual membership or non-membership

of this or that "school" apart) is that sci.math does
not have more than one "school" of mathematics.
Maths,
insofar as it gets done here at all, gets done within
one "school". And then there are people like me who
sit in school, but sometimes stare out of the window,

and forget to pay attention to the lesson; and there
are people outside the school (some of whom want to
burn the school down); and perhaps somewhere there is
a Galois or Ramanujan, who can't get into the school,
but is doing mathematics anyway (while perhaps, in
the
case of Galois, also wanting to burn the school
down).

perhaps galois theory is the foundation of math



However, I haven't seen any evidence of the latter.
What
we have is a variety of opinions as to how the school
is
run, and whether all its rules make sense; but there
is
no other school.

Nor do I think there should be another school.
Mathematics
isn't /about/ its foundations. The existence of
different
opinions about how mathematics is justified doesn't
lead
to the creation of different mathematics. I know
this
has to be argued for (especially in view of the
claims
of Intuitionism, in particular); I suppose I'm just
saying
that whatever the problems with the current orthodoxy
in
mathematics, the dragon (or is it angels with flaming
swords?) guards a real treasure; and I for one would
like
to be admitted into Cantor's paradise (without
necessarily
assuming that it is the whole world of mathematics).


with all respect but i strongly dissagree on that !


Perhaps the house of mathematics has other mansions
too,
but I'd rather see some ... er ... constructive
effort
to build those than see Cantor's house being torn
down.

thats impossible because if you create another mansion cantorians will tear it down , calling it inconsistant with cantor...

therefore you have to defend. and the best defense is attack.


I'm sorry about all the mixed metaphors, and I know I

haven't written this at all clearly. I am interested
in
problems in the foundations of mathematics,
especially
to do with whether everything in mathematics is a set

(which I must say does seem a rather barmy idea), and

how you apply mathematics to the "real world"
(especially
how set theory accounts for such applications).

i have asked for examples of applications of cantor like a 1000 times and conjectured like a 100 times that it does not have that...

didnt get an example ...


But
it is
a really tragic mistake to allow one's worries about
the
/form/ in which mathematics is presented to deprive
one
of contact with its /substance/.

I am not aware of any language other than that of set

theory in which mathematics can be presented.


every domain of math has its own language ...


(I am
certainly not against efforts to do so, even if such
efforts must be experimental and toy-like in the
early
stages; but I haven't even seen any early
constructive
efforts in sci.math. Here I mean "constructive" in
the
everyday English sense.)

Apropos of that word that I just used in another
sense,
I have a vague question, which perhaps someone here
can
answer. Do schools of constructivism differ in
respect
of whether they regard non-constructive mathematics
as
meaningless or worthless? Do some constructivists
want
to tear down the non-constructive edifice, while
others
see their work as taking place within the same
edifice
as other mathematicians, but limiting attention to
the
"constructive" part of it?

yes, yes, yes and yes

and i am some kind of constructivist ....


--
Angus Rodgers
(twirlip@ eats spam; reply to angusrod@)
Contains mild peril

tommy1729
.

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